Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
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: | \( x^{14} - 2 x^{13} - 18 x^{12} + 34 x^{11} + 124 x^{10} - 216 x^{9} - 420 x^{8} + 647 x^{7} + 750 x^{6} - 939 x^{5} - 717 x^{4} + 604 x^{3} + 352 x^{2} - 128 x - 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 2001) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.55124\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.55124 | −1.80400 | −0.901998 | − | 0.431740i | \(-0.857900\pi\) | ||||
−0.901998 | + | 0.431740i | \(0.857900\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.50880 | 2.25440 | ||||||||
\(5\) | 1.64740 | 0.736739 | 0.368369 | − | 0.929680i | \(-0.379916\pi\) | ||||
0.368369 | + | 0.929680i | \(0.379916\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.91756 | −1.10273 | −0.551366 | − | 0.834263i | \(-0.685893\pi\) | ||||
−0.551366 | + | 0.834263i | \(0.685893\pi\) | |||||||
\(8\) | −6.40055 | −2.26294 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.20290 | −1.32907 | ||||||||
\(11\) | 6.56108 | 1.97824 | 0.989120 | − | 0.147113i | \(-0.0469980\pi\) | ||||
0.989120 | + | 0.147113i | \(0.0469980\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.20247 | 1.44290 | 0.721452 | − | 0.692464i | \(-0.243475\pi\) | ||||
0.721452 | + | 0.692464i | \(0.243475\pi\) | |||||||
\(14\) | 7.44337 | 1.98933 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 7.31171 | 1.82793 | ||||||||
\(17\) | 1.25844 | 0.305216 | 0.152608 | − | 0.988287i | \(-0.451233\pi\) | ||||
0.152608 | + | 0.988287i | \(0.451233\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.89571 | −1.12315 | −0.561576 | − | 0.827425i | \(-0.689805\pi\) | ||||
−0.561576 | + | 0.827425i | \(0.689805\pi\) | |||||||
\(20\) | 7.42779 | 1.66091 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −16.7389 | −3.56874 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.28608 | −0.457216 | ||||||||
\(26\) | −13.2727 | −2.60299 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −13.1547 | −2.48600 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.43452 | −0.437253 | −0.218627 | − | 0.975809i | \(-0.570158\pi\) | ||||
−0.218627 | + | 0.975809i | \(0.570158\pi\) | |||||||
\(32\) | −5.85279 | −1.03464 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.21057 | −0.550608 | ||||||||
\(35\) | −4.80637 | −0.812425 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.46802 | 0.405741 | 0.202870 | − | 0.979206i | \(-0.434973\pi\) | ||||
0.202870 | + | 0.979206i | \(0.434973\pi\) | |||||||
\(38\) | 12.4901 | 2.02616 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.5443 | −1.66719 | ||||||||
\(41\) | 6.73385 | 1.05165 | 0.525825 | − | 0.850593i | \(-0.323757\pi\) | ||||
0.525825 | + | 0.850593i | \(0.323757\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.485941 | 0.0741053 | 0.0370526 | − | 0.999313i | \(-0.488203\pi\) | ||||
0.0370526 | + | 0.999313i | \(0.488203\pi\) | |||||||
\(44\) | 29.5826 | 4.45975 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.55124 | −0.376159 | ||||||||
\(47\) | 2.92199 | 0.426216 | 0.213108 | − | 0.977029i | \(-0.431641\pi\) | ||||
0.213108 | + | 0.977029i | \(0.431641\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.51213 | 0.216019 | ||||||||
\(50\) | 5.83233 | 0.824816 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 23.4569 | 3.25289 | ||||||||
\(53\) | 7.90067 | 1.08524 | 0.542620 | − | 0.839978i | \(-0.317432\pi\) | ||||
0.542620 | + | 0.839978i | \(0.317432\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.8087 | 1.45745 | ||||||||
\(56\) | 18.6740 | 2.49541 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.55124 | −0.334994 | ||||||||
\(59\) | 1.28036 | 0.166688 | 0.0833441 | − | 0.996521i | \(-0.473440\pi\) | ||||
0.0833441 | + | 0.996521i | \(0.473440\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.7703 | 1.50703 | 0.753515 | − | 0.657431i | \(-0.228357\pi\) | ||||
0.753515 | + | 0.657431i | \(0.228357\pi\) | |||||||
\(62\) | 6.21104 | 0.788803 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.308435 | 0.0385543 | ||||||||
\(65\) | 8.57053 | 1.06304 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.52581 | 0.430747 | 0.215373 | − | 0.976532i | \(-0.430903\pi\) | ||||
0.215373 | + | 0.976532i | \(0.430903\pi\) | |||||||
\(68\) | 5.67404 | 0.688079 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 12.2622 | 1.46561 | ||||||||
\(71\) | −9.97469 | −1.18378 | −0.591889 | − | 0.806020i | \(-0.701618\pi\) | ||||
−0.591889 | + | 0.806020i | \(0.701618\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.56126 | −0.650896 | −0.325448 | − | 0.945560i | \(-0.605515\pi\) | ||||
−0.325448 | + | 0.945560i | \(0.605515\pi\) | |||||||
\(74\) | −6.29651 | −0.731954 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −22.0738 | −2.53204 | ||||||||
\(77\) | −19.1423 | −2.18147 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.84862 | −0.658021 | −0.329011 | − | 0.944326i | \(-0.606715\pi\) | ||||
−0.329011 | + | 0.944326i | \(0.606715\pi\) | |||||||
\(80\) | 12.0453 | 1.34670 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −17.1796 | −1.89717 | ||||||||
\(83\) | 10.9870 | 1.20598 | 0.602991 | − | 0.797748i | \(-0.293976\pi\) | ||||
0.602991 | + | 0.797748i | \(0.293976\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.07314 | 0.224864 | ||||||||
\(86\) | −1.23975 | −0.133686 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −41.9945 | −4.47663 | ||||||||
\(89\) | −16.6318 | −1.76297 | −0.881483 | − | 0.472216i | \(-0.843454\pi\) | ||||
−0.881483 | + | 0.472216i | \(0.843454\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.1785 | −1.59114 | ||||||||
\(92\) | 4.50880 | 0.470075 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.45469 | −0.768893 | ||||||||
\(95\) | −8.06517 | −0.827469 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.97784 | 0.708492 | 0.354246 | − | 0.935152i | \(-0.384737\pi\) | ||||
0.354246 | + | 0.935152i | \(0.384737\pi\) | |||||||
\(98\) | −3.85780 | −0.389697 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −10.3075 | −1.03075 | ||||||||
\(101\) | −4.13909 | −0.411855 | −0.205927 | − | 0.978567i | \(-0.566021\pi\) | ||||
−0.205927 | + | 0.978567i | \(0.566021\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.8987 | 1.27095 | 0.635473 | − | 0.772123i | \(-0.280805\pi\) | ||||
0.635473 | + | 0.772123i | \(0.280805\pi\) | |||||||
\(104\) | −33.2987 | −3.26520 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −20.1565 | −1.95777 | ||||||||
\(107\) | 20.4276 | 1.97481 | 0.987406 | − | 0.158207i | \(-0.0505714\pi\) | ||||
0.987406 | + | 0.158207i | \(0.0505714\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.37849 | 0.323601 | 0.161800 | − | 0.986824i | \(-0.448270\pi\) | ||||
