Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, 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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.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: | \(48.2216577807\) |
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: | \( x^{14} - x^{13} - 21 x^{12} + 20 x^{11} + 167 x^{10} - 148 x^{9} - 627 x^{8} + 497 x^{7} + 1123 x^{6} + \cdots - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 2013) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(2.45909\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.45909 | 1.73884 | 0.869421 | − | 0.494071i | \(-0.164492\pi\) | ||||
0.869421 | + | 0.494071i | \(0.164492\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.04715 | 2.02357 | ||||||||
\(5\) | 1.85442 | 0.829322 | 0.414661 | − | 0.909976i | \(-0.363900\pi\) | ||||
0.414661 | + | 0.909976i | \(0.363900\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.32343 | 0.878174 | 0.439087 | − | 0.898445i | \(-0.355302\pi\) | ||||
0.439087 | + | 0.898445i | \(0.355302\pi\) | |||||||
\(8\) | 5.03413 | 1.77983 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.56020 | 1.44206 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.54120 | 1.81420 | 0.907101 | − | 0.420913i | \(-0.138290\pi\) | ||||
0.907101 | + | 0.420913i | \(0.138290\pi\) | |||||||
\(14\) | 5.71353 | 1.52701 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.28511 | 1.07128 | ||||||||
\(17\) | −2.94936 | −0.715325 | −0.357663 | − | 0.933851i | \(-0.616426\pi\) | ||||
−0.357663 | + | 0.933851i | \(0.616426\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.42989 | 1.47512 | 0.737558 | − | 0.675283i | \(-0.235979\pi\) | ||||
0.737558 | + | 0.675283i | \(0.235979\pi\) | |||||||
\(20\) | 7.50511 | 1.67819 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.45909 | 0.524281 | ||||||||
\(23\) | 1.80034 | 0.375397 | 0.187699 | − | 0.982227i | \(-0.439897\pi\) | ||||
0.187699 | + | 0.982227i | \(0.439897\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.56112 | −0.312225 | ||||||||
\(26\) | 16.0854 | 3.15461 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 9.40326 | 1.77705 | ||||||||
\(29\) | −8.87924 | −1.64883 | −0.824417 | − | 0.565983i | \(-0.808497\pi\) | ||||
−0.824417 | + | 0.565983i | \(0.808497\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.72079 | 0.488669 | 0.244335 | − | 0.969691i | \(-0.421431\pi\) | ||||
0.244335 | + | 0.969691i | \(0.421431\pi\) | |||||||
\(32\) | 0.469234 | 0.0829497 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.25276 | −1.24384 | ||||||||
\(35\) | 4.30862 | 0.728289 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.53485 | −0.581126 | −0.290563 | − | 0.956856i | \(-0.593843\pi\) | ||||
−0.290563 | + | 0.956856i | \(0.593843\pi\) | |||||||
\(38\) | 15.8117 | 2.56500 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 9.33540 | 1.47606 | ||||||||
\(41\) | 2.27369 | 0.355091 | 0.177545 | − | 0.984113i | \(-0.443184\pi\) | ||||
0.177545 | + | 0.984113i | \(0.443184\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.10603 | −0.473665 | −0.236832 | − | 0.971550i | \(-0.576109\pi\) | ||||
−0.236832 | + | 0.971550i | \(0.576109\pi\) | |||||||
\(44\) | 4.04715 | 0.610131 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.42721 | 0.652757 | ||||||||
\(47\) | −11.7194 | −1.70945 | −0.854724 | − | 0.519082i | \(-0.826274\pi\) | ||||
−0.854724 | + | 0.519082i | \(0.826274\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.60167 | −0.228811 | ||||||||
\(50\) | −3.83895 | −0.542910 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 26.4732 | 3.67117 | ||||||||
\(53\) | −7.91063 | −1.08661 | −0.543304 | − | 0.839536i | \(-0.682827\pi\) | ||||
−0.543304 | + | 0.839536i | \(0.682827\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.85442 | 0.250050 | ||||||||
\(56\) | 11.6965 | 1.56300 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −21.8349 | −2.86706 | ||||||||
\(59\) | 5.84081 | 0.760409 | 0.380204 | − | 0.924903i | \(-0.375854\pi\) | ||||
0.380204 | + | 0.924903i | \(0.375854\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 6.69069 | 0.849719 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.41633 | −0.927042 | ||||||||
\(65\) | 12.1301 | 1.50456 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.0882 | −1.23246 | −0.616232 | − | 0.787564i | \(-0.711342\pi\) | ||||
−0.616232 | + | 0.787564i | \(0.711342\pi\) | |||||||
\(68\) | −11.9365 | −1.44751 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 10.5953 | 1.26638 | ||||||||
\(71\) | −13.7123 | −1.62735 | −0.813676 | − | 0.581319i | \(-0.802537\pi\) | ||||
−0.813676 | + | 0.581319i | \(0.802537\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.7140 | −1.72214 | −0.861070 | − | 0.508486i | \(-0.830205\pi\) | ||||
−0.861070 | + | 0.508486i | \(0.830205\pi\) | |||||||
\(74\) | −8.69254 | −1.01049 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 26.0227 | 2.98501 | ||||||||
\(77\) | 2.32343 | 0.264779 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.60431 | 0.405517 | 0.202758 | − | 0.979229i | \(-0.435009\pi\) | ||||
0.202758 | + | 0.979229i | \(0.435009\pi\) | |||||||
\(80\) | 7.94640 | 0.888435 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.59122 | 0.617447 | ||||||||
\(83\) | 5.22564 | 0.573589 | 0.286794 | − | 0.957992i | \(-0.407410\pi\) | ||||
0.286794 | + | 0.957992i | \(0.407410\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.46935 | −0.593235 | ||||||||
\(86\) | −7.63802 | −0.823629 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.03413 | 0.536640 | ||||||||
\(89\) | 14.1984 | 1.50502 | 0.752511 | − | 0.658579i | \(-0.228842\pi\) | ||||
0.752511 | + | 0.658579i | \(0.228842\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.1980 | 1.59318 | ||||||||
\(92\) | 7.28625 | 0.759644 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −28.8191 | −2.97246 | ||||||||
\(95\) | 11.9237 | 1.22335 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.9948 | 1.82709 | 0.913547 | − | 0.406734i | \(-0.133332\pi\) | ||||
0.913547 | + | 0.406734i | \(0.133332\pi\) | |||||||
\(98\) | −3.93867 | −0.397866 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.31810 | −0.631810 | ||||||||
\(101\) | 16.6067 | 1.65243 | 0.826216 | − | 0.563354i | \(-0.190489\pi\) | ||||
0.826216 | + | 0.563354i | \(0.190489\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.44597 | 0.733673 | 0.366836 | − | 0.930285i | \(-0.380441\pi\) | ||||
0.366836 | + | 0.930285i | \(0.380441\pi\) | |||||||
\(104\) | 32.9292 | 3.22898 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −19.4530 | −1.88944 | ||||||||
\(107\) | −12.3092 | −1.18997 | −0.594986 | − | 0.803736i | \(-0.702842\pi\) | ||||
