Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, 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("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.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: | \(64.1677830643\) |
Analytic rank: | \(0\) |
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: | \( x^{15} - x^{14} - 37 x^{13} + 39 x^{12} + 537 x^{11} - 616 x^{10} - 3853 x^{9} + 4929 x^{8} + \cdots + 3381 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1148) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.93225\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-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 | ||||||||
\(3\) | −1.93225 | −1.11558 | −0.557792 | − | 0.829981i | \(-0.688351\pi\) | ||||
−0.557792 | + | 0.829981i | \(0.688351\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.475465 | −0.212635 | −0.106317 | − | 0.994332i | \(-0.533906\pi\) | ||||
−0.106317 | + | 0.994332i | \(0.533906\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.733587 | 0.244529 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.608408 | 0.183442 | 0.0917210 | − | 0.995785i | \(-0.470763\pi\) | ||||
0.0917210 | + | 0.995785i | \(0.470763\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.258249 | 0.0716255 | 0.0358127 | − | 0.999359i | \(-0.488598\pi\) | ||||
0.0358127 | + | 0.999359i | \(0.488598\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.918718 | 0.237212 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.67585 | 1.61913 | 0.809566 | − | 0.587029i | \(-0.199703\pi\) | ||||
0.809566 | + | 0.587029i | \(0.199703\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.55857 | −1.96347 | −0.981735 | − | 0.190252i | \(-0.939070\pi\) | ||||
−0.981735 | + | 0.190252i | \(0.939070\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.540802 | −0.112765 | −0.0563825 | − | 0.998409i | \(-0.517957\pi\) | ||||
−0.0563825 | + | 0.998409i | \(0.517957\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.77393 | −0.954787 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.37927 | 0.842792 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.17655 | 1.70404 | 0.852021 | − | 0.523508i | \(-0.175377\pi\) | ||||
0.852021 | + | 0.523508i | \(0.175377\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.19512 | −0.573861 | −0.286930 | − | 0.957951i | \(-0.592635\pi\) | ||||
−0.286930 | + | 0.957951i | \(0.592635\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.17560 | −0.204645 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.11667 | 0.347979 | 0.173989 | − | 0.984748i | \(-0.444334\pi\) | ||||
0.173989 | + | 0.984748i | \(0.444334\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.499002 | −0.0799043 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.45997 | −1.44263 | −0.721316 | − | 0.692606i | \(-0.756462\pi\) | ||||
−0.721316 | + | 0.692606i | \(0.756462\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.348795 | −0.0519953 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.21836 | −0.761176 | −0.380588 | − | 0.924745i | \(-0.624278\pi\) | ||||
−0.380588 | + | 0.924745i | \(0.624278\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.8994 | −1.80628 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.1314 | 1.52901 | 0.764507 | − | 0.644615i | \(-0.222982\pi\) | ||||
0.764507 | + | 0.644615i | \(0.222982\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.289277 | −0.0390061 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 16.5373 | 2.19042 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.80041 | −0.885338 | −0.442669 | − | 0.896685i | \(-0.645968\pi\) | ||||
−0.442669 | + | 0.896685i | \(0.645968\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.40208 | 0.179517 | 0.0897587 | − | 0.995964i | \(-0.471390\pi\) | ||||
0.0897587 | + | 0.995964i | \(0.471390\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.122789 | −0.0152301 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.9998 | 1.95468 | 0.977340 | − | 0.211674i | \(-0.0678915\pi\) | ||||
0.977340 | + | 0.211674i | \(0.0678915\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.04496 | 0.125799 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.72154 | 0.441665 | 0.220833 | − | 0.975312i | \(-0.429123\pi\) | ||||
0.220833 | + | 0.975312i | \(0.429123\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.31128 | −1.08980 | −0.544902 | − | 0.838500i | \(-0.683433\pi\) | ||||
−0.544902 | + | 0.838500i | \(0.683433\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.22443 | 1.06515 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.46345 | 0.614686 | 0.307343 | − | 0.951599i | \(-0.400560\pi\) | ||||
0.307343 | + | 0.951599i | \(0.400560\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.6626 | −1.18473 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.971073 | 0.106589 | 0.0532945 | − | 0.998579i | \(-0.483028\pi\) | ||||
0.0532945 | + | 0.998579i | \(0.483028\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.17414 | −0.344284 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −17.7314 | −1.90100 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.78989 | 1.03773 | 0.518863 | − | 0.854857i | \(-0.326355\pi\) | ||||
0.518863 | + | 0.854857i | \(0.326355\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.17377 | 0.640190 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.06930 | 0.417502 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.26994 | 0.332012 | 0.166006 | − | 0.986125i | \(-0.446913\pi\) | ||||
0.166006 | + | 0.986125i | \(0.446913\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.446320 | 0.0448569 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.3557 | −1.52795 | −0.763973 | − | 0.645248i | \(-0.776754\pi\) | ||||
−0.763973 | + | 0.645248i | \(0.776754\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.9051 | −1.56717 | −0.783586 | − | 0.621283i | \(-0.786612\pi\) | ||||
