Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(1,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, 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("4012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0359812909\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 5 x^{14} - 16 x^{13} + 123 x^{12} - 76 x^{11} - 630 x^{10} + 937 x^{9} + 1083 x^{8} - 2602 x^{7} + \cdots - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.18786\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4012.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.460784 | −0.266034 | −0.133017 | − | 0.991114i | \(-0.542466\pi\) | ||||
−0.133017 | + | 0.991114i | \(0.542466\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.730164 | −0.326539 | −0.163270 | − | 0.986582i | \(-0.552204\pi\) | ||||
−0.163270 | + | 0.986582i | \(0.552204\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.58746 | 1.35593 | 0.677965 | − | 0.735094i | \(-0.262862\pi\) | ||||
0.677965 | + | 0.735094i | \(0.262862\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.78768 | −0.929226 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.02705 | 0.912689 | 0.456345 | − | 0.889803i | \(-0.349158\pi\) | ||||
0.456345 | + | 0.889803i | \(0.349158\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.246566 | 0.0683851 | 0.0341926 | − | 0.999415i | \(-0.489114\pi\) | ||||
0.0341926 | + | 0.999415i | \(0.489114\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.336448 | 0.0868704 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.29765 | −0.756532 | −0.378266 | − | 0.925697i | \(-0.623480\pi\) | ||||
−0.378266 | + | 0.925697i | \(0.623480\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.65304 | −0.360723 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.34754 | −1.94910 | −0.974549 | − | 0.224175i | \(-0.928031\pi\) | ||||
−0.974549 | + | 0.224175i | \(0.928031\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.46686 | −0.893372 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.66687 | 0.513239 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.632935 | −0.117533 | −0.0587666 | − | 0.998272i | \(-0.518717\pi\) | ||||
−0.0587666 | + | 0.998272i | \(0.518717\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.50261 | 0.269876 | 0.134938 | − | 0.990854i | \(-0.456916\pi\) | ||||
0.134938 | + | 0.990854i | \(0.456916\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.39482 | −0.242806 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.61943 | −0.442764 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.91272 | −1.13644 | −0.568222 | − | 0.822875i | \(-0.692369\pi\) | ||||
−0.568222 | + | 0.822875i | \(0.692369\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.113614 | −0.0181928 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.28210 | −0.824926 | −0.412463 | − | 0.910974i | \(-0.635331\pi\) | ||||
−0.412463 | + | 0.910974i | \(0.635331\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.83103 | 0.431728 | 0.215864 | − | 0.976423i | \(-0.430743\pi\) | ||||
0.215864 | + | 0.976423i | \(0.430743\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.03546 | 0.303429 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.15459 | 1.04360 | 0.521802 | − | 0.853067i | \(-0.325260\pi\) | ||||
0.521802 | + | 0.853067i | \(0.325260\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.86984 | 0.838549 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.460784 | −0.0645227 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.4716 | −1.57575 | −0.787876 | − | 0.615834i | \(-0.788819\pi\) | ||||
−0.787876 | + | 0.615834i | \(0.788819\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.21024 | −0.298029 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.51950 | 0.201263 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.09602 | −0.268368 | −0.134184 | − | 0.990956i | \(-0.542841\pi\) | ||||
−0.134184 | + | 0.990956i | \(0.542841\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.0007 | −1.25997 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.180034 | −0.0223304 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.17171 | 0.753995 | 0.376997 | − | 0.926214i | \(-0.376957\pi\) | ||||
0.376997 | + | 0.926214i | \(0.376957\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.30720 | 0.518526 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.38615 | 1.11393 | 0.556965 | − | 0.830536i | \(-0.311966\pi\) | ||||
0.556965 | + | 0.830536i | \(0.311966\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.44514 | −0.286182 | −0.143091 | − | 0.989710i | \(-0.545704\pi\) | ||||
−0.143091 | + | 0.989710i | \(0.545704\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.05826 | 0.237667 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.8594 | 1.23754 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.46383 | 0.839746 | 0.419873 | − | 0.907583i | \(-0.362075\pi\) | ||||
0.419873 | + | 0.907583i | \(0.362075\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.13418 | 0.792687 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.8110 | −1.40619 | −0.703093 | − | 0.711097i | \(-0.748198\pi\) | ||||
−0.703093 | + | 0.711097i | \(0.748198\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.730164 | −0.0791974 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.291646 | 0.0312678 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.0018 | −1.69619 | −0.848094 | − | 0.529846i | \(-0.822250\pi\) | ||||
−0.848094 | + | 0.529846i | \(0.822250\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.884545 | 0.0927255 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.692376 | −0.0717961 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.40782 | 0.247037 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.15215 | 0.624656 | 0.312328 | − | 0.949974i | \(-0.398891\pi\) | ||||
0.312328 | + | 0.949974i | \(0.398891\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.43844 | −0.848095 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.57276 | 0.952525 | 0.476262 | − | 0.879303i | \(-0.341991\pi\) | ||||
0.476262 | + | 0.879303i | \(0.341991\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.8901 | −1.07303 | −0.536517 | − | 0.843889i | \(-0.680260\pi\) | ||||
−0.536517 | + | 0.843889i | \(0.680260\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.20699 | 0.117790 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.25952 | 0.218436 | 0.109218 | − | 0.994018i | \(-0.465165\pi\) | ||||