−0.594986 | + | 0.803736i | \(0.702842\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.4228 | −1.38146 | −0.690728 | − | 0.723115i | \(-0.742710\pi\) | ||||
−0.690728 | + | 0.723115i | \(0.742710\pi\) | |||||||
\(110\) | 4.56020 | 0.434798 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.95616 | 0.940768 | ||||||||
\(113\) | 7.36553 | 0.692891 | 0.346446 | − | 0.938070i | \(-0.387389\pi\) | ||||
0.346446 | + | 0.938070i | \(0.387389\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.33859 | 0.311325 | ||||||||
\(116\) | −35.9356 | −3.33654 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 14.3631 | 1.32223 | ||||||||
\(119\) | −6.85263 | −0.628180 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.45909 | 0.222636 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 11.0115 | 0.988858 | ||||||||
\(125\) | −12.1671 | −1.08826 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.7526 | 0.954136 | 0.477068 | − | 0.878867i | \(-0.341700\pi\) | ||||
0.477068 | + | 0.878867i | \(0.341700\pi\) | |||||||
\(128\) | −19.1759 | −1.69493 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 29.8291 | 2.61619 | ||||||||
\(131\) | 14.8878 | 1.30076 | 0.650378 | − | 0.759611i | \(-0.274611\pi\) | ||||
0.650378 | + | 0.759611i | \(0.274611\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.9394 | 1.29541 | ||||||||
\(134\) | −24.8077 | −2.14306 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −14.8475 | −1.27316 | ||||||||
\(137\) | 12.2986 | 1.05074 | 0.525371 | − | 0.850873i | \(-0.323926\pi\) | ||||
0.525371 | + | 0.850873i | \(0.323926\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.3998 | −1.30620 | −0.653099 | − | 0.757273i | \(-0.726531\pi\) | ||||
−0.653099 | + | 0.757273i | \(0.726531\pi\) | |||||||
\(140\) | 17.4376 | 1.47375 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −33.7199 | −2.82971 | ||||||||
\(143\) | 6.54120 | 0.547002 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.4658 | −1.36741 | ||||||||
\(146\) | −36.1831 | −2.99453 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −14.3061 | −1.17595 | ||||||||
\(149\) | −20.3781 | −1.66944 | −0.834721 | − | 0.550673i | \(-0.814371\pi\) | ||||
−0.834721 | + | 0.550673i | \(0.814371\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.79859 | 0.471883 | 0.235941 | − | 0.971767i | \(-0.424183\pi\) | ||||
0.235941 | + | 0.971767i | \(0.424183\pi\) | |||||||
\(152\) | 32.3689 | 2.62546 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.71353 | 0.460410 | ||||||||
\(155\) | 5.04550 | 0.405264 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.4274 | 0.991817 | 0.495909 | − | 0.868375i | \(-0.334835\pi\) | ||||
0.495909 | + | 0.868375i | \(0.334835\pi\) | |||||||
\(158\) | 8.86334 | 0.705129 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.870157 | 0.0687920 | ||||||||
\(161\) | 4.18297 | 0.329664 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.7740 | 1.23551 | 0.617757 | − | 0.786369i | \(-0.288042\pi\) | ||||
0.617757 | + | 0.786369i | \(0.288042\pi\) | |||||||
\(164\) | 9.20195 | 0.718552 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.8503 | 0.997380 | ||||||||
\(167\) | 11.8094 | 0.913840 | 0.456920 | − | 0.889508i | \(-0.348953\pi\) | ||||
0.456920 | + | 0.889508i | \(0.348953\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 29.7873 | 2.29133 | ||||||||
\(170\) | −13.4497 | −1.03154 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −12.5706 | −0.958496 | ||||||||
\(173\) | −24.1903 | −1.83916 | −0.919578 | − | 0.392907i | \(-0.871469\pi\) | ||||
−0.919578 | + | 0.392907i | \(0.871469\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.62716 | −0.274188 | ||||||||
\(176\) | 4.28511 | 0.323002 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 34.9151 | 2.61700 | ||||||||
\(179\) | 13.3687 | 0.999224 | 0.499612 | − | 0.866249i | \(-0.333476\pi\) | ||||
0.499612 | + | 0.866249i | \(0.333476\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.9666 | −1.40977 | −0.704887 | − | 0.709320i | \(-0.749002\pi\) | ||||
−0.704887 | + | 0.709320i | \(0.749002\pi\) | |||||||
\(182\) | 37.3734 | 2.77030 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.06316 | 0.668145 | ||||||||
\(185\) | −6.55510 | −0.481941 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.94936 | −0.215679 | ||||||||
\(188\) | −47.4301 | −3.45920 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 29.3215 | 2.12721 | ||||||||
\(191\) | −11.3313 | −0.819908 | −0.409954 | − | 0.912106i | \(-0.634455\pi\) | ||||
−0.409954 | + | 0.912106i | \(0.634455\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.588060 | 0.0423295 | 0.0211647 | − | 0.999776i | \(-0.493263\pi\) | ||||
0.0211647 | + | 0.999776i | \(0.493263\pi\) | |||||||
\(194\) | 44.2509 | 3.17703 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.48221 | −0.463015 | ||||||||
\(197\) | −26.5822 | −1.89390 | −0.946952 | − | 0.321376i | \(-0.895855\pi\) | ||||
−0.946952 | + | 0.321376i | \(0.895855\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.56330 | −0.323484 | −0.161742 | − | 0.986833i | \(-0.551711\pi\) | ||||
−0.161742 | + | 0.986833i | \(0.551711\pi\) | |||||||
\(200\) | −7.85891 | −0.555709 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 40.8375 | 2.87332 | ||||||||
\(203\) | −20.6303 | −1.44796 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.21637 | 0.294484 | ||||||||
\(206\) | 18.3103 | 1.27574 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 28.0298 | 1.94351 | ||||||||
\(209\) | 6.42989 | 0.444764 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.2987 | 1.25973 | 0.629867 | − | 0.776703i | \(-0.283109\pi\) | ||||
0.629867 | + | 0.776703i | \(0.283109\pi\) | |||||||
\(212\) | −32.0155 | −2.19883 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −30.2694 | −2.06917 | ||||||||
\(215\) | −5.75988 | −0.392821 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.32157 | 0.429136 | ||||||||
\(218\) | −35.4671 | −2.40213 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.50511 | 0.505995 | ||||||||
\(221\) | −19.2923 | −1.29774 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.67679 | −0.313181 | −0.156590 | − | 0.987664i | \(-0.550050\pi\) | ||||
−0.156590 | + | 0.987664i | \(0.550050\pi\) | |||||||
\(224\) | 1.09023 | 0.0728442 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.1125 | 1.20483 | ||||||||
\(227\) | −9.63473 | −0.639480 | −0.319740 | − | 0.947505i | \(-0.603596\pi\) | ||||
−0.319740 | + | 0.947505i | \(0.603596\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.6987 | 1.30173 | 0.650863 | − | 0.759195i | \(-0.274407\pi\) | ||||
0.650863 | + | 0.759195i | \(0.274407\pi\) | |||||||
