Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(85,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.85");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.j (of order \(3\), 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: | \(14.8684813214\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 7 x^{17} + 81 x^{16} - 470 x^{15} + 2687 x^{14} - 12243 x^{13} + 43732 x^{12} + \cdots + 5500612092612 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 85.1 | ||
Root | \(6.01410 + 1.36338i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.85 |
Dual form | 252.4.j.b.169.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −5.01410 | + | 1.36338i | −0.964964 | + | 0.262382i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.333146 | + | 0.577025i | −0.0297975 | + | 0.0516107i | −0.880540 | − | 0.473973i | \(-0.842820\pi\) |
0.850742 | + | 0.525583i | \(0.176153\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.50000 | − | 6.06218i | −0.188982 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 23.2824 | − | 13.6722i | 0.862311 | − | 0.506379i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.42273 | − | 11.1245i | −0.176048 | − | 0.304924i | 0.764476 | − | 0.644653i | \(-0.222998\pi\) |
−0.940523 | + | 0.339729i | \(0.889665\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.93360 | + | 5.08115i | −0.0625873 | + | 0.108404i | −0.895621 | − | 0.444818i | \(-0.853269\pi\) |
0.833034 | + | 0.553222i | \(0.186602\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.883722 | − | 3.34747i | 0.0152117 | − | 0.0576208i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 10.4753 | 0.149449 | 0.0747243 | − | 0.997204i | \(-0.476192\pi\) | ||||
0.0747243 | + | 0.997204i | \(0.476192\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 25.8933 | 0.312649 | 0.156324 | − | 0.987706i | \(-0.450035\pi\) | ||||
0.156324 | + | 0.987706i | \(0.450035\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 25.8144 | + | 25.6245i | 0.268246 | + | 0.266273i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −32.0287 | + | 55.4753i | −0.290367 | + | 0.502930i | −0.973896 | − | 0.226993i | \(-0.927111\pi\) |
0.683530 | + | 0.729923i | \(0.260444\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 62.2780 | + | 107.869i | 0.498224 | + | 0.862950i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −98.0998 | + | 100.297i | −0.699234 | + | 0.714893i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 81.4630 | + | 141.098i | 0.521631 | + | 0.903491i | 0.999683 | + | 0.0251601i | \(0.00800956\pi\) |
−0.478052 | + | 0.878331i | \(0.658657\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −59.6865 | + | 103.380i | −0.345807 | + | 0.598955i | −0.985500 | − | 0.169675i | \(-0.945728\pi\) |
0.639693 | + | 0.768630i | \(0.279061\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 47.3711 | + | 47.0227i | 0.249886 | + | 0.248049i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.66404 | 0.0225248 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 292.816 | 1.30104 | 0.650522 | − | 0.759487i | \(-0.274550\pi\) | ||||
0.650522 | + | 0.759487i | \(0.274550\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.78184 | − | 29.4770i | 0.0319511 | − | 0.121028i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −196.421 | + | 340.212i | −0.748191 | + | 1.29591i | 0.200497 | + | 0.979694i | \(0.435744\pi\) |
−0.948689 | + | 0.316211i | \(0.897589\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 70.7394 | + | 122.524i | 0.250876 | + | 0.434530i | 0.963767 | − | 0.266745i | \(-0.0859481\pi\) |
−0.712891 | + | 0.701274i | \(0.752615\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.132792 | + | 17.9894i | 0.000439901 | + | 0.0595933i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 99.6313 | + | 172.566i | 0.309207 | + | 0.535562i | 0.978189 | − | 0.207716i | \(-0.0666031\pi\) |
−0.668982 | + | 0.743278i | \(0.733270\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −24.5000 | + | 42.4352i | −0.0714286 | + | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −52.5241 | + | 14.2818i | −0.144213 | + | 0.0392127i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 375.572 | 0.973374 | 0.486687 | − | 0.873576i | \(-0.338205\pi\) | ||||
0.486687 | + | 0.873576i | \(0.338205\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.55882 | 0.0209831 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −129.832 | + | 35.3024i | −0.301695 | + | 0.0820336i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −226.870 | + | 392.950i | −0.500608 | + | 0.867079i | 0.499391 | + | 0.866377i | \(0.333557\pi\) |
−1.00000 | 0.000702659i | \(0.999776\pi\) | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 126.869 | + | 219.744i | 0.266294 | + | 0.461234i | 0.967902 | − | 0.251329i | \(-0.0808675\pi\) |
−0.701608 | + | 0.712563i | \(0.747534\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −164.372 | − | 93.2892i | −0.328713 | − | 0.186561i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.95463 | − | 3.38552i | −0.00372988 | − | 0.00646035i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 432.744 | − | 749.534i | 0.789075 | − | 1.36672i | −0.137458 | − | 0.990508i | \(-0.543893\pi\) |
0.926534 | − | 0.376211i | \(-0.122773\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 84.9611 | − | 321.826i | 0.148234 | − | 0.561497i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −712.205 | −1.19047 | −0.595234 | − | 0.803553i | \(-0.702940\pi\) | ||||
−0.595234 | + | 0.803553i | \(0.702940\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 527.665 | 0.846006 | 0.423003 | − | 0.906128i | \(-0.360976\pi\) | ||||
0.423003 | + | 0.906128i | \(0.360976\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −459.334 | − | 455.956i | −0.707191 | − | 0.701990i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −44.9591 | + | 77.8714i | −0.0665398 | + | 0.115250i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −142.073 | − | 246.078i | −0.202335 | − | 0.350454i | 0.746945 | − | 0.664885i | \(-0.231520\pi\) |
−0.949280 | + | 0.314431i | \(0.898186\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 355.140 | − | 636.645i | 0.487161 | − | 0.873312i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −29.5309 | − | 51.1489i | −0.0390534 | − | 0.0676425i | 0.845838 | − | 0.533440i | \(-0.179101\pi\) |
−0.884891 | + | 0.465797i | \(0.845768\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.48979 | + | 6.04450i | −0.00445319 | + | 0.00771315i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −600.834 | − | 596.415i | −0.740415 | − | 0.734970i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −189.928 | −0.226206 | −0.113103 | − | 0.993583i | \(-0.536079\pi\) | ||||
−0.113103 | + | 0.993583i | \(0.536079\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 41.0704 | 0.0473115 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 158.328 | − | 599.733i | 0.176536 | − | 0.668704i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.62624 | + | 14.9411i | −0.00931614 | + | 0.0161360i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 143.777 | + | 249.030i | 0.150499 | + | 0.260671i | 0.931411 | − | 0.363969i | \(-0.118579\pi\) |
−0.780912 | + | 0.624641i | \(0.785245\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −301.633 | − | 171.192i | −0.306215 | − | 0.173792i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −92.3450 | − | 159.946i | −0.0909770 | − | 0.157577i | 0.816946 | − | 0.576715i | \(-0.195666\pi\) |
−0.907922 | + | 0.419138i | \(0.862332\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 58.2990 | − | 100.977i | 0.0557706 | − | 0.0965976i | −0.836792 | − | 0.547521i | \(-0.815572\pi\) |
0.892563 | + | 0.450923i | \(0.148905\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −23.3860 | + | 6.35885i | −0.0217356 | + | 0.00591010i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 31.0814 | 0.0280818 | 0.0140409 | − | 0.999901i | \(-0.495530\pi\) | ||||