0.109218 | + | 0.994018i | \(0.465165\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.83175 | −0.271233 | −0.135616 | − | 0.990761i | \(-0.543301\pi\) | ||||
−0.135616 | + | 0.990761i | \(0.543301\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.18527 | 0.302332 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.90955 | 0.179636 | 0.0898179 | − | 0.995958i | \(-0.471371\pi\) | ||||
0.0898179 | + | 0.995958i | \(0.471371\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.82524 | 0.636457 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.687347 | −0.0635452 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.58746 | 0.328862 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.83698 | −0.166998 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.43391 | 0.219458 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.91236 | 0.618260 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.41498 | −0.214295 | −0.107147 | − | 0.994243i | \(-0.534172\pi\) | ||||
−0.107147 | + | 0.994243i | \(0.534172\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.30449 | −0.114854 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.69389 | −0.846959 | −0.423480 | − | 0.905906i | \(-0.639191\pi\) | ||||
−0.423480 | + | 0.905906i | \(0.639191\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.8302 | −1.02581 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.94725 | −0.167593 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.0213 | −1.53967 | −0.769833 | − | 0.638245i | \(-0.779661\pi\) | ||||
−0.769833 | + | 0.638245i | \(0.779661\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.41812 | 0.798834 | 0.399417 | − | 0.916769i | \(-0.369213\pi\) | ||||
0.399417 | + | 0.916769i | \(0.369213\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.29672 | −0.277634 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.746367 | 0.0624144 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.462146 | 0.0383792 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.70473 | −0.223082 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.83474 | 0.314154 | 0.157077 | − | 0.987586i | \(-0.449793\pi\) | ||||
0.157077 | + | 0.987586i | \(0.449793\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.8793 | −0.885343 | −0.442671 | − | 0.896684i | \(-0.645969\pi\) | ||||
−0.442671 | + | 0.896684i | \(0.645969\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.78768 | −0.225370 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.09715 | −0.0881250 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.51455 | −0.280492 | −0.140246 | − | 0.990117i | \(-0.544789\pi\) | ||||
−0.140246 | + | 0.990117i | \(0.544789\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.28595 | 0.419203 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −33.5339 | −2.64284 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.02497 | −0.706890 | −0.353445 | − | 0.935455i | \(-0.614990\pi\) | ||||
−0.353445 | + | 0.935455i | \(0.614990\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.01844 | 0.0792857 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.5178 | 0.891274 | 0.445637 | − | 0.895214i | \(-0.352977\pi\) | ||||
0.445637 | + | 0.895214i | \(0.352977\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9392 | −0.995323 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.19278 | 0.702989 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.1297 | −1.60646 | −0.803231 | − | 0.595668i | \(-0.796888\pi\) | ||||
−0.803231 | + | 0.595668i | \(0.796888\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.0247 | −1.21135 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.460784 | 0.0346346 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.801336 | −0.0598947 | −0.0299473 | − | 0.999551i | \(-0.509534\pi\) | ||||
−0.0299473 | + | 0.999551i | \(0.509534\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.06063 | −0.153165 | −0.0765826 | − | 0.997063i | \(-0.524401\pi\) | ||||
−0.0765826 | + | 0.997063i | \(0.524401\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.965813 | 0.0713950 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.04742 | 0.371093 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.02705 | 0.221360 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.56728 | 0.695917 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.09740 | −0.513550 | −0.256775 | − | 0.966471i | \(-0.582660\pi\) | ||||
−0.256775 | + | 0.966471i | \(0.582660\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.4816 | 1.83421 | 0.917103 | − | 0.398651i | \(-0.130521\pi\) | ||||
0.917103 | + | 0.398651i | \(0.130521\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0829566 | 0.00594064 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.9188 | −0.849181 | −0.424590 | − | 0.905386i | \(-0.639582\pi\) | ||||
−0.424590 | + | 0.905386i | \(0.639582\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.0007 | −0.850710 | −0.425355 | − | 0.905027i | \(-0.639851\pi\) | ||||
−0.425355 | + | 0.905027i | \(0.639851\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.84383 | −0.200588 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.27063 | −0.159367 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.85680 | 0.269371 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 26.0579 | 1.81115 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.98214 | −0.690479 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.4785 | −1.20327 | −0.601636 | − | 0.798770i | \(-0.705484\pi\) | ||||
−0.601636 | + | 0.798770i | \(0.705484\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.32499 | −0.296343 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.06712 | −0.140976 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.39053 | 0.365933 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.12668 | 0.0761340 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.246566 | 0.0165858 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.15686 | −0.0774692 | −0.0387346 | − | 0.999250i | \(-0.512333\pi\) | ||||
−0.0387346 | + | 0.999250i | \(0.512333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.4522 | 0.830145 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.30390 | −0.551149 | −0.275575 | − | 0.961280i | \(-0.588868\pi\) | ||||
−0.275575 | + | 0.961280i | \(0.588868\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.89289 | −0.125086 | −0.0625429 | − | 0.998042i | \(-0.519921\pi\) | ||||