\(230\) | 8.20991 | 0.541345 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −44.6993 | −2.93465 | ||||||||
\(233\) | −9.18049 | −0.601434 | −0.300717 | − | 0.953713i | \(-0.597226\pi\) | ||||
−0.300717 | + | 0.953713i | \(0.597226\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.7327 | −1.41768 | ||||||||
\(236\) | 23.6386 | 1.53874 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −16.8513 | −1.09231 | ||||||||
\(239\) | 7.54022 | 0.487736 | 0.243868 | − | 0.969808i | \(-0.421584\pi\) | ||||
0.243868 | + | 0.969808i | \(0.421584\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.7468 | 1.20759 | 0.603794 | − | 0.797141i | \(-0.293655\pi\) | ||||
0.603794 | + | 0.797141i | \(0.293655\pi\) | |||||||
\(242\) | 2.45909 | 0.158077 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.04715 | 0.259092 | ||||||||
\(245\) | −2.97018 | −0.189758 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 42.0592 | 2.67616 | ||||||||
\(248\) | 13.6968 | 0.869750 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −29.9200 | −1.89231 | ||||||||
\(251\) | 11.1054 | 0.700965 | 0.350482 | − | 0.936569i | \(-0.386018\pi\) | ||||
0.350482 | + | 0.936569i | \(0.386018\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.80034 | 0.113187 | ||||||||
\(254\) | 26.4416 | 1.65909 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.3228 | −2.02017 | ||||||||
\(257\) | −14.2372 | −0.888092 | −0.444046 | − | 0.896004i | \(-0.646457\pi\) | ||||
−0.444046 | + | 0.896004i | \(0.646457\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.21298 | −0.510330 | ||||||||
\(260\) | 49.0924 | 3.04458 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 36.6106 | 2.26181 | ||||||||
\(263\) | −23.3083 | −1.43725 | −0.718627 | − | 0.695396i | \(-0.755229\pi\) | ||||
−0.718627 | + | 0.695396i | \(0.755229\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.6696 | −0.901148 | ||||||||
\(266\) | 36.7374 | 2.25251 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −40.8283 | −2.49398 | ||||||||
\(269\) | 0.631304 | 0.0384913 | 0.0192456 | − | 0.999815i | \(-0.493874\pi\) | ||||
0.0192456 | + | 0.999815i | \(0.493874\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0422 | −0.731510 | −0.365755 | − | 0.930711i | \(-0.619189\pi\) | ||||
−0.365755 | + | 0.930711i | \(0.619189\pi\) | |||||||
\(272\) | −12.6383 | −0.766312 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 30.2435 | 1.82708 | ||||||||
\(275\) | −1.56112 | −0.0941393 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.99666 | 0.300220 | 0.150110 | − | 0.988669i | \(-0.452037\pi\) | ||||
0.150110 | + | 0.988669i | \(0.452037\pi\) | |||||||
\(278\) | −37.8697 | −2.27127 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 21.6901 | 1.29623 | ||||||||
\(281\) | 21.8369 | 1.30268 | 0.651340 | − | 0.758786i | \(-0.274207\pi\) | ||||
0.651340 | + | 0.758786i | \(0.274207\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.38159 | 0.557678 | 0.278839 | − | 0.960338i | \(-0.410050\pi\) | ||||
0.278839 | + | 0.960338i | \(0.410050\pi\) | |||||||
\(284\) | −55.4957 | −3.29307 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 16.0854 | 0.951151 | ||||||||
\(287\) | 5.28276 | 0.311831 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.30127 | −0.488310 | ||||||||
\(290\) | −40.4911 | −2.37772 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −59.5496 | −3.48488 | ||||||||
\(293\) | −2.56663 | −0.149944 | −0.0749720 | − | 0.997186i | \(-0.523887\pi\) | ||||
−0.0749720 | + | 0.997186i | \(0.523887\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.8313 | 0.630624 | ||||||||
\(296\) | −17.7949 | −1.03431 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −50.1118 | −2.90290 | ||||||||
\(299\) | 11.7764 | 0.681046 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.21664 | −0.415960 | ||||||||
\(302\) | 14.2593 | 0.820530 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 27.5528 | 1.58026 | ||||||||
\(305\) | 1.85442 | 0.106184 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.7513 | 0.670681 | 0.335341 | − | 0.942097i | \(-0.391149\pi\) | ||||
0.335341 | + | 0.942097i | \(0.391149\pi\) | |||||||
\(308\) | 9.40326 | 0.535801 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 12.4074 | 0.704690 | ||||||||
\(311\) | −0.0431092 | −0.00244450 | −0.00122225 | − | 0.999999i | \(-0.500389\pi\) | ||||
−0.00122225 | + | 0.999999i | \(0.500389\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.75221 | −0.551227 | −0.275614 | − | 0.961268i | \(-0.588881\pi\) | ||||
−0.275614 | + | 0.961268i | \(0.588881\pi\) | |||||||
\(314\) | 30.5602 | 1.72461 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.5872 | 0.820593 | ||||||||
\(317\) | 12.6416 | 0.710023 | 0.355011 | − | 0.934862i | \(-0.384477\pi\) | ||||
0.355011 | + | 0.934862i | \(0.384477\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.87924 | −0.497142 | ||||||||
\(320\) | −13.7530 | −0.768816 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.2863 | 0.573234 | ||||||||
\(323\) | −18.9641 | −1.05519 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.2116 | −0.566439 | ||||||||
\(326\) | 38.7897 | 2.14836 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.4460 | 0.632002 | ||||||||
\(329\) | −27.2292 | −1.50119 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.4514 | 1.34397 | 0.671986 | − | 0.740564i | \(-0.265441\pi\) | ||||
0.671986 | + | 0.740564i | \(0.265441\pi\) | |||||||
\(332\) | 21.1489 | 1.16070 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 29.0405 | 1.58902 | ||||||||
\(335\) | −18.7077 | −1.02211 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.71105 | 0.147680 | 0.0738402 | − | 0.997270i | \(-0.476475\pi\) | ||||
0.0738402 | + | 0.997270i | \(0.476475\pi\) | |||||||
\(338\) | 73.2497 | 3.98426 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −22.1353 | −1.20045 | ||||||||
\(341\) | 2.72079 | 0.147339 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9854 | −1.07911 | ||||||||
\(344\) | −15.6362 | −0.843045 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −59.4863 | −3.19800 | ||||||||
\(347\) | 16.5889 | 0.890541 | 0.445271 | − | 0.895396i | \(-0.353108\pi\) | ||||
0.445271 | + | 0.895396i | \(0.353108\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.3034 | 1.30093 | 0.650465 | − | 0.759536i | \(-0.274574\pi\) | ||||
0.650465 | + | 0.759536i | \(0.274574\pi\) | |||||||
\(350\) | −8.91954 | −0.476769 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.469234 | 0.0250103 | ||||||||
\(353\) | 1.04268 | 0.0554963 | 0.0277482 | − | 0.999615i | \(-0.491166\pi\) | ||||
0.0277482 | + | 0.999615i | \(0.491166\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.4284 | −1.34960 | ||||||||