0.0140409 | + | 0.999901i | \(0.495530\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1531.46 | 1.34576 | 0.672879 | − | 0.739753i | \(-0.265058\pi\) | ||||
0.672879 | + | 0.739753i | \(0.265058\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1468.21 | + | 399.219i | −1.25546 | + | 0.341371i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −702.471 | + | 1216.72i | −0.584804 | + | 1.01291i | 0.410095 | + | 0.912043i | \(0.365495\pi\) |
−0.994900 | + | 0.100868i | \(0.967838\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −21.3404 | − | 36.9627i | −0.0173044 | − | 0.0299721i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.16934 | + | 158.410i | 0.000923978 | + | 0.125171i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −36.6634 | − | 63.5030i | −0.0282431 | − | 0.0489185i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 582.997 | − | 1009.78i | 0.438014 | − | 0.758663i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 521.039 | − | 1973.65i | 0.381955 | − | 1.44681i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −166.277 | −0.118978 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 151.277 | 0.105698 | 0.0528489 | − | 0.998603i | \(-0.483170\pi\) | ||||
0.0528489 | + | 0.998603i | \(0.483170\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −521.741 | − | 517.904i | −0.356099 | − | 0.353480i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1020.83 | + | 1768.13i | −0.680841 | + | 1.17925i | 0.293884 | + | 0.955841i | \(0.405052\pi\) |
−0.974725 | + | 0.223410i | \(0.928281\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −90.6265 | − | 156.970i | −0.0590851 | − | 0.102338i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −25.1922 | − | 90.0195i | −0.0160607 | − | 0.0573900i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −281.424 | − | 487.441i | −0.175501 | − | 0.303977i | 0.764833 | − | 0.644228i | \(-0.222821\pi\) |
−0.940335 | + | 0.340251i | \(0.889488\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 233.361 | − | 404.193i | 0.142399 | − | 0.246642i | −0.786001 | − | 0.618226i | \(-0.787852\pi\) |
0.928399 | + | 0.371584i | \(0.121185\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −734.835 | − | 729.431i | −0.438895 | − | 0.435668i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 75.3669 | 0.0440734 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −108.556 | −0.0621731 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 64.9902 | − | 246.177i | 0.0364646 | − | 0.138125i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 375.931 | − | 651.132i | 0.206695 | − | 0.358005i | −0.743977 | − | 0.668205i | \(-0.767063\pi\) |
0.950671 | + | 0.310200i | \(0.100396\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −285.901 | − | 495.196i | −0.154082 | − | 0.266877i | 0.778643 | − | 0.627468i | \(-0.215909\pi\) |
−0.932724 | + | 0.360591i | \(0.882575\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 243.889 | − | 143.220i | 0.128871 | − | 0.0756776i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −39.7686 | − | 68.8812i | −0.0206083 | − | 0.0356947i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 407.686 | − | 706.133i | 0.207241 | − | 0.358952i | −0.743603 | − | 0.668621i | \(-0.766885\pi\) |
0.950845 | + | 0.309669i | \(0.100218\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1883.16 | + | 512.047i | −0.939271 | + | 0.255396i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 448.401 | 0.219497 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1926.66 | 0.925812 | 0.462906 | − | 0.886407i | \(-0.346807\pi\) | ||||
0.462906 | + | 0.886407i | \(0.346807\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −42.9148 | + | 11.6689i | −0.0202479 | + | 0.00550559i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1344.59 | + | 2328.90i | −0.623040 | + | 1.07914i | 0.365877 | + | 0.930663i | \(0.380769\pi\) |
−0.988916 | + | 0.148473i | \(0.952564\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1081.29 | + | 1872.85i | 0.492166 | + | 0.852456i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 602.858 | − | 354.019i | 0.269601 | − | 0.158319i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 183.966 | + | 318.639i | 0.0808479 | + | 0.140033i | 0.903614 | − | 0.428347i | \(-0.140904\pi\) |
−0.822766 | + | 0.568380i | \(0.807571\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 435.946 | − | 755.081i | 0.188311 | − | 0.326164i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 601.808 | − | 2279.60i | 0.255563 | − | 0.968051i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 894.591 | 0.373547 | 0.186773 | − | 0.982403i | \(-0.440197\pi\) | ||||
0.186773 | + | 0.982403i | \(0.440197\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1074.33 | −0.441183 | −0.220592 | − | 0.975366i | \(-0.570799\pi\) | ||||
−0.220592 | + | 0.975366i | \(0.570799\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −935.728 | − | 928.847i | −0.377984 | − | 0.375204i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −97.5504 | + | 168.962i | −0.0387678 | + | 0.0671479i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −67.2798 | − | 116.532i | −0.0263101 | − | 0.0455704i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 951.366 | + | 243.660i | 0.366146 | + | 0.0937761i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 427.628 | + | 740.673i | 0.162000 | + | 0.280593i | 0.935586 | − | 0.353099i | \(-0.114872\pi\) |
−0.773586 | + | 0.633692i | \(0.781539\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 42.2904 | − | 73.2491i | 0.0157727 | − | 0.0273191i | −0.858031 | − | 0.513597i | \(-0.828313\pi\) |
0.873804 | + | 0.486278i | \(0.161646\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 14.4165 | + | 14.3105i | 0.00529428 | + | 0.00525535i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −132.433 | −0.0478956 | −0.0239478 | − | 0.999713i | \(-0.507624\pi\) | ||||
−0.0239478 | + | 0.999713i | \(0.507624\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 964.275 | 0.343496 | 0.171748 | − | 0.985141i | \(-0.445059\pi\) | ||||
0.171748 | + | 0.985141i | \(0.445059\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1147.92 | + | 4348.23i | −0.402827 | + | 1.52587i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 570.241 | − | 987.686i | 0.197158 | − | 0.341488i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −130.874 | − | 226.680i | −0.0445884 | − | 0.0772294i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.7667 | + | 1729.50i | 0.00428669 | + | 0.580718i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −166.306 | − | 288.050i | −0.0550411 | − | 0.0953341i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1039.03 | + | 1799.66i | −0.339004 | + | 0.587173i | −0.984246 | − | 0.176806i | \(-0.943423\pi\) |
0.645241 | + | 0.763979i | \(0.276757\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3571.07 | − | 971.005i | 1.14876 | − | 0.312357i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −94.2661 | −0.0299018 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 835.611 | 0.261405 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2645.76 | + | 719.407i | −0.816366 | + | 0.221977i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −30.7303 | + | 53.2264i | −0.00935358 | + | 0.0162009i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 323.227 | + | 559.845i | 0.0970622 | + | 0.168117i | 0.910467 | − | 0.413581i | \(-0.135722\pi\) |
−0.813405 | + | 0.581697i | \(0.802389\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2924.79 | + | 1659.96i | 0.866604 | + | 0.491841i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −891.831 | − | 1544.70i | −0.260762 | − | 0.451653i | 0.705683 | − | 0.708528i | \(-0.250640\pi\) |
−0.966445 | + | 0.256875i | \(0.917307\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3364.13 | + | 5826.84i | −0.970777 | + | 1.68143i | −0.277556 | + | 0.960709i | \(0.589525\pi\) |
−0.693220 | + | 0.720726i | \(0.743809\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 119.261 | − | 451.751i | 0.0339689 | − | 0.128671i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4058.14 | 1.14102 | 0.570509 | − | 0.821291i | \(-0.306746\pi\) | ||||