−0.0625429 | + | 0.998042i | \(0.519921\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.00384 | −0.329228 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.9586 | 1.30753 | 0.653765 | − | 0.756698i | \(-0.273189\pi\) | ||||
0.653765 | + | 0.756698i | \(0.273189\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.22402 | −0.340777 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.43921 | −0.223401 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.8152 | −0.958317 | −0.479159 | − | 0.877728i | \(-0.659058\pi\) | ||||
−0.479159 | + | 0.877728i | \(0.659058\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.4606 | 0.802659 | 0.401329 | − | 0.915934i | \(-0.368548\pi\) | ||||
0.401329 | + | 0.915934i | \(0.368548\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.2879 | −0.724121 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.28594 | −0.273819 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.813088 | −0.0517355 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.90309 | 0.374093 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.01178 | 0.568819 | 0.284409 | − | 0.958703i | \(-0.408203\pi\) | ||||
0.284409 | + | 0.958703i | \(0.408203\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −28.2955 | −1.77892 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.336448 | 0.0210692 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.6924 | −0.791733 | −0.395866 | − | 0.918308i | \(-0.629556\pi\) | ||||
−0.395866 | + | 0.918308i | \(0.629556\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −24.7991 | −1.54094 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.76442 | 0.109215 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.11094 | −0.253492 | −0.126746 | − | 0.991935i | \(-0.540453\pi\) | ||||
−0.126746 | + | 0.991935i | \(0.540453\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.37618 | 0.514544 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.37338 | 0.451243 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.418438 | 0.0255126 | 0.0127563 | − | 0.999919i | \(-0.495939\pi\) | ||||
0.0127563 | + | 0.999919i | \(0.495939\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.0474225 | 0.00288071 | 0.00144036 | − | 0.999999i | \(-0.499542\pi\) | ||||
0.00144036 | + | 0.999999i | \(0.499542\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.407584 | −0.0246681 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.5214 | −0.815371 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.65391 | 0.519963 | 0.259982 | − | 0.965614i | \(-0.416284\pi\) | ||||
0.259982 | + | 0.965614i | \(0.416284\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.18878 | −0.250776 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.9356 | −1.54719 | −0.773593 | − | 0.633683i | \(-0.781542\pi\) | ||||
−0.773593 | + | 0.633683i | \(0.781542\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.4240 | 1.15463 | 0.577317 | − | 0.816520i | \(-0.304100\pi\) | ||||
0.577317 | + | 0.816520i | \(0.304100\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.10949 | −0.0657203 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.9493 | −1.11854 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.83481 | −0.166180 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.9316 | 0.872316 | 0.436158 | − | 0.899870i | \(-0.356339\pi\) | ||||
0.436158 | + | 0.899870i | \(0.356339\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.730164 | 0.0425118 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.07274 | 0.468428 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.30479 | −0.133289 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.1562 | 0.585394 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.41097 | −0.253404 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.53044 | 0.0876327 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.0048 | 1.31295 | 0.656476 | − | 0.754347i | \(-0.272046\pi\) | ||||
0.656476 | + | 0.754347i | \(0.272046\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.01799 | 0.285463 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.73030 | −0.438345 | −0.219173 | − | 0.975686i | \(-0.570336\pi\) | ||||
−0.219173 | + | 0.975686i | \(0.570336\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.755472 | 0.0427018 | 0.0213509 | − | 0.999772i | \(-0.493203\pi\) | ||||
0.0213509 | + | 0.999772i | \(0.493203\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.30213 | 0.411428 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.47493 | −0.195172 | −0.0975858 | − | 0.995227i | \(-0.531112\pi\) | ||||
−0.0975858 | + | 0.995227i | \(0.531112\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.91593 | −0.107271 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.04115 | −0.0581114 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.29765 | −0.183486 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.10138 | −0.0610934 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.30483 | 0.0721571 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 25.6668 | 1.41505 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.88263 | −0.543199 | −0.271599 | − | 0.962410i | \(-0.587553\pi\) | ||||
−0.271599 | + | 0.962410i | \(0.587553\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 19.2704 | 1.05601 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.50636 | −0.246209 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.9833 | 1.03409 | 0.517043 | − | 0.855959i | \(-0.327033\pi\) | ||||
0.517043 | + | 0.855959i | \(0.327033\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.879892 | −0.0477892 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.54846 | 0.246313 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.05440 | −0.218917 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.14496 | −0.169319 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.95522 | −0.158645 | −0.0793223 | − | 0.996849i | \(-0.525276\pi\) | ||||
−0.0793223 | + | 0.996849i | \(0.525276\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.6175 | 1.26421 | 0.632107 | − | 0.774881i | \(-0.282190\pi\) | ||||
0.632107 | + | 0.774881i | \(0.282190\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.657559 | 0.0350979 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.1935 | 0.648997 | 0.324499 | − | 0.945886i | \(-0.394804\pi\) | ||||