−0.783586 | + | 0.621283i | \(0.786612\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.33023 | −0.901988 | −0.450994 | − | 0.892527i | \(-0.648930\pi\) | ||||
−0.450994 | + | 0.892527i | \(0.648930\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.1284 | −1.25747 | −0.628736 | − | 0.777619i | \(-0.716428\pi\) | ||||
−0.628736 | + | 0.777619i | \(0.716428\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.08994 | −0.388200 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.66144 | −0.814800 | −0.407400 | − | 0.913250i | \(-0.633565\pi\) | ||||
−0.407400 | + | 0.913250i | \(0.633565\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.257133 | 0.0239778 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.189448 | 0.0175145 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6298 | −0.966349 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.93225 | 0.174225 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.64717 | 0.415655 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.3874 | 1.36541 | 0.682705 | − | 0.730694i | \(-0.260803\pi\) | ||||
0.682705 | + | 0.730694i | \(0.260803\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 18.2790 | 1.60938 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.68476 | −0.671421 | −0.335710 | − | 0.941965i | \(-0.608976\pi\) | ||||
−0.335710 | + | 0.941965i | \(0.608976\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.08219 | −0.179207 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.5241 | 1.66805 | 0.834026 | − | 0.551725i | \(-0.186030\pi\) | ||||
0.834026 | + | 0.551725i | \(0.186030\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.3761 | −1.04972 | −0.524862 | − | 0.851188i | \(-0.675883\pi\) | ||||
−0.524862 | + | 0.851188i | \(0.675883\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.0832 | 0.849157 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.157121 | 0.0131391 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.36313 | −0.362338 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.81485 | −0.476371 | −0.238186 | − | 0.971220i | \(-0.576553\pi\) | ||||
−0.238186 | + | 0.971220i | \(0.576553\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.96305 | 0.485266 | 0.242633 | − | 0.970118i | \(-0.421989\pi\) | ||||
0.242633 | + | 0.970118i | \(0.421989\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.89732 | 0.395925 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.51917 | 0.122023 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.8012 | −1.26108 | −0.630538 | − | 0.776159i | \(-0.717166\pi\) | ||||
−0.630538 | + | 0.776159i | \(0.717166\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −21.5086 | −1.70575 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.1423 | 1.34269 | 0.671345 | − | 0.741145i | \(-0.265717\pi\) | ||||
0.671345 | + | 0.741145i | \(0.265717\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.558956 | 0.0435146 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.3673 | 1.11178 | 0.555888 | − | 0.831257i | \(-0.312378\pi\) | ||||
0.555888 | + | 0.831257i | \(0.312378\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9333 | −0.994870 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.27845 | −0.480125 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 25.2690 | 1.92116 | 0.960582 | − | 0.277996i | \(-0.0896701\pi\) | ||||
0.960582 | + | 0.277996i | \(0.0896701\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.1401 | 0.987670 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.2626 | 1.51450 | 0.757250 | − | 0.653125i | \(-0.226543\pi\) | ||||
0.757250 | + | 0.653125i | \(0.226543\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.26666 | 0.614456 | 0.307228 | − | 0.951636i | \(-0.400599\pi\) | ||||
0.307228 | + | 0.951636i | \(0.400599\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.70916 | −0.200267 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.00640 | −0.0739923 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.06164 | 0.297017 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.2773 | 1.53957 | 0.769786 | − | 0.638302i | \(-0.220363\pi\) | ||||
0.769786 | + | 0.638302i | \(0.220363\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.1778 | −0.732615 | −0.366307 | − | 0.930494i | \(-0.619378\pi\) | ||||
−0.366307 | + | 0.930494i | \(0.619378\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.237258 | 0.0169904 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.0683 | 1.07357 | 0.536787 | − | 0.843718i | \(-0.319638\pi\) | ||||
0.536787 | + | 0.843718i | \(0.319638\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.57936 | 0.324622 | 0.162311 | − | 0.986740i | \(-0.448105\pi\) | ||||
0.162311 | + | 0.986740i | \(0.448105\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −30.9155 | −2.18061 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.475465 | 0.0332080 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.396725 | −0.0275743 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.20711 | −0.360183 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.2177 | −1.73606 | −0.868028 | − | 0.496515i | \(-0.834613\pi\) | ||||
−0.868028 | + | 0.496515i | \(0.834613\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.19094 | −0.492715 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.49789 | 0.306753 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.9917 | 1.21577 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.72403 | 0.115971 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.02063 | −0.604066 | −0.302033 | − | 0.953298i | \(-0.597665\pi\) | ||||
−0.302033 | + | 0.953298i | \(0.597665\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.50209 | −0.233473 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.7610 | 1.17884 | 0.589421 | − | 0.807826i | \(-0.299356\pi\) | ||||