0.570509 | + | 0.821291i | \(0.306746\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −132.767 | −0.0368543 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1047.86 | + | 1040.16i | 0.287199 | + | 0.285087i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3028.96 | + | 5246.31i | −0.819779 | + | 1.41990i | 0.0860660 | + | 0.996289i | \(0.472570\pi\) |
−0.905845 | + | 0.423609i | \(0.860763\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1589.77 | + | 2753.55i | 0.424920 | + | 0.735984i | 0.996413 | − | 0.0846236i | \(-0.0269688\pi\) |
−0.571493 | + | 0.820607i | \(0.693635\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −912.721 | + | 3676.39i | −0.240951 | + | 0.970537i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.3241 | − | 28.2742i | −0.00425678 | − | 0.00737296i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −75.9606 | + | 131.568i | −0.0195678 | + | 0.0338925i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 217.806 | + | 216.204i | 0.0554333 | + | 0.0550256i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5356.03 | 1.34689 | 0.673446 | − | 0.739237i | \(-0.264813\pi\) | ||||
0.673446 | + | 0.739237i | \(0.264813\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 822.846 | 0.204474 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.25723 | − | 35.0656i | 0.00227337 | − | 0.00861135i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3133.65 | + | 5427.63i | −0.760589 | + | 1.31738i | 0.181958 | + | 0.983306i | \(0.441756\pi\) |
−0.942547 | + | 0.334073i | \(0.891577\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1024.86 | − | 1775.10i | −0.245874 | − | 0.425867i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3825.78 | + | 2171.32i | 0.907317 | + | 0.514948i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1168.34 | − | 2023.63i | −0.273928 | − | 0.474458i | 0.695936 | − | 0.718104i | \(-0.254990\pi\) |
−0.969864 | + | 0.243646i | \(0.921656\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −125.120 | + | 216.715i | −0.0290041 | + | 0.0502365i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 952.320 | − | 258.944i | 0.218281 | − | 0.0593525i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2551.67 | 0.578358 | 0.289179 | − | 0.957275i | \(-0.406618\pi\) | ||||
0.289179 | + | 0.957275i | \(0.406618\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7057.24 | −1.58191 | −0.790954 | − | 0.611876i | \(-0.790415\pi\) | ||||
−0.790954 | + | 0.611876i | \(0.790415\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −205.931 | + | 55.9945i | −0.0456539 | + | 0.0124137i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 799.990 | − | 1385.62i | 0.175422 | − | 0.303841i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 547.265 | + | 947.890i | 0.118707 | + | 0.205607i | 0.919256 | − | 0.393661i | \(-0.128792\pi\) |
−0.800548 | + | 0.599268i | \(0.795458\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 23.7911 | + | 3222.98i | 0.00510516 | + | 0.691595i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3525.49 | − | 6106.34i | −0.748446 | − | 1.29635i | −0.948567 | − | 0.316576i | \(-0.897467\pi\) |
0.200121 | − | 0.979771i | \(-0.435866\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2669.52 | − | 4623.75i | 0.560730 | − | 0.971212i | −0.436703 | − | 0.899606i | \(-0.643854\pi\) |
0.997433 | − | 0.0716068i | \(-0.0228127\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 22.8825 | − | 86.6769i | 0.00475593 | − | 0.0180151i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2749.90 | 0.565580 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4803.27 | −0.977665 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1060.44 | − | 1052.64i | −0.213621 | − | 0.212050i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4031.27 | − | 6982.36i | 0.803785 | − | 1.39220i | −0.113323 | − | 0.993558i | \(-0.536150\pi\) |
0.917108 | − | 0.398638i | \(-0.130517\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −151.161 | − | 261.819i | −0.0298337 | − | 0.0516735i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1745.82 | + | 447.133i | 0.341086 | + | 0.0873578i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −187.919 | − | 325.485i | −0.0363465 | − | 0.0629541i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 495.176 | − | 857.670i | 0.0948221 | − | 0.164237i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 681.095 | + | 676.086i | 0.129135 | + | 0.128185i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −169.064 | −0.0317395 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2099.74 | −0.390354 | −0.195177 | − | 0.980768i | \(-0.562528\pi\) | ||||
−0.195177 | + | 0.980768i | \(0.562528\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −154.647 | + | 585.792i | −0.0284712 | + | 0.107846i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1546.53 | − | 2678.67i | 0.281980 | − | 0.488403i | −0.689893 | − | 0.723912i | \(-0.742342\pi\) |
0.971872 | + | 0.235509i | \(0.0756756\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1263.36 | − | 2188.20i | −0.228144 | − | 0.395158i | 0.729114 | − | 0.684393i | \(-0.239933\pi\) |
−0.957258 | + | 0.289235i | \(0.906599\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 108.590 | − | 63.7678i | 0.0194234 | − | 0.0114061i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4947.20 | − | 8568.79i | −0.876537 | − | 1.51821i | −0.855117 | − | 0.518436i | \(-0.826515\pi\) |
−0.0214203 | − | 0.999771i | \(-0.506819\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1046.43 | − | 1812.47i | 0.183664 | − | 0.318115i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −155.845 | + | 42.3757i | −0.0270979 | + | 0.00736817i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 271.239 | 0.0467249 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −730.796 | −0.124730 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7678.91 | + | 2087.96i | −1.29861 | + | 0.353103i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 697.419 | − | 1207.97i | 0.116869 | − | 0.202423i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2679.68 | − | 4641.34i | −0.444980 | − | 0.770728i | 0.553071 | − | 0.833134i | \(-0.313456\pi\) |
−0.998051 | + | 0.0624063i | \(0.980123\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6817.46 | − | 4003.45i | 1.12191 | − | 0.658822i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 288.333 | + | 499.408i | 0.0470249 | + | 0.0814495i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5067.01 | + | 8776.32i | −0.819044 | + | 1.41863i | 0.0873440 | + | 0.996178i | \(0.472162\pi\) |
−0.906388 | + | 0.422447i | \(0.861171\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1863.42 | − | 7058.47i | 0.298545 | − | 1.13086i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1533.40 | 0.243514 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 157.397 | + | 156.240i | 0.0245623 | + | 0.0243816i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 319.080 | − | 552.663i | 0.0493635 | − | 0.0855000i | −0.840288 | − | 0.542140i | \(-0.817614\pi\) |
0.889651 | + | 0.456640i | \(0.150947\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4694.26 | − | 8130.70i | −0.719995 | − | 1.24707i | −0.961001 | − | 0.276544i | \(-0.910811\pi\) |
0.241007 | − | 0.970524i | \(-0.422522\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −221.836 | − | 792.690i | −0.0337343 | − | 0.120543i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3799.82 | − | 6581.48i | −0.572929 | − | 0.992342i | −0.996263 | − | 0.0863688i | \(-0.972474\pi\) |
0.423334 | − | 0.905974i | \(-0.360860\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 237.268 | − | 410.960i | 0.0354729 | − | 0.0614408i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 270.413 | + | 268.424i | 0.0400890 | + | 0.0397941i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9242.70 | 1.35881 | 0.679403 | − | 0.733766i | \(-0.262239\pi\) | ||||