0.324499 | + | 0.945886i | \(0.394804\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.85342 | −0.363742 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.65304 | −0.0874883 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.6189 | −0.982668 | −0.491334 | − | 0.870971i | \(-0.663490\pi\) | ||||
−0.491334 | + | 0.870971i | \(0.663490\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.12552 | −0.427659 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.846451 | 0.0444272 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.78535 | 0.0934496 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.9392 | −0.675423 | −0.337712 | − | 0.941250i | \(-0.609653\pi\) | ||||
−0.337712 | + | 0.941250i | \(0.609653\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.7248 | 0.766543 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −41.1540 | −2.13661 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.3949 | −0.745339 | −0.372669 | − | 0.927964i | \(-0.621557\pi\) | ||||
−0.372669 | + | 0.927964i | \(0.621557\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.18510 | −0.164478 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.156060 | −0.00803752 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.49864 | −0.282446 | −0.141223 | − | 0.989978i | \(-0.545103\pi\) | ||||
−0.141223 | + | 0.989978i | \(0.545103\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.11278 | 0.0570097 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −34.4463 | −1.76013 | −0.880063 | − | 0.474858i | \(-0.842500\pi\) | ||||
−0.880063 | + | 0.474858i | \(0.842500\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.92914 | −0.404106 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.89200 | −0.401173 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.4972 | −1.19136 | −0.595678 | − | 0.803223i | \(-0.703117\pi\) | ||||
−0.595678 | + | 0.803223i | \(0.703117\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.34754 | −0.472726 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.46679 | 0.225320 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.44981 | −0.274210 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.7637 | −1.34323 | −0.671615 | − | 0.740901i | \(-0.734399\pi\) | ||||
−0.671615 | + | 0.740901i | \(0.734399\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.45115 | 0.272899 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.5833 | 0.778193 | 0.389096 | − | 0.921197i | \(-0.372787\pi\) | ||||
0.389096 | + | 0.921197i | \(0.372787\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.370491 | 0.0184555 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.20912 | −0.258843 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.9251 | −1.03722 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.01222 | 0.396179 | 0.198089 | − | 0.980184i | \(-0.436526\pi\) | ||||
0.198089 | + | 0.980184i | \(0.436526\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.30394 | 0.409603 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.58746 | −0.176527 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.35411 | 0.459175 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.33972 | −0.212517 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.81791 | 0.430783 | 0.215392 | − | 0.976528i | \(-0.430897\pi\) | ||||
0.215392 | + | 0.976528i | \(0.430897\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.9729 | 1.80195 | 0.900976 | − | 0.433870i | \(-0.142852\pi\) | ||||
0.900976 | + | 0.433870i | \(0.142852\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −19.9447 | −0.969744 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.46686 | −0.216675 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.51939 | −0.363889 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.343914 | −0.0166043 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.9266 | −0.767159 | −0.383580 | − | 0.923508i | \(-0.625309\pi\) | ||||
−0.383580 | + | 0.923508i | \(0.625309\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.41602 | 0.164164 | 0.0820818 | − | 0.996626i | \(-0.473843\pi\) | ||||
0.0820818 | + | 0.996626i | \(0.473843\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.212950 | −0.0102101 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 30.8249 | 1.47455 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.5643 | −0.742844 | −0.371422 | − | 0.928464i | \(-0.621130\pi\) | ||||
−0.371422 | + | 0.928464i | \(0.621130\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.3632 | −0.779201 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.4245 | −1.11293 | −0.556465 | − | 0.830871i | \(-0.687843\pi\) | ||||
−0.556465 | + | 0.830871i | \(0.687843\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.6839 | 0.553872 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.76699 | −0.0835755 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.8925 | −0.608437 | −0.304218 | − | 0.952602i | \(-0.598395\pi\) | ||||
−0.304218 | + | 0.952602i | \(0.598395\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.9892 | −0.752901 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.01299 | 0.235531 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.645863 | −0.0302785 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.3779 | −0.532237 | −0.266118 | − | 0.963940i | \(-0.585741\pi\) | ||||
−0.266118 | + | 0.963940i | \(0.585741\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.66687 | 0.124479 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.5554 | 0.817635 | 0.408817 | − | 0.912616i | \(-0.365941\pi\) | ||||
0.408817 | + | 0.912616i | \(0.365941\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.72624 | −0.359069 | −0.179534 | − | 0.983752i | \(-0.557459\pi\) | ||||
−0.179534 | + | 0.983752i | \(0.557459\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.505548 | 0.0234442 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 38.0061 | 1.75871 | 0.879356 | − | 0.476165i | \(-0.157974\pi\) | ||||
0.879356 | + | 0.476165i | \(0.157974\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.1407 | 1.02236 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.61945 | 0.0746202 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.56967 | 0.394034 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.7301 | 0.675865 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 31.9793 | 1.46423 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.1244 | −0.873817 | −0.436908 | − | 0.899506i | \(-0.643927\pi\) | ||||
