Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.a (trivial) |
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: | yes |
Analytic conductor: | \(32.1397868136\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} - 22 x^{12} + 18 x^{11} + 187 x^{10} - 118 x^{9} - 772 x^{8} + 346 x^{7} + 1581 x^{6} - 443 x^{5} - 1429 x^{4} + 193 x^{3} + 386 x^{2} - 3 x - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.582976\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.582976 | −0.412227 | −0.206113 | − | 0.978528i | \(-0.566082\pi\) | ||||
−0.206113 | + | 0.978528i | \(0.566082\pi\) | |||||||
\(3\) | −0.367598 | −0.212233 | −0.106116 | − | 0.994354i | \(-0.533842\pi\) | ||||
−0.106116 | + | 0.994354i | \(0.533842\pi\) | |||||||
\(4\) | −1.66014 | −0.830069 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.214301 | 0.0874880 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.13377 | 0.754403 | ||||||||
\(9\) | −2.86487 | −0.954957 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.0267004 | 0.00805047 | 0.00402524 | − | 0.999992i | \(-0.498719\pi\) | ||||
0.00402524 | + | 0.999992i | \(0.498719\pi\) | |||||||
\(12\) | 0.610264 | 0.176168 | ||||||||
\(13\) | −3.10813 | −0.862040 | −0.431020 | − | 0.902342i | \(-0.641846\pi\) | ||||
−0.431020 | + | 0.902342i | \(0.641846\pi\) | |||||||
\(14\) | −0.582976 | −0.155807 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.07634 | 0.519084 | ||||||||
\(17\) | −8.10612 | −1.96602 | −0.983012 | − | 0.183543i | \(-0.941243\pi\) | ||||
−0.983012 | + | 0.183543i | \(0.941243\pi\) | |||||||
\(18\) | 1.67015 | 0.393659 | ||||||||
\(19\) | −4.14248 | −0.950349 | −0.475175 | − | 0.879891i | \(-0.657615\pi\) | ||||
−0.475175 | + | 0.879891i | \(0.657615\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.367598 | −0.0802165 | ||||||||
\(22\) | −0.0155657 | −0.00331862 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −0.784372 | −0.160109 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.81197 | 0.355356 | ||||||||
\(27\) | 2.15592 | 0.414906 | ||||||||
\(28\) | −1.66014 | −0.313737 | ||||||||
\(29\) | −1.48754 | −0.276229 | −0.138115 | − | 0.990416i | \(-0.544104\pi\) | ||||
−0.138115 | + | 0.990416i | \(0.544104\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.35245 | 1.14093 | 0.570467 | − | 0.821320i | \(-0.306762\pi\) | ||||
0.570467 | + | 0.821320i | \(0.306762\pi\) | |||||||
\(32\) | −5.47800 | −0.968383 | ||||||||
\(33\) | −0.00981502 | −0.00170858 | ||||||||
\(34\) | 4.72568 | 0.810447 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.75608 | 0.792681 | ||||||||
\(37\) | 10.8928 | 1.79077 | 0.895383 | − | 0.445296i | \(-0.146902\pi\) | ||||
0.895383 | + | 0.445296i | \(0.146902\pi\) | |||||||
\(38\) | 2.41497 | 0.391759 | ||||||||
\(39\) | 1.14254 | 0.182953 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.32684 | −1.30043 | −0.650217 | − | 0.759748i | \(-0.725322\pi\) | ||||
−0.650217 | + | 0.759748i | \(0.725322\pi\) | |||||||
\(42\) | 0.214301 | 0.0330674 | ||||||||
\(43\) | −3.73815 | −0.570063 | −0.285031 | − | 0.958518i | \(-0.592004\pi\) | ||||
−0.285031 | + | 0.958518i | \(0.592004\pi\) | |||||||
\(44\) | −0.0443264 | −0.00668245 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.582976 | 0.0859552 | ||||||||
\(47\) | −11.9018 | −1.73606 | −0.868030 | − | 0.496512i | \(-0.834614\pi\) | ||||
−0.868030 | + | 0.496512i | \(0.834614\pi\) | |||||||
\(48\) | −0.763258 | −0.110167 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.97980 | 0.417255 | ||||||||
\(52\) | 5.15992 | 0.715553 | ||||||||
\(53\) | 13.1021 | 1.79971 | 0.899853 | − | 0.436194i | \(-0.143674\pi\) | ||||
0.899853 | + | 0.436194i | \(0.143674\pi\) | |||||||
\(54\) | −1.25685 | −0.171035 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.13377 | 0.285138 | ||||||||
\(57\) | 1.52277 | 0.201695 | ||||||||
\(58\) | 0.867201 | 0.113869 | ||||||||
\(59\) | −1.06393 | −0.138512 | −0.0692560 | − | 0.997599i | \(-0.522063\pi\) | ||||
−0.0692560 | + | 0.997599i | \(0.522063\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.897659 | 0.114933 | 0.0574667 | − | 0.998347i | \(-0.481698\pi\) | ||||
0.0574667 | + | 0.998347i | \(0.481698\pi\) | |||||||
\(62\) | −3.70333 | −0.470323 | ||||||||
\(63\) | −2.86487 | −0.360940 | ||||||||
\(64\) | −0.959128 | −0.119891 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.00572192 | 0.000704320 0 | ||||||||
\(67\) | 12.4481 | 1.52078 | 0.760388 | − | 0.649469i | \(-0.225009\pi\) | ||||
0.760388 | + | 0.649469i | \(0.225009\pi\) | |||||||
\(68\) | 13.4573 | 1.63194 | ||||||||
\(69\) | 0.367598 | 0.0442536 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.6084 | −1.37766 | −0.688832 | − | 0.724921i | \(-0.741876\pi\) | ||||
−0.688832 | + | 0.724921i | \(0.741876\pi\) | |||||||
\(72\) | −6.11299 | −0.720423 | ||||||||
\(73\) | 3.27293 | 0.383068 | 0.191534 | − | 0.981486i | \(-0.438654\pi\) | ||||
0.191534 | + | 0.981486i | \(0.438654\pi\) | |||||||
\(74\) | −6.35025 | −0.738202 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.87709 | 0.788856 | ||||||||
\(77\) | 0.0267004 | 0.00304279 | ||||||||
\(78\) | −0.666075 | −0.0754182 | ||||||||
\(79\) | −4.17218 | −0.469407 | −0.234703 | − | 0.972067i | \(-0.575412\pi\) | ||||
−0.234703 | + | 0.972067i | \(0.575412\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.80210 | 0.866900 | ||||||||
\(82\) | 4.85435 | 0.536074 | ||||||||
\(83\) | −0.986115 | −0.108240 | −0.0541201 | − | 0.998534i | \(-0.517235\pi\) | ||||
−0.0541201 | + | 0.998534i | \(0.517235\pi\) | |||||||
\(84\) | 0.610264 | 0.0665853 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.17925 | 0.234995 | ||||||||
\(87\) | 0.546817 | 0.0586250 | ||||||||
\(88\) | 0.0569726 | 0.00607330 | ||||||||
\(89\) | −17.0415 | −1.80639 | −0.903196 | − | 0.429228i | \(-0.858786\pi\) | ||||
−0.903196 | + | 0.429228i | \(0.858786\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.10813 | −0.325820 | ||||||||
\(92\) | 1.66014 | 0.173081 | ||||||||
\(93\) | −2.33515 | −0.242144 | ||||||||
\(94\) | 6.93848 | 0.715650 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.01370 | 0.205523 | ||||||||
\(97\) | −7.08771 | −0.719648 | −0.359824 | − | 0.933020i | \(-0.617163\pi\) | ||||
−0.359824 | + | 0.933020i | \(0.617163\pi\) | |||||||
\(98\) | −0.582976 | −0.0588895 | ||||||||
\(99\) | −0.0764932 | −0.00768786 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.26346 | 0.623237 | 0.311619 | − | 0.950207i | \(-0.399129\pi\) | ||||
0.311619 | + | 0.950207i | \(0.399129\pi\) | |||||||
\(102\) | −1.73715 | −0.172004 | ||||||||
\(103\) | −0.647440 | −0.0637941 | −0.0318971 | − | 0.999491i | \(-0.510155\pi\) | ||||
−0.0318971 | + | 0.999491i | \(0.510155\pi\) | |||||||
\(104\) | −6.63204 | −0.650325 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.63819 | −0.741886 | ||||||||
\(107\) | 17.8099 | 1.72175 | 0.860875 | − | 0.508817i | \(-0.169917\pi\) | ||||
0.860875 | + | 0.508817i | \(0.169917\pi\) | |||||||