0.679403 | + | 0.733766i | \(0.262239\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6188.54 | −0.902251 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1546.49 | + | 5857.99i | −0.223608 | + | 0.847010i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −175.789 | + | 304.476i | −0.0252088 | + | 0.0436630i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1536.15 | − | 2660.69i | −0.218491 | − | 0.378438i | 0.735856 | − | 0.677138i | \(-0.236780\pi\) |
−0.954347 | + | 0.298700i | \(0.903447\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 78.2939 | + | 10606.5i | 0.0110456 | + | 1.49634i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1314.50 | − | 2276.79i | −0.183950 | − | 0.318611i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3034.26 | − | 5255.49i | 0.421201 | − | 0.729542i | −0.574856 | − | 0.818255i | \(-0.694942\pi\) |
0.996057 | + | 0.0887126i | \(0.0282753\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 833.730 | − | 226.699i | 0.114810 | − | 0.0312178i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −955.920 | −0.130590 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2794.68 | 0.378768 | 0.189384 | − | 0.981903i | \(-0.439351\pi\) | ||||
0.189384 | + | 0.981903i | \(0.439351\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −758.516 | + | 206.247i | −0.101995 | + | 0.0277332i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2782.83 | − | 4820.00i | 0.371269 | − | 0.643056i | −0.618492 | − | 0.785791i | \(-0.712256\pi\) |
0.989761 | + | 0.142735i | \(0.0455895\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −29.9559 | − | 51.8851i | −0.00396543 | − | 0.00686833i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3322.16 | + | 1885.49i | 0.436370 | + | 0.247661i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4489.99 | − | 7776.90i | −0.585223 | − | 1.01364i | −0.994848 | − | 0.101382i | \(-0.967674\pi\) |
0.409625 | − | 0.912254i | \(-0.365660\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −335.509 | + | 581.119i | −0.0433949 | + | 0.0751622i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2707.91 | − | 10257.3i | 0.347572 | − | 1.31658i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 189.324 | 0.0241163 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7081.82 | −0.895280 | −0.447640 | − | 0.894214i | \(-0.647735\pi\) | ||||
−0.447640 | + | 0.894214i | \(0.647735\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 668.420 | + | 663.504i | 0.0838668 | + | 0.0832500i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1004.78 | − | 1740.34i | 0.125128 | − | 0.216729i | −0.796655 | − | 0.604435i | \(-0.793399\pi\) |
0.921783 | + | 0.387706i | \(0.126732\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −350.193 | − | 606.552i | −0.0432862 | − | 0.0749739i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 249.047 | + | 417.020i | 0.0305561 | + | 0.0511652i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1880.68 | − | 3257.43i | −0.229046 | − | 0.396719i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7193.40 | + | 12459.3i | −0.869659 | + | 1.50629i | −0.00731400 | + | 0.999973i | \(0.502328\pi\) |
−0.862345 | + | 0.506321i | \(0.831005\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2075.65 | + | 2060.39i | 0.249111 | + | 0.247279i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3176.17 | 0.378424 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 39.3523 | 0.00465477 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −619.027 | + | 2344.82i | −0.0726951 | + | 0.275363i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5240.11 | + | 9076.13i | −0.610969 | + | 1.05823i | 0.380108 | + | 0.924942i | \(0.375887\pi\) |
−0.991077 | + | 0.133287i | \(0.957447\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6528.75 | + | 11308.1i | 0.755800 | + | 1.30908i | 0.944976 | + | 0.327140i | \(0.106085\pi\) |
−0.189176 | + | 0.981943i | \(0.560582\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4679.03 | + | 2655.58i | 0.537830 | + | 0.305245i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 652.379 | + | 1129.95i | 0.0744589 | + | 0.128967i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 888.084 | − | 1538.21i | 0.100650 | − | 0.174330i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −377.897 | + | 102.754i | −0.0425292 | + | 0.0115641i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11283.3 | 1.26101 | 0.630507 | − | 0.776184i | \(-0.282847\pi\) | ||||
0.630507 | + | 0.776184i | \(0.282847\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8081.40 | −0.896923 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 544.312 | − | 148.003i | 0.0599948 | − | 0.0163131i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −829.328 | + | 1436.44i | −0.0907829 | + | 0.157241i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4058.00 | − | 7028.67i | −0.441180 | − | 0.764146i | 0.556598 | − | 0.830782i | \(-0.312107\pi\) |
−0.997777 | + | 0.0666366i | \(0.978773\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.76574 | + | 1322.96i | 0.00105450 | + | 0.142853i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1996.63 | + | 3458.26i | 0.214137 | + | 0.370896i | 0.953005 | − | 0.302954i | \(-0.0979727\pi\) |
−0.738868 | + | 0.673850i | \(0.764639\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 63.2738 | − | 109.593i | 0.00674037 | − | 0.0116747i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −997.217 | + | 3777.38i | −0.105518 | + | 0.399695i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18616.4 | −1.95671 | −0.978356 | − | 0.206928i | \(-0.933653\pi\) | ||||
−0.978356 | + | 0.206928i | \(0.933653\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5046.24 | 0.526870 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2108.68 | + | 2093.17i | 0.218707 | + | 0.217098i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.6824 | + | 23.6987i | −0.00140976 | + | 0.00244178i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −734.233 | − | 1271.73i | −0.0751553 | − | 0.130173i | 0.825999 | − | 0.563672i | \(-0.190612\pi\) |
−0.901154 | + | 0.433500i | \(0.857279\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1027.62 | + | 1050.63i | −0.104500 | + | 0.106840i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4674.37 | − | 8096.25i | −0.472250 | − | 0.817961i | 0.527246 | − | 0.849713i | \(-0.323225\pi\) |
−0.999496 | + | 0.0317519i | \(0.989891\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1461.07 | − | 2530.64i | 0.146655 | − | 0.254015i | −0.783334 | − | 0.621601i | \(-0.786482\pi\) |
0.929989 | + | 0.367586i | \(0.119816\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 293.315 | + | 291.158i | 0.0292519 | + | 0.0290368i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13329.0 | 1.32075 | 0.660376 | − | 0.750936i | \(-0.270397\pi\) | ||||
0.660376 | + | 0.750936i | \(0.270397\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6058.41 | −0.596485 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1081.45 | + | 4096.45i | −0.105798 | + | 0.400753i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 908.680 | − | 1573.88i | 0.0883322 | − | 0.152996i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1612.58 | + | 2793.08i | 0.155769 | + | 0.269800i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8744.22 | − | 5134.91i | 0.839351 | − | 0.492896i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3950.87 | + | 6843.11i | 0.376868 | + | 0.652755i | 0.990605 | − | 0.136756i | \(-0.0436676\pi\) |
−0.613736 | + | 0.789511i | \(0.710334\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −859.006 | + | 1487.84i | −0.0814289 | + | 0.141039i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2248.33 | + | 611.341i | −0.211806 | + | 0.0575921i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −191.595 | −0.0179379 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16390.6 | 1.52511 | 0.762555 | − | 0.646923i | \(-0.223944\pi\) | ||||