\(356\) | 57.4628 | 3.04552 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 32.8749 | 1.73749 | ||||||||
\(359\) | −9.78110 | −0.516226 | −0.258113 | − | 0.966115i | \(-0.583101\pi\) | ||||
−0.258113 | + | 0.966115i | \(0.583101\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.3434 | 1.17597 | ||||||||
\(362\) | −46.6406 | −2.45138 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 61.5086 | 3.22393 | ||||||||
\(365\) | −27.2859 | −1.42821 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.48502 | 0.286316 | 0.143158 | − | 0.989700i | \(-0.454274\pi\) | ||||
0.143158 | + | 0.989700i | \(0.454274\pi\) | |||||||
\(368\) | 7.71467 | 0.402155 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −16.1196 | −0.838019 | ||||||||
\(371\) | −18.3798 | −0.954231 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.6216 | −1.11952 | −0.559761 | − | 0.828654i | \(-0.689107\pi\) | ||||
−0.559761 | + | 0.828654i | \(0.689107\pi\) | |||||||
\(374\) | −7.25276 | −0.375031 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −58.9969 | −3.04254 | ||||||||
\(377\) | −58.0809 | −2.99132 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.0189 | 1.49060 | 0.745301 | − | 0.666729i | \(-0.232306\pi\) | ||||
0.745301 | + | 0.666729i | \(0.232306\pi\) | |||||||
\(380\) | 48.2570 | 2.47553 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −27.8649 | −1.42569 | ||||||||
\(383\) | 3.92201 | 0.200406 | 0.100203 | − | 0.994967i | \(-0.468051\pi\) | ||||
0.100203 | + | 0.994967i | \(0.468051\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.30862 | 0.219587 | ||||||||
\(386\) | 1.44610 | 0.0736043 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 72.8276 | 3.69726 | ||||||||
\(389\) | 25.9769 | 1.31708 | 0.658541 | − | 0.752545i | \(-0.271174\pi\) | ||||
0.658541 | + | 0.752545i | \(0.271174\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.30986 | −0.268531 | ||||||||
\(392\) | −8.06304 | −0.407245 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −65.3681 | −3.29320 | ||||||||
\(395\) | 6.68391 | 0.336304 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.1899 | 0.963114 | 0.481557 | − | 0.876415i | \(-0.340071\pi\) | ||||
0.481557 | + | 0.876415i | \(0.340071\pi\) | |||||||
\(398\) | −11.2216 | −0.562488 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.68959 | −0.334480 | ||||||||
\(401\) | −9.45087 | −0.471954 | −0.235977 | − | 0.971759i | \(-0.575829\pi\) | ||||
−0.235977 | + | 0.971759i | \(0.575829\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.7972 | 0.886544 | ||||||||
\(404\) | 67.2099 | 3.34382 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −50.7319 | −2.51778 | ||||||||
\(407\) | −3.53485 | −0.175216 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.7554 | −1.27352 | −0.636762 | − | 0.771061i | \(-0.719727\pi\) | ||||
−0.636762 | + | 0.771061i | \(0.719727\pi\) | |||||||
\(410\) | 10.3685 | 0.512062 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 30.1349 | 1.48464 | ||||||||
\(413\) | 13.5707 | 0.667771 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.69054 | 0.475690 | ||||||||
\(416\) | 3.06935 | 0.150487 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 15.8117 | 0.773376 | ||||||||
\(419\) | 7.79219 | 0.380674 | 0.190337 | − | 0.981719i | \(-0.439042\pi\) | ||||
0.190337 | + | 0.981719i | \(0.439042\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.5371 | −1.39081 | −0.695407 | − | 0.718616i | \(-0.744776\pi\) | ||||
−0.695407 | + | 0.718616i | \(0.744776\pi\) | |||||||
\(422\) | 44.9983 | 2.19048 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −39.8231 | −1.93398 | ||||||||
\(425\) | 4.60432 | 0.223342 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.32343 | 0.112439 | ||||||||
\(428\) | −49.8170 | −2.40800 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −14.1641 | −0.683054 | ||||||||
\(431\) | 0.647148 | 0.0311720 | 0.0155860 | − | 0.999879i | \(-0.495039\pi\) | ||||
0.0155860 | + | 0.999879i | \(0.495039\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.4583 | −0.887052 | −0.443526 | − | 0.896262i | \(-0.646273\pi\) | ||||
−0.443526 | + | 0.896262i | \(0.646273\pi\) | |||||||
\(434\) | 15.5453 | 0.746201 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −58.3713 | −2.79548 | ||||||||
\(437\) | 11.5760 | 0.553755 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.86799 | 0.423246 | 0.211623 | − | 0.977351i | \(-0.432125\pi\) | ||||
0.211623 | + | 0.977351i | \(0.432125\pi\) | |||||||
\(440\) | 9.33540 | 0.445048 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −47.4417 | −2.25657 | ||||||||
\(443\) | −11.3375 | −0.538661 | −0.269330 | − | 0.963048i | \(-0.586802\pi\) | ||||
−0.269330 | + | 0.963048i | \(0.586802\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.3297 | 1.24815 | ||||||||
\(446\) | −11.5007 | −0.544572 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −17.2313 | −0.814104 | ||||||||
\(449\) | 17.3627 | 0.819397 | 0.409698 | − | 0.912221i | \(-0.365634\pi\) | ||||
0.409698 | + | 0.912221i | \(0.365634\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.27369 | 0.107064 | ||||||||
\(452\) | 29.8094 | 1.40212 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −23.6927 | −1.11195 | ||||||||
\(455\) | 28.1835 | 1.32126 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.9050 | −0.790783 | −0.395391 | − | 0.918513i | \(-0.629391\pi\) | ||||
−0.395391 | + | 0.918513i | \(0.629391\pi\) | |||||||
\(458\) | 48.4409 | 2.26350 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 13.5118 | 0.629990 | ||||||||
\(461\) | 31.3017 | 1.45786 | 0.728932 | − | 0.684586i | \(-0.240017\pi\) | ||||
0.728932 | + | 0.684586i | \(0.240017\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.3893 | −0.994044 | −0.497022 | − | 0.867738i | \(-0.665573\pi\) | ||||
−0.497022 | + | 0.867738i | \(0.665573\pi\) | |||||||
\(464\) | −38.0485 | −1.76636 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −22.5757 | −1.04580 | ||||||||
\(467\) | −38.0400 | −1.76028 | −0.880142 | − | 0.474711i | \(-0.842552\pi\) | ||||
−0.880142 | + | 0.474711i | \(0.842552\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.4391 | −1.08232 | ||||||||
\(470\) | −53.4427 | −2.46513 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 29.4034 | 1.35340 | ||||||||
\(473\) | −3.10603 | −0.142815 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.0379 | −0.460568 | ||||||||
\(476\) | −27.7336 | −1.27117 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.5421 | 0.848096 | ||||||||
\(479\) | −36.1392 | −1.65124 | −0.825621 | − | 0.564226i | \(-0.809175\pi\) | ||||
−0.825621 | + | 0.564226i | \(0.809175\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.1222 | −1.05428 | ||||||||