−0.436908 | + | 0.899506i | \(0.643927\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.70444 | −0.0777159 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.4519 | 0.703085 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.49208 | −0.203975 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.573377 | −0.0259822 | −0.0129911 | − | 0.999916i | \(-0.504135\pi\) | ||||
−0.0129911 | + | 0.999916i | \(0.504135\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.15856 | 0.188057 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.7805 | −0.937809 | −0.468905 | − | 0.883249i | \(-0.655351\pi\) | ||||
−0.468905 | + | 0.883249i | \(0.655351\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.632935 | −0.0285060 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.16144 | 0.276936 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 33.6724 | 1.51041 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.8442 | 0.977881 | 0.488941 | − | 0.872317i | \(-0.337384\pi\) | ||||
0.488941 | + | 0.872317i | \(0.337384\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.30722 | −0.237109 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.74549 | −0.0778274 | −0.0389137 | − | 0.999243i | \(-0.512390\pi\) | ||||
−0.0389137 | + | 0.999243i | \(0.512390\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.98968 | −0.311037 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.96218 | 0.264790 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 32.6471 | 1.44706 | 0.723528 | − | 0.690295i | \(-0.242519\pi\) | ||||
0.723528 | + | 0.690295i | \(0.242519\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.77183 | −0.388043 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.79439 | −0.388282 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.95156 | 0.350388 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.6573 | 0.952486 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.73623 | 0.427373 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.8552 | −0.782249 | −0.391125 | − | 0.920338i | \(-0.627914\pi\) | ||||
−0.391125 | + | 0.920338i | \(0.627914\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.4320 | 1.37443 | 0.687213 | − | 0.726456i | \(-0.258834\pi\) | ||||
0.687213 | + | 0.726456i | \(0.258834\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.38391 | 0.322260 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.50261 | 0.0654545 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 64.3766 | 2.79898 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.78768 | 0.120975 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.30239 | −0.0564127 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.64982 | −0.0713280 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.369243 | 0.0159340 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.7683 | 0.765334 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.4853 | 1.09570 | 0.547850 | − | 0.836577i | \(-0.315447\pi\) | ||||
0.547850 | + | 0.836577i | \(0.315447\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.949504 | 0.0407471 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.06764 | 0.0885681 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.8260 | −0.462885 | −0.231443 | − | 0.972849i | \(-0.574345\pi\) | ||||
−0.231443 | + | 0.972849i | \(0.574345\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.84303 | 0.249375 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.08720 | 0.0889176 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.7761 | 1.13864 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.32577 | −0.0987234 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.2776 | 1.49476 | 0.747380 | − | 0.664397i | \(-0.231312\pi\) | ||||
0.747380 | + | 0.664397i | \(0.231312\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.698036 | 0.0295238 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.39482 | −0.0588891 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.8279 | −0.919935 | −0.459967 | − | 0.887936i | \(-0.652139\pi\) | ||||
−0.459967 | + | 0.887936i | \(0.652139\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.39429 | −0.0586581 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 25.5936 | 1.07483 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −42.7780 | −1.79335 | −0.896673 | − | 0.442694i | \(-0.854023\pi\) | ||||
−0.896673 | + | 0.442694i | \(0.854023\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.13885 | −0.0895081 | −0.0447540 | − | 0.998998i | \(-0.514250\pi\) | ||||
−0.0447540 | + | 0.998998i | \(0.514250\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.27037 | 0.136622 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 41.7542 | 1.74127 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.6451 | −0.859466 | −0.429733 | − | 0.902956i | \(-0.641392\pi\) | ||||
−0.429733 | + | 0.902956i | \(0.641392\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.7415 | −0.487961 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −45.9588 | −1.90669 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −34.7252 | −1.43817 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.501876 | 0.0207500 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.40288 | 0.0991775 | 0.0495887 | − | 0.998770i | \(-0.484209\pi\) | ||||
0.0495887 | + | 0.998770i | \(0.484209\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.95506 | −0.204170 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.49200 | 0.225911 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.2998 | −0.422961 | −0.211480 | − | 0.977382i | \(-0.567828\pi\) | ||||
−0.211480 | + | 0.977382i | \(0.567828\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.61943 | −0.107386 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.52975 | 0.226318 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 38.2784 | 1.56401 | 0.782006 | − | 0.623271i | \(-0.214197\pi\) | ||||
0.782006 | + | 0.623271i | \(0.214197\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.5870 | 1.00292 | 0.501462 | − | 0.865180i | \(-0.332796\pi\) | ||||
0.501462 | + | 0.865180i | \(0.332796\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.2047 | −0.700632 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.34130 | 0.0545314 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.35623 | 0.298580 | 0.149290 | − | 0.988793i | \(-0.452301\pi\) | ||||
0.149290 | + | 0.988793i | \(0.452301\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.04627 | 0.0423969 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.76408 | 0.0713670 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.0629 | 0.689164 | 0.344582 | − | 0.938756i | \(-0.388021\pi\) | ||||