0.589421 | + | 0.807826i | \(0.299356\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.5866 | 1.42648 | 0.713242 | − | 0.700918i | \(-0.247226\pi\) | ||||
0.713242 | + | 0.700918i | \(0.247226\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.03999 | −0.395693 | −0.197846 | − | 0.980233i | \(-0.563395\pi\) | ||||
−0.197846 | + | 0.980233i | \(0.563395\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.48115 | 0.161852 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.5567 | −0.685734 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.84860 | −0.507683 | −0.253842 | − | 0.967246i | \(-0.581694\pi\) | ||||
−0.253842 | + | 0.967246i | \(0.581694\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.3385 | −1.69661 | −0.848306 | − | 0.529506i | \(-0.822377\pi\) | ||||
−0.848306 | + | 0.529506i | \(0.822377\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.46500 | 0.478880 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.21024 | −0.140634 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.87635 | −0.118909 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.7507 | −0.741699 | −0.370849 | − | 0.928693i | \(-0.620933\pi\) | ||||
−0.370849 | + | 0.928693i | \(0.620933\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.329029 | −0.0206858 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.13322 | 0.384077 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.0458 | −1.18805 | −0.594023 | − | 0.804448i | \(-0.702461\pi\) | ||||
−0.594023 | + | 0.804448i | \(0.702461\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.73179 | 0.416688 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.7032 | −0.721651 | −0.360825 | − | 0.932633i | \(-0.617505\pi\) | ||||
−0.360825 | + | 0.932633i | \(0.617505\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.29259 | −0.325121 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.9165 | −1.15767 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.1797 | 1.53524 | 0.767618 | − | 0.640908i | \(-0.221442\pi\) | ||||
0.767618 | + | 0.640908i | \(0.221442\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.2398 | 0.804262 | 0.402131 | − | 0.915582i | \(-0.368270\pi\) | ||||
0.402131 | + | 0.915582i | \(0.368270\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.90450 | −0.175148 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.96026 | 0.177865 | 0.0889323 | − | 0.996038i | \(-0.471655\pi\) | ||||
0.0889323 | + | 0.996038i | \(0.471655\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.34390 | −0.140326 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.8626 | 0.707666 | 0.353833 | − | 0.935309i | \(-0.384878\pi\) | ||||
0.353833 | + | 0.935309i | \(0.384878\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.4471 | −1.45323 | −0.726615 | − | 0.687044i | \(-0.758908\pi\) | ||||
−0.726615 | + | 0.687044i | \(0.758908\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.86291 | −0.465759 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 27.5670 | 1.62159 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.31834 | −0.370388 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 31.9974 | 1.86931 | 0.934653 | − | 0.355561i | \(-0.115710\pi\) | ||||
0.934653 | + | 0.355561i | \(0.115710\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.23336 | 0.188254 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.66439 | 0.154603 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.139662 | −0.00807685 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 29.6710 | 1.70455 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.666639 | −0.0381716 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.37931 | −0.0787211 | −0.0393606 | − | 0.999225i | \(-0.512532\pi\) | ||||
−0.0393606 | + | 0.999225i | \(0.512532\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 30.7326 | 1.74831 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.57209 | 0.372669 | 0.186335 | − | 0.982486i | \(-0.440339\pi\) | ||||
0.186335 | + | 0.982486i | \(0.440339\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.2077 | 0.576976 | 0.288488 | − | 0.957484i | \(-0.406847\pi\) | ||||
0.288488 | + | 0.957484i | \(0.406847\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.3693 | −0.638565 | −0.319282 | − | 0.947660i | \(-0.603442\pi\) | ||||
−0.319282 | + | 0.947660i | \(0.603442\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.58309 | 0.312593 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.0283 | 1.00624 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −57.1357 | −3.17912 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.23286 | −0.0683870 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 25.3673 | 1.40282 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.3419 | 1.06313 | 0.531564 | − | 0.847018i | \(-0.321605\pi\) | ||||
0.531564 | + | 0.847018i | \(0.321605\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.55276 | 0.0850909 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.60733 | −0.415633 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.0087 | 0.708629 | 0.354315 | − | 0.935126i | \(-0.384714\pi\) | ||||
0.354315 | + | 0.935126i | \(0.384714\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.7361 | 0.908978 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.94394 | −0.105270 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.496845 | −0.0267492 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.25837 | 0.497015 | 0.248508 | − | 0.968630i | \(-0.420060\pi\) | ||||
0.248508 | + | 0.968630i | \(0.420060\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.45465 | 0.184923 | 0.0924615 | − | 0.995716i | \(-0.470527\pi\) | ||||
0.0924615 | + | 0.995716i | \(0.470527\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.13094 | 0.0603653 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.57050 | 0.402937 | 0.201468 | − | 0.979495i | \(-0.435429\pi\) | ||||