\(108\) | −3.57912 | −0.344401 | ||||||||
\(109\) | −4.16066 | −0.398519 | −0.199259 | − | 0.979947i | \(-0.563854\pi\) | ||||
−0.199259 | + | 0.979947i | \(0.563854\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.00418 | −0.380060 | ||||||||
\(112\) | 2.07634 | 0.196195 | ||||||||
\(113\) | 2.35008 | 0.221077 | 0.110539 | − | 0.993872i | \(-0.464742\pi\) | ||||
0.110539 | + | 0.993872i | \(0.464742\pi\) | |||||||
\(114\) | −0.887737 | −0.0831442 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.46952 | 0.229290 | ||||||||
\(117\) | 8.90439 | 0.823211 | ||||||||
\(118\) | 0.620247 | 0.0570984 | ||||||||
\(119\) | −8.10612 | −0.743087 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9993 | −0.999935 | ||||||||
\(122\) | −0.523314 | −0.0473786 | ||||||||
\(123\) | 3.06093 | 0.275995 | ||||||||
\(124\) | −10.5460 | −0.947054 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.67015 | 0.148789 | ||||||||
\(127\) | −11.0139 | −0.977323 | −0.488662 | − | 0.872473i | \(-0.662515\pi\) | ||||
−0.488662 | + | 0.872473i | \(0.662515\pi\) | |||||||
\(128\) | 11.5152 | 1.01781 | ||||||||
\(129\) | 1.37414 | 0.120986 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.25785 | 0.721492 | 0.360746 | − | 0.932664i | \(-0.382522\pi\) | ||||
0.360746 | + | 0.932664i | \(0.382522\pi\) | |||||||
\(132\) | 0.0162943 | 0.00141824 | ||||||||
\(133\) | −4.14248 | −0.359198 | ||||||||
\(134\) | −7.25694 | −0.626904 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −17.2966 | −1.48317 | ||||||||
\(137\) | 18.1430 | 1.55006 | 0.775031 | − | 0.631923i | \(-0.217734\pi\) | ||||
0.775031 | + | 0.631923i | \(0.217734\pi\) | |||||||
\(138\) | −0.214301 | −0.0182425 | ||||||||
\(139\) | −10.9562 | −0.929292 | −0.464646 | − | 0.885497i | \(-0.653818\pi\) | ||||
−0.464646 | + | 0.885497i | \(0.653818\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.37509 | 0.368449 | ||||||||
\(142\) | 6.76742 | 0.567909 | ||||||||
\(143\) | −0.0829883 | −0.00693983 | ||||||||
\(144\) | −5.94844 | −0.495703 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.90804 | −0.157911 | ||||||||
\(147\) | −0.367598 | −0.0303190 | ||||||||
\(148\) | −18.0836 | −1.48646 | ||||||||
\(149\) | 11.2894 | 0.924864 | 0.462432 | − | 0.886655i | \(-0.346977\pi\) | ||||
0.462432 | + | 0.886655i | \(0.346977\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.60271 | −0.293185 | −0.146592 | − | 0.989197i | \(-0.546831\pi\) | ||||
−0.146592 | + | 0.989197i | \(0.546831\pi\) | |||||||
\(152\) | −8.83911 | −0.716946 | ||||||||
\(153\) | 23.2230 | 1.87747 | ||||||||
\(154\) | −0.0155657 | −0.00125432 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.89678 | −0.151864 | ||||||||
\(157\) | −7.96765 | −0.635888 | −0.317944 | − | 0.948110i | \(-0.602992\pi\) | ||||
−0.317944 | + | 0.948110i | \(0.602992\pi\) | |||||||
\(158\) | 2.43228 | 0.193502 | ||||||||
\(159\) | −4.81629 | −0.381957 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | −4.54844 | −0.357359 | ||||||||
\(163\) | 15.4157 | 1.20745 | 0.603724 | − | 0.797193i | \(-0.293683\pi\) | ||||
0.603724 | + | 0.797193i | \(0.293683\pi\) | |||||||
\(164\) | 13.8237 | 1.07945 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.574882 | 0.0446195 | ||||||||
\(167\) | 14.6991 | 1.13745 | 0.568726 | − | 0.822527i | \(-0.307436\pi\) | ||||
0.568726 | + | 0.822527i | \(0.307436\pi\) | |||||||
\(168\) | −0.784372 | −0.0605156 | ||||||||
\(169\) | −3.33954 | −0.256888 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.8677 | 0.907543 | ||||||||
\(172\) | 6.20585 | 0.473192 | ||||||||
\(173\) | −6.31055 | −0.479782 | −0.239891 | − | 0.970800i | \(-0.577112\pi\) | ||||
−0.239891 | + | 0.970800i | \(0.577112\pi\) | |||||||
\(174\) | −0.318782 | −0.0241668 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.0554390 | 0.00417888 | ||||||||
\(177\) | 0.391099 | 0.0293968 | ||||||||
\(178\) | 9.93478 | 0.744643 | ||||||||
\(179\) | 12.0397 | 0.899892 | 0.449946 | − | 0.893056i | \(-0.351443\pi\) | ||||
0.449946 | + | 0.893056i | \(0.351443\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.4656 | 1.29821 | 0.649103 | − | 0.760700i | \(-0.275144\pi\) | ||||
0.649103 | + | 0.760700i | \(0.275144\pi\) | |||||||
\(182\) | 1.81197 | 0.134312 | ||||||||
\(183\) | −0.329978 | −0.0243927 | ||||||||
\(184\) | −2.13377 | −0.157304 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.36134 | 0.0998181 | ||||||||
\(187\) | −0.216437 | −0.0158274 | ||||||||
\(188\) | 19.7587 | 1.44105 | ||||||||
\(189\) | 2.15592 | 0.156820 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.2513 | −0.741756 | −0.370878 | − | 0.928682i | \(-0.620943\pi\) | ||||
−0.370878 | + | 0.928682i | \(0.620943\pi\) | |||||||
\(192\) | 0.352574 | 0.0254448 | ||||||||
\(193\) | 12.8854 | 0.927514 | 0.463757 | − | 0.885963i | \(-0.346501\pi\) | ||||
0.463757 | + | 0.885963i | \(0.346501\pi\) | |||||||
\(194\) | 4.13197 | 0.296658 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.66014 | −0.118581 | ||||||||
\(197\) | 18.5512 | 1.32172 | 0.660858 | − | 0.750511i | \(-0.270192\pi\) | ||||
0.660858 | + | 0.750511i | \(0.270192\pi\) | |||||||
\(198\) | 0.0445937 | 0.00316914 | ||||||||
\(199\) | 4.77181 | 0.338265 | 0.169132 | − | 0.985593i | \(-0.445903\pi\) | ||||
0.169132 | + | 0.985593i | \(0.445903\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.57589 | −0.322759 | ||||||||
\(202\) | −3.65145 | −0.256915 | ||||||||
\(203\) | −1.48754 | −0.104405 | ||||||||
\(204\) | −4.94687 | −0.346350 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.377442 | 0.0262976 | ||||||||
\(207\) | 2.86487 | 0.199122 | ||||||||
\(208\) | −6.45352 | −0.447471 | ||||||||
\(209\) | −0.110606 | −0.00765076 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.82154 | 0.125400 | 0.0626999 | − | 0.998032i | \(-0.480029\pi\) | ||||
0.0626999 | + | 0.998032i | \(0.480029\pi\) | |||||||
\(212\) | −21.7512 | −1.49388 | ||||||||
\(213\) | 4.26723 | 0.292386 | ||||||||
\(214\) | −10.3828 | −0.709751 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.60024 | 0.313007 | ||||||||
\(217\) | 6.35245 | 0.431233 | ||||||||
\(218\) | 2.42556 | 0.164280 | ||||||||
\(219\) | −1.20312 | −0.0812996 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.1949 | 1.69479 | ||||||||
\(222\) | 2.33434 | 0.156671 | ||||||||
\(223\) | 26.9390 | 1.80397 | 0.901983 | − | 0.431771i | \(-0.142111\pi\) | ||||
0.901983 | + | 0.431771i | \(0.142111\pi\) | |||||||
\(224\) | −5.47800 | −0.366015 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.37004 | −0.0911339 | ||||||||
\(227\) | −0.201134 | −0.0133497 | −0.00667486 | − | 0.999978i | \(-0.502125\pi\) | ||||
−0.00667486 | + | 0.999978i | \(0.502125\pi\) | |||||||
\(228\) | −2.52800 | −0.167421 | ||||||||
\(229\) | 25.8753 | 1.70989 | 0.854943 | − | 0.518723i | \(-0.173592\pi\) | ||||
0.854943 | + | 0.518723i | \(0.173592\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.00981502 | −0.000645781 0 | ||||||||
\(232\) | −3.17408 | −0.208388 | ||||||||