0.344582 | + | 0.938756i | \(0.388021\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.77715 | −0.0716617 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.7525 | 0.835465 | 0.417732 | − | 0.908570i | \(-0.362825\pi\) | ||||
0.417732 | + | 0.908570i | \(0.362825\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.1578 | 1.61408 | 0.807039 | − | 0.590498i | \(-0.201069\pi\) | ||||
0.807039 | + | 0.590498i | \(0.201069\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −24.9287 | −1.00035 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −57.4058 | −2.29991 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.2872 | 0.691486 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.59961 | 0.183691 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.91272 | −0.275628 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.1145 | −0.681317 | −0.340658 | − | 0.940187i | \(-0.610650\pi\) | ||||
−0.340658 | + | 0.940187i | \(0.610650\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.05383 | 0.320111 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.76333 | 0.0699756 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.44730 | 0.0573443 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −26.1656 | −1.03509 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.23231 | −0.0486734 | −0.0243367 | − | 0.999704i | \(-0.507747\pi\) | ||||
−0.0243367 | + | 0.999704i | \(0.507747\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.3579 | 0.408477 | 0.204238 | − | 0.978921i | \(-0.434528\pi\) | ||||
0.204238 | + | 0.978921i | \(0.434528\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.952494 | 0.0375044 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.2491 | 1.11059 | 0.555293 | − | 0.831655i | \(-0.312606\pi\) | ||||
0.555293 | + | 0.831655i | \(0.312606\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.02705 | −0.118822 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.48387 | −0.0973505 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.27302 | −0.245482 | −0.122741 | − | 0.992439i | \(-0.539168\pi\) | ||||
−0.122741 | + | 0.992439i | \(0.539168\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.07813 | 0.276565 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.81626 | 0.265928 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.2529 | 1.02267 | 0.511333 | − | 0.859382i | \(-0.329152\pi\) | ||||
0.511333 | + | 0.859382i | \(0.329152\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.2578 | 0.632354 | 0.316177 | − | 0.948700i | \(-0.397601\pi\) | ||||
0.316177 | + | 0.948700i | \(0.397601\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.113614 | −0.00441239 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.63795 | 0.334965 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.91639 | 0.229084 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.533064 | 0.0206094 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.34476 | −0.244937 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.56894 | 0.214667 | 0.107333 | − | 0.994223i | \(-0.465769\pi\) | ||||
0.107333 | + | 0.994223i | \(0.465769\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11.9125 | −0.458514 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.9781 | −0.652520 | −0.326260 | − | 0.945280i | \(-0.605788\pi\) | ||||
−0.326260 | + | 0.945280i | \(0.605788\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.0706 | 0.846991 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.82630 | 0.146624 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.0449 | −1.18790 | −0.593950 | − | 0.804502i | \(-0.702432\pi\) | ||||
−0.593950 | + | 0.804502i | \(0.702432\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.1585 | 0.502761 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.872214 | 0.0332770 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.82852 | −0.107758 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.9628 | −0.455088 | −0.227544 | − | 0.973768i | \(-0.573069\pi\) | ||||
−0.227544 | + | 0.973768i | \(0.573069\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −30.2725 | −1.14996 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.87676 | −0.260851 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.28210 | −0.200074 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.19659 | −0.347847 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.0871 | 0.494293 | 0.247147 | − | 0.968978i | \(-0.420507\pi\) | ||||
0.247147 | + | 0.968978i | \(0.420507\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.7957 | 0.859756 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.40714 | 0.0906583 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 34.3418 | 1.29156 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.13830 | 0.230529 | 0.115264 | − | 0.993335i | \(-0.463228\pi\) | ||||
0.115264 | + | 0.993335i | \(0.463228\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.8067 | −0.780314 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.0457 | −0.526014 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.544970 | −0.0203807 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.82662 | 0.254945 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.6983 | 0.809211 | 0.404606 | − | 0.914491i | \(-0.367409\pi\) | ||||
0.404606 | + | 0.914491i | \(0.367409\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −39.0678 | −1.45496 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.74165 | −0.213534 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.82723 | 0.105001 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.3740 | 0.718542 | 0.359271 | − | 0.933233i | \(-0.383025\pi\) | ||||
0.359271 | + | 0.933233i | \(0.383025\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.2013 | −0.600047 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.83103 | 0.104709 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.0353 | 0.555342 | 0.277671 | − | 0.960676i | \(-0.410437\pi\) | ||||
0.277671 | + | 0.960676i | \(0.410437\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.97489 | 0.0728451 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.6821 | 0.688163 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.9931 | −0.698671 | −0.349336 | − | 0.936998i | \(-0.613593\pi\) | ||||