\(482\) | 46.1001 | 2.09980 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.04715 | 0.183961 | ||||||||
\(485\) | 33.3699 | 1.51525 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.8680 | −0.900306 | −0.450153 | − | 0.892951i | \(-0.648631\pi\) | ||||
−0.450153 | + | 0.892951i | \(0.648631\pi\) | |||||||
\(488\) | 5.03413 | 0.227884 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7.30395 | −0.329959 | ||||||||
\(491\) | 23.2929 | 1.05119 | 0.525597 | − | 0.850733i | \(-0.323842\pi\) | ||||
0.525597 | + | 0.850733i | \(0.323842\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.1881 | 1.17945 | ||||||||
\(494\) | 103.427 | 4.65342 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11.6589 | 0.523500 | ||||||||
\(497\) | −31.8596 | −1.42910 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.7308 | −0.838504 | −0.419252 | − | 0.907870i | \(-0.637708\pi\) | ||||
−0.419252 | + | 0.907870i | \(0.637708\pi\) | |||||||
\(500\) | −49.2420 | −2.20217 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 27.3092 | 1.21887 | ||||||||
\(503\) | 22.9645 | 1.02393 | 0.511967 | − | 0.859005i | \(-0.328917\pi\) | ||||
0.511967 | + | 0.859005i | \(0.328917\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 30.7959 | 1.37040 | ||||||||
\(506\) | 4.42721 | 0.196814 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 43.5172 | 1.93076 | ||||||||
\(509\) | 16.0499 | 0.711398 | 0.355699 | − | 0.934601i | \(-0.384243\pi\) | ||||
0.355699 | + | 0.934601i | \(0.384243\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −34.1869 | −1.51234 | ||||||||
\(512\) | −41.1329 | −1.81784 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −35.0106 | −1.54425 | ||||||||
\(515\) | 13.8080 | 0.608451 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.7194 | −0.515418 | ||||||||
\(518\) | −20.1965 | −0.887383 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 61.0647 | 2.67786 | ||||||||
\(521\) | 31.7652 | 1.39166 | 0.695829 | − | 0.718208i | \(-0.255037\pi\) | ||||
0.695829 | + | 0.718208i | \(0.255037\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.3136 | 0.931979 | 0.465990 | − | 0.884790i | \(-0.345698\pi\) | ||||
0.465990 | + | 0.884790i | \(0.345698\pi\) | |||||||
\(524\) | 60.2532 | 2.63217 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −57.3174 | −2.49916 | ||||||||
\(527\) | −8.02460 | −0.349557 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.7588 | −0.859077 | ||||||||
\(530\) | −36.0740 | −1.56695 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 60.4619 | 2.62136 | ||||||||
\(533\) | 14.8726 | 0.644206 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.8264 | −0.986870 | ||||||||
\(536\) | −50.7851 | −2.19358 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.55244 | 0.0669302 | ||||||||
\(539\) | −1.60167 | −0.0689890 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.7223 | 1.14888 | 0.574440 | − | 0.818547i | \(-0.305220\pi\) | ||||
0.574440 | + | 0.818547i | \(0.305220\pi\) | |||||||
\(542\) | −29.6128 | −1.27198 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.38394 | −0.0593360 | ||||||||
\(545\) | −26.7460 | −1.14567 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.28637 | −0.0550010 | −0.0275005 | − | 0.999622i | \(-0.508755\pi\) | ||||
−0.0275005 | + | 0.999622i | \(0.508755\pi\) | |||||||
\(548\) | 49.7744 | 2.12626 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.83895 | −0.163694 | ||||||||
\(551\) | −57.0925 | −2.43222 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.37436 | 0.356114 | ||||||||
\(554\) | 12.2873 | 0.522036 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −62.3254 | −2.64319 | ||||||||
\(557\) | −5.02337 | −0.212847 | −0.106424 | − | 0.994321i | \(-0.533940\pi\) | ||||
−0.106424 | + | 0.994321i | \(0.533940\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.3171 | −0.859324 | ||||||||
\(560\) | 18.4629 | 0.780200 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 53.6990 | 2.26516 | ||||||||
\(563\) | −27.1450 | −1.14402 | −0.572012 | − | 0.820245i | \(-0.693837\pi\) | ||||
−0.572012 | + | 0.820245i | \(0.693837\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.6588 | 0.574630 | ||||||||
\(566\) | 23.0702 | 0.969714 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −69.0296 | −2.89642 | ||||||||
\(569\) | 16.5905 | 0.695511 | 0.347756 | − | 0.937585i | \(-0.386944\pi\) | ||||
0.347756 | + | 0.937585i | \(0.386944\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.50125 | −0.272069 | −0.136035 | − | 0.990704i | \(-0.543436\pi\) | ||||
−0.136035 | + | 0.990704i | \(0.543436\pi\) | |||||||
\(572\) | 26.4732 | 1.10690 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 12.9908 | 0.542225 | ||||||||
\(575\) | −2.81056 | −0.117208 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.0196890 | 0.000819665 0 | 0.000409832 | − | 1.00000i | \(-0.499870\pi\) | ||||
0.000409832 | 1.00000i | \(0.499870\pi\) | ||||||||
\(578\) | −20.4136 | −0.849094 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −66.6397 | −2.76706 | ||||||||
\(581\) | 12.1414 | 0.503711 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.91063 | −0.327625 | ||||||||
\(584\) | −74.0721 | −3.06513 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.31159 | −0.260729 | ||||||||
\(587\) | −4.04780 | −0.167070 | −0.0835352 | − | 0.996505i | \(-0.526621\pi\) | ||||
−0.0835352 | + | 0.996505i | \(0.526621\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.4944 | 0.720844 | ||||||||
\(590\) | 26.6352 | 1.09656 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −15.1472 | −0.622548 | ||||||||
\(593\) | 3.29700 | 0.135391 | 0.0676957 | − | 0.997706i | \(-0.478435\pi\) | ||||
0.0676957 | + | 0.997706i | \(0.478435\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.7077 | −0.520963 | ||||||||
\(596\) | −82.4734 | −3.37824 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 28.9593 | 1.18423 | ||||||||
\(599\) | −21.4453 | −0.876232 | −0.438116 | − | 0.898918i | \(-0.644354\pi\) | ||||
−0.438116 | + | 0.898918i | \(0.644354\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.2402 | −0.540080 | −0.270040 | − | 0.962849i | \(-0.587037\pi\) | ||||
−0.270040 | + | 0.962849i | \(0.587037\pi\) | |||||||
\(602\) | −17.7464 | −0.723289 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 23.4678 | 0.954890 | ||||||||
\(605\) | 1.85442 | 0.0753929 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.8370 | −1.41399 | −0.706995 | − | 0.707218i | \(-0.749950\pi\) | ||||
−0.706995 | + | 0.707218i | \(0.749950\pi\) | |||||||
\(608\) | 3.01712 | 0.122360 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.56020 | 0.184637 | ||||||||
\(611\) | −76.6588 | −3.10128 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.0906 | −0.488335 | −0.244167 | − | 0.969733i | \(-0.578515\pi\) | ||||