0.161800 | + | 0.986824i | \(0.448270\pi\) | |||||||
\(110\) | −27.5756 | −2.62923 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −21.3323 | −2.01571 | ||||||||
\(113\) | 8.18175 | 0.769674 | 0.384837 | − | 0.922984i | \(-0.374258\pi\) | ||||
0.384837 | + | 0.922984i | \(0.374258\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.64740 | 0.153621 | ||||||||
\(116\) | 4.50880 | 0.418632 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.26649 | −0.300705 | ||||||||
\(119\) | −3.67156 | −0.336571 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 32.0477 | 2.91343 | ||||||||
\(122\) | −30.0287 | −2.71867 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −10.9768 | −0.985744 | ||||||||
\(125\) | −12.0031 | −1.07359 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.53978 | 0.580312 | 0.290156 | − | 0.956979i | \(-0.406293\pi\) | ||||
0.290156 | + | 0.956979i | \(0.406293\pi\) | |||||||
\(128\) | 10.9187 | 0.965086 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −21.8654 | −1.91773 | ||||||||
\(131\) | −14.4084 | −1.25887 | −0.629435 | − | 0.777053i | \(-0.716714\pi\) | ||||
−0.629435 | + | 0.777053i | \(0.716714\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.2835 | 1.23854 | ||||||||
\(134\) | −8.99518 | −0.777065 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.05469 | −0.690684 | ||||||||
\(137\) | 14.8821 | 1.27146 | 0.635730 | − | 0.771911i | \(-0.280699\pi\) | ||||
0.635730 | + | 0.771911i | \(0.280699\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.3393 | −1.13142 | −0.565711 | − | 0.824603i | \(-0.691398\pi\) | ||||
−0.565711 | + | 0.824603i | \(0.691398\pi\) | |||||||
\(140\) | −21.6710 | −1.83153 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 25.4478 | 2.13553 | ||||||||
\(143\) | 34.1338 | 2.85441 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.64740 | 0.136809 | ||||||||
\(146\) | 14.1881 | 1.17421 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.1278 | 0.914702 | ||||||||
\(149\) | −18.6630 | −1.52893 | −0.764465 | − | 0.644665i | \(-0.776997\pi\) | ||||
−0.764465 | + | 0.644665i | \(0.776997\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.5101 | −0.855300 | −0.427650 | − | 0.903945i | \(-0.640658\pi\) | ||||
−0.427650 | + | 0.903945i | \(0.640658\pi\) | |||||||
\(152\) | 31.3352 | 2.54162 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 48.8365 | 3.93536 | ||||||||
\(155\) | −4.01063 | −0.322141 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.85993 | 0.786908 | 0.393454 | − | 0.919344i | \(-0.371280\pi\) | ||||
0.393454 | + | 0.919344i | \(0.371280\pi\) | |||||||
\(158\) | 14.9212 | 1.18707 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9.64188 | −0.762257 | ||||||||
\(161\) | −2.91756 | −0.229936 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.33183 | −0.104317 | −0.0521584 | − | 0.998639i | \(-0.516610\pi\) | ||||
−0.0521584 | + | 0.998639i | \(0.516610\pi\) | |||||||
\(164\) | 30.3616 | 2.37084 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −28.0305 | −2.17559 | ||||||||
\(167\) | −15.9888 | −1.23725 | −0.618625 | − | 0.785687i | \(-0.712310\pi\) | ||||
−0.618625 | + | 0.785687i | \(0.712310\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.0656 | 1.08197 | ||||||||
\(170\) | −5.28908 | −0.405654 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.19101 | 0.167063 | ||||||||
\(173\) | 5.44324 | 0.413842 | 0.206921 | − | 0.978358i | \(-0.433656\pi\) | ||||
0.206921 | + | 0.978358i | \(0.433656\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.66977 | 0.504187 | ||||||||
\(176\) | 47.9727 | 3.61608 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 42.4316 | 3.18038 | ||||||||
\(179\) | 5.56852 | 0.416210 | 0.208105 | − | 0.978106i | \(-0.433270\pi\) | ||||
0.208105 | + | 0.978106i | \(0.433270\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.79673 | 0.356538 | 0.178269 | − | 0.983982i | \(-0.442950\pi\) | ||||
0.178269 | + | 0.983982i | \(0.442950\pi\) | |||||||
\(182\) | 38.7239 | 2.87041 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.40055 | −0.471855 | ||||||||
\(185\) | 4.06582 | 0.298925 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.25670 | 0.603790 | ||||||||
\(188\) | 13.1747 | 0.960863 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 20.5762 | 1.49275 | ||||||||
\(191\) | 14.5446 | 1.05241 | 0.526206 | − | 0.850357i | \(-0.323614\pi\) | ||||
0.526206 | + | 0.850357i | \(0.323614\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.2537 | −1.74582 | −0.872911 | − | 0.487880i | \(-0.837771\pi\) | ||||
−0.872911 | + | 0.487880i | \(0.837771\pi\) | |||||||
\(194\) | −17.8021 | −1.27812 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.81790 | 0.486993 | ||||||||
\(197\) | 13.2341 | 0.942892 | 0.471446 | − | 0.881895i | \(-0.343732\pi\) | ||||
0.471446 | + | 0.881895i | \(0.343732\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.7549 | −1.25861 | −0.629307 | − | 0.777157i | \(-0.716661\pi\) | ||||
−0.629307 | + | 0.777157i | \(0.716661\pi\) | |||||||
\(200\) | 14.6322 | 1.03465 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.5598 | 0.742984 | ||||||||
\(203\) | −2.91756 | −0.204772 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.0933 | 0.774792 | ||||||||
\(206\) | −32.9076 | −2.29278 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 38.0389 | 2.63752 | ||||||||
\(209\) | −32.1211 | −2.22186 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.27562 | −0.569717 | −0.284859 | − | 0.958570i | \(-0.591947\pi\) | ||||
−0.284859 | + | 0.958570i | \(0.591947\pi\) | |||||||
\(212\) | 35.6226 | 2.44657 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −52.1157 | −3.56255 | ||||||||
\(215\) | 0.800538 | 0.0545962 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.10285 | 0.482173 | ||||||||
\(218\) | −8.61933 | −0.583775 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 48.7343 | 3.28567 | ||||||||
\(221\) | 6.54697 | 0.440397 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.09231 | 0.207077 | 0.103538 | − | 0.994625i | \(-0.466984\pi\) | ||||
0.103538 | + | 0.994625i | \(0.466984\pi\) | |||||||
\(224\) | 17.0758 | 1.14093 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −20.8736 | −1.38849 | ||||||||
\(227\) | −17.4806 | −1.16023 | −0.580115 | − | 0.814534i | \(-0.696992\pi\) | ||||
−0.580115 | + | 0.814534i | \(0.696992\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.5863 | 1.36038 | 0.680191 | − | 0.733035i | \(-0.261897\pi\) | ||||
0.680191 | + | 0.733035i | \(0.261897\pi\) | |||||||
\(230\) | −4.20290 | −0.277131 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.40055 | −0.420217 | ||||||||