\(233\) | −8.30873 | −0.544323 | −0.272162 | − | 0.962252i | \(-0.587739\pi\) | ||||
−0.272162 | + | 0.962252i | \(0.587739\pi\) | |||||||
\(234\) | −5.19105 | −0.339349 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.76627 | 0.114975 | ||||||||
\(237\) | 1.53369 | 0.0996236 | ||||||||
\(238\) | 4.72568 | 0.306320 | ||||||||
\(239\) | −18.5838 | −1.20209 | −0.601043 | − | 0.799217i | \(-0.705248\pi\) | ||||
−0.601043 | + | 0.799217i | \(0.705248\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.9684 | 1.60836 | 0.804178 | − | 0.594389i | \(-0.202606\pi\) | ||||
0.804178 | + | 0.594389i | \(0.202606\pi\) | |||||||
\(242\) | 6.41232 | 0.412200 | ||||||||
\(243\) | −9.33579 | −0.598891 | ||||||||
\(244\) | −1.49024 | −0.0954027 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.78445 | −0.113772 | ||||||||
\(247\) | 12.8753 | 0.819239 | ||||||||
\(248\) | 13.5547 | 0.860724 | ||||||||
\(249\) | 0.362494 | 0.0229721 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.55142 | 0.224163 | 0.112082 | − | 0.993699i | \(-0.464248\pi\) | ||||
0.112082 | + | 0.993699i | \(0.464248\pi\) | |||||||
\(252\) | 4.75608 | 0.299605 | ||||||||
\(253\) | −0.0267004 | −0.00167864 | ||||||||
\(254\) | 6.42083 | 0.402879 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.79481 | −0.299676 | ||||||||
\(257\) | −13.0752 | −0.815607 | −0.407803 | − | 0.913070i | \(-0.633705\pi\) | ||||
−0.407803 | + | 0.913070i | \(0.633705\pi\) | |||||||
\(258\) | −0.801090 | −0.0498737 | ||||||||
\(259\) | 10.8928 | 0.676846 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.26161 | 0.263787 | ||||||||
\(262\) | −4.81413 | −0.297418 | ||||||||
\(263\) | −14.6392 | −0.902693 | −0.451347 | − | 0.892349i | \(-0.649056\pi\) | ||||
−0.451347 | + | 0.892349i | \(0.649056\pi\) | |||||||
\(264\) | −0.0209430 | −0.00128895 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.41497 | 0.148071 | ||||||||
\(267\) | 6.26442 | 0.383376 | ||||||||
\(268\) | −20.6655 | −1.26235 | ||||||||
\(269\) | 4.50049 | 0.274400 | 0.137200 | − | 0.990543i | \(-0.456190\pi\) | ||||
0.137200 | + | 0.990543i | \(0.456190\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.3892 | −1.05632 | −0.528161 | − | 0.849144i | \(-0.677118\pi\) | ||||
−0.528161 | + | 0.849144i | \(0.677118\pi\) | |||||||
\(272\) | −16.8310 | −1.02053 | ||||||||
\(273\) | 1.14254 | 0.0691498 | ||||||||
\(274\) | −10.5770 | −0.638977 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.610264 | −0.0367336 | ||||||||
\(277\) | 9.94437 | 0.597499 | 0.298750 | − | 0.954332i | \(-0.403430\pi\) | ||||
0.298750 | + | 0.954332i | \(0.403430\pi\) | |||||||
\(278\) | 6.38720 | 0.383079 | ||||||||
\(279\) | −18.1990 | −1.08954 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.03201 | 0.240530 | 0.120265 | − | 0.992742i | \(-0.461626\pi\) | ||||
0.120265 | + | 0.992742i | \(0.461626\pi\) | |||||||
\(282\) | −2.55057 | −0.151884 | ||||||||
\(283\) | −18.5270 | −1.10132 | −0.550659 | − | 0.834730i | \(-0.685623\pi\) | ||||
−0.550659 | + | 0.834730i | \(0.685623\pi\) | |||||||
\(284\) | 19.2715 | 1.14356 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.0483802 | 0.00286078 | ||||||||
\(287\) | −8.32684 | −0.491518 | ||||||||
\(288\) | 15.6938 | 0.924765 | ||||||||
\(289\) | 48.7092 | 2.86525 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.60543 | 0.152733 | ||||||||
\(292\) | −5.43352 | −0.317973 | ||||||||
\(293\) | −9.00421 | −0.526032 | −0.263016 | − | 0.964792i | \(-0.584717\pi\) | ||||
−0.263016 | + | 0.964792i | \(0.584717\pi\) | |||||||
\(294\) | 0.214301 | 0.0124983 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 23.2428 | 1.35096 | ||||||||
\(297\) | 0.0575638 | 0.00334019 | ||||||||
\(298\) | −6.58145 | −0.381253 | ||||||||
\(299\) | 3.10813 | 0.179748 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.73815 | −0.215464 | ||||||||
\(302\) | 2.10030 | 0.120858 | ||||||||
\(303\) | −2.30244 | −0.132271 | ||||||||
\(304\) | −8.60118 | −0.493311 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −13.5385 | −0.773942 | ||||||||
\(307\) | 16.5249 | 0.943123 | 0.471562 | − | 0.881833i | \(-0.343691\pi\) | ||||
0.471562 | + | 0.881833i | \(0.343691\pi\) | |||||||
\(308\) | −0.0443264 | −0.00252573 | ||||||||
\(309\) | 0.237998 | 0.0135392 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.67017 | 0.548345 | 0.274173 | − | 0.961680i | \(-0.411596\pi\) | ||||
0.274173 | + | 0.961680i | \(0.411596\pi\) | |||||||
\(312\) | 2.43793 | 0.138020 | ||||||||
\(313\) | 21.6189 | 1.22197 | 0.610986 | − | 0.791642i | \(-0.290773\pi\) | ||||
0.610986 | + | 0.791642i | \(0.290773\pi\) | |||||||
\(314\) | 4.64495 | 0.262130 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.92639 | 0.389640 | ||||||||
\(317\) | 2.10547 | 0.118255 | 0.0591276 | − | 0.998250i | \(-0.481168\pi\) | ||||
0.0591276 | + | 0.998250i | \(0.481168\pi\) | |||||||
\(318\) | 2.80778 | 0.157453 | ||||||||
\(319\) | −0.0397179 | −0.00222378 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.54689 | −0.365412 | ||||||||
\(322\) | 0.582976 | 0.0324880 | ||||||||
\(323\) | 33.5794 | 1.86841 | ||||||||
\(324\) | −12.9526 | −0.719587 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.98697 | −0.497742 | ||||||||
\(327\) | 1.52945 | 0.0845788 | ||||||||
\(328\) | −17.7676 | −0.981052 | ||||||||
\(329\) | −11.9018 | −0.656169 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.3019 | 1.77547 | 0.887737 | − | 0.460352i | \(-0.152277\pi\) | ||||
0.887737 | + | 0.460352i | \(0.152277\pi\) | |||||||
\(332\) | 1.63709 | 0.0898469 | ||||||||
\(333\) | −31.2065 | −1.71011 | ||||||||
\(334\) | −8.56925 | −0.468888 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.763258 | −0.0416391 | ||||||||
\(337\) | 19.8860 | 1.08326 | 0.541629 | − | 0.840618i | \(-0.317808\pi\) | ||||
0.541629 | + | 0.840618i | \(0.317808\pi\) | |||||||
\(338\) | 1.94687 | 0.105896 | ||||||||
\(339\) | −0.863886 | −0.0469198 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.169613 | 0.00918506 | ||||||||
\(342\) | −6.91857 | −0.374113 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −7.97637 | −0.430057 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.67890 | 0.197779 | ||||||||
\(347\) | −3.71949 | −0.199672 | −0.0998362 | − | 0.995004i | \(-0.531832\pi\) | ||||
−0.0998362 | + | 0.995004i | \(0.531832\pi\) | |||||||
\(348\) | −0.907793 | −0.0486628 | ||||||||
\(349\) | 14.6645 | 0.784975 | 0.392487 | − | 0.919757i | \(-0.371615\pi\) | ||||
0.392487 | + | 0.919757i | \(0.371615\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.70086 | −0.357666 | ||||||||
\(352\) | −0.146265 | −0.00779595 | ||||||||
\(353\) | 26.0664 | 1.38738 | 0.693688 | − | 0.720275i | \(-0.255984\pi\) | ||||
0.693688 | + | 0.720275i | \(0.255984\pi\) | |||||||
\(354\) | −0.228002 | −0.0121182 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 28.2912 | 1.49943 | ||||||||
\(357\) | 2.97980 | 0.157708 | ||||||||
\(358\) | −7.01888 | −0.370959 | ||||||||