−0.349336 | + | 0.936998i | \(0.613593\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.374658 | 0.0137634 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.0861 | −1.25050 | −0.625249 | − | 0.780425i | \(-0.715003\pi\) | ||||
−0.625249 | + | 0.780425i | \(0.715003\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.79999 | −0.102584 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 35.7129 | 1.30667 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.10594 | 0.296185 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.5082 | 0.930807 | 0.465404 | − | 0.885099i | \(-0.345909\pi\) | ||||
0.465404 | + | 0.885099i | \(0.345909\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.15248 | −0.151325 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.94365 | 0.289099 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.0372384 | 0.00135345 | 0.000676727 | − | 1.00000i | \(-0.499785\pi\) | ||||
0.000676727 | 1.00000i | \(0.499785\pi\) | ||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.0381 | 0.473253 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.2584 | −0.951867 | −0.475933 | − | 0.879481i | \(-0.657890\pi\) | ||||
−0.475933 | + | 0.879481i | \(0.657890\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.1588 | −0.367773 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.03546 | 0.0735922 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.246566 | −0.00890299 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40.8728 | −1.47391 | −0.736956 | − | 0.675940i | \(-0.763738\pi\) | ||||
−0.736956 | + | 0.675940i | \(0.763738\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.84847 | 0.210628 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.5570 | 1.45874 | 0.729368 | − | 0.684122i | \(-0.239814\pi\) | ||||
0.729368 | + | 0.684122i | \(0.239814\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.71193 | −0.241100 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.4270 | 0.409942 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.4185 | 0.624083 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.4123 | 1.01667 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.68796 | −0.0603226 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.56620 | 0.0915915 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.18689 | −0.0779541 | −0.0389771 | − | 0.999240i | \(-0.512410\pi\) | ||||
−0.0389771 | + | 0.999240i | \(0.512410\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.89426 | 0.0674373 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.85044 | 0.243574 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.516808 | −0.0183524 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.85961 | −0.136886 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.26665 | −0.221976 | −0.110988 | − | 0.993822i | \(-0.535402\pi\) | ||||
−0.110988 | + | 0.993822i | \(0.535402\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.15459 | 0.253111 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 44.6079 | 1.57614 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.40155 | −0.261195 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.4852 | 0.862991 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.192809 | −0.00678721 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.1334 | −0.496903 | −0.248451 | − | 0.968644i | \(-0.579922\pi\) | ||||
−0.248451 | + | 0.968644i | \(0.579922\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.3432 | −0.363200 | −0.181600 | − | 0.983372i | \(-0.558128\pi\) | ||||
−0.181600 | + | 0.983372i | \(0.558128\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.0218515 | −0.000766366 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.58970 | 0.230827 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.33574 | −0.326616 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.46583 | −0.0861630 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.63288 | 0.231489 | 0.115744 | − | 0.993279i | \(-0.463075\pi\) | ||||
0.115744 | + | 0.993279i | \(0.463075\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.3078 | 0.742743 | 0.371372 | − | 0.928484i | \(-0.378888\pi\) | ||||
0.371372 | + | 0.928484i | \(0.378888\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.23045 | 0.216916 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.1096 | 0.838374 | 0.419187 | − | 0.907900i | \(-0.362315\pi\) | ||||
0.419187 | + | 0.907900i | \(0.362315\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.7139 | 1.41405 | 0.707027 | − | 0.707187i | \(-0.250036\pi\) | ||||
0.707027 | + | 0.707187i | \(0.250036\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.98758 | −0.138328 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.86984 | 0.203378 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.40988 | −0.291036 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.00725 | 0.138511 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.9413 | −0.895595 | −0.447797 | − | 0.894135i | \(-0.647791\pi\) | ||||
−0.447797 | + | 0.894135i | \(0.647791\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5994 | −0.986186 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.9507 | 0.411604 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.44774 | 0.325012 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.59009 | −0.226438 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.95025 | −0.307172 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 64.6170 | 2.21504 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 51.2128 | 1.75349 | 0.876746 | − | 0.480953i | \(-0.159709\pi\) | ||||
0.876746 | + | 0.480953i | \(0.159709\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.71223 | −0.229553 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.7595 | −0.982405 | −0.491203 | − | 0.871045i | \(-0.663443\pi\) | ||||
−0.491203 | + | 0.871045i | \(0.663443\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.8391 | 0.676903 | 0.338451 | − | 0.940984i | \(-0.390097\pi\) | ||||
0.338451 | + | 0.940984i | \(0.390097\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.73154 | 0.297570 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42.6777 | −1.45277 | −0.726384 | − | 0.687289i | \(-0.758800\pi\) | ||||
−0.726384 | + | 0.687289i | \(0.758800\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.4281 | 0.524573 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.460784 | −0.0156490 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 22.5934 | 0.766427 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.52174 | 0.0515620 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −17.1502 | −0.580447 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24.7978 | 0.838318 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44.9566 | −1.51808 | −0.759038 | − | 0.651046i | \(-0.774331\pi\) | ||||