0.201468 | + | 0.979495i | \(0.435429\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.76946 | −0.0939133 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.2984 | −0.807419 | −0.403710 | − | 0.914887i | \(-0.632279\pi\) | ||||
−0.403710 | + | 0.914887i | \(0.632279\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 54.2491 | 2.85522 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 20.5395 | 1.07804 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.42719 | 0.231730 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.1193 | −0.580421 | −0.290211 | − | 0.956963i | \(-0.593725\pi\) | ||||
−0.290211 | + | 0.956963i | \(0.593725\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.733587 | −0.0381890 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.7948 | 1.59449 | 0.797247 | − | 0.603653i | \(-0.206289\pi\) | ||||
0.797247 | + | 0.603653i | \(0.206289\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.97949 | −0.463699 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.36984 | 0.122053 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.7083 | 0.806881 | 0.403441 | − | 0.915006i | \(-0.367814\pi\) | ||||
0.403441 | + | 0.915006i | \(0.367814\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −29.7323 | −1.52323 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.295229 | 0.0150855 | 0.00754274 | − | 0.999972i | \(-0.497599\pi\) | ||||
0.00754274 | + | 0.999972i | \(0.497599\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.93971 | −0.352765 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.05446 | 0.306974 | 0.153487 | − | 0.988151i | \(-0.450950\pi\) | ||||
0.153487 | + | 0.988151i | \(0.450950\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.61031 | −0.182581 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.8489 | 0.749027 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.59768 | −0.130703 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.1683 | 1.16278 | 0.581392 | − | 0.813623i | \(-0.302508\pi\) | ||||
0.581392 | + | 0.813623i | \(0.302508\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 35.4197 | 1.76878 | 0.884388 | − | 0.466752i | \(-0.154576\pi\) | ||||
0.884388 | + | 0.466752i | \(0.154576\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.825137 | −0.0411030 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.06970 | 0.251916 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.28780 | 0.0638339 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.5932 | −1.01827 | −0.509135 | − | 0.860687i | \(-0.670035\pi\) | ||||
−0.509135 | + | 0.860687i | \(0.670035\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −37.7253 | −1.86085 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.461712 | −0.0226645 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 23.9136 | 1.17105 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 37.3854 | 1.82640 | 0.913198 | − | 0.407517i | \(-0.133605\pi\) | ||||
0.913198 | + | 0.407517i | \(0.133605\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.03447 | 0.440313 | 0.220156 | − | 0.975465i | \(-0.429343\pi\) | ||||
0.220156 | + | 0.975465i | \(0.429343\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.82812 | −0.186130 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −31.8701 | −1.54593 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.303597 | −0.0146578 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.86857 | 0.282679 | 0.141340 | − | 0.989961i | \(-0.454859\pi\) | ||||
0.141340 | + | 0.989961i | \(0.454859\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.3406 | 1.31391 | 0.656953 | − | 0.753931i | \(-0.271845\pi\) | ||||
0.656953 | + | 0.753931i | \(0.271845\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.43066 | 0.404219 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.62849 | 0.221411 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.0278 | 1.43315 | 0.716574 | − | 0.697512i | \(-0.245709\pi\) | ||||
0.716574 | + | 0.697512i | \(0.245709\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.60397 | −0.361276 | −0.180638 | − | 0.983550i | \(-0.557816\pi\) | ||||
−0.180638 | + | 0.983550i | \(0.557816\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.65476 | −0.220657 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.2357 | 0.531432 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.589677 | 0.0278286 | 0.0139143 | − | 0.999903i | \(-0.495571\pi\) | ||||
0.0139143 | + | 0.999903i | \(0.495571\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.608408 | −0.0286488 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.5221 | −0.541356 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.29570 | 0.0606101 | 0.0303051 | − | 0.999541i | \(-0.490352\pi\) | ||||
0.0303051 | + | 0.999541i | \(0.490352\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 29.2354 | 1.36459 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.0668 | 1.02775 | 0.513876 | − | 0.857864i | \(-0.328209\pi\) | ||||
0.513876 | + | 0.857864i | \(0.328209\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.1079 | −0.934493 | −0.467246 | − | 0.884127i | \(-0.654754\pi\) | ||||
−0.467246 | + | 0.884127i | \(0.654754\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.93541 | −0.136127 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.8752 | 1.38246 | 0.691230 | − | 0.722635i | \(-0.257069\pi\) | ||||
0.691230 | + | 0.722635i | \(0.257069\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 30.5319 | 1.40684 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.75552 | −0.264639 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 40.8580 | 1.87470 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.16585 | 0.373888 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −38.5445 | −1.76115 | −0.880573 | − | 0.473911i | \(-0.842842\pi\) | ||||