0.762555 | + | 0.646923i | \(0.223944\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9660.45 | + | 2626.76i | −0.893376 | + | 0.242917i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7105.46 | + | 12307.0i | −0.653085 | + | 1.13118i | 0.329285 | + | 0.944231i | \(0.393192\pi\) |
−0.982370 | + | 0.186946i | \(0.940141\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 853.347 | + | 1478.04i | 0.0779570 | + | 0.135026i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 199.270 | − | 117.018i | 0.0180940 | − | 0.0106254i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2492.72 | + | 4317.51i | 0.224977 | + | 0.389672i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1833.28 | − | 3175.33i | 0.164467 | − | 0.284865i | −0.771999 | − | 0.635624i | \(-0.780743\pi\) |
0.936466 | + | 0.350759i | \(0.114076\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3566.74 | − | 13510.5i | 0.318065 | − | 1.20480i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21619.5 | 1.91643 | 0.958215 | − | 0.286050i | \(-0.0923423\pi\) | ||||
0.958215 | + | 0.286050i | \(0.0923423\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 123.057 | 0.0108435 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7975.08 | − | 7916.43i | −0.698592 | − | 0.693454i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3117.99 | − | 5400.52i | 0.271518 | − | 0.470283i | −0.697733 | − | 0.716358i | \(-0.745808\pi\) |
0.969251 | + | 0.246075i | \(0.0791410\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1846.83 | − | 3198.80i | −0.159880 | − | 0.276921i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2540.13 | + | 2597.01i | −0.218615 | + | 0.223510i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 38.8441 | + | 67.2800i | 0.00332365 | + | 0.00575672i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1279.81 | − | 2216.70i | 0.108870 | − | 0.188569i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1356.85 | − | 1346.87i | −0.114757 | − | 0.113913i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18726.1 | −1.57468 | −0.787339 | − | 0.616520i | \(-0.788542\pi\) | ||||
−0.787339 | + | 0.616520i | \(0.788542\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7182.40 | 0.600506 | 0.300253 | − | 0.953860i | \(-0.402929\pi\) | ||||
0.300253 | + | 0.953860i | \(0.402929\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1156.42 | + | 4380.41i | −0.0961336 | + | 0.364146i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −625.232 | + | 1082.93i | −0.0516803 | + | 0.0895130i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4031.83 | + | 6983.33i | 0.331374 | + | 0.573957i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 90.4306 | + | 12250.6i | 0.00739049 | + | 1.00119i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1152.44 | − | 1996.09i | −0.0936545 | − | 0.162214i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.3546 | + | 17.9348i | −0.000836767 | + | 0.00144932i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4485.57 | + | 1219.67i | −0.360459 | + | 0.0980120i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 629.427 | 0.0502994 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2106.61 | 0.167412 | 0.0837061 | − | 0.996490i | \(-0.473324\pi\) | ||||
0.0837061 | + | 0.996490i | \(0.473324\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5386.79 | − | 1464.72i | 0.425726 | − | 0.115759i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −510.200 | + | 883.693i | −0.0401001 | + | 0.0694555i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9802.22 | + | 16977.9i | 0.766202 | + | 1.32710i | 0.939609 | + | 0.342251i | \(0.111189\pi\) |
−0.173406 | + | 0.984850i | \(0.555477\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5958.20 | + | 3381.58i | 0.463188 | + | 0.262882i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2109.35 | + | 3653.49i | 0.163087 | + | 0.282476i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −994.511 | + | 1722.54i | −0.0764754 | + | 0.132459i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 258.768 | − | 980.192i | 0.0197912 | − | 0.0749673i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5686.70 | −0.432591 | −0.216296 | − | 0.976328i | \(-0.569397\pi\) | ||||
−0.216296 | + | 0.976328i | \(0.569397\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −830.085 | −0.0628065 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 496.225 | + | 492.575i | 0.0373452 | + | 0.0370705i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7670.07 | + | 13284.9i | −0.574165 | + | 0.994482i | 0.421967 | + | 0.906611i | \(0.361340\pi\) |
−0.996132 | + | 0.0878713i | \(0.971994\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −468.050 | − | 810.687i | −0.0348514 | − | 0.0603643i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5102.44 | + | 75.3337i | −0.377923 | + | 0.00557975i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7758.53 | + | 13438.2i | 0.571625 | + | 0.990083i | 0.996399 | + | 0.0847838i | \(0.0270199\pi\) |
−0.424775 | + | 0.905299i | \(0.639647\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1945.26 | + | 3369.29i | −0.142568 | + | 0.246936i | −0.928463 | − | 0.371425i | \(-0.878869\pi\) |
0.785895 | + | 0.618360i | \(0.212203\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3153.98 | − | 3130.79i | −0.229947 | − | 0.228256i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7978.73 | −0.578671 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4707.77 | 0.339666 | 0.169833 | − | 0.985473i | \(-0.445677\pi\) | ||||
0.169833 | + | 0.985473i | \(0.445677\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −112.182 | + | 424.936i | −0.00805202 | + | 0.0305004i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −206.716 | + | 358.043i | −0.0147608 | + | 0.0255665i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2412.20 | − | 4178.05i | −0.171360 | − | 0.296805i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −91.7962 | − | 52.0989i | −0.00648770 | − | 0.00368209i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7095.56 | + | 12289.9i | 0.498918 | + | 0.864152i | 0.999999 | − | 0.00124845i | \(-0.000397393\pi\) |
−0.501081 | + | 0.865401i | \(0.667064\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1545.48 | + | 2676.85i | −0.108116 | + | 0.187263i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 664.031 | − | 180.556i | 0.0462176 | − | 0.0125670i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11109.6 | 0.769338 | 0.384669 | − | 0.923054i | \(-0.374316\pi\) | ||||
0.384669 | + | 0.923054i | \(0.374316\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 48.8571 | 0.00336629 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4834.97 | + | 1314.67i | −0.331461 | + | 0.0901272i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9711.46 | + | 16820.7i | −0.662436 | + | 1.14737i | 0.317537 | + | 0.948246i | \(0.397144\pi\) |
−0.979974 | + | 0.199128i | \(0.936189\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5722.99 | − | 9912.50i | −0.388428 | − | 0.672778i | 0.603810 | − | 0.797128i | \(-0.293649\pi\) |
−0.992238 | + | 0.124351i | \(0.960315\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −172.492 | − | 23367.5i | −0.0116491 | − | 1.57811i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 388.446 | + | 672.808i | 0.0261034 | + | 0.0452125i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13050.4 | − | 22604.0i | 0.872651 | − | 1.51148i | 0.0134073 | − | 0.999910i | \(-0.495732\pi\) |
0.859244 | − | 0.511566i | \(-0.170934\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1512.66 | + | 5729.81i | −0.100650 | + | 0.381254i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1169.11 | −0.0774097 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10725.6 | 0.706690 | 0.353345 | − | 0.935493i | \(-0.385044\pi\) | ||||
0.353345 | + | 0.935493i | \(0.385044\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 965.265 | + | 958.166i | 0.0632898 | + | 0.0628244i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8848.51 | + | 15326.1i | −0.577354 | + | 1.00001i | 0.418427 | + | 0.908250i | \(0.362581\pi\) |