\(233\) | −7.89100 | −0.516957 | −0.258478 | − | 0.966017i | \(-0.583221\pi\) | ||||
−0.258478 | + | 0.966017i | \(0.583221\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.81368 | 0.314010 | ||||||||
\(236\) | 5.77288 | 0.375782 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.36701 | 0.607173 | ||||||||
\(239\) | −19.9245 | −1.28881 | −0.644405 | − | 0.764684i | \(-0.722895\pi\) | ||||
−0.644405 | + | 0.764684i | \(0.722895\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.8421 | 0.698399 | 0.349200 | − | 0.937048i | \(-0.386454\pi\) | ||||
0.349200 | + | 0.937048i | \(0.386454\pi\) | |||||||
\(242\) | −81.7614 | −5.25582 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 53.0699 | 3.39745 | ||||||||
\(245\) | 2.49108 | 0.159149 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.4697 | −1.62060 | ||||||||
\(248\) | 15.5823 | 0.989476 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 30.6227 | 1.93675 | ||||||||
\(251\) | 21.9174 | 1.38342 | 0.691708 | − | 0.722177i | \(-0.256858\pi\) | ||||
0.691708 | + | 0.722177i | \(0.256858\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.56108 | 0.412491 | ||||||||
\(254\) | −16.6845 | −1.04688 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −28.4730 | −1.77956 | ||||||||
\(257\) | 3.65769 | 0.228161 | 0.114080 | − | 0.993472i | \(-0.463608\pi\) | ||||
0.114080 | + | 0.993472i | \(0.463608\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.20059 | −0.447423 | ||||||||
\(260\) | 38.6428 | 2.39653 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 36.7593 | 2.27100 | ||||||||
\(263\) | −26.5342 | −1.63617 | −0.818085 | − | 0.575098i | \(-0.804964\pi\) | ||||
−0.818085 | + | 0.575098i | \(0.804964\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.0155 | 0.799538 | ||||||||
\(266\) | −36.4406 | −2.23431 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15.8972 | 0.971076 | ||||||||
\(269\) | 18.9277 | 1.15404 | 0.577022 | − | 0.816729i | \(-0.304215\pi\) | ||||
0.577022 | + | 0.816729i | \(0.304215\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.52707 | −0.0927629 | −0.0463814 | − | 0.998924i | \(-0.514769\pi\) | ||||
−0.0463814 | + | 0.998924i | \(0.514769\pi\) | |||||||
\(272\) | 9.20132 | 0.557912 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −37.9677 | −2.29371 | ||||||||
\(275\) | −14.9992 | −0.904483 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.7373 | −1.78674 | −0.893370 | − | 0.449322i | \(-0.851666\pi\) | ||||
−0.893370 | + | 0.449322i | \(0.851666\pi\) | |||||||
\(278\) | 34.0316 | 2.04108 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 30.7634 | 1.83847 | ||||||||
\(281\) | 28.9096 | 1.72460 | 0.862301 | − | 0.506397i | \(-0.169023\pi\) | ||||
0.862301 | + | 0.506397i | \(0.169023\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.7138 | 0.636871 | 0.318436 | − | 0.947944i | \(-0.396843\pi\) | ||||
0.318436 | + | 0.947944i | \(0.396843\pi\) | |||||||
\(284\) | −44.9739 | −2.66871 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −87.0833 | −5.14935 | ||||||||
\(287\) | −19.6464 | −1.15969 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.4163 | −0.906843 | ||||||||
\(290\) | −4.20290 | −0.246803 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −25.0746 | −1.46738 | ||||||||
\(293\) | 18.4098 | 1.07551 | 0.537757 | − | 0.843100i | \(-0.319272\pi\) | ||||
0.537757 | + | 0.843100i | \(0.319272\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.10926 | 0.122806 | ||||||||
\(296\) | −15.7967 | −0.918165 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 47.6136 | 2.75818 | ||||||||
\(299\) | 5.20247 | 0.300866 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.41776 | −0.0817183 | ||||||||
\(302\) | 26.8137 | 1.54296 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −35.7960 | −2.05304 | ||||||||
\(305\) | 19.3903 | 1.11029 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.79956 | 0.502217 | 0.251109 | − | 0.967959i | \(-0.419205\pi\) | ||||
0.251109 | + | 0.967959i | \(0.419205\pi\) | |||||||
\(308\) | −86.3089 | −4.91791 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 10.2321 | 0.581142 | ||||||||
\(311\) | 15.0932 | 0.855856 | 0.427928 | − | 0.903813i | \(-0.359244\pi\) | ||||
0.427928 | + | 0.903813i | \(0.359244\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.7920 | −1.00567 | −0.502833 | − | 0.864384i | \(-0.667709\pi\) | ||||
−0.502833 | + | 0.864384i | \(0.667709\pi\) | |||||||
\(314\) | −25.1550 | −1.41958 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −26.3703 | −1.48344 | ||||||||
\(317\) | 14.9547 | 0.839938 | 0.419969 | − | 0.907538i | \(-0.362041\pi\) | ||||
0.419969 | + | 0.907538i | \(0.362041\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.56108 | 0.367350 | ||||||||
\(320\) | 0.508114 | 0.0284044 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.44337 | 0.414803 | ||||||||
\(323\) | −6.16093 | −0.342804 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.8933 | −0.659719 | ||||||||
\(326\) | 3.39781 | 0.188187 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −43.1004 | −2.37982 | ||||||||
\(329\) | −8.52507 | −0.470002 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.5635 | 0.800480 | 0.400240 | − | 0.916410i | \(-0.368927\pi\) | ||||
0.400240 | + | 0.916410i | \(0.368927\pi\) | |||||||
\(332\) | 49.5383 | 2.71877 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 40.7912 | 2.23199 | ||||||||
\(335\) | 5.80842 | 0.317348 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.2334 | −1.32008 | −0.660039 | − | 0.751231i | \(-0.729460\pi\) | ||||
−0.660039 | + | 0.751231i | \(0.729460\pi\) | |||||||
\(338\) | −35.8848 | −1.95188 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.34740 | 0.506934 | ||||||||
\(341\) | −15.9731 | −0.864991 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.0112 | 0.864522 | ||||||||
\(344\) | −3.11029 | −0.167696 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.8870 | −0.746569 | ||||||||
\(347\) | −8.45970 | −0.454140 | −0.227070 | − | 0.973878i | \(-0.572915\pi\) | ||||
−0.227070 | + | 0.973878i | \(0.572915\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.28519 | −0.0687946 | −0.0343973 | − | 0.999408i | \(-0.510951\pi\) | ||||
−0.0343973 | + | 0.999408i | \(0.510951\pi\) | |||||||
\(350\) | −17.0162 | −0.909552 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −38.4006 | −2.04676 | ||||||||
\(353\) | 13.9545 | 0.742725 | 0.371363 | − | 0.928488i | \(-0.378891\pi\) | ||||
0.371363 | + | 0.928488i | \(0.378891\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.4323 | −0.872135 | ||||||||
\(356\) | −74.9895 | −3.97443 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.2066 | −0.750842 | ||||||||