−0.880573 | + | 0.473911i | \(0.842842\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.546629 | 0.0249241 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.55474 | −0.0705973 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.7629 | −0.850226 | −0.425113 | − | 0.905140i | \(-0.639766\pi\) | ||||
−0.425113 | + | 0.905140i | \(0.639766\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −33.1232 | −1.49788 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.61032 | −0.0726725 | −0.0363363 | − | 0.999340i | \(-0.511569\pi\) | ||||
−0.0363363 | + | 0.999340i | \(0.511569\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 61.2613 | 2.75907 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.212210 | −0.00953813 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.49401 | −0.201179 | −0.100590 | − | 0.994928i | \(-0.532073\pi\) | ||||
−0.100590 | + | 0.994928i | \(0.532073\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −27.7613 | −1.24028 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.671350 | −0.0299340 | −0.0149670 | − | 0.999888i | \(-0.504764\pi\) | ||||
−0.0149670 | + | 0.999888i | \(0.504764\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.30109 | 0.324894 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 24.9904 | 1.10986 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.5947 | 1.00149 | 0.500745 | − | 0.865595i | \(-0.333059\pi\) | ||||
0.500745 | + | 0.865595i | \(0.333059\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −37.4803 | −1.65480 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.56231 | 0.333235 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.17490 | −0.139632 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −48.8260 | −2.14322 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.35329 | −0.0592888 | −0.0296444 | − | 0.999561i | \(-0.509437\pi\) | ||||
−0.0296444 | + | 0.999561i | \(0.509437\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.5312 | −0.722858 | −0.361429 | − | 0.932400i | \(-0.617711\pi\) | ||||
−0.361429 | + | 0.932400i | \(0.617711\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.3301 | −0.929156 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7075 | −0.987284 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.98869 | −0.216491 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.258249 | −0.0111860 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.43620 | 0.191794 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −39.1524 | −1.68955 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.33057 | −0.272172 | −0.136086 | − | 0.990697i | \(-0.543452\pi\) | ||||
−0.136086 | + | 0.990697i | \(0.543452\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.9732 | −0.685477 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.24210 | 0.267382 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.5272 | 1.21973 | 0.609867 | − | 0.792503i | \(-0.291223\pi\) | ||||
0.609867 | + | 0.792503i | \(0.291223\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.02854 | 0.0438972 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −78.5381 | −3.34584 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.94462 | 0.0825447 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −39.1109 | −1.65718 | −0.828591 | − | 0.559855i | \(-0.810857\pi\) | ||||
−0.828591 | + | 0.559855i | \(0.810857\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.44303 | −0.103329 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.84811 | −0.331347 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.1984 | 1.23057 | 0.615284 | − | 0.788306i | \(-0.289042\pi\) | ||||
0.615284 | + | 0.788306i | \(0.289042\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.11822 | 0.173255 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.3981 | 0.561679 | 0.280840 | − | 0.959755i | \(-0.409387\pi\) | ||||
0.280840 | + | 0.959755i | \(0.409387\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.05488 | −0.0859941 | −0.0429970 | − | 0.999075i | \(-0.513691\pi\) | ||||
−0.0429970 | + | 0.999075i | \(0.513691\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −41.1131 | −1.71752 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.58175 | 0.107667 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.0423 | 0.834372 | 0.417186 | − | 0.908821i | \(-0.363016\pi\) | ||||
0.417186 | + | 0.908821i | \(0.363016\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.6661 | 0.817294 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.77243 | 0.280486 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.0900761 | −0.00372419 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.2770 | 0.713098 | 0.356549 | − | 0.934277i | \(-0.383953\pi\) | ||||
0.356549 | + | 0.934277i | \(0.383953\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.3457 | 1.12676 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −29.1158 | −1.19766 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.43785 | −0.182241 | −0.0911203 | − | 0.995840i | \(-0.529045\pi\) | ||||
−0.0911203 | + | 0.995840i | \(0.529045\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.84846 | −0.362144 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.5564 | 1.49366 | 0.746828 | − | 0.665017i | \(-0.231576\pi\) | ||||
0.746828 | + | 0.665017i | \(0.231576\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.7836 | 0.521453 | 0.260726 | − | 0.965413i | \(-0.416038\pi\) | ||||
0.260726 | + | 0.965413i | \(0.416038\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.7372 | 0.477976 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.05412 | 0.205479 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.7778 | −0.640401 | −0.320200 | − | 0.947350i | \(-0.603750\pi\) | ||||
−0.320200 | + | 0.947350i | \(0.603750\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.34764 | −0.0545196 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.3571 | 1.71079 | 0.855394 | − | 0.517978i | \(-0.173315\pi\) | ||||