\(359\) | −16.6347 | −0.877944 | −0.438972 | − | 0.898501i | \(-0.644657\pi\) | ||||
−0.438972 | + | 0.898501i | \(0.644657\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.83989 | −0.0968361 | ||||||||
\(362\) | −10.1820 | −0.535155 | ||||||||
\(363\) | 4.04332 | 0.212219 | ||||||||
\(364\) | 5.15992 | 0.270453 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.192369 | 0.0100553 | ||||||||
\(367\) | 31.7676 | 1.65825 | 0.829127 | − | 0.559061i | \(-0.188838\pi\) | ||||
0.829127 | + | 0.559061i | \(0.188838\pi\) | |||||||
\(368\) | −2.07634 | −0.108237 | ||||||||
\(369\) | 23.8553 | 1.24186 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.1021 | 0.680225 | ||||||||
\(372\) | 3.87667 | 0.200996 | ||||||||
\(373\) | 0.115224 | 0.00596609 | 0.00298304 | − | 0.999996i | \(-0.499050\pi\) | ||||
0.00298304 | + | 0.999996i | \(0.499050\pi\) | |||||||
\(374\) | 0.126177 | 0.00652448 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −25.3958 | −1.30969 | ||||||||
\(377\) | 4.62347 | 0.238121 | ||||||||
\(378\) | −1.25685 | −0.0646453 | ||||||||
\(379\) | −37.6368 | −1.93327 | −0.966635 | − | 0.256157i | \(-0.917544\pi\) | ||||
−0.966635 | + | 0.256157i | \(0.917544\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.04868 | 0.207420 | ||||||||
\(382\) | 5.97625 | 0.305772 | ||||||||
\(383\) | 34.0526 | 1.74000 | 0.870002 | − | 0.493048i | \(-0.164117\pi\) | ||||
0.870002 | + | 0.493048i | \(0.164117\pi\) | |||||||
\(384\) | −4.23295 | −0.216012 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.51190 | −0.382346 | ||||||||
\(387\) | 10.7093 | 0.544386 | ||||||||
\(388\) | 11.7666 | 0.597358 | ||||||||
\(389\) | 5.56952 | 0.282386 | 0.141193 | − | 0.989982i | \(-0.454906\pi\) | ||||
0.141193 | + | 0.989982i | \(0.454906\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.10612 | 0.409944 | ||||||||
\(392\) | 2.13377 | 0.107772 | ||||||||
\(393\) | −3.03557 | −0.153124 | ||||||||
\(394\) | −10.8149 | −0.544847 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.126989 | 0.00638146 | ||||||||
\(397\) | −36.4612 | −1.82994 | −0.914968 | − | 0.403526i | \(-0.867784\pi\) | ||||
−0.914968 | + | 0.403526i | \(0.867784\pi\) | |||||||
\(398\) | −2.78185 | −0.139442 | ||||||||
\(399\) | 1.52277 | 0.0762337 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.33616 | −0.166600 | −0.0833000 | − | 0.996525i | \(-0.526546\pi\) | ||||
−0.0833000 | + | 0.996525i | \(0.526546\pi\) | |||||||
\(402\) | 2.66764 | 0.133050 | ||||||||
\(403\) | −19.7442 | −0.983531 | ||||||||
\(404\) | −10.3982 | −0.517330 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.867201 | 0.0430385 | ||||||||
\(407\) | 0.290842 | 0.0144165 | ||||||||
\(408\) | 6.35821 | 0.314778 | ||||||||
\(409\) | −3.62760 | −0.179373 | −0.0896866 | − | 0.995970i | \(-0.528587\pi\) | ||||
−0.0896866 | + | 0.995970i | \(0.528587\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.66934 | −0.328974 | ||||||||
\(412\) | 1.07484 | 0.0529535 | ||||||||
\(413\) | −1.06393 | −0.0523526 | ||||||||
\(414\) | −1.67015 | −0.0820835 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 17.0263 | 0.834785 | ||||||||
\(417\) | 4.02748 | 0.197226 | ||||||||
\(418\) | 0.0644806 | 0.00315385 | ||||||||
\(419\) | −14.5798 | −0.712268 | −0.356134 | − | 0.934435i | \(-0.615905\pi\) | ||||
−0.356134 | + | 0.934435i | \(0.615905\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.7980 | −1.06237 | −0.531184 | − | 0.847257i | \(-0.678253\pi\) | ||||
−0.531184 | + | 0.847257i | \(0.678253\pi\) | |||||||
\(422\) | −1.06191 | −0.0516931 | ||||||||
\(423\) | 34.0972 | 1.65786 | ||||||||
\(424\) | 27.9568 | 1.35770 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.48769 | −0.120529 | ||||||||
\(427\) | 0.897659 | 0.0434408 | ||||||||
\(428\) | −29.5669 | −1.42917 | ||||||||
\(429\) | 0.0305063 | 0.00147286 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.6012 | −1.66668 | −0.833341 | − | 0.552759i | \(-0.813575\pi\) | ||||
−0.833341 | + | 0.552759i | \(0.813575\pi\) | |||||||
\(432\) | 4.47641 | 0.215371 | ||||||||
\(433\) | −10.5948 | −0.509153 | −0.254577 | − | 0.967053i | \(-0.581936\pi\) | ||||
−0.254577 | + | 0.967053i | \(0.581936\pi\) | |||||||
\(434\) | −3.70333 | −0.177766 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.90727 | 0.330798 | ||||||||
\(437\) | 4.14248 | 0.198162 | ||||||||
\(438\) | 0.701393 | 0.0335138 | ||||||||
\(439\) | −37.4013 | −1.78507 | −0.892534 | − | 0.450979i | \(-0.851075\pi\) | ||||
−0.892534 | + | 0.450979i | \(0.851075\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.86487 | −0.136422 | ||||||||
\(442\) | −14.6880 | −0.698637 | ||||||||
\(443\) | −1.77797 | −0.0844739 | −0.0422370 | − | 0.999108i | \(-0.513448\pi\) | ||||
−0.0422370 | + | 0.999108i | \(0.513448\pi\) | |||||||
\(444\) | 6.64749 | 0.315476 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −15.7048 | −0.743643 | ||||||||
\(447\) | −4.14996 | −0.196286 | ||||||||
\(448\) | −0.959128 | −0.0453145 | ||||||||
\(449\) | 39.3938 | 1.85911 | 0.929554 | − | 0.368687i | \(-0.120193\pi\) | ||||
0.929554 | + | 0.368687i | \(0.120193\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.222330 | −0.0104691 | ||||||||
\(452\) | −3.90146 | −0.183509 | ||||||||
\(453\) | 1.32435 | 0.0622234 | ||||||||
\(454\) | 0.117256 | 0.00550311 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.24924 | 0.152160 | ||||||||
\(457\) | −3.78655 | −0.177127 | −0.0885637 | − | 0.996071i | \(-0.528228\pi\) | ||||
−0.0885637 | + | 0.996071i | \(0.528228\pi\) | |||||||
\(458\) | −15.0847 | −0.704860 | ||||||||
\(459\) | −17.4761 | −0.815715 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.3471 | −1.73943 | −0.869715 | − | 0.493554i | \(-0.835697\pi\) | ||||
−0.869715 | + | 0.493554i | \(0.835697\pi\) | |||||||
\(462\) | 0.00572192 | 0.000266208 0 | ||||||||
\(463\) | 12.1071 | 0.562664 | 0.281332 | − | 0.959610i | \(-0.409224\pi\) | ||||
0.281332 | + | 0.959610i | \(0.409224\pi\) | |||||||
\(464\) | −3.08864 | −0.143386 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.84379 | 0.224384 | ||||||||
\(467\) | 0.197125 | 0.00912185 | 0.00456093 | − | 0.999990i | \(-0.498548\pi\) | ||||
0.00456093 | + | 0.999990i | \(0.498548\pi\) | |||||||
\(468\) | −14.7825 | −0.683322 | ||||||||
\(469\) | 12.4481 | 0.574799 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.92889 | 0.134956 | ||||||||
\(472\) | −2.27019 | −0.104494 | ||||||||
\(473\) | −0.0998102 | −0.00458928 | ||||||||
\(474\) | −0.894102 | −0.0410675 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 13.4573 | 0.616814 | ||||||||
\(477\) | −37.5357 | −1.71864 | ||||||||
\(478\) | 10.8339 | 0.495532 | ||||||||
\(479\) | 32.8344 | 1.50024 | 0.750121 | − | 0.661301i | \(-0.229995\pi\) | ||||
0.750121 | + | 0.661301i | \(0.229995\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −33.8562 | −1.54371 | ||||||||
\(482\) | −14.5560 | −0.663007 | ||||||||
\(483\) | 0.367598 | 0.0167263 | ||||||||