\(359\) | 30.4675 | 1.60801 | 0.804007 | − | 0.594620i | \(-0.202697\pi\) | ||||
0.804007 | + | 0.594620i | \(0.202697\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.96794 | 0.261471 | ||||||||
\(362\) | −12.2376 | −0.643194 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −68.4368 | −3.58706 | ||||||||
\(365\) | −9.16161 | −0.479540 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.18438 | 0.270623 | 0.135311 | − | 0.990803i | \(-0.456797\pi\) | ||||
0.135311 | + | 0.990803i | \(0.456797\pi\) | |||||||
\(368\) | 7.31171 | 0.381149 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −10.3729 | −0.539259 | ||||||||
\(371\) | −23.0506 | −1.19673 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.9429 | 0.929048 | 0.464524 | − | 0.885561i | \(-0.346225\pi\) | ||||
0.464524 | + | 0.885561i | \(0.346225\pi\) | |||||||
\(374\) | −21.0648 | −1.08923 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −18.7024 | −0.964501 | ||||||||
\(377\) | 5.20247 | 0.267941 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.6550 | −1.16371 | −0.581853 | − | 0.813294i | \(-0.697672\pi\) | ||||
−0.581853 | + | 0.813294i | \(0.697672\pi\) | |||||||
\(380\) | −36.3643 | −1.86545 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −37.1068 | −1.89855 | ||||||||
\(383\) | 11.7444 | 0.600113 | 0.300056 | − | 0.953921i | \(-0.402994\pi\) | ||||
0.300056 | + | 0.953921i | \(0.402994\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −31.5350 | −1.60717 | ||||||||
\(386\) | 61.8770 | 3.14946 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 31.4617 | 1.59723 | ||||||||
\(389\) | −10.7623 | −0.545671 | −0.272835 | − | 0.962061i | \(-0.587961\pi\) | ||||
−0.272835 | + | 0.962061i | \(0.587961\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.25844 | 0.0636419 | ||||||||
\(392\) | −9.67847 | −0.488837 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −33.7634 | −1.70097 | ||||||||
\(395\) | −9.63500 | −0.484790 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.03714 | 0.252807 | 0.126403 | − | 0.991979i | \(-0.459657\pi\) | ||||
0.126403 | + | 0.991979i | \(0.459657\pi\) | |||||||
\(398\) | 45.2970 | 2.27053 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −16.7152 | −0.835758 | ||||||||
\(401\) | −28.6191 | −1.42917 | −0.714586 | − | 0.699548i | \(-0.753385\pi\) | ||||
−0.714586 | + | 0.699548i | \(0.753385\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.6655 | −0.630914 | ||||||||
\(404\) | −18.6623 | −0.928486 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.44337 | 0.369408 | ||||||||
\(407\) | 16.1929 | 0.802652 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.44849 | 0.368304 | 0.184152 | − | 0.982898i | \(-0.441046\pi\) | ||||
0.184152 | + | 0.982898i | \(0.441046\pi\) | |||||||
\(410\) | −28.3017 | −1.39772 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 58.1577 | 2.86523 | ||||||||
\(413\) | −3.73551 | −0.183813 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.1000 | 0.888493 | ||||||||
\(416\) | −30.4490 | −1.49288 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 81.9485 | 4.00823 | ||||||||
\(419\) | −2.54093 | −0.124133 | −0.0620663 | − | 0.998072i | \(-0.519769\pi\) | ||||
−0.0620663 | + | 0.998072i | \(0.519769\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.17670 | −0.398508 | −0.199254 | − | 0.979948i | \(-0.563852\pi\) | ||||
−0.199254 | + | 0.979948i | \(0.563852\pi\) | |||||||
\(422\) | 21.1131 | 1.02777 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −50.5686 | −2.45583 | ||||||||
\(425\) | −2.87689 | −0.139550 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −34.3404 | −1.66185 | ||||||||
\(428\) | 92.1041 | 4.45202 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.04236 | −0.0984914 | ||||||||
\(431\) | −23.9124 | −1.15182 | −0.575910 | − | 0.817513i | \(-0.695352\pi\) | ||||
−0.575910 | + | 0.817513i | \(0.695352\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.1094 | −0.533884 | −0.266942 | − | 0.963713i | \(-0.586013\pi\) | ||||
−0.266942 | + | 0.963713i | \(0.586013\pi\) | |||||||
\(434\) | −18.1211 | −0.869839 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.2330 | 0.729526 | ||||||||
\(437\) | −4.89571 | −0.234193 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.6475 | −0.889997 | −0.444998 | − | 0.895531i | \(-0.646796\pi\) | ||||
−0.444998 | + | 0.895531i | \(0.646796\pi\) | |||||||
\(440\) | −69.1817 | −3.29811 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −16.7029 | −0.794474 | ||||||||
\(443\) | 4.40464 | 0.209271 | 0.104635 | − | 0.994511i | \(-0.466632\pi\) | ||||
0.104635 | + | 0.994511i | \(0.466632\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −27.3992 | −1.29884 | ||||||||
\(446\) | −7.88922 | −0.373565 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.899875 | −0.0425151 | ||||||||
\(449\) | 22.6058 | 1.06684 | 0.533418 | − | 0.845852i | \(-0.320907\pi\) | ||||
0.533418 | + | 0.845852i | \(0.320907\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 44.1813 | 2.08042 | ||||||||
\(452\) | 36.8899 | 1.73516 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 44.5972 | 2.09305 | ||||||||
\(455\) | −25.0050 | −1.17225 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 36.8455 | 1.72356 | 0.861781 | − | 0.507281i | \(-0.169349\pi\) | ||||
0.861781 | + | 0.507281i | \(0.169349\pi\) | |||||||
\(458\) | −52.5206 | −2.45413 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.42779 | 0.346323 | ||||||||
\(461\) | −8.77617 | −0.408747 | −0.204373 | − | 0.978893i | \(-0.565516\pi\) | ||||
−0.204373 | + | 0.978893i | \(0.565516\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.87863 | −0.273203 | −0.136602 | − | 0.990626i | \(-0.543618\pi\) | ||||
−0.136602 | + | 0.990626i | \(0.543618\pi\) | |||||||
\(464\) | 7.31171 | 0.339438 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.1318 | 0.932588 | ||||||||
\(467\) | −4.25825 | −0.197048 | −0.0985241 | − | 0.995135i | \(-0.531412\pi\) | ||||
−0.0985241 | + | 0.995135i | \(0.531412\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.2868 | −0.474998 | ||||||||
\(470\) | −12.2808 | −0.566473 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.19499 | −0.377205 | ||||||||
\(473\) | 3.18830 | 0.146598 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.1920 | 0.513523 | ||||||||
\(476\) | −16.5543 | −0.758767 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 50.8322 | 2.32501 | ||||||||
\(479\) | −33.3895 | −1.52561 | −0.762803 | − | 0.646631i | \(-0.776177\pi\) | ||||
−0.762803 | + | 0.646631i | \(0.776177\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.8398 | 0.585445 | ||||||||