0.855394 | + | 0.517978i | \(0.173315\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.918718 | −0.0370463 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.74340 | −0.271479 | −0.135739 | − | 0.990745i | \(-0.543341\pi\) | ||||
−0.135739 | + | 0.990745i | \(0.543341\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.13188 | 0.0856874 | 0.0428437 | − | 0.999082i | \(-0.486358\pi\) | ||||
0.0428437 | + | 0.999082i | \(0.486358\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.36832 | −0.0950374 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.6601 | 0.866404 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.0614 | 0.401815 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.1306 | 0.563424 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.8631 | 1.14902 | 0.574511 | − | 0.818497i | \(-0.305192\pi\) | ||||
0.574511 | + | 0.818497i | \(0.305192\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 48.7268 | 1.93672 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.31617 | −0.290333 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.73007 | 0.108000 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.1831 | −0.757685 | −0.378843 | − | 0.925461i | \(-0.623678\pi\) | ||||
−0.378843 | + | 0.925461i | \(0.623678\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.3924 | 1.27743 | 0.638716 | − | 0.769442i | \(-0.279466\pi\) | ||||
0.638716 | + | 0.769442i | \(0.279466\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.69104 | −0.342209 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 35.4947 | 1.39544 | 0.697719 | − | 0.716371i | \(-0.254198\pi\) | ||||
0.697719 | + | 0.716371i | \(0.254198\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.13743 | −0.162408 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.0785 | 1.52926 | 0.764630 | − | 0.644469i | \(-0.222922\pi\) | ||||
0.764630 | + | 0.644469i | \(0.222922\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.65384 | 0.142767 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.83063 | −0.266488 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.6445 | 0.765242 | 0.382621 | − | 0.923905i | \(-0.375022\pi\) | ||||
0.382621 | + | 0.923905i | \(0.375022\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.5191 | 0.448041 | 0.224020 | − | 0.974584i | \(-0.428082\pi\) | ||||
0.224020 | + | 0.974584i | \(0.428082\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.33126 | −0.129376 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.96269 | −0.192156 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.4301 | 0.673887 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.853035 | 0.0329310 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.9330 | 0.652719 | 0.326359 | − | 0.945246i | \(-0.394178\pi\) | ||||
0.326359 | + | 0.945246i | \(0.394178\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −20.9064 | −0.804686 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.3909 | −1.01429 | −0.507143 | − | 0.861862i | \(-0.669298\pi\) | ||||
−0.507143 | + | 0.861862i | \(0.669298\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −34.3188 | −1.31510 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.8163 | −1.02610 | −0.513049 | − | 0.858359i | \(-0.671484\pi\) | ||||
−0.513049 | + | 0.858359i | \(0.671484\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.28301 | −0.354686 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −41.7107 | −1.59136 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.87467 | 0.109516 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.1588 | 1.14730 | 0.573648 | − | 0.819102i | \(-0.305528\pi\) | ||||
0.573648 | + | 0.819102i | \(0.305528\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.88439 | 0.223207 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.67585 | −0.252866 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.6708 | 0.441429 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.1146 | −0.684178 | −0.342089 | − | 0.939668i | \(-0.611134\pi\) | ||||
−0.342089 | + | 0.939668i | \(0.611134\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.1157 | −0.683246 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.79420 | −0.180560 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.7306 | 1.41700 | 0.708501 | − | 0.705709i | \(-0.249372\pi\) | ||||
0.708501 | + | 0.705709i | \(0.249372\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.00791 | 0.150308 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.72793 | 0.0647114 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.0747056 | −0.00279383 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.1654 | 0.566364 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.6396 | −1.03078 | −0.515391 | − | 0.856955i | \(-0.672353\pi\) | ||||
−0.515391 | + | 0.856955i | \(0.672353\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 50.8926 | 1.89271 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −43.8082 | −1.62700 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.3955 | 1.34983 | 0.674917 | − | 0.737894i | \(-0.264180\pi\) | ||||
0.674917 | + | 0.737894i | \(0.264180\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.5636 | 0.650504 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −63.1533 | −2.33581 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.5815 | 0.686323 | 0.343161 | − | 0.939276i | \(-0.388502\pi\) | ||||
0.343161 | + | 0.939276i | \(0.388502\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.73438 | 0.358571 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.9347 | −0.733309 | −0.366654 | − | 0.930357i | \(-0.619497\pi\) | ||||
−0.366654 | + | 0.930357i | \(0.619497\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.27074 | 0.156890 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.00507 | −0.220305 | −0.110152 | − | 0.993915i | \(-0.535134\pi\) | ||||