−0.995781 | + | 0.0917563i | \(0.970752\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13563.1 | + | 23492.0i | 0.880691 | + | 1.52540i | 0.850574 | + | 0.525856i | \(0.176255\pi\) |
0.0301173 | + | 0.999546i | \(0.490412\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2421.98 | − | 8654.48i | −0.156507 | − | 0.559247i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 664.749 | + | 1151.38i | 0.0427490 | + | 0.0740434i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7729.36 | + | 13387.6i | −0.494679 | + | 0.856809i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1226.59 | + | 1217.57i | 0.0781267 | + | 0.0775521i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3067.33 | 0.194439 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19730.4 | 1.24478 | 0.622389 | − | 0.782708i | \(-0.286162\pi\) | ||||
0.622389 | + | 0.782708i | \(0.286162\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2756.20 | − | 10440.2i | 0.173063 | − | 0.655549i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −50.3971 | + | 87.2904i | −0.00314953 | + | 0.00545514i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −143.746 | − | 248.976i | −0.00894104 | − | 0.0154863i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16581.8 | + | 9737.43i | −1.02655 | + | 0.602827i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 943.282 | + | 1633.81i | 0.0581239 | + | 0.100674i | 0.893623 | − | 0.448818i | \(-0.148155\pi\) |
−0.835499 | + | 0.549491i | \(0.814821\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5903.79 | − | 10225.7i | 0.362088 | − | 0.627155i | −0.626216 | − | 0.779650i | \(-0.715397\pi\) |
0.988304 | + | 0.152494i | \(0.0487306\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 472.660 | − | 128.520i | 0.0288542 | − | 0.00784571i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19045.5 | −1.15727 | −0.578636 | − | 0.815586i | \(-0.696415\pi\) | ||||
−0.578636 | + | 0.815586i | \(0.696415\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5828.48 | 0.352524 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4189.84 | + | 1139.25i | −0.252247 | + | 0.0685881i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4517.88 | − | 7825.19i | 0.270748 | − | 0.468949i | −0.698306 | − | 0.715799i | \(-0.746062\pi\) |
0.969053 | + | 0.246851i | \(0.0793958\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −680.169 | − | 1178.09i | −0.0405747 | − | 0.0702774i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12285.3 | − | 7214.35i | 0.729521 | − | 0.428400i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11234.0 | − | 19457.8i | −0.664057 | − | 1.15018i | −0.979540 | − | 0.201249i | \(-0.935500\pi\) |
0.315483 | − | 0.948931i | \(-0.397833\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1074.65 | − | 1861.35i | 0.0632362 | − | 0.109528i | −0.832674 | − | 0.553763i | \(-0.813191\pi\) |
0.895910 | + | 0.444235i | \(0.146525\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 81.5169 | − | 308.779i | 0.00477505 | − | 0.0180875i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 120.767 | 0.00704234 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10436.6 | −0.605858 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2383.97 | − | 2366.44i | −0.137772 | − | 0.136759i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1629.69 | − | 2822.71i | 0.0937609 | − | 0.162399i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11245.1 | + | 19477.1i | 0.644083 | + | 1.11558i | 0.984513 | + | 0.175314i | \(0.0560941\pi\) |
−0.340430 | + | 0.940270i | \(0.610573\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16928.3 | − | 4335.63i | −0.965292 | − | 0.247227i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3592.77 | + | 6222.86i | 0.203961 | + | 0.353270i | 0.949801 | − | 0.312854i | \(-0.101285\pi\) |
−0.745840 | + | 0.666125i | \(0.767952\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1006.44 | − | 1743.21i | 0.0568831 | − | 0.0985245i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6577.74 | + | 6529.36i | 0.370131 | + | 0.367409i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12056.1 | −0.675421 | −0.337711 | − | 0.941250i | \(-0.609653\pi\) | ||||
−0.337711 | + | 0.941250i | \(0.609653\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 375.021 | 0.0209180 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8923.89 | − | 33803.0i | 0.495586 | − | 1.87724i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1101.78 | + | 1908.34i | −0.0609208 | + | 0.105518i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15029.9 | − | 26032.5i | −0.827443 | − | 1.43317i | −0.900038 | − | 0.435812i | \(-0.856461\pi\) |
0.0725947 | − | 0.997362i | \(-0.476872\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17.9208 | + | 2427.72i | 0.000982329 | + | 0.133076i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 155.486 | + | 269.310i | 0.00848623 | + | 0.0146986i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2057.57 | + | 3563.81i | −0.111816 | + | 0.193671i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20347.9 | + | 5532.78i | −1.10104 | + | 0.299383i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5029.65 | −0.270994 | −0.135497 | − | 0.990778i | \(-0.543263\pi\) | ||||
−0.135497 | + | 0.990778i | \(0.543263\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7581.97 | 0.406770 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 665.707 | − | 181.012i | 0.0355631 | − | 0.00966992i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −646.415 | + | 1119.62i | −0.0343861 | + | 0.0595584i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −732.843 | − | 1269.32i | −0.0388187 | − | 0.0672360i | 0.845963 | − | 0.533241i | \(-0.179026\pi\) |
−0.884782 | + | 0.466005i | \(0.845693\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6672.23 | − | 3786.82i | −0.351938 | − | 0.199742i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3823.36 | − | 6622.25i | −0.200822 | − | 0.347833i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −25.1082 | + | 43.4886i | −0.00131328 | + | 0.00227466i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8034.80 | − | 30435.2i | 0.418501 | − | 1.58525i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19500.5 | 1.01147 | 0.505735 | − | 0.862689i | \(-0.331221\pi\) | ||||
0.505735 | + | 0.862689i | \(0.331221\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −816.186 | −0.0421586 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11725.4 | − | 11639.1i | −0.603142 | − | 0.598706i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10146.7 | + | 17574.6i | −0.519778 | + | 0.900283i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5587.94 | − | 9678.60i | −0.285069 | − | 0.493754i | 0.687557 | − | 0.726131i | \(-0.258683\pi\) |
−0.972626 | + | 0.232376i | \(0.925350\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −435.839 | − | 19678.2i | −0.0221429 | − | 0.999755i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 741.014 | + | 1283.47i | 0.0374930 | + | 0.0649398i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18392.5 | − | 31856.7i | 0.926795 | − | 1.60526i | 0.138147 | − | 0.990412i | \(-0.455885\pi\) |
0.788648 | − | 0.614844i | \(-0.210781\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 120.399 | + | 119.514i | 0.00604217 | + | 0.00599774i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11117.6 | −0.555660 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20277.2 | −1.00935 | −0.504675 | − | 0.863309i | \(-0.668388\pi\) | ||||
−0.504675 | + | 0.863309i | \(0.668388\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 201.498 | − | 763.256i | 0.00998947 | − | 0.0378393i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1326.46 | + | 2297.49i | −0.0654952 | + | 0.113441i | −0.896914 | − | 0.442206i | \(-0.854196\pi\) |