−0.244167 | + | 0.969733i | \(0.578515\pi\) | |||||||
\(614\) | 28.8975 | 1.16621 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.6965 | 0.471263 | ||||||||
\(617\) | 25.9928 | 1.04643 | 0.523215 | − | 0.852201i | \(-0.324733\pi\) | ||||
0.523215 | + | 0.852201i | \(0.324733\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.1655 | 0.890908 | 0.445454 | − | 0.895305i | \(-0.353042\pi\) | ||||
0.445454 | + | 0.895305i | \(0.353042\pi\) | |||||||
\(620\) | 20.4199 | 0.820082 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.106010 | −0.00425060 | ||||||||
\(623\) | 32.9889 | 1.32167 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.7573 | −0.590291 | ||||||||
\(626\) | −23.9816 | −0.958498 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 50.2957 | 2.00702 | ||||||||
\(629\) | 10.4256 | 0.415694 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.8967 | 0.672649 | 0.336324 | − | 0.941746i | \(-0.390816\pi\) | ||||
0.336324 | + | 0.941746i | \(0.390816\pi\) | |||||||
\(632\) | 18.1446 | 0.721752 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 31.0869 | 1.23462 | ||||||||
\(635\) | 19.9398 | 0.791286 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.4769 | −0.415109 | ||||||||
\(638\) | −21.8349 | −0.864452 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −35.5602 | −1.40564 | ||||||||
\(641\) | −15.5118 | −0.612680 | −0.306340 | − | 0.951922i | \(-0.599104\pi\) | ||||
−0.306340 | + | 0.951922i | \(0.599104\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.4440 | 1.12172 | 0.560861 | − | 0.827910i | \(-0.310470\pi\) | ||||
0.560861 | + | 0.827910i | \(0.310470\pi\) | |||||||
\(644\) | 16.9291 | 0.667099 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −46.6344 | −1.83481 | ||||||||
\(647\) | −10.2252 | −0.401993 | −0.200996 | − | 0.979592i | \(-0.564418\pi\) | ||||
−0.200996 | + | 0.979592i | \(0.564418\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.84081 | 0.229272 | ||||||||
\(650\) | −25.1114 | −0.984948 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 63.8396 | 2.50015 | ||||||||
\(653\) | 17.9727 | 0.703325 | 0.351663 | − | 0.936127i | \(-0.385616\pi\) | ||||
0.351663 | + | 0.936127i | \(0.385616\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.6083 | 1.07874 | ||||||||
\(656\) | 9.74301 | 0.380401 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −66.9591 | −2.61034 | ||||||||
\(659\) | −29.6229 | −1.15394 | −0.576972 | − | 0.816764i | \(-0.695766\pi\) | ||||
−0.576972 | + | 0.816764i | \(0.695766\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.7945 | −1.08108 | −0.540540 | − | 0.841319i | \(-0.681780\pi\) | ||||
−0.540540 | + | 0.841319i | \(0.681780\pi\) | |||||||
\(662\) | 60.1284 | 2.33696 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 26.3066 | 1.02089 | ||||||||
\(665\) | 27.7039 | 1.07431 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.9857 | −0.618968 | ||||||||
\(668\) | 47.7945 | 1.84922 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −46.0040 | −1.77729 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.3964 | 0.477846 | 0.238923 | − | 0.971039i | \(-0.423206\pi\) | ||||
0.238923 | + | 0.971039i | \(0.423206\pi\) | |||||||
\(674\) | 6.66674 | 0.256793 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 120.553 | 4.63667 | ||||||||
\(677\) | −34.3788 | −1.32128 | −0.660642 | − | 0.750701i | \(-0.729716\pi\) | ||||
−0.660642 | + | 0.750701i | \(0.729716\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41.8096 | 1.60451 | ||||||||
\(680\) | −27.5335 | −1.05586 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.69069 | 0.256200 | ||||||||
\(683\) | −38.8947 | −1.48826 | −0.744132 | − | 0.668033i | \(-0.767137\pi\) | ||||
−0.744132 | + | 0.668033i | \(0.767137\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.8068 | 0.871404 | ||||||||
\(686\) | −49.1460 | −1.87640 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −13.3097 | −0.507427 | ||||||||
\(689\) | −51.7450 | −1.97133 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.0503 | 0.610583 | 0.305291 | − | 0.952259i | \(-0.401246\pi\) | ||||
0.305291 | + | 0.952259i | \(0.401246\pi\) | |||||||
\(692\) | −97.9018 | −3.72167 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 40.7938 | 1.54851 | ||||||||
\(695\) | −28.5578 | −1.08326 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.70593 | −0.254005 | ||||||||
\(698\) | 59.7643 | 2.26211 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −14.6797 | −0.554839 | ||||||||
\(701\) | −13.3561 | −0.504454 | −0.252227 | − | 0.967668i | \(-0.581163\pi\) | ||||
−0.252227 | + | 0.967668i | \(0.581163\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.7287 | −0.857229 | ||||||||
\(704\) | −7.41633 | −0.279514 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.56405 | 0.0964994 | ||||||||
\(707\) | 38.5846 | 1.45112 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.35828 | 0.126123 | 0.0630615 | − | 0.998010i | \(-0.479914\pi\) | ||||
0.0630615 | + | 0.998010i | \(0.479914\pi\) | |||||||
\(710\) | −62.5308 | −2.34674 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 71.4764 | 2.67869 | ||||||||
\(713\) | 4.89836 | 0.183445 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.1301 | 0.453641 | ||||||||
\(716\) | 54.1051 | 2.02200 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −24.0526 | −0.897637 | ||||||||
\(719\) | −27.5080 | −1.02588 | −0.512938 | − | 0.858426i | \(-0.671443\pi\) | ||||
−0.512938 | + | 0.858426i | \(0.671443\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.3002 | 0.644292 | ||||||||
\(722\) | 54.9446 | 2.04483 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −76.7605 | −2.85278 | ||||||||
\(725\) | 13.8616 | 0.514807 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.693006 | 0.0257022 | 0.0128511 | − | 0.999917i | \(-0.495909\pi\) | ||||
0.0128511 | + | 0.999917i | \(0.495909\pi\) | |||||||
\(728\) | 76.5088 | 2.83560 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −67.0986 | −2.48343 | ||||||||
\(731\) | 9.16080 | 0.338824 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.4941 | 1.20020 | 0.600098 | − | 0.799927i | \(-0.295128\pi\) | ||||
0.600098 | + | 0.799927i | \(0.295128\pi\) | |||||||
\(734\) | 13.4882 | 0.497858 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.844782 | 0.0311391 | ||||||||
\(737\) | −10.0882 | −0.371602 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.7986 | 0.544374 | 0.272187 | − | 0.962244i | \(-0.412253\pi\) | ||||
0.272187 | + | 0.962244i | \(0.412253\pi\) | |||||||
\(740\) | −26.5295 | −0.975243 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −45.1976 | −1.65926 | ||||||||