\(482\) | −27.6607 | −1.25991 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 144.497 | 6.56805 | ||||||||
\(485\) | 11.4953 | 0.521974 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.38462 | −0.334629 | −0.167314 | − | 0.985904i | \(-0.553510\pi\) | ||||
−0.167314 | + | 0.985904i | \(0.553510\pi\) | |||||||
\(488\) | −75.3363 | −3.41031 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.35533 | −0.287105 | ||||||||
\(491\) | 42.4415 | 1.91536 | 0.957679 | − | 0.287838i | \(-0.0929364\pi\) | ||||
0.957679 | + | 0.287838i | \(0.0929364\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.25844 | 0.0566771 | ||||||||
\(494\) | 64.9793 | 2.92356 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −17.8005 | −0.799267 | ||||||||
\(497\) | 29.1017 | 1.30539 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 40.0787 | 1.79417 | 0.897086 | − | 0.441857i | \(-0.145680\pi\) | ||||
0.897086 | + | 0.441857i | \(0.145680\pi\) | |||||||
\(500\) | −54.1195 | −2.42030 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −55.9166 | −2.49568 | ||||||||
\(503\) | 0.118814 | 0.00529764 | 0.00264882 | − | 0.999996i | \(-0.499157\pi\) | ||||
0.00264882 | + | 0.999996i | \(0.499157\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.81872 | −0.303429 | ||||||||
\(506\) | −16.7389 | −0.744133 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 29.4866 | 1.30826 | ||||||||
\(509\) | 3.69720 | 0.163876 | 0.0819378 | − | 0.996637i | \(-0.473889\pi\) | ||||
0.0819378 | + | 0.996637i | \(0.473889\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.2253 | 0.717764 | ||||||||
\(512\) | 50.8040 | 2.24524 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.33164 | −0.411601 | ||||||||
\(515\) | 21.2493 | 0.936356 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.1714 | 0.843158 | ||||||||
\(518\) | 18.3704 | 0.807150 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −54.8561 | −2.40560 | ||||||||
\(521\) | −9.03211 | −0.395704 | −0.197852 | − | 0.980232i | \(-0.563397\pi\) | ||||
−0.197852 | + | 0.980232i | \(0.563397\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.2806 | −0.493267 | −0.246634 | − | 0.969109i | \(-0.579324\pi\) | ||||
−0.246634 | + | 0.969109i | \(0.579324\pi\) | |||||||
\(524\) | −64.9648 | −2.83800 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 67.6950 | 2.95164 | ||||||||
\(527\) | −3.06369 | −0.133456 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −33.2057 | −1.44236 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 64.4015 | 2.79216 | ||||||||
\(533\) | 35.0326 | 1.51743 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 33.6524 | 1.45492 | ||||||||
\(536\) | −22.5672 | −0.974752 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −48.2891 | −2.08189 | ||||||||
\(539\) | 9.92121 | 0.427337 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.8519 | 0.552548 | 0.276274 | − | 0.961079i | \(-0.410900\pi\) | ||||
0.276274 | + | 0.961079i | \(0.410900\pi\) | |||||||
\(542\) | 3.89592 | 0.167344 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.36537 | −0.315787 | ||||||||
\(545\) | 5.56572 | 0.238409 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.1104 | −1.54397 | −0.771985 | − | 0.635641i | \(-0.780736\pi\) | ||||
−0.771985 | + | 0.635641i | \(0.780736\pi\) | |||||||
\(548\) | 67.1003 | 2.86638 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 38.2664 | 1.63168 | ||||||||
\(551\) | −4.89571 | −0.208564 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.0637 | 0.725621 | ||||||||
\(554\) | 75.8668 | 3.22327 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −60.1442 | −2.55068 | ||||||||
\(557\) | −25.5611 | −1.08306 | −0.541529 | − | 0.840682i | \(-0.682155\pi\) | ||||
−0.541529 | + | 0.840682i | \(0.682155\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.52809 | 0.106927 | ||||||||
\(560\) | −35.1428 | −1.48505 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −73.7552 | −3.11117 | ||||||||
\(563\) | 17.3413 | 0.730850 | 0.365425 | − | 0.930841i | \(-0.380924\pi\) | ||||
0.365425 | + | 0.930841i | \(0.380924\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.4786 | 0.567049 | ||||||||
\(566\) | −27.3335 | −1.14891 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 63.8435 | 2.67881 | ||||||||
\(569\) | 42.8650 | 1.79699 | 0.898497 | − | 0.438980i | \(-0.144660\pi\) | ||||
0.898497 | + | 0.438980i | \(0.144660\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.5508 | 1.40406 | 0.702028 | − | 0.712149i | \(-0.252278\pi\) | ||||
0.702028 | + | 0.712149i | \(0.252278\pi\) | |||||||
\(572\) | 153.903 | 6.43499 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 50.1226 | 2.09208 | ||||||||
\(575\) | −2.28608 | −0.0953362 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.4048 | 1.34903 | 0.674514 | − | 0.738262i | \(-0.264353\pi\) | ||||
0.674514 | + | 0.738262i | \(0.264353\pi\) | |||||||
\(578\) | 39.3307 | 1.63594 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.42779 | 0.308422 | ||||||||
\(581\) | −32.0552 | −1.32987 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 51.8369 | 2.14686 | ||||||||
\(584\) | 35.5951 | 1.47294 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −46.9678 | −1.94022 | ||||||||
\(587\) | −34.5477 | −1.42593 | −0.712967 | − | 0.701197i | \(-0.752649\pi\) | ||||
−0.712967 | + | 0.701197i | \(0.752649\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.9187 | 0.491102 | ||||||||
\(590\) | −5.38121 | −0.221541 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 18.0455 | 0.741664 | ||||||||
\(593\) | 17.2013 | 0.706371 | 0.353186 | − | 0.935553i | \(-0.385098\pi\) | ||||
0.353186 | + | 0.935553i | \(0.385098\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.04851 | −0.247965 | ||||||||
\(596\) | −84.1477 | −3.44682 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −13.2727 | −0.542762 | ||||||||
\(599\) | 32.8586 | 1.34257 | 0.671283 | − | 0.741201i | \(-0.265743\pi\) | ||||
0.671283 | + | 0.741201i | \(0.265743\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.47346 | 0.0601038 | 0.0300519 | − | 0.999548i | \(-0.490433\pi\) | ||||
0.0300519 | + | 0.999548i | \(0.490433\pi\) | |||||||
\(602\) | 3.61704 | 0.147420 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −47.3880 | −1.92819 | ||||||||
\(605\) | 52.7954 | 2.14644 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.3362 | −0.541300 | −0.270650 | − | 0.962678i | \(-0.587239\pi\) | ||||
−0.270650 | + | 0.962678i | \(0.587239\pi\) | |||||||
\(608\) | 28.6536 | 1.16206 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −49.4693 | −2.00295 | ||||||||
\(611\) | 15.2016 | 0.614989 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.1307 | 0.530345 | 0.265173 | − | 0.964201i | \(-0.414571\pi\) | ||||