0.831418 | + | 0.555647i | \(0.187529\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 250.480 | + | 433.844i | 0.0123179 | + | 0.0213353i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1386.87 | − | 787.117i | −0.0679289 | − | 0.0385530i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −108.785 | − | 188.421i | −0.00530696 | − | 0.00919193i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13048.0 | − | 22599.8i | 0.633992 | − | 1.09811i | −0.352736 | − | 0.935723i | \(-0.614749\pi\) |
0.986728 | − | 0.162383i | \(-0.0519180\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −26855.7 | + | 7302.30i | −1.29970 | + | 0.353400i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 380.987 | 0.0183650 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35450.1 | 1.70206 | 0.851028 | − | 0.525120i | \(-0.175979\pi\) | ||||
0.851028 | + | 0.525120i | \(0.175979\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4125.83 | + | 1121.85i | −0.197310 | + | 0.0536503i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17487.1 | − | 30288.6i | 0.832993 | − | 1.44279i | −0.0626608 | − | 0.998035i | \(-0.519959\pi\) |
0.895654 | − | 0.444752i | \(-0.146708\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5360.12 | − | 9284.00i | −0.254324 | − | 0.440502i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.39104 | + | 188.444i | 6.57425e−5 | + | 0.00890613i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1331.09 | − | 2305.51i | −0.0626634 | − | 0.108536i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3406.79 | − | 5900.72i | 0.159755 | − | 0.276704i | −0.775025 | − | 0.631930i | \(-0.782263\pi\) |
0.934780 | + | 0.355226i | \(0.115596\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8312.49 | − | 31487.0i | 0.388284 | − | 1.47079i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15398.2 | −0.716475 | −0.358238 | − | 0.933630i | \(-0.616622\pi\) | ||||
−0.358238 | + | 0.933630i | \(0.616622\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14868.6 | −0.689157 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7558.87 | + | 7503.28i | 0.349000 | + | 0.346433i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5085.99 | + | 8809.20i | −0.233921 | + | 0.405164i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4574.30 | + | 7922.92i | 0.209579 | + | 0.363002i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −22143.2 | − | 5671.23i | −1.01064 | − | 0.258842i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 271.638 | + | 470.490i | 0.0123505 | + | 0.0213917i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4472.23 | + | 7746.14i | −0.202564 | + | 0.350851i | −0.949354 | − | 0.314209i | \(-0.898261\pi\) |
0.746790 | + | 0.665060i | \(0.231594\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8617.16 | + | 8553.79i | 0.388820 | + | 0.385961i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9834.59 | 0.442071 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1488.73 | −0.0666664 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 331.901 | − | 1257.22i | 0.0148067 | − | 0.0560866i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18050.5 | − | 31264.3i | 0.802233 | − | 1.38951i | −0.115909 | − | 0.993260i | \(-0.536978\pi\) |
0.918143 | − | 0.396249i | \(-0.129688\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1043.66 | + | 1807.68i | 0.0462105 | + | 0.0800390i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4421.99 | + | 2596.74i | −0.195060 | + | 0.114546i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3389.05 | − | 5870.00i | −0.148938 | − | 0.257967i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −149.383 | + | 258.739i | −0.00654045 | + | 0.0113284i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12794.3 | + | 3478.90i | −0.558094 | + | 0.151751i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −33907.0 | −1.47355 | −0.736777 | − | 0.676135i | \(-0.763653\pi\) | ||||
−0.736777 | + | 0.676135i | \(0.763653\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22570.9 | 0.977276 | 0.488638 | − | 0.872487i | \(-0.337494\pi\) | ||||
0.488638 | + | 0.872487i | \(0.337494\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 35385.7 | − | 9621.69i | 1.52648 | − | 0.415065i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −641.857 | + | 1111.73i | −0.0275869 | + | 0.0477818i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1831.68 | + | 3172.56i | 0.0784360 | + | 0.135855i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 956.218 | − | 561.524i | 0.0407973 | − | 0.0239576i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22320.7 | + | 38660.7i | 0.948842 | + | 1.64344i | 0.747870 | + | 0.663846i | \(0.231077\pi\) |
0.200972 | + | 0.979597i | \(0.435590\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16364.7 | + | 28344.5i | −0.693121 | + | 1.20052i | 0.277689 | + | 0.960671i | \(0.410431\pi\) |
−0.970810 | + | 0.239849i | \(0.922902\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2122.10 | + | 8038.34i | −0.0895540 | + | 0.339223i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33603.0 | −1.41293 | −0.706464 | − | 0.707749i | \(-0.749711\pi\) | ||||
−0.706464 | + | 0.707749i | \(0.749711\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5729.17 | 0.240027 | 0.120013 | − | 0.992772i | \(-0.461706\pi\) | ||||
0.120013 | + | 0.992772i | \(0.461706\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4036.37 | − | 4006.69i | −0.168496 | − | 0.167257i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −256.644 | + | 444.521i | −0.0106749 | + | 0.0184895i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −895.890 | − | 1551.73i | −0.0371300 | − | 0.0643110i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4513.44 | − | 16127.9i | −0.186389 | − | 0.666025i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17013.6 | + | 29468.3i | 0.700087 | + | 1.21259i | 0.968435 | + | 0.249265i | \(0.0801889\pi\) |
−0.268348 | + | 0.963322i | \(0.586478\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1077.94 | + | 1867.05i | −0.0441978 | + | 0.0765529i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 26002.4 | + | 25811.2i | 1.06236 | + | 1.05455i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1440.91 | −0.0586611 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8161.96 | −0.331108 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7081.33 | + | 26823.5i | −0.286255 | + | 1.08431i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9378.51 | + | 16244.1i | −0.377780 | + | 0.654335i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19266.6 | − | 33370.7i | −0.773358 | − | 1.33950i | −0.935713 | − | 0.352763i | \(-0.885242\pi\) |
0.162355 | − | 0.986732i | \(-0.448091\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.43843 | + | 465.804i | 0.000137534 | + | 0.0186318i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6348.27 | + | 10995.5i | 0.253037 | + | 0.438273i | 0.964361 | − | 0.264592i | \(-0.0852372\pi\) |
−0.711323 | + | 0.702865i | \(0.751904\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3887.48 | + | 6733.31i | −0.154411 | + | 0.267448i | −0.932844 | − | 0.360279i | \(-0.882681\pi\) |
0.778433 | + | 0.627727i | \(0.216015\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13788.3 | + | 3749.15i | −0.545764 | + | 0.148398i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3051.19 | 0.120352 | 0.0601759 | − | 0.998188i | \(-0.480834\pi\) | ||||
0.0601759 | + | 0.998188i | \(0.480834\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −245.150 | −0.00963624 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24084.1 | − | 6548.67i | 0.943412 | − | 0.256522i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1824.99 | + | 3160.98i | −0.0712412 | + | 0.123393i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2538.99 | + | 4397.67i | 0.0987722 | + | 0.171078i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6752.27 | + | 3832.25i | 0.261775 | + | 0.148570i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 581.970 | + | 1008.00i | 0.0224848 | + | 0.0389448i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13335.6 | + | 23098.0i | −0.513469 | + | 0.889354i | 0.486409 | + | 0.873731i | \(0.338307\pi\) |