\(743\) | 24.8498 | 0.911649 | 0.455825 | − | 0.890070i | \(-0.349344\pi\) | ||||
0.455825 | + | 0.890070i | \(0.349344\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −37.7896 | −1.38451 | ||||||||
\(746\) | −53.1695 | −1.94667 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −11.9365 | −0.436442 | ||||||||
\(749\) | −28.5995 | −1.04500 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.05201 | −0.293822 | −0.146911 | − | 0.989150i | \(-0.546933\pi\) | ||||
−0.146911 | + | 0.989150i | \(0.546933\pi\) | |||||||
\(752\) | −50.2189 | −1.83129 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −142.826 | −5.20143 | ||||||||
\(755\) | 10.7530 | 0.391343 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.7999 | 1.51924 | 0.759622 | − | 0.650365i | \(-0.225384\pi\) | ||||
0.759622 | + | 0.650365i | \(0.225384\pi\) | |||||||
\(758\) | 71.3602 | 2.59192 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 60.0255 | 2.17736 | ||||||||
\(761\) | 50.6166 | 1.83485 | 0.917425 | − | 0.397909i | \(-0.130264\pi\) | ||||
0.917425 | + | 0.397909i | \(0.130264\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.5104 | −1.21316 | ||||||||
\(764\) | −45.8596 | −1.65914 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.64460 | 0.348474 | ||||||||
\(767\) | 38.2059 | 1.37953 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.3462 | 1.45492 | 0.727461 | − | 0.686149i | \(-0.240700\pi\) | ||||
0.727461 | + | 0.686149i | \(0.240700\pi\) | |||||||
\(770\) | 10.5953 | 0.381828 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.37997 | 0.0856568 | ||||||||
\(773\) | −11.9238 | −0.428869 | −0.214434 | − | 0.976738i | \(-0.568791\pi\) | ||||
−0.214434 | + | 0.976738i | \(0.568791\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.24750 | −0.152575 | ||||||||
\(776\) | 90.5881 | 3.25192 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 63.8797 | 2.29020 | ||||||||
\(779\) | 14.6196 | 0.523800 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.7123 | −0.490665 | ||||||||
\(782\) | −13.0574 | −0.466933 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.86336 | −0.245120 | ||||||||
\(785\) | 23.0457 | 0.822536 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −48.7632 | −1.73822 | −0.869111 | − | 0.494618i | \(-0.835308\pi\) | ||||
−0.869111 | + | 0.494618i | \(0.835308\pi\) | |||||||
\(788\) | −107.582 | −3.83245 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 16.4364 | 0.584779 | ||||||||
\(791\) | 17.1133 | 0.608479 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.54120 | 0.232285 | ||||||||
\(794\) | 47.1898 | 1.67470 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.4684 | −0.654594 | ||||||||
\(797\) | 19.5299 | 0.691785 | 0.345893 | − | 0.938274i | \(-0.387576\pi\) | ||||
0.345893 | + | 0.938274i | \(0.387576\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.5647 | 1.22281 | ||||||||
\(800\) | −0.732533 | −0.0258989 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −23.2406 | −0.820654 | ||||||||
\(803\) | −14.7140 | −0.519245 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.75698 | 0.273398 | ||||||||
\(806\) | 43.7651 | 1.54156 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 83.6005 | 2.94106 | ||||||||
\(809\) | 26.1404 | 0.919049 | 0.459524 | − | 0.888165i | \(-0.348020\pi\) | ||||
0.459524 | + | 0.888165i | \(0.348020\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.3822 | 1.38289 | 0.691447 | − | 0.722427i | \(-0.256973\pi\) | ||||
0.691447 | + | 0.722427i | \(0.256973\pi\) | |||||||
\(812\) | −83.4939 | −2.93006 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.69254 | −0.304673 | ||||||||
\(815\) | 29.2516 | 1.02464 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.9714 | −0.698711 | ||||||||
\(818\) | −63.3350 | −2.21446 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 17.0643 | 0.595911 | ||||||||
\(821\) | −18.4817 | −0.645016 | −0.322508 | − | 0.946567i | \(-0.604526\pi\) | ||||
−0.322508 | + | 0.946567i | \(0.604526\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.67700 | −0.128172 | −0.0640861 | − | 0.997944i | \(-0.520413\pi\) | ||||
−0.0640861 | + | 0.997944i | \(0.520413\pi\) | |||||||
\(824\) | 37.4840 | 1.30582 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 33.3717 | 1.16115 | ||||||||
\(827\) | 3.52277 | 0.122499 | 0.0612493 | − | 0.998123i | \(-0.480492\pi\) | ||||
0.0612493 | + | 0.998123i | \(0.480492\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.1379 | 1.25512 | 0.627560 | − | 0.778568i | \(-0.284054\pi\) | ||||
0.627560 | + | 0.778568i | \(0.284054\pi\) | |||||||
\(830\) | 23.8299 | 0.827150 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −48.5117 | −1.68184 | ||||||||
\(833\) | 4.72392 | 0.163674 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.8996 | 0.757868 | ||||||||
\(836\) | 26.0227 | 0.900014 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 19.1617 | 0.661931 | ||||||||
\(839\) | −40.7462 | −1.40672 | −0.703358 | − | 0.710836i | \(-0.748317\pi\) | ||||
−0.703358 | + | 0.710836i | \(0.748317\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 49.8409 | 1.71865 | ||||||||
\(842\) | −70.1755 | −2.41841 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 74.0576 | 2.54917 | ||||||||
\(845\) | 55.2381 | 1.90025 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.32343 | 0.0798340 | ||||||||
\(848\) | −33.8979 | −1.16406 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 11.3225 | 0.388357 | ||||||||
\(851\) | −6.36394 | −0.218153 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.9702 | 1.47127 | 0.735636 | − | 0.677377i | \(-0.236883\pi\) | ||||
0.735636 | + | 0.677377i | \(0.236883\pi\) | |||||||
\(854\) | 5.71353 | 0.195513 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −61.9660 | −2.11795 | ||||||||
\(857\) | 51.7558 | 1.76794 | 0.883972 | − | 0.467540i | \(-0.154859\pi\) | ||||
0.883972 | + | 0.467540i | \(0.154859\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.73686 | −0.229859 | −0.114929 | − | 0.993374i | \(-0.536664\pi\) | ||||
−0.114929 | + | 0.993374i | \(0.536664\pi\) | |||||||
\(860\) | −23.3111 | −0.794902 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.59140 | 0.0542033 | ||||||||
\(863\) | −24.2044 | −0.823929 | −0.411964 | − | 0.911200i | \(-0.635157\pi\) | ||||
−0.411964 | + | 0.911200i | \(0.635157\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −44.8590 | −1.52525 | ||||||||
\(866\) | −45.3908 | −1.54244 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 25.5843 | 0.868389 | ||||||||
\(869\) | 3.60431 | 0.122268 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −65.9886 | −2.23594 | ||||||||
\(872\) | −72.6064 | −2.45876 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 28.4665 | 0.962892 | ||||||||