0.265173 | + | 0.964201i | \(0.414571\pi\) | |||||||
\(614\) | −22.4498 | −0.905998 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 122.521 | 4.93653 | ||||||||
\(617\) | 41.4164 | 1.66736 | 0.833681 | − | 0.552247i | \(-0.186229\pi\) | ||||
0.833681 | + | 0.552247i | \(0.186229\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.0601 | −1.36899 | −0.684496 | − | 0.729017i | \(-0.739978\pi\) | ||||
−0.684496 | + | 0.729017i | \(0.739978\pi\) | |||||||
\(620\) | −18.0831 | −0.726236 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −38.5063 | −1.54396 | ||||||||
\(623\) | 48.5241 | 1.94408 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.34343 | −0.333737 | ||||||||
\(626\) | 45.3917 | 1.81422 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 44.4565 | 1.77401 | ||||||||
\(629\) | 3.10585 | 0.123838 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.31051 | −0.211408 | −0.105704 | − | 0.994398i | \(-0.533710\pi\) | ||||
−0.105704 | + | 0.994398i | \(0.533710\pi\) | |||||||
\(632\) | 37.4344 | 1.48906 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −38.1529 | −1.51524 | ||||||||
\(635\) | 10.7736 | 0.427538 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.86681 | 0.311694 | ||||||||
\(638\) | −16.7389 | −0.662698 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 17.9874 | 0.711016 | ||||||||
\(641\) | 27.3092 | 1.07865 | 0.539323 | − | 0.842099i | \(-0.318680\pi\) | ||||
0.539323 | + | 0.842099i | \(0.318680\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.1059 | −1.38444 | −0.692220 | − | 0.721686i | \(-0.743367\pi\) | ||||
−0.692220 | + | 0.721686i | \(0.743367\pi\) | |||||||
\(644\) | −13.1547 | −0.518367 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15.7180 | 0.618416 | ||||||||
\(647\) | 28.1684 | 1.10741 | 0.553706 | − | 0.832712i | \(-0.313213\pi\) | ||||
0.553706 | + | 0.832712i | \(0.313213\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.40052 | 0.329749 | ||||||||
\(650\) | 30.3425 | 1.19013 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.00495 | −0.235172 | ||||||||
\(653\) | −27.6829 | −1.08331 | −0.541657 | − | 0.840599i | \(-0.682203\pi\) | ||||
−0.541657 | + | 0.840599i | \(0.682203\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23.7364 | −0.927458 | ||||||||
\(656\) | 49.2360 | 1.92234 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 21.7495 | 0.847883 | ||||||||
\(659\) | 32.3726 | 1.26106 | 0.630530 | − | 0.776165i | \(-0.282838\pi\) | ||||
0.630530 | + | 0.776165i | \(0.282838\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.6507 | −0.530950 | −0.265475 | − | 0.964118i | \(-0.585529\pi\) | ||||
−0.265475 | + | 0.964118i | \(0.585529\pi\) | |||||||
\(662\) | −37.1548 | −1.44406 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −70.3229 | −2.72906 | ||||||||
\(665\) | 23.5306 | 0.912477 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −72.0903 | −2.78926 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −14.8186 | −0.572494 | ||||||||
\(671\) | 77.2257 | 2.98126 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.5130 | −1.36892 | −0.684462 | − | 0.729048i | \(-0.739963\pi\) | ||||
−0.684462 | + | 0.729048i | \(0.739963\pi\) | |||||||
\(674\) | 61.8252 | 2.38142 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 63.4193 | 2.43920 | ||||||||
\(677\) | 3.45875 | 0.132930 | 0.0664652 | − | 0.997789i | \(-0.478828\pi\) | ||||
0.0664652 | + | 0.997789i | \(0.478828\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.3582 | −0.781277 | ||||||||
\(680\) | −13.2693 | −0.508853 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 40.7511 | 1.56044 | ||||||||
\(683\) | −30.8279 | −1.17960 | −0.589798 | − | 0.807551i | \(-0.700792\pi\) | ||||
−0.589798 | + | 0.807551i | \(0.700792\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.5167 | 0.936734 | ||||||||
\(686\) | −40.8483 | −1.55959 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.55306 | 0.135459 | ||||||||
\(689\) | 41.1029 | 1.56590 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.5507 | 1.16220 | 0.581102 | − | 0.813831i | \(-0.302622\pi\) | ||||
0.581102 | + | 0.813831i | \(0.302622\pi\) | |||||||
\(692\) | 24.5425 | 0.932966 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.5827 | 0.819268 | ||||||||
\(695\) | −21.9751 | −0.833563 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.47412 | 0.320980 | ||||||||
\(698\) | 3.27882 | 0.124105 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 30.0727 | 1.13664 | ||||||||
\(701\) | −23.9520 | −0.904656 | −0.452328 | − | 0.891852i | \(-0.649406\pi\) | ||||
−0.452328 | + | 0.891852i | \(0.649406\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.0827 | −0.455708 | ||||||||
\(704\) | 2.02366 | 0.0762697 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −35.6013 | −1.33987 | ||||||||
\(707\) | 12.0760 | 0.454165 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.3049 | 0.387007 | 0.193503 | − | 0.981100i | \(-0.438015\pi\) | ||||
0.193503 | + | 0.981100i | \(0.438015\pi\) | |||||||
\(710\) | 41.9226 | 1.57333 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 106.453 | 3.98948 | ||||||||
\(713\) | −2.43452 | −0.0911736 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 56.2319 | 2.10295 | ||||||||
\(716\) | 25.1074 | 0.938306 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −77.7298 | −2.90085 | ||||||||
\(719\) | 47.4660 | 1.77018 | 0.885092 | − | 0.465416i | \(-0.154095\pi\) | ||||
0.885092 | + | 0.465416i | \(0.154095\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −37.6327 | −1.40151 | ||||||||
\(722\) | −12.6744 | −0.471692 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 21.6275 | 0.803781 | ||||||||
\(725\) | −2.28608 | −0.0849029 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.6344 | 1.54414 | 0.772068 | − | 0.635540i | \(-0.219222\pi\) | ||||
0.772068 | + | 0.635540i | \(0.219222\pi\) | |||||||
\(728\) | 97.1507 | 3.60064 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 23.3734 | 0.865089 | ||||||||
\(731\) | 0.611526 | 0.0226181 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.0455 | 0.998948 | 0.499474 | − | 0.866329i | \(-0.333527\pi\) | ||||
0.499474 | + | 0.866329i | \(0.333527\pi\) | |||||||
\(734\) | −13.2266 | −0.488202 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.85279 | −0.215737 | ||||||||
\(737\) | 23.1331 | 0.852120 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.7406 | 1.46188 | 0.730942 | − | 0.682440i | \(-0.239081\pi\) | ||||
0.730942 | + | 0.682440i | \(0.239081\pi\) | |||||||
\(740\) | 18.3320 | 0.673897 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 58.8076 | 2.15889 | ||||||||