−0.110152 | + | 0.993915i | \(0.535134\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.76476 | 0.101293 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.712366 | 0.0260641 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.2815 | 0.557632 | 0.278816 | − | 0.960345i | \(-0.410058\pi\) | ||||
0.278816 | + | 0.960345i | \(0.410058\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.7053 | 0.827428 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.83523 | −0.103184 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.8279 | −1.26584 | −0.632921 | − | 0.774217i | \(-0.718144\pi\) | ||||
−0.632921 | + | 0.774217i | \(0.718144\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.635765 | 0.0230768 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.2028 | −0.877350 | −0.438675 | − | 0.898646i | \(-0.644552\pi\) | ||||
−0.438675 | + | 0.898646i | \(0.644552\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.32851 | −0.0841873 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.75620 | −0.0634128 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.20909 | −0.296027 | −0.148014 | − | 0.988985i | \(-0.547288\pi\) | ||||
−0.148014 | + | 0.988985i | \(0.547288\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 36.8013 | 1.32537 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.17621 | −0.222143 | −0.111071 | − | 0.993812i | \(-0.535428\pi\) | ||||
−0.111071 | + | 0.993812i | \(0.535428\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.2533 | 0.547914 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.55857 | 0.306643 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.26421 | 0.0810199 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 40.1866 | 1.43615 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.51294 | 0.268148 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.0855 | −0.787262 | −0.393631 | − | 0.919269i | \(-0.628781\pi\) | ||||
−0.393631 | + | 0.919269i | \(0.628781\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.6135 | 0.805062 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.362085 | 0.0128580 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.2266 | 0.362701 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27.3116 | 0.967425 | 0.483713 | − | 0.875227i | \(-0.339288\pi\) | ||||
0.483713 | + | 0.875227i | \(0.339288\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34.8370 | −1.23245 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.18174 | 0.253754 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.66506 | −0.199916 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −48.6535 | −1.71269 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.5846 | 0.407294 | 0.203647 | − | 0.979044i | \(-0.434721\pi\) | ||||
0.203647 | + | 0.979044i | \(0.434721\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.9836 | −1.22844 | −0.614221 | − | 0.789134i | \(-0.710530\pi\) | ||||
−0.614221 | + | 0.789134i | \(0.710530\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.5826 | −0.897222 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.15058 | −0.285502 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 80.9638 | 2.83256 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.3594 | 0.815249 | 0.407625 | − | 0.913150i | \(-0.366357\pi\) | ||||
0.407625 | + | 0.913150i | \(0.366357\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.52046 | 0.192431 | 0.0962156 | − | 0.995361i | \(-0.469326\pi\) | ||||
0.0962156 | + | 0.995361i | \(0.469326\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.61222 | 0.195392 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.6872 | −1.17142 | −0.585710 | − | 0.810521i | \(-0.699184\pi\) | ||||
−0.585710 | + | 0.810521i | \(0.699184\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.9791 | 0.728635 | 0.364318 | − | 0.931275i | \(-0.381302\pi\) | ||||
0.364318 | + | 0.931275i | \(0.381302\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.71995 | −0.198423 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.83117 | −0.236402 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.9923 | −0.483645 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.6347 | 1.47191 | 0.735957 | − | 0.677029i | \(-0.236733\pi\) | ||||
0.735957 | + | 0.677029i | \(0.236733\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 55.2090 | 1.90376 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22.9216 | −0.789461 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.14934 | 0.211544 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 47.2379 | 1.62120 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.14470 | −0.0392398 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.48928 | −0.187949 | −0.0939746 | − | 0.995575i | \(-0.529957\pi\) | ||||
−0.0939746 | + | 0.995575i | \(0.529957\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.98519 | 0.102091 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.7723 | 1.05116 | 0.525581 | − | 0.850743i | \(-0.323848\pi\) | ||||
0.525581 | + | 0.850743i | \(0.323848\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.1640 | 0.415030 | 0.207515 | − | 0.978232i | \(-0.433462\pi\) | ||||
0.207515 | + | 0.978232i | \(0.433462\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.631149 | −0.0214846 | −0.0107423 | − | 0.999942i | \(-0.503419\pi\) | ||||
−0.0107423 | + | 0.999942i | \(0.503419\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.0145 | −0.408506 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −53.2663 | −1.80902 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.32401 | 0.112759 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.13192 | 0.140005 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.39879 | 0.0811866 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.79128 | 0.229325 | 0.114663 | − | 0.993404i | \(-0.463421\pi\) | ||||