−0.999878 | + | 0.0156231i | \(0.995027\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10693.6 | + | 40506.4i | −0.410336 | + | 1.55432i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31214.1 | 1.19368 | 0.596839 | − | 0.802361i | \(-0.296423\pi\) | ||||
0.596839 | + | 0.802361i | \(0.296423\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14463.8 | 0.551240 | 0.275620 | − | 0.961267i | \(-0.411117\pi\) | ||||
0.275620 | + | 0.961267i | \(0.411117\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1114.90 | + | 1106.70i | 0.0423467 | + | 0.0420352i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18953.4 | − | 32828.3i | 0.717467 | − | 1.24269i | −0.244533 | − | 0.969641i | \(-0.578635\pi\) |
0.962000 | − | 0.273049i | \(-0.0880320\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −529.468 | − | 917.065i | −0.0199750 | − | 0.0345977i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9363.32 | + | 138.242i | −0.352057 | + | 0.00519785i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2579.78 | + | 4468.32i | 0.0966732 | + | 0.167443i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −298.029 | + | 516.201i | −0.0111307 | + | 0.0192790i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1386.00 | + | 1375.81i | 0.0515911 | + | 0.0512117i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19449.0 | −0.721534 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3934.22 | 0.145469 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1313.53 | + | 4975.55i | −0.0484071 | + | 0.183362i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 357.908 | − | 619.914i | 0.0131461 | − | 0.0227698i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19035.0 | + | 32969.6i | 0.696853 | + | 1.20699i | 0.969552 | + | 0.244886i | \(0.0787506\pi\) |
−0.272698 | + | 0.962100i | \(0.587916\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4336.84 | − | 2461.37i | −0.158244 | − | 0.0898113i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12993.3 | − | 22505.1i | −0.472545 | − | 0.818472i | 0.526961 | − | 0.849889i | \(-0.323331\pi\) |
−0.999506 | + | 0.0314170i | \(0.989998\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −379.337 | + | 657.031i | −0.0137505 | + | 0.0238166i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 847.702 | − | 230.498i | 0.0306275 | − | 0.00832789i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14291.6 | 0.514667 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40516.5 | −1.45432 | −0.727158 | − | 0.686470i | \(-0.759159\pi\) | ||||
−0.727158 | + | 0.686470i | \(0.759159\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10528.3 | − | 2862.74i | 0.376677 | − | 0.102422i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2089.32 | − | 3618.82i | 0.0745081 | − | 0.129052i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18236.0 | + | 31585.7i | 0.648212 | + | 1.12274i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −23.2381 | − | 3148.06i | −0.000823343 | − | 0.111538i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20238.2 | + | 35053.5i | 0.714739 | + | 1.23796i | 0.963060 | + | 0.269287i | \(0.0867880\pi\) |
−0.248321 | + | 0.968678i | \(0.579879\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −634.386 | + | 1098.79i | −0.0223321 | + | 0.0386803i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4102.42 | + | 15539.6i | −0.143952 | + | 0.545278i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 89.6559 | 0.00313590 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17086.6 | −0.595727 | −0.297863 | − | 0.954609i | \(-0.596274\pi\) | ||||
−0.297863 | + | 0.954609i | \(0.596274\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9317.95 | + | 9249.42i | 0.323834 | + | 0.321452i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19327.3 | − | 33475.9i | 0.669557 | − | 1.15971i | −0.308471 | − | 0.951234i | \(-0.599817\pi\) |
0.978028 | − | 0.208473i | \(-0.0668493\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12582.2 | − | 21793.0i | −0.434500 | − | 0.752576i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −457.542 | + | 467.788i | −0.0157501 | + | 0.0161028i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18207.0 | − | 31535.5i | −0.624761 | − | 1.08212i | −0.988587 | − | 0.150651i | \(-0.951863\pi\) |
0.363826 | − | 0.931467i | \(-0.381470\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1547.96 | + | 2681.14i | −0.0529492 | + | 0.0917108i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 36488.2 | + | 36219.9i | 1.24418 | + | 1.23503i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17374.5 | −0.590573 | −0.295286 | − | 0.955409i | \(-0.595415\pi\) | ||||
−0.295286 | + | 0.955409i | \(0.595415\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −569.849 | −0.0193088 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2775.82 | + | 10514.6i | −0.0937613 | + | 0.355160i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1969.97 | + | 3412.08i | −0.0663333 | + | 0.114893i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7770.54 | + | 13459.0i | 0.260835 | + | 0.451780i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 723.650 | − | 424.952i | 0.0242153 | − | 0.0142200i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 28.1777 | + | 48.8052i | 0.000939971 | + | 0.00162808i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2257.27 | + | 3909.71i | −0.0750661 | + | 0.130018i | −0.901115 | − | 0.433580i | \(-0.857250\pi\) |
0.826049 | + | 0.563598i | \(0.190583\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1360.02 | + | 369.802i | −0.0450879 | + | 0.0122598i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19368.2 | 0.640118 | 0.320059 | − | 0.947398i | \(-0.396297\pi\) | ||||
0.320059 | + | 0.947398i | \(0.396297\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3267.05 | −0.107643 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3664.28 | − | 996.351i | 0.120360 | − | 0.0327269i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3259.56 | + | 5645.73i | −0.106738 | + | 0.184875i | −0.914447 | − | 0.404706i | \(-0.867374\pi\) |
0.807709 | + | 0.589581i | \(0.200707\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1219.86 | + | 2112.86i | 0.0398231 | + | 0.0689756i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 35656.1 | − | 20938.5i | 1.16046 | − | 0.681463i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13969.7 | + | 24196.2i | 0.453269 | + | 0.785085i | 0.998587 | − | 0.0531443i | \(-0.0169243\pi\) |
−0.545318 | + | 0.838229i | \(0.683591\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 44.1194 | − | 76.4170i | 0.00142717 | − | 0.00247193i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1850.02 | + | 7007.71i | −0.0596623 | + | 0.225996i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9062.76 | −0.291384 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25423.9 | −0.814952 | −0.407476 | − | 0.913216i | \(-0.633591\pi\) | ||||
−0.407476 | + | 0.913216i | \(0.633591\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19764.1 | + | 19618.7i | 0.631615 | + | 0.626970i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −321.244 | + | 556.411i | −0.0102353 | + | 0.0177281i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12766.2 | + | 22111.7i | 0.405526 | + | 0.702391i | 0.994382 | − | 0.105846i | \(-0.0337552\pi\) |
−0.588857 | + | 0.808237i | \(0.700422\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −28725.2 | + | 29368.5i | −0.909735 | + | 0.930107i |
(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 | 252.4.j.b.85.1 | ✓ | 18 | |
3.2 | odd | 2 | 756.4.j.b.253.6 | 18 | |||
9.2 | odd | 6 | 756.4.j.b.505.6 | 18 | |||
9.4 | even | 3 | 2268.4.a.i.1.6 | 9 | |||
9.5 | odd | 6 | 2268.4.a.h.1.4 | 9 | |||
9.7 | even | 3 | inner | 252.4.j.b.169.1 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.j.b.85.1 | ✓ | 18 | 1.1 | even | 1 | trivial | |
252.4.j.b.169.1 | yes | 18 | 9.7 | even | 3 | inner | |
756.4.j.b.253.6 | 18 | 3.2 | odd | 2 | |||
756.4.j.b.505.6 | 18 | 9.2 | odd | 6 | |||
2268.4.a.h.1.4 | 9 | 9.5 | odd | 6 | |||
2268.4.a.i.1.6 | 9 | 9.4 | even | 3 |