\(743\) | −35.1971 | −1.29126 | −0.645629 | − | 0.763651i | \(-0.723405\pi\) | ||||
−0.645629 | + | 0.763651i | \(0.723405\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30.7453 | −1.12642 | ||||||||
\(746\) | −45.7766 | −1.67600 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 37.2278 | 1.36118 | ||||||||
\(749\) | −59.5987 | −2.17769 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.2429 | −0.446750 | −0.223375 | − | 0.974733i | \(-0.571707\pi\) | ||||
−0.223375 | + | 0.974733i | \(0.571707\pi\) | |||||||
\(752\) | 21.3648 | 0.779092 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −13.2727 | −0.483364 | ||||||||
\(755\) | −17.3143 | −0.630132 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.7925 | −0.683025 | −0.341513 | − | 0.939877i | \(-0.610939\pi\) | ||||
−0.341513 | + | 0.939877i | \(0.610939\pi\) | |||||||
\(758\) | 57.7981 | 2.09932 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 51.6216 | 1.87251 | ||||||||
\(761\) | 39.8907 | 1.44604 | 0.723019 | − | 0.690828i | \(-0.242754\pi\) | ||||
0.723019 | + | 0.690828i | \(0.242754\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.85694 | −0.356845 | ||||||||
\(764\) | 65.5789 | 2.37256 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −29.9628 | −1.08260 | ||||||||
\(767\) | 6.66101 | 0.240515 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.6742 | −1.17826 | −0.589131 | − | 0.808038i | \(-0.700530\pi\) | ||||
−0.589131 | + | 0.808038i | \(0.700530\pi\) | |||||||
\(770\) | 80.4532 | 2.89933 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −109.355 | −3.93578 | ||||||||
\(773\) | 0.742529 | 0.0267069 | 0.0133535 | − | 0.999911i | \(-0.495749\pi\) | ||||
0.0133535 | + | 0.999911i | \(0.495749\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.56552 | 0.199919 | ||||||||
\(776\) | −44.6620 | −1.60327 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 27.4572 | 0.984388 | ||||||||
\(779\) | −32.9670 | −1.18116 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −65.4447 | −2.34180 | ||||||||
\(782\) | −3.21057 | −0.114810 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 11.0563 | 0.394866 | ||||||||
\(785\) | 16.2432 | 0.579746 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.6413 | −0.628846 | −0.314423 | − | 0.949283i | \(-0.601811\pi\) | ||||
−0.314423 | + | 0.949283i | \(0.601811\pi\) | |||||||
\(788\) | 59.6701 | 2.12566 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 24.5812 | 0.874558 | ||||||||
\(791\) | −23.8707 | −0.848745 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 61.2344 | 2.17450 | ||||||||
\(794\) | −12.8509 | −0.456062 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −80.0535 | −2.83742 | ||||||||
\(797\) | 9.68090 | 0.342915 | 0.171458 | − | 0.985192i | \(-0.445152\pi\) | ||||
0.171458 | + | 0.985192i | \(0.445152\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.67714 | 0.130088 | ||||||||
\(800\) | 13.3800 | 0.473053 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 73.0142 | 2.57822 | ||||||||
\(803\) | −36.4879 | −1.28763 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.80637 | −0.169402 | ||||||||
\(806\) | 32.3127 | 1.13817 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 26.4925 | 0.932001 | ||||||||
\(809\) | 29.2901 | 1.02978 | 0.514892 | − | 0.857255i | \(-0.327832\pi\) | ||||
0.514892 | + | 0.857255i | \(0.327832\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.53571 | 0.159270 | 0.0796352 | − | 0.996824i | \(-0.474624\pi\) | ||||
0.0796352 | + | 0.996824i | \(0.474624\pi\) | |||||||
\(812\) | −13.1547 | −0.461639 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −41.3119 | −1.44798 | ||||||||
\(815\) | −2.19405 | −0.0768542 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.37902 | −0.0832315 | ||||||||
\(818\) | −19.0029 | −0.664419 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 50.0176 | 1.74669 | ||||||||
\(821\) | −6.70897 | −0.234145 | −0.117072 | − | 0.993123i | \(-0.537351\pi\) | ||||
−0.117072 | + | 0.993123i | \(0.537351\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.24785 | −0.252644 | −0.126322 | − | 0.991989i | \(-0.540317\pi\) | ||||
−0.126322 | + | 0.991989i | \(0.540317\pi\) | |||||||
\(824\) | −82.5588 | −2.87607 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.53017 | 0.331597 | ||||||||
\(827\) | −14.4279 | −0.501707 | −0.250853 | − | 0.968025i | \(-0.580711\pi\) | ||||
−0.250853 | + | 0.968025i | \(0.580711\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43.7318 | −1.51887 | −0.759433 | − | 0.650585i | \(-0.774524\pi\) | ||||
−0.759433 | + | 0.650585i | \(0.774524\pi\) | |||||||
\(830\) | −46.1773 | −1.60284 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.60462 | 0.0556302 | ||||||||
\(833\) | 1.90292 | 0.0659323 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.3399 | −0.911529 | ||||||||
\(836\) | −144.828 | −5.00897 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.48251 | 0.223935 | ||||||||
\(839\) | 35.6685 | 1.23141 | 0.615706 | − | 0.787976i | \(-0.288871\pi\) | ||||
0.615706 | + | 0.787976i | \(0.288871\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 20.8607 | 0.718907 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −37.3132 | −1.28437 | ||||||||
\(845\) | 23.1717 | 0.797131 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −93.5011 | −3.21274 | ||||||||
\(848\) | 57.7674 | 1.98374 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 7.33962 | 0.251747 | ||||||||
\(851\) | 2.46802 | 0.0846027 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.4978 | 1.28390 | 0.641950 | − | 0.766746i | \(-0.278126\pi\) | ||||
0.641950 | + | 0.766746i | \(0.278126\pi\) | |||||||
\(854\) | 87.6105 | 2.99797 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −130.748 | −4.46888 | ||||||||
\(857\) | −42.6622 | −1.45731 | −0.728656 | − | 0.684879i | \(-0.759855\pi\) | ||||
−0.728656 | + | 0.684879i | \(0.759855\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.7446 | 0.605439 | 0.302720 | − | 0.953080i | \(-0.402105\pi\) | ||||
0.302720 | + | 0.953080i | \(0.402105\pi\) | |||||||
\(860\) | 3.60947 | 0.123082 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 61.0062 | 2.07788 | ||||||||
\(863\) | 12.6765 | 0.431512 | 0.215756 | − | 0.976447i | \(-0.430778\pi\) | ||||
0.215756 | + | 0.976447i | \(0.430778\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.96718 | 0.304893 | ||||||||
\(866\) | 28.3427 | 0.963124 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 32.0254 | 1.08701 | ||||||||
\(869\) | −38.3732 | −1.30172 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.3429 | 0.621526 | ||||||||
\(872\) | −21.6242 | −0.732288 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 12.4901 | 0.422484 | ||||||||