\(875\) | −28.2694 | −0.955679 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.49029 | −0.219162 | −0.109581 | − | 0.993978i | \(-0.534951\pi\) | ||||
−0.109581 | + | 0.993978i | \(0.534951\pi\) | |||||||
\(878\) | 21.8072 | 0.735958 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.94640 | 0.267873 | ||||||||
\(881\) | −27.3311 | −0.920807 | −0.460403 | − | 0.887710i | \(-0.652295\pi\) | ||||
−0.460403 | + | 0.887710i | \(0.652295\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.5968 | 0.895055 | 0.447528 | − | 0.894270i | \(-0.352305\pi\) | ||||
0.447528 | + | 0.894270i | \(0.352305\pi\) | |||||||
\(884\) | −78.0790 | −2.62608 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −27.8800 | −0.936647 | ||||||||
\(887\) | −0.875150 | −0.0293846 | −0.0146923 | − | 0.999892i | \(-0.504677\pi\) | ||||
−0.0146923 | + | 0.999892i | \(0.504677\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.9828 | 0.837897 | ||||||||
\(890\) | 64.7473 | 2.17033 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18.9277 | −0.633745 | ||||||||
\(893\) | −75.3543 | −2.52164 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.7912 | 0.828678 | ||||||||
\(896\) | −44.5539 | −1.48844 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 42.6966 | 1.42480 | ||||||||
\(899\) | −24.1586 | −0.805734 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.3313 | 0.777278 | ||||||||
\(902\) | 5.59122 | 0.186167 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 37.0791 | 1.23323 | ||||||||
\(905\) | −35.1720 | −1.16916 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.9567 | −1.39315 | −0.696575 | − | 0.717484i | \(-0.745294\pi\) | ||||
−0.696575 | + | 0.717484i | \(0.745294\pi\) | |||||||
\(908\) | −38.9932 | −1.29403 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 69.3059 | 2.29747 | ||||||||
\(911\) | −28.2659 | −0.936493 | −0.468246 | − | 0.883598i | \(-0.655114\pi\) | ||||
−0.468246 | + | 0.883598i | \(0.655114\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.22564 | 0.172943 | ||||||||
\(914\) | −41.5710 | −1.37505 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 79.7235 | 2.63414 | ||||||||
\(917\) | 34.5908 | 1.14229 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.4057 | −0.640136 | −0.320068 | − | 0.947395i | \(-0.603706\pi\) | ||||
−0.320068 | + | 0.947395i | \(0.603706\pi\) | |||||||
\(920\) | 16.8069 | 0.554107 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 76.9738 | 2.53500 | ||||||||
\(923\) | −89.6949 | −2.95234 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.51834 | 0.181442 | ||||||||
\(926\) | −52.5982 | −1.72849 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.16644 | −0.136770 | ||||||||
\(929\) | −32.2579 | −1.05835 | −0.529174 | − | 0.848513i | \(-0.677498\pi\) | ||||
−0.529174 | + | 0.848513i | \(0.677498\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.2986 | −0.337522 | ||||||||
\(932\) | −37.1548 | −1.21705 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −93.5441 | −3.06086 | ||||||||
\(935\) | −5.46935 | −0.178867 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.4476 | −0.798669 | −0.399334 | − | 0.916805i | \(-0.630759\pi\) | ||||
−0.399334 | + | 0.916805i | \(0.630759\pi\) | |||||||
\(938\) | −57.6390 | −1.88198 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −87.9554 | −2.86879 | ||||||||
\(941\) | 6.11565 | 0.199365 | 0.0996823 | − | 0.995019i | \(-0.468217\pi\) | ||||
0.0996823 | + | 0.995019i | \(0.468217\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.09342 | 0.133300 | ||||||||
\(944\) | 25.0285 | 0.814609 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.63802 | −0.248333 | ||||||||
\(947\) | −26.7450 | −0.869094 | −0.434547 | − | 0.900649i | \(-0.643092\pi\) | ||||
−0.434547 | + | 0.900649i | \(0.643092\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −96.2470 | −3.12431 | ||||||||
\(950\) | −24.6840 | −0.800856 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −34.4971 | −1.11806 | ||||||||
\(953\) | −12.5656 | −0.407041 | −0.203520 | − | 0.979071i | \(-0.565238\pi\) | ||||
−0.203520 | + | 0.979071i | \(0.565238\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.0131 | −0.679967 | ||||||||
\(956\) | 30.5164 | 0.986970 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −88.8697 | −2.87125 | ||||||||
\(959\) | 28.5750 | 0.922735 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.5973 | −0.761203 | ||||||||
\(962\) | −56.8596 | −1.83323 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 75.8711 | 2.44364 | ||||||||
\(965\) | 1.09051 | 0.0351048 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.19458 | −0.102731 | −0.0513655 | − | 0.998680i | \(-0.516357\pi\) | ||||
−0.0513655 | + | 0.998680i | \(0.516357\pi\) | |||||||
\(968\) | 5.03413 | 0.161803 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 82.0598 | 2.63478 | ||||||||
\(971\) | 29.2651 | 0.939161 | 0.469581 | − | 0.882890i | \(-0.344405\pi\) | ||||
0.469581 | + | 0.882890i | \(0.344405\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −35.7805 | −1.14707 | ||||||||
\(974\) | −48.8574 | −1.56549 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.28511 | 0.137163 | ||||||||
\(977\) | 15.0225 | 0.480614 | 0.240307 | − | 0.970697i | \(-0.422752\pi\) | ||||
0.240307 | + | 0.970697i | \(0.422752\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.1984 | 0.453781 | ||||||||
\(980\) | −12.0208 | −0.383989 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 57.2795 | 1.82786 | ||||||||
\(983\) | 0.886011 | 0.0282594 | 0.0141297 | − | 0.999900i | \(-0.495502\pi\) | ||||
0.0141297 | + | 0.999900i | \(0.495502\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −49.2946 | −1.57066 | ||||||||
\(986\) | 64.3990 | 2.05088 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 170.220 | 5.41541 | ||||||||
\(989\) | −5.59191 | −0.177812 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.8350 | 0.630079 | 0.315040 | − | 0.949079i | \(-0.397982\pi\) | ||||
0.315040 | + | 0.949079i | \(0.397982\pi\) | |||||||
\(992\) | 1.27669 | 0.0405349 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −78.3457 | −2.48498 | ||||||||
\(995\) | −8.46228 | −0.268272 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.9119 | −0.567275 | −0.283638 | − | 0.958932i | \(-0.591541\pi\) | ||||
−0.283638 | + | 0.958932i | \(0.591541\pi\) | |||||||
\(998\) | −46.0607 | −1.45803 | ||||||||
\(999\) | 0 | 0 |
(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 | 6039.2.a.j.1.13 | 14 | ||
3.2 | odd | 2 | 2013.2.a.h.1.2 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.h.1.2 | ✓ | 14 | 3.2 | odd | 2 | ||
6039.2.a.j.1.13 | 14 | 1.1 | even | 1 | trivial |