0.114663 | + | 0.993404i | \(0.463421\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −61.8269 | −2.08537 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.5322 | −1.26449 | −0.632247 | − | 0.774767i | \(-0.717867\pi\) | ||||
−0.632247 | + | 0.774767i | \(0.717867\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0969 | 0.676313 | 0.338157 | − | 0.941090i | \(-0.390197\pi\) | ||||
0.338157 | + | 0.941090i | \(0.390197\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.24766 | −0.210013 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.9581 | −0.804433 | −0.402217 | − | 0.915544i | \(-0.631760\pi\) | ||||
−0.402217 | + | 0.915544i | \(0.631760\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.48722 | −0.217330 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 44.6617 | 1.49455 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.63418 | −0.322035 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.269861 | 0.00901041 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −29.3202 | −0.977882 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 74.3115 | 2.47568 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.93051 | −0.130655 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.8339 | 0.459346 | 0.229673 | − | 0.973268i | \(-0.426234\pi\) | ||||
0.229673 | + | 0.973268i | \(0.426234\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.2647 | −0.373627 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.1585 | 0.369697 | 0.184849 | − | 0.982767i | \(-0.440820\pi\) | ||||
0.184849 | + | 0.982767i | \(0.440820\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.590809 | 0.0195529 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.28811 | 0.0425837 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −31.9623 | −1.05434 | −0.527169 | − | 0.849761i | \(-0.676746\pi\) | ||||
−0.527169 | + | 0.849761i | \(0.676746\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.66516 | 0.0878201 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.961084 | 0.0316345 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.1049 | −0.332245 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.6677 | −0.383219 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.0007 | −0.689011 | −0.344505 | − | 0.938784i | \(-0.611953\pi\) | ||||
−0.344505 | + | 0.938784i | \(0.611953\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.6989 | −0.415744 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.93117 | −0.0631561 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.6936 | 0.480019 | 0.240009 | − | 0.970771i | \(-0.422850\pi\) | ||||
0.240009 | + | 0.970771i | \(0.422850\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.7239 | −0.643666 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.2667 | 0.497680 | 0.248840 | − | 0.968545i | \(-0.419951\pi\) | ||||
0.248840 | + | 0.968545i | \(0.419951\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.540802 | 0.0176109 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.8411 | −0.709740 | −0.354870 | − | 0.934916i | \(-0.615475\pi\) | ||||
−0.354870 | + | 0.934916i | \(0.615475\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.40463 | −0.0780576 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.9684 | 0.712373 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.7302 | −1.57853 | −0.789264 | − | 0.614055i | \(-0.789537\pi\) | ||||
−0.789264 | + | 0.614055i | \(0.789537\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.1166 | −0.327366 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.7879 | −0.348724 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.7912 | −0.670684 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.84454 | −0.220562 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.83920 | 0.155779 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.1717 | −0.809467 | −0.404734 | − | 0.914435i | \(-0.632636\pi\) | ||||
−0.404734 | + | 0.914435i | \(0.632636\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 110.401 | 3.54658 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46.2440 | 1.48404 | 0.742020 | − | 0.670378i | \(-0.233868\pi\) | ||||
0.742020 | + | 0.670378i | \(0.233868\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.38220 | 0.0762915 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.1753 | 0.357529 | 0.178765 | − | 0.983892i | \(-0.442790\pi\) | ||||
0.178765 | + | 0.983892i | \(0.442790\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.95625 | 0.190363 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.63082 | −0.307489 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.8140 | −0.568179 | −0.284090 | − | 0.958798i | \(-0.591691\pi\) | ||||
−0.284090 | + | 0.958798i | \(0.591691\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.16447 | −0.228279 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.11597 | 0.162678 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.45574 | −0.141541 | −0.0707706 | − | 0.997493i | \(-0.522546\pi\) | ||||
−0.0707706 | + | 0.997493i | \(0.522546\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −37.3734 | −1.18601 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.17733 | −0.0690259 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.9717 | −1.10756 | −0.553782 | − | 0.832662i | \(-0.686816\pi\) | ||||
−0.553782 | + | 0.832662i | \(0.686816\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.26949 | 0.293274 |
(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 | 8036.2.a.q.1.4 | 15 | ||
7.2 | even | 3 | 1148.2.i.e.165.12 | ✓ | 30 | ||
7.4 | even | 3 | 1148.2.i.e.821.12 | yes | 30 | ||
7.6 | odd | 2 | 8036.2.a.r.1.12 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.i.e.165.12 | ✓ | 30 | 7.2 | even | 3 | ||
1148.2.i.e.821.12 | yes | 30 | 7.4 | even | 3 | ||
8036.2.a.q.1.4 | 15 | 1.1 | even | 1 | trivial | ||
8036.2.a.r.1.12 | 15 | 7.6 | odd | 2 |