\(875\) | 35.0196 | 1.18388 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.131207 | 0.00443054 | 0.00221527 | − | 0.999998i | \(-0.499295\pi\) | ||||
0.00221527 | + | 0.999998i | \(0.499295\pi\) | |||||||
\(878\) | 47.5742 | 1.60555 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 79.0301 | 2.66410 | ||||||||
\(881\) | 52.2114 | 1.75905 | 0.879523 | − | 0.475856i | \(-0.157862\pi\) | ||||
0.879523 | + | 0.475856i | \(0.157862\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.7337 | 1.67367 | 0.836836 | − | 0.547453i | \(-0.184403\pi\) | ||||
0.836836 | + | 0.547453i | \(0.184403\pi\) | |||||||
\(884\) | 29.5190 | 0.992832 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.2373 | −0.377523 | ||||||||
\(887\) | −1.15616 | −0.0388200 | −0.0194100 | − | 0.999812i | \(-0.506179\pi\) | ||||
−0.0194100 | + | 0.999812i | \(0.506179\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.0802 | −0.639929 | ||||||||
\(890\) | 69.9017 | 2.34311 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.9426 | 0.466834 | ||||||||
\(893\) | −14.3052 | −0.478706 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.17356 | 0.306638 | ||||||||
\(896\) | −31.8559 | −1.06423 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −57.6728 | −1.92457 | ||||||||
\(899\) | −2.43452 | −0.0811959 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.94248 | 0.331232 | ||||||||
\(902\) | −112.717 | −3.75306 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −52.3677 | −1.74172 | ||||||||
\(905\) | 7.90212 | 0.262676 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.3077 | −1.13917 | −0.569585 | − | 0.821933i | \(-0.692896\pi\) | ||||
−0.569585 | + | 0.821933i | \(0.692896\pi\) | |||||||
\(908\) | −78.8168 | −2.61563 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 63.7936 | 2.11474 | ||||||||
\(911\) | 41.4208 | 1.37233 | 0.686167 | − | 0.727444i | \(-0.259292\pi\) | ||||
0.686167 | + | 0.727444i | \(0.259292\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 72.0866 | 2.38572 | ||||||||
\(914\) | −94.0016 | −3.10930 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 92.8197 | 3.06685 | ||||||||
\(917\) | 42.0374 | 1.38820 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.42221 | −0.211849 | −0.105925 | − | 0.994374i | \(-0.533780\pi\) | ||||
−0.105925 | + | 0.994374i | \(0.533780\pi\) | |||||||
\(920\) | −10.5443 | −0.347634 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 22.3901 | 0.737378 | ||||||||
\(923\) | −51.8930 | −1.70808 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.64210 | −0.185511 | ||||||||
\(926\) | 14.9978 | 0.492857 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.85279 | −0.192127 | ||||||||
\(929\) | −26.4758 | −0.868641 | −0.434321 | − | 0.900758i | \(-0.643012\pi\) | ||||
−0.434321 | + | 0.900758i | \(0.643012\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.40295 | −0.242622 | ||||||||
\(932\) | −35.5790 | −1.16543 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10.8638 | 0.355474 | ||||||||
\(935\) | 13.6021 | 0.444835 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.44658 | 0.177932 | 0.0889660 | − | 0.996035i | \(-0.471644\pi\) | ||||
0.0889660 | + | 0.996035i | \(0.471644\pi\) | |||||||
\(938\) | 26.2439 | 0.856895 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 21.7040 | 0.707905 | ||||||||
\(941\) | −9.09767 | −0.296576 | −0.148288 | − | 0.988944i | \(-0.547376\pi\) | ||||
−0.148288 | + | 0.988944i | \(0.547376\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.73385 | 0.219284 | ||||||||
\(944\) | 9.36160 | 0.304694 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.13410 | −0.264462 | ||||||||
\(947\) | 42.5878 | 1.38392 | 0.691959 | − | 0.721937i | \(-0.256748\pi\) | ||||
0.691959 | + | 0.721937i | \(0.256748\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.9323 | −0.939181 | ||||||||
\(950\) | −28.5534 | −0.926394 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 23.5000 | 0.761639 | ||||||||
\(953\) | −11.7665 | −0.381155 | −0.190577 | − | 0.981672i | \(-0.561036\pi\) | ||||
−0.190577 | + | 0.981672i | \(0.561036\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.9608 | 0.775353 | ||||||||
\(956\) | −89.8358 | −2.90550 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 85.1845 | 2.75219 | ||||||||
\(959\) | −43.4192 | −1.40208 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.0731 | −0.808810 | ||||||||
\(962\) | −32.7574 | −1.05614 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 48.8848 | 1.57447 | ||||||||
\(965\) | −39.9555 | −1.28621 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.0505 | 0.966360 | 0.483180 | − | 0.875521i | \(-0.339482\pi\) | ||||
0.483180 | + | 0.875521i | \(0.339482\pi\) | |||||||
\(968\) | −205.123 | −6.59291 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −29.3272 | −0.941638 | ||||||||
\(971\) | −35.1648 | −1.12849 | −0.564246 | − | 0.825607i | \(-0.690833\pi\) | ||||
−0.564246 | + | 0.825607i | \(0.690833\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 38.9181 | 1.24766 | ||||||||
\(974\) | 18.8399 | 0.603669 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 86.0608 | 2.75474 | ||||||||
\(977\) | 26.7076 | 0.854452 | 0.427226 | − | 0.904145i | \(-0.359491\pi\) | ||||
0.427226 | + | 0.904145i | \(0.359491\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −109.122 | −3.48757 | ||||||||
\(980\) | 11.2318 | 0.358786 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −108.278 | −3.45530 | ||||||||
\(983\) | −20.0805 | −0.640468 | −0.320234 | − | 0.947338i | \(-0.603762\pi\) | ||||
−0.320234 | + | 0.947338i | \(0.603762\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.8019 | 0.694665 | ||||||||
\(986\) | −3.21057 | −0.102245 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −114.838 | −3.65349 | ||||||||
\(989\) | 0.485941 | 0.0154520 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.1961 | 0.832146 | 0.416073 | − | 0.909331i | \(-0.363406\pi\) | ||||
0.416073 | + | 0.909331i | \(0.363406\pi\) | |||||||
\(992\) | 14.2488 | 0.452398 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −74.2453 | −2.35492 | ||||||||
\(995\) | −29.2494 | −0.927269 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.6800 | 1.25668 | 0.628340 | − | 0.777939i | \(-0.283735\pi\) | ||||
0.628340 | + | 0.777939i | \(0.283735\pi\) | |||||||
\(998\) | −102.250 | −3.23668 | ||||||||
\(999\) | 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 | 6003.2.a.p.1.1 | 14 | ||
3.2 | odd | 2 | 2001.2.a.m.1.14 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.m.1.14 | ✓ | 14 | 3.2 | odd | 2 | ||
6003.2.a.p.1.1 | 14 | 1.1 | even | 1 | trivial |