\(484\) | 18.2603 | 0.830015 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5.44254 | 0.246879 | ||||||||
\(487\) | −28.9171 | −1.31036 | −0.655179 | − | 0.755473i | \(-0.727407\pi\) | ||||
−0.655179 | + | 0.755473i | \(0.727407\pi\) | |||||||
\(488\) | 1.91540 | 0.0867062 | ||||||||
\(489\) | −5.66677 | −0.256260 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.57281 | −0.341756 | −0.170878 | − | 0.985292i | \(-0.554660\pi\) | ||||
−0.170878 | + | 0.985292i | \(0.554660\pi\) | |||||||
\(492\) | −5.08157 | −0.229095 | ||||||||
\(493\) | 12.0582 | 0.543074 | ||||||||
\(494\) | −7.50602 | −0.337712 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.1898 | 0.592241 | ||||||||
\(497\) | −11.6084 | −0.520708 | ||||||||
\(498\) | −0.211326 | −0.00946972 | ||||||||
\(499\) | 29.5306 | 1.32197 | 0.660986 | − | 0.750398i | \(-0.270138\pi\) | ||||
0.660986 | + | 0.750398i | \(0.270138\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.40337 | −0.241405 | ||||||||
\(502\) | −2.07039 | −0.0924061 | ||||||||
\(503\) | 14.8127 | 0.660468 | 0.330234 | − | 0.943899i | \(-0.392872\pi\) | ||||
0.330234 | + | 0.943899i | \(0.392872\pi\) | |||||||
\(504\) | −6.11299 | −0.272294 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.0155657 | 0.000691980 0 | ||||||||
\(507\) | 1.22761 | 0.0545200 | ||||||||
\(508\) | 18.2846 | 0.811246 | ||||||||
\(509\) | 29.5150 | 1.30823 | 0.654115 | − | 0.756395i | \(-0.273041\pi\) | ||||
0.654115 | + | 0.756395i | \(0.273041\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.27293 | 0.144786 | ||||||||
\(512\) | −20.2351 | −0.894271 | ||||||||
\(513\) | −8.93083 | −0.394306 | ||||||||
\(514\) | 7.62251 | 0.336215 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.28126 | −0.100427 | ||||||||
\(517\) | −0.317784 | −0.0139761 | ||||||||
\(518\) | −6.35025 | −0.279014 | ||||||||
\(519\) | 2.31975 | 0.101826 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.76947 | −0.296576 | −0.148288 | − | 0.988944i | \(-0.547376\pi\) | ||||
−0.148288 | + | 0.988944i | \(0.547376\pi\) | |||||||
\(522\) | −2.48442 | −0.108740 | ||||||||
\(523\) | 37.6825 | 1.64774 | 0.823870 | − | 0.566779i | \(-0.191811\pi\) | ||||
0.823870 | + | 0.566779i | \(0.191811\pi\) | |||||||
\(524\) | −13.7092 | −0.598888 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.53432 | 0.372114 | ||||||||
\(527\) | −51.4938 | −2.24310 | ||||||||
\(528\) | −0.0203793 | −0.000886895 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.04803 | 0.132273 | ||||||||
\(532\) | 6.87709 | 0.298159 | ||||||||
\(533\) | 25.8809 | 1.12103 | ||||||||
\(534\) | −3.65201 | −0.158038 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 26.5614 | 1.14728 | ||||||||
\(537\) | −4.42578 | −0.190987 | ||||||||
\(538\) | −2.62368 | −0.113115 | ||||||||
\(539\) | 0.0267004 | 0.00115007 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.7575 | −1.27937 | −0.639687 | − | 0.768636i | \(-0.720936\pi\) | ||||
−0.639687 | + | 0.768636i | \(0.720936\pi\) | |||||||
\(542\) | 10.1375 | 0.435444 | ||||||||
\(543\) | −6.42031 | −0.275522 | ||||||||
\(544\) | 44.4054 | 1.90386 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.666075 | −0.0285054 | ||||||||
\(547\) | −11.6592 | −0.498510 | −0.249255 | − | 0.968438i | \(-0.580186\pi\) | ||||
−0.249255 | + | 0.968438i | \(0.580186\pi\) | |||||||
\(548\) | −30.1199 | −1.28666 | ||||||||
\(549\) | −2.57168 | −0.109757 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.16210 | 0.262514 | ||||||||
\(552\) | 0.784372 | 0.0333851 | ||||||||
\(553\) | −4.17218 | −0.177419 | ||||||||
\(554\) | −5.79733 | −0.246305 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.1888 | 0.771377 | ||||||||
\(557\) | 13.9900 | 0.592777 | 0.296389 | − | 0.955067i | \(-0.404218\pi\) | ||||
0.296389 | + | 0.955067i | \(0.404218\pi\) | |||||||
\(558\) | 10.6096 | 0.449139 | ||||||||
\(559\) | 11.6187 | 0.491417 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.0795617 | 0.00335910 | ||||||||
\(562\) | −2.35057 | −0.0991527 | ||||||||
\(563\) | −34.0803 | −1.43631 | −0.718157 | − | 0.695882i | \(-0.755014\pi\) | ||||
−0.718157 | + | 0.695882i | \(0.755014\pi\) | |||||||
\(564\) | −7.26325 | −0.305838 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10.8008 | 0.453992 | ||||||||
\(567\) | 7.80210 | 0.327658 | ||||||||
\(568\) | −24.7697 | −1.03931 | ||||||||
\(569\) | −5.07887 | −0.212917 | −0.106459 | − | 0.994317i | \(-0.533951\pi\) | ||||
−0.106459 | + | 0.994317i | \(0.533951\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.1865 | 0.970326 | 0.485163 | − | 0.874424i | \(-0.338760\pi\) | ||||
0.485163 | + | 0.874424i | \(0.338760\pi\) | |||||||
\(572\) | 0.137772 | 0.00576054 | ||||||||
\(573\) | 3.76835 | 0.157425 | ||||||||
\(574\) | 4.85435 | 0.202617 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.74778 | 0.114491 | ||||||||
\(577\) | 8.26129 | 0.343922 | 0.171961 | − | 0.985104i | \(-0.444990\pi\) | ||||
0.171961 | + | 0.985104i | \(0.444990\pi\) | |||||||
\(578\) | −28.3963 | −1.18113 | ||||||||
\(579\) | −4.73666 | −0.196849 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.986115 | −0.0409110 | ||||||||
\(582\) | −1.51890 | −0.0629606 | ||||||||
\(583\) | 0.349830 | 0.0144885 | ||||||||
\(584\) | 6.98370 | 0.288987 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.24924 | 0.216844 | ||||||||
\(587\) | 31.4936 | 1.29988 | 0.649940 | − | 0.759985i | \(-0.274794\pi\) | ||||
0.649940 | + | 0.759985i | \(0.274794\pi\) | |||||||
\(588\) | 0.610264 | 0.0251669 | ||||||||
\(589\) | −26.3149 | −1.08429 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.81938 | −0.280512 | ||||||||
\(592\) | 22.6171 | 0.929559 | ||||||||
\(593\) | −29.1504 | −1.19707 | −0.598533 | − | 0.801098i | \(-0.704249\pi\) | ||||
−0.598533 | + | 0.801098i | \(0.704249\pi\) | |||||||
\(594\) | −0.0335584 | −0.00137692 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −18.7420 | −0.767701 | ||||||||
\(597\) | −1.75411 | −0.0717909 | ||||||||
\(598\) | −1.81197 | −0.0740968 | ||||||||
\(599\) | −22.2900 | −0.910744 | −0.455372 | − | 0.890301i | \(-0.650494\pi\) | ||||
−0.455372 | + | 0.890301i | \(0.650494\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.35959 | −0.340995 | −0.170497 | − | 0.985358i | \(-0.554537\pi\) | ||||
−0.170497 | + | 0.985358i | \(0.554537\pi\) | |||||||
\(602\) | 2.17925 | 0.0888198 | ||||||||
\(603\) | −35.6622 | −1.45228 | ||||||||
\(604\) | 5.98100 | 0.243364 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.34227 | 0.0545258 | ||||||||
\(607\) | 12.2796 | 0.498412 | 0.249206 | − | 0.968450i | \(-0.419830\pi\) | ||||
0.249206 | + | 0.968450i | \(0.419830\pi\) | |||||||
\(608\) | 22.6925 | 0.920303 | ||||||||
\(609\) | 0.546817 | 0.0221582 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 36.9924 | 1.49655 | ||||||||
\(612\) | −38.5534 | −1.55843 | ||||||||
\(613\) | −5.40643 | −0.218364 | −0.109182 | − | 0.994022i | \(-0.534823\pi\) | ||||
−0.109182 | + | 0.994022i | \(0.534823\pi\) | |||||||