−0.759038 | + | 0.651046i | \(0.774331\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.88026 | −0.232066 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.1003 | 0.744577 | 0.372288 | − | 0.928117i | \(-0.378573\pi\) | ||||
0.372288 | + | 0.928117i | \(0.378573\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.3716 | 0.651908 | 0.325954 | − | 0.945386i | \(-0.394315\pi\) | ||||
0.325954 | + | 0.945386i | \(0.394315\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.336448 | −0.0113096 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −50.9927 | −1.71217 | −0.856084 | − | 0.516836i | \(-0.827110\pi\) | ||||
−0.856084 | + | 0.516836i | \(0.827110\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.66363 | −0.290569 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.5955 | 0.723477 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −23.5933 | −0.789520 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.585107 | 0.0195580 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.06201 | 0.0354594 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.951052 | −0.0317194 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.4716 | −0.382176 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.67981 | −0.155734 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.50460 | 0.0500145 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.3821 | −1.17484 | −0.587421 | − | 0.809282i | \(-0.699857\pi\) | ||||
−0.587421 | + | 0.809282i | \(0.699857\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −26.6858 | −0.885111 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.45651 | 0.180782 | 0.0903911 | − | 0.995906i | \(-0.471188\pi\) | ||||
0.0903911 | + | 0.995906i | \(0.471188\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −38.7794 | −1.28341 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.705202 | −0.0233132 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −34.7764 | −1.14842 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.4690 | −0.873130 | −0.436565 | − | 0.899673i | \(-0.643805\pi\) | ||||
−0.436565 | + | 0.899673i | \(0.643805\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.6002 | −0.349289 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.31431 | 0.0761763 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.8782 | 1.01527 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 30.3581 | 0.997092 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26.5891 | −0.872359 | −0.436180 | − | 0.899860i | \(-0.643669\pi\) | ||||
−0.436180 | + | 0.899860i | \(0.643669\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.3567 | −0.634389 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.56200 | 0.116615 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.21024 | −0.0722826 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.79458 | −0.0912949 | −0.0456475 | − | 0.998958i | \(-0.514535\pi\) | ||||
−0.0456475 | + | 0.998958i | \(0.514535\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.348109 | −0.0113601 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.7467 | 1.23051 | 0.615254 | − | 0.788329i | \(-0.289054\pi\) | ||||
0.615254 | + | 0.788329i | \(0.289054\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 49.3747 | 1.60786 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.98568 | −0.227244 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.8014 | 0.578469 | 0.289234 | − | 0.957258i | \(-0.406599\pi\) | ||||
0.289234 | + | 0.957258i | \(0.406599\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.602888 | −0.0195706 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.60119 | 0.0519222 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.1287 | 0.587247 | 0.293624 | − | 0.955921i | \(-0.405139\pi\) | ||||
0.293624 | + | 0.955921i | \(0.405139\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.18227 | 0.167694 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.882828 | 0.0285378 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −64.6508 | −2.08768 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.7422 | −0.927167 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.29882 | −0.202977 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18.6057 | −0.598940 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53.1217 | 1.70828 | 0.854139 | − | 0.520044i | \(-0.174085\pi\) | ||||
0.854139 | + | 0.520044i | \(0.174085\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.51950 | 0.0488135 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.1364 | −0.485751 | −0.242875 | − | 0.970057i | \(-0.578091\pi\) | ||||
−0.242875 | + | 0.970057i | \(0.578091\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 33.7871 | 1.08316 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.507497 | 0.0162529 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.4909 | 0.399618 | 0.199809 | − | 0.979835i | \(-0.435968\pi\) | ||||
0.199809 | + | 0.979835i | \(0.435968\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −48.4382 | −1.54809 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.89402 | 0.252037 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.8821 | −1.20825 | −0.604125 | − | 0.796889i | \(-0.706477\pi\) | ||||
−0.604125 | + | 0.796889i | \(0.706477\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.70269 | 0.277291 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.8268 | −0.376452 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −26.4632 | −0.841480 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.0553 | 1.74889 | 0.874445 | − | 0.485124i | \(-0.161226\pi\) | ||||
0.874445 | + | 0.485124i | \(0.161226\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.55376 | 0.144509 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.76250 | 0.277790 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.0927 | −1.26975 | −0.634874 | − | 0.772616i | \(-0.718948\pi\) | ||||
−0.634874 | + | 0.772616i | \(0.718948\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −18.4353 | −0.583268 |
(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 | 4012.2.a.h.1.7 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.a.h.1.7 | ✓ | 15 | 1.1 | even | 1 | trivial |