\(614\) | −9.63360 | −0.388780 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.0569726 | 0.00229549 | ||||||||
\(617\) | 4.26177 | 0.171572 | 0.0857862 | − | 0.996314i | \(-0.472660\pi\) | ||||
0.0857862 | + | 0.996314i | \(0.472660\pi\) | |||||||
\(618\) | −0.138747 | −0.00558122 | ||||||||
\(619\) | 22.7559 | 0.914636 | 0.457318 | − | 0.889303i | \(-0.348810\pi\) | ||||
0.457318 | + | 0.889303i | \(0.348810\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.15592 | −0.0865139 | ||||||||
\(622\) | −5.63748 | −0.226042 | ||||||||
\(623\) | −17.0415 | −0.682752 | ||||||||
\(624\) | 2.37230 | 0.0949681 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −12.6033 | −0.503729 | ||||||||
\(627\) | 0.0406585 | 0.00162374 | ||||||||
\(628\) | 13.2274 | 0.527831 | ||||||||
\(629\) | −88.2984 | −3.52069 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.6945 | −1.38117 | −0.690583 | − | 0.723253i | \(-0.742646\pi\) | ||||
−0.690583 | + | 0.723253i | \(0.742646\pi\) | |||||||
\(632\) | −8.90249 | −0.354122 | ||||||||
\(633\) | −0.669594 | −0.0266140 | ||||||||
\(634\) | −1.22744 | −0.0487479 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7.99571 | 0.317051 | ||||||||
\(637\) | −3.10813 | −0.123149 | ||||||||
\(638\) | 0.0231546 | 0.000916700 0 | ||||||||
\(639\) | 33.2566 | 1.31561 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.9845 | 1.02633 | 0.513163 | − | 0.858291i | \(-0.328474\pi\) | ||||
0.513163 | + | 0.858291i | \(0.328474\pi\) | |||||||
\(642\) | 3.81668 | 0.150633 | ||||||||
\(643\) | −8.23620 | −0.324804 | −0.162402 | − | 0.986725i | \(-0.551924\pi\) | ||||
−0.162402 | + | 0.986725i | \(0.551924\pi\) | |||||||
\(644\) | 1.66014 | 0.0654186 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −19.5760 | −0.770208 | ||||||||
\(647\) | −20.2308 | −0.795354 | −0.397677 | − | 0.917526i | \(-0.630183\pi\) | ||||
−0.397677 | + | 0.917526i | \(0.630183\pi\) | |||||||
\(648\) | 16.6479 | 0.653992 | ||||||||
\(649\) | −0.0284074 | −0.00111509 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.33515 | −0.0915217 | ||||||||
\(652\) | −25.5921 | −1.00227 | ||||||||
\(653\) | −37.3573 | −1.46190 | −0.730952 | − | 0.682429i | \(-0.760924\pi\) | ||||
−0.730952 | + | 0.682429i | \(0.760924\pi\) | |||||||
\(654\) | −0.891633 | −0.0348656 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −17.2893 | −0.675035 | ||||||||
\(657\) | −9.37653 | −0.365813 | ||||||||
\(658\) | 6.93848 | 0.270490 | ||||||||
\(659\) | 22.8235 | 0.889077 | 0.444538 | − | 0.895760i | \(-0.353368\pi\) | ||||
0.444538 | + | 0.895760i | \(0.353368\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.10581 | −0.198593 | −0.0992964 | − | 0.995058i | \(-0.531659\pi\) | ||||
−0.0992964 | + | 0.995058i | \(0.531659\pi\) | |||||||
\(662\) | −18.8312 | −0.731897 | ||||||||
\(663\) | −9.26159 | −0.359690 | ||||||||
\(664\) | −2.10415 | −0.0816567 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 18.1927 | 0.704951 | ||||||||
\(667\) | 1.48754 | 0.0575978 | ||||||||
\(668\) | −24.4026 | −0.944165 | ||||||||
\(669\) | −9.90272 | −0.382861 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.0239679 | 0.000925269 0 | ||||||||
\(672\) | 2.01370 | 0.0776803 | ||||||||
\(673\) | −17.4364 | −0.672123 | −0.336061 | − | 0.941840i | \(-0.609095\pi\) | ||||
−0.336061 | + | 0.941840i | \(0.609095\pi\) | |||||||
\(674\) | −11.5930 | −0.446547 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.54410 | 0.213235 | ||||||||
\(677\) | 10.2077 | 0.392312 | 0.196156 | − | 0.980573i | \(-0.437154\pi\) | ||||
0.196156 | + | 0.980573i | \(0.437154\pi\) | |||||||
\(678\) | 0.503625 | 0.0193416 | ||||||||
\(679\) | −7.08771 | −0.272002 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.0739364 | 0.00283325 | ||||||||
\(682\) | −0.0988804 | −0.00378633 | ||||||||
\(683\) | 11.6087 | 0.444196 | 0.222098 | − | 0.975024i | \(-0.428710\pi\) | ||||
0.222098 | + | 0.975024i | \(0.428710\pi\) | |||||||
\(684\) | −19.7020 | −0.753324 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.582976 | −0.0222581 | ||||||||
\(687\) | −9.51170 | −0.362894 | ||||||||
\(688\) | −7.76167 | −0.295911 | ||||||||
\(689\) | −40.7229 | −1.55142 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.04770 | 0.115940 | 0.0579700 | − | 0.998318i | \(-0.481537\pi\) | ||||
0.0579700 | + | 0.998318i | \(0.481537\pi\) | |||||||
\(692\) | 10.4764 | 0.398252 | ||||||||
\(693\) | −0.0764932 | −0.00290574 | ||||||||
\(694\) | 2.16837 | 0.0823103 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.16678 | 0.0442269 | ||||||||
\(697\) | 67.4984 | 2.55668 | ||||||||
\(698\) | −8.54908 | −0.323587 | ||||||||
\(699\) | 3.05427 | 0.115523 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.6080 | −1.04274 | −0.521370 | − | 0.853331i | \(-0.674579\pi\) | ||||
−0.521370 | + | 0.853331i | \(0.674579\pi\) | |||||||
\(702\) | 3.90645 | 0.147439 | ||||||||
\(703\) | −45.1232 | −1.70185 | ||||||||
\(704\) | −0.0256091 | −0.000965179 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.1961 | −0.571914 | ||||||||
\(707\) | 6.26346 | 0.235562 | ||||||||
\(708\) | −0.649279 | −0.0244014 | ||||||||
\(709\) | 10.7441 | 0.403504 | 0.201752 | − | 0.979437i | \(-0.435337\pi\) | ||||
0.201752 | + | 0.979437i | \(0.435337\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.9528 | 0.448263 | ||||||||
\(712\) | −36.3627 | −1.36275 | ||||||||
\(713\) | −6.35245 | −0.237901 | ||||||||
\(714\) | −1.73715 | −0.0650112 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −19.9876 | −0.746972 | ||||||||
\(717\) | 6.83137 | 0.255122 | ||||||||
\(718\) | 9.69761 | 0.361912 | ||||||||
\(719\) | 18.6767 | 0.696522 | 0.348261 | − | 0.937398i | \(-0.386772\pi\) | ||||
0.348261 | + | 0.937398i | \(0.386772\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.647440 | −0.0241119 | ||||||||
\(722\) | 1.07261 | 0.0399184 | ||||||||
\(723\) | −9.17834 | −0.341346 | ||||||||
\(724\) | −28.9953 | −1.07760 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.35716 | −0.0874824 | ||||||||
\(727\) | 34.5497 | 1.28138 | 0.640688 | − | 0.767801i | \(-0.278649\pi\) | ||||
0.640688 | + | 0.767801i | \(0.278649\pi\) | |||||||
\(728\) | −6.63204 | −0.245800 | ||||||||
\(729\) | −19.9745 | −0.739796 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.3019 | 1.12076 | ||||||||
\(732\) | 0.547809 | 0.0202476 | ||||||||
\(733\) | −26.7884 | −0.989454 | −0.494727 | − | 0.869049i | \(-0.664732\pi\) | ||||
−0.494727 | + | 0.869049i | \(0.664732\pi\) | |||||||
\(734\) | −18.5197 | −0.683576 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.47800 | 0.201922 | ||||||||
\(737\) | 0.332369 | 0.0122430 | ||||||||
\(738\) | −13.9071 | −0.511927 | ||||||||
\(739\) | 30.0904 | 1.10689 | 0.553447 | − | 0.832885i | \(-0.313312\pi\) | ||||
0.553447 | + | 0.832885i | \(0.313312\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.73296 | −0.173869 | ||||||||
\(742\) | −7.63819 | −0.280407 | ||||||||
\(743\) | 32.4616 | 1.19090 | 0.595450 | − | 0.803392i | \(-0.296974\pi\) | ||||
0.595450 | + | 0.803392i | \(0.296974\pi\) | |||||||
\(744\) | −4.98268 | −0.182674 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.0671730 | −0.00245938 | ||||||||
\(747\) | 2.82509 | 0.103365 | ||||||||
\(748\) | 0.359315 | 0.0131379 | ||||||||
\(749\) | 17.8099 | 0.650760 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.3064 | 1.32484 | 0.662420 | − | 0.749133i | \(-0.269529\pi\) | ||||
0.662420 | + | 0.749133i | \(0.269529\pi\) | |||||||
\(752\) | −24.7122 | −0.901161 | ||||||||
\(753\) | −1.30549 | −0.0475749 | ||||||||
\(754\) | −2.69537 | −0.0981597 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.57912 | −0.130171 | ||||||||
\(757\) | −12.4321 | −0.451853 | −0.225926 | − | 0.974144i | \(-0.572541\pi\) | ||||
−0.225926 | + | 0.974144i | \(0.572541\pi\) | |||||||
\(758\) | 21.9413 | 0.796945 | ||||||||
\(759\) | 0.00981502 | 0.000356263 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.8319 | −1.26266 | −0.631329 | − | 0.775515i | \(-0.717490\pi\) | ||||
−0.631329 | + | 0.775515i | \(0.717490\pi\) | |||||||
\(762\) | −2.36028 | −0.0855041 | ||||||||
\(763\) | −4.16066 | −0.150626 | ||||||||
\(764\) | 17.0185 | 0.615709 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.8518 | −0.717276 | ||||||||
\(767\) | 3.30684 | 0.119403 | ||||||||
\(768\) | 1.76256 | 0.0636010 | ||||||||
\(769\) | 41.4728 | 1.49555 | 0.747774 | − | 0.663953i | \(-0.231123\pi\) | ||||
0.747774 | + | 0.663953i | \(0.231123\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.80641 | 0.173099 | ||||||||
\(772\) | −21.3916 | −0.769901 | ||||||||
\(773\) | −29.0392 | −1.04447 | −0.522234 | − | 0.852802i | \(-0.674901\pi\) | ||||
−0.522234 | + | 0.852802i | \(0.674901\pi\) | |||||||
\(774\) | −6.24328 | −0.224410 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −15.1236 | −0.542905 | ||||||||
\(777\) | −4.00418 | −0.143649 | ||||||||
\(778\) | −3.24690 | −0.116407 | ||||||||
\(779\) | 34.4938 | 1.23587 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.309949 | −0.0110908 | ||||||||
\(782\) | −4.72568 | −0.168990 | ||||||||
\(783\) | −3.20701 | −0.114609 | ||||||||
\(784\) | 2.07634 | 0.0741549 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.76967 | 0.0631219 | ||||||||
\(787\) | 5.23260 | 0.186522 | 0.0932610 | − | 0.995642i | \(-0.470271\pi\) | ||||
0.0932610 | + | 0.995642i | \(0.470271\pi\) | |||||||
\(788\) | −30.7975 | −1.09712 | ||||||||
\(789\) | 5.38135 | 0.191581 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.35008 | 0.0835593 | ||||||||
\(792\) | −0.163219 | −0.00579974 | ||||||||
\(793\) | −2.79004 | −0.0990772 | ||||||||
\(794\) | 21.2560 | 0.754348 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.92187 | −0.280783 | ||||||||
\(797\) | −36.0192 | −1.27587 | −0.637933 | − | 0.770092i | \(-0.720210\pi\) | ||||
−0.637933 | + | 0.770092i | \(0.720210\pi\) | |||||||
\(798\) | −0.887737 | −0.0314256 | ||||||||
\(799\) | 96.4776 | 3.41313 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 48.8216 | 1.72503 | ||||||||
\(802\) | 1.94490 | 0.0686770 | ||||||||
\(803\) | 0.0873886 | 0.00308388 | ||||||||
\(804\) | 7.59662 | 0.267912 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.5104 | 0.405437 | ||||||||
\(807\) | −1.65437 | −0.0582367 | ||||||||
\(808\) | 13.3648 | 0.470172 | ||||||||
\(809\) | −1.76325 | −0.0619925 | −0.0309962 | − | 0.999520i | \(-0.509868\pi\) | ||||
−0.0309962 | + | 0.999520i | \(0.509868\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.9994 | −0.737388 | −0.368694 | − | 0.929551i | \(-0.620195\pi\) | ||||
−0.368694 | + | 0.929551i | \(0.620195\pi\) | |||||||
\(812\) | 2.46952 | 0.0866633 | ||||||||
\(813\) | 6.39226 | 0.224186 | ||||||||
\(814\) | −0.169554 | −0.00594287 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.18706 | 0.216590 | ||||||||
\(817\) | 15.4852 | 0.541759 | ||||||||
\(818\) | 2.11480 | 0.0739424 | ||||||||
\(819\) | 8.90439 | 0.311145 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.7805 | 0.480942 | 0.240471 | − | 0.970656i | \(-0.422698\pi\) | ||||
0.240471 | + | 0.970656i | \(0.422698\pi\) | |||||||
\(822\) | 3.88807 | 0.135612 | ||||||||
\(823\) | 27.1880 | 0.947715 | 0.473857 | − | 0.880602i | \(-0.342861\pi\) | ||||
0.473857 | + | 0.880602i | \(0.342861\pi\) | |||||||
\(824\) | −1.38149 | −0.0481265 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.620247 | 0.0215812 | ||||||||
\(827\) | 34.4957 | 1.19953 | 0.599766 | − | 0.800175i | \(-0.295260\pi\) | ||||
0.599766 | + | 0.800175i | \(0.295260\pi\) | |||||||
\(828\) | −4.75608 | −0.165285 | ||||||||
\(829\) | 33.2015 | 1.15314 | 0.576568 | − | 0.817049i | \(-0.304392\pi\) | ||||
0.576568 | + | 0.817049i | \(0.304392\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.65553 | −0.126809 | ||||||||
\(832\) | 2.98109 | 0.103351 | ||||||||
\(833\) | −8.10612 | −0.280860 | ||||||||
\(834\) | −2.34792 | −0.0813019 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.183621 | 0.00635066 | ||||||||
\(837\) | 13.6954 | 0.473381 | ||||||||
\(838\) | 8.49965 | 0.293616 | ||||||||
\(839\) | 25.4737 | 0.879451 | 0.439726 | − | 0.898132i | \(-0.355076\pi\) | ||||
0.439726 | + | 0.898132i | \(0.355076\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.7872 | −0.923697 | ||||||||
\(842\) | 12.7077 | 0.437936 | ||||||||
\(843\) | −1.48216 | −0.0510483 | ||||||||
\(844\) | −3.02401 | −0.104091 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −19.8779 | −0.683415 | ||||||||
\(847\) | −10.9993 | −0.377940 | ||||||||
\(848\) | 27.2043 | 0.934199 | ||||||||
\(849\) | 6.81050 | 0.233736 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.8928 | −0.373401 | ||||||||
\(852\) | −7.08419 | −0.242700 | ||||||||
\(853\) | −33.0155 | −1.13043 | −0.565215 | − | 0.824944i | \(-0.691207\pi\) | ||||
−0.565215 | + | 0.824944i | \(0.691207\pi\) | |||||||
\(854\) | −0.523314 | −0.0179074 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 38.0023 | 1.29889 | ||||||||
\(857\) | 32.6486 | 1.11525 | 0.557627 | − | 0.830091i | \(-0.311712\pi\) | ||||
0.557627 | + | 0.830091i | \(0.311712\pi\) | |||||||
\(858\) | −0.0177845 | −0.000607152 0 | ||||||||
\(859\) | −34.8450 | −1.18890 | −0.594448 | − | 0.804134i | \(-0.702630\pi\) | ||||
−0.594448 | + | 0.804134i | \(0.702630\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.06093 | 0.104316 | ||||||||
\(862\) | 20.1717 | 0.687051 | ||||||||
\(863\) | −26.8030 | −0.912385 | −0.456192 | − | 0.889881i | \(-0.650787\pi\) | ||||
−0.456192 | + | 0.889881i | \(0.650787\pi\) | |||||||
\(864\) | −11.8101 | −0.401788 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.17651 | 0.209886 | ||||||||
\(867\) | −17.9054 | −0.608100 | ||||||||
\(868\) | −10.5460 | −0.357953 | ||||||||
\(869\) | −0.111399 | −0.00377895 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −38.6902 | −1.31097 | ||||||||
\(872\) | −8.87790 | −0.300644 | ||||||||
\(873\) | 20.3054 | 0.687233 | ||||||||
\(874\) | −2.41497 | −0.0816874 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.99735 | 0.0674843 | ||||||||
\(877\) | 51.2702 | 1.73127 | 0.865635 | − | 0.500675i | \(-0.166915\pi\) | ||||
0.865635 | + | 0.500675i | \(0.166915\pi\) | |||||||
\(878\) | 21.8041 | 0.735853 | ||||||||
\(879\) | 3.30993 | 0.111641 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.0726 | −0.743646 | −0.371823 | − | 0.928304i | \(-0.621267\pi\) | ||||
−0.371823 | + | 0.928304i | \(0.621267\pi\) | |||||||
\(882\) | 1.67015 | 0.0562370 | ||||||||
\(883\) | 23.5847 | 0.793687 | 0.396844 | − | 0.917886i | \(-0.370105\pi\) | ||||
0.396844 | + | 0.917886i | \(0.370105\pi\) | |||||||
\(884\) | −41.8270 | −1.40679 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.03651 | 0.0348224 | ||||||||
\(887\) | −14.6114 | −0.490602 | −0.245301 | − | 0.969447i | \(-0.578887\pi\) | ||||
−0.245301 | + | 0.969447i | \(0.578887\pi\) | |||||||
\(888\) | −8.54401 | −0.286718 | ||||||||
\(889\) | −11.0139 | −0.369393 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.208319 | 0.00697896 | ||||||||
\(892\) | −44.7224 | −1.49742 | ||||||||
\(893\) | 49.3030 | 1.64986 | ||||||||
\(894\) | 2.41933 | 0.0809145 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 11.5152 | 0.384694 | ||||||||
\(897\) | −1.14254 | −0.0381484 | ||||||||
\(898\) | −22.9656 | −0.766373 | ||||||||
\(899\) | −9.44953 | −0.315160 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −106.207 | −3.53826 | ||||||||
\(902\) | 0.129613 | 0.00431565 | ||||||||
\(903\) | 1.37414 | 0.0457285 | ||||||||
\(904\) | 5.01454 | 0.166781 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.772065 | −0.0256501 | ||||||||
\(907\) | −10.0900 | −0.335034 | −0.167517 | − | 0.985869i | \(-0.553575\pi\) | ||||
−0.167517 | + | 0.985869i | \(0.553575\pi\) | |||||||
\(908\) | 0.333910 | 0.0110812 | ||||||||
\(909\) | −17.9440 | −0.595165 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.5530 | −1.50924 | −0.754619 | − | 0.656163i | \(-0.772179\pi\) | ||||
−0.754619 | + | 0.656163i | \(0.772179\pi\) | |||||||
\(912\) | 3.16178 | 0.104697 | ||||||||
\(913\) | −0.0263297 | −0.000871385 0 | ||||||||
\(914\) | 2.20747 | 0.0730166 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −42.9565 | −1.41932 | ||||||||
\(917\) | 8.25785 | 0.272698 | ||||||||
\(918\) | 10.1882 | 0.336260 | ||||||||
\(919\) | 41.8047 | 1.37901 | 0.689504 | − | 0.724282i | \(-0.257829\pi\) | ||||
0.689504 | + | 0.724282i | \(0.257829\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.07451 | −0.200162 | ||||||||
\(922\) | 21.7725 | 0.717039 | ||||||||
\(923\) | 36.0804 | 1.18760 | ||||||||
\(924\) | 0.0162943 | 0.000536043 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −7.05815 | −0.231945 | ||||||||
\(927\) | 1.85483 | 0.0609207 | ||||||||
\(928\) | 8.14876 | 0.267496 | ||||||||
\(929\) | 8.45666 | 0.277454 | 0.138727 | − | 0.990331i | \(-0.455699\pi\) | ||||
0.138727 | + | 0.990331i | \(0.455699\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.14248 | −0.135764 | ||||||||
\(932\) | 13.7936 | 0.451826 | ||||||||
\(933\) | −3.55474 | −0.116377 | ||||||||
\(934\) | −0.114919 | −0.00376027 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 19.0000 | 0.621033 | ||||||||
\(937\) | 26.1767 | 0.855155 | 0.427578 | − | 0.903979i | \(-0.359367\pi\) | ||||
0.427578 | + | 0.903979i | \(0.359367\pi\) | |||||||
\(938\) | −7.25694 | −0.236947 | ||||||||
\(939\) | −7.94706 | −0.259343 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38.0124 | −1.23917 | −0.619585 | − | 0.784929i | \(-0.712699\pi\) | ||||
−0.619585 | + | 0.784929i | \(0.712699\pi\) | |||||||
\(942\) | −1.70748 | −0.0556326 | ||||||||
\(943\) | 8.32684 | 0.271159 | ||||||||
\(944\) | −2.20908 | −0.0718995 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.0581870 | 0.00189182 | ||||||||
\(947\) | −16.9759 | −0.551642 | −0.275821 | − | 0.961209i | \(-0.588950\pi\) | ||||
−0.275821 | + | 0.961209i | \(0.588950\pi\) | |||||||
\(948\) | −2.54613 | −0.0826945 | ||||||||
\(949\) | −10.1727 | −0.330219 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.773969 | −0.0250977 | ||||||||
\(952\) | −17.2966 | −0.560587 | ||||||||
\(953\) | −3.41279 | −0.110551 | −0.0552756 | − | 0.998471i | \(-0.517604\pi\) | ||||
−0.0552756 | + | 0.998471i | \(0.517604\pi\) | |||||||
\(954\) | 21.8824 | 0.708470 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 30.8517 | 0.997815 | ||||||||
\(957\) | 0.0146002 | 0.000471959 0 | ||||||||
\(958\) | −19.1417 | −0.618440 | ||||||||
\(959\) | 18.1430 | 0.585869 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.35365 | 0.301731 | ||||||||
\(962\) | 19.7374 | 0.636359 | ||||||||
\(963\) | −51.0231 | −1.64420 | ||||||||
\(964\) | −41.4510 | −1.33505 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.214301 | −0.00689502 | ||||||||
\(967\) | −43.4582 | −1.39752 | −0.698761 | − | 0.715355i | \(-0.746265\pi\) | ||||
−0.698761 | + | 0.715355i | \(0.746265\pi\) | |||||||
\(968\) | −23.4700 | −0.754354 | ||||||||
\(969\) | −12.3437 | −0.396538 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −56.8918 | −1.82575 | −0.912873 | − | 0.408244i | \(-0.866141\pi\) | ||||
−0.912873 | + | 0.408244i | \(0.866141\pi\) | |||||||
\(972\) | 15.4987 | 0.497121 | ||||||||
\(973\) | −10.9562 | −0.351239 | ||||||||
\(974\) | 16.8580 | 0.540165 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.86384 | 0.0596602 | ||||||||
\(977\) | 49.9260 | 1.59727 | 0.798637 | − | 0.601813i | \(-0.205555\pi\) | ||||
0.798637 | + | 0.601813i | \(0.205555\pi\) | |||||||
\(978\) | 3.30359 | 0.105637 | ||||||||
\(979\) | −0.455014 | −0.0145423 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.9197 | 0.380568 | ||||||||
\(982\) | 4.41477 | 0.140881 | ||||||||
\(983\) | −16.2972 | −0.519798 | −0.259899 | − | 0.965636i | \(-0.583689\pi\) | ||||
−0.259899 | + | 0.965636i | \(0.583689\pi\) | |||||||
\(984\) | 6.53134 | 0.208212 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.02964 | −0.223869 | ||||||||
\(987\) | 4.37509 | 0.139261 | ||||||||
\(988\) | −21.3749 | −0.680025 | ||||||||
\(989\) | 3.73815 | 0.118866 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.1841 | 1.46709 | 0.733544 | − | 0.679642i | \(-0.237865\pi\) | ||||
0.733544 | + | 0.679642i | \(0.237865\pi\) | |||||||
\(992\) | −34.7988 | −1.10486 | ||||||||
\(993\) | −11.8741 | −0.376814 | ||||||||
\(994\) | 6.76742 | 0.214650 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.601791 | −0.0190685 | ||||||||
\(997\) | −33.5035 | −1.06107 | −0.530533 | − | 0.847664i | \(-0.678008\pi\) | ||||
−0.530533 | + | 0.847664i | \(0.678008\pi\) | |||||||
\(998\) | −17.2157 | −0.544952 | ||||||||
\(999\) | 23.4840 | 0.743000 |
(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 | 4025.2.a.bb.1.6 | yes | 14 | |
5.4 | even | 2 | 4025.2.a.ba.1.9 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4025.2.a.ba.1.9 | ✓ | 14 | 5.4 | even | 2 | ||
4025.2.a.bb.1.6 | yes | 14 | 1.1 | even | 1 | trivial |