Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3380,2,Mod(1,3380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3380, 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("3380.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3380.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: | \(26.9894358832\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 19x^{7} + 16x^{6} + 106x^{5} - 87x^{4} - 153x^{3} + 149x^{2} - 26x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.161999\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3380.1 |
$q$-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 | ||||||||
\(3\) | −0.161999 | −0.0935300 | −0.0467650 | − | 0.998906i | \(-0.514891\pi\) | ||||
−0.0467650 | + | 0.998906i | \(0.514891\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.89771 | −0.717268 | −0.358634 | − | 0.933478i | \(-0.616757\pi\) | ||||
−0.358634 | + | 0.933478i | \(0.616757\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.97376 | −0.991252 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.35728 | −1.61528 | −0.807641 | − | 0.589674i | \(-0.799256\pi\) | ||||
−0.807641 | + | 0.589674i | \(0.799256\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.161999 | 0.0418279 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.71387 | 1.87089 | 0.935445 | − | 0.353473i | \(-0.114999\pi\) | ||||
0.935445 | + | 0.353473i | \(0.114999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.553719 | −0.127032 | −0.0635160 | − | 0.997981i | \(-0.520231\pi\) | ||||
−0.0635160 | + | 0.997981i | \(0.520231\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.307427 | 0.0670861 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.14988 | −0.656795 | −0.328398 | − | 0.944540i | \(-0.606509\pi\) | ||||
−0.328398 | + | 0.944540i | \(0.606509\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.967741 | 0.186242 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.54250 | −0.657826 | −0.328913 | − | 0.944360i | \(-0.606682\pi\) | ||||
−0.328913 | + | 0.944360i | \(0.606682\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.01423 | −1.08019 | −0.540094 | − | 0.841605i | \(-0.681611\pi\) | ||||
−0.540094 | + | 0.841605i | \(0.681611\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.867873 | 0.151077 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.89771 | 0.320772 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.8657 | 1.78631 | 0.893157 | − | 0.449746i | \(-0.148485\pi\) | ||||
0.893157 | + | 0.449746i | \(0.148485\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.74983 | −1.36649 | −0.683247 | − | 0.730187i | \(-0.739433\pi\) | ||||
−0.683247 | + | 0.730187i | \(0.739433\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.25198 | −0.495923 | −0.247961 | − | 0.968770i | \(-0.579761\pi\) | ||||
−0.247961 | + | 0.968770i | \(0.579761\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.97376 | 0.443301 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.81442 | −1.43158 | −0.715790 | − | 0.698315i | \(-0.753933\pi\) | ||||
−0.715790 | + | 0.698315i | \(0.753933\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.39868 | −0.485526 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.24964 | −0.174984 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.87818 | 1.21951 | 0.609756 | − | 0.792590i | \(-0.291268\pi\) | ||||
0.609756 | + | 0.792590i | \(0.291268\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.35728 | 0.722376 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.0897018 | 0.0118813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.4174 | 1.74680 | 0.873401 | − | 0.487002i | \(-0.161909\pi\) | ||||
0.873401 | + | 0.487002i | \(0.161909\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.551418 | −0.0706018 | −0.0353009 | − | 0.999377i | \(-0.511239\pi\) | ||||
−0.0353009 | + | 0.999377i | \(0.511239\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.64334 | 0.710994 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.46051 | −0.544938 | −0.272469 | − | 0.962165i | \(-0.587840\pi\) | ||||
−0.272469 | + | 0.962165i | \(0.587840\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.510276 | 0.0614301 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.17861 | 0.970623 | 0.485311 | − | 0.874341i | \(-0.338706\pi\) | ||||
0.485311 | + | 0.874341i | \(0.338706\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.6129 | 1.47623 | 0.738113 | − | 0.674677i | \(-0.235717\pi\) | ||||
0.738113 | + | 0.674677i | \(0.235717\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.161999 | −0.0187060 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.1666 | 1.15859 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.4130 | 1.50908 | 0.754540 | − | 0.656255i | \(-0.227860\pi\) | ||||
0.754540 | + | 0.656255i | \(0.227860\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.76450 | 0.973833 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.42318 | −0.595271 | −0.297636 | − | 0.954680i | \(-0.596198\pi\) | ||||
−0.297636 | + | 0.954680i | \(0.596198\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.71387 | −0.836687 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.573881 | 0.0615265 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.46756 | 0.155561 | 0.0777804 | − | 0.996971i | \(-0.475217\pi\) | ||||
0.0777804 | + | 0.996971i | \(0.475217\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.974297 | 0.101030 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.553719 | 0.0568104 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.69045 | 0.577777 | 0.288889 | − | 0.957363i | \(-0.406714\pi\) | ||||
0.288889 | + | 0.957363i | \(0.406714\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.9313 | 1.60115 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.80029 | 0.676654 | 0.338327 | − | 0.941029i | \(-0.390139\pi\) | ||||
0.338327 | + | 0.941029i | \(0.390139\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.9081 | 1.27187 | 0.635936 | − | 0.771742i | \(-0.280614\pi\) | ||||
0.635936 | + | 0.771742i | \(0.280614\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.307427 | −0.0300018 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.23968 | −0.409865 | −0.204933 | − | 0.978776i | \(-0.565697\pi\) | ||||
−0.204933 | + | 0.978776i | \(0.565697\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00088 | −0.670563 | −0.335281 | − | 0.942118i | \(-0.608831\pi\) | ||||
−0.335281 | + | 0.942118i | \(0.608831\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.76023 | −0.167074 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.29176 | 0.215590 | 0.107795 | − | 0.994173i | \(-0.465621\pi\) | ||||
0.107795 | + | 0.994173i | \(0.465621\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.14988 | 0.293728 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.6387 | −1.34193 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.7005 | 1.60914 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.41746 | 0.127808 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.526702 | −0.0467372 | −0.0233686 | − | 0.999727i | \(-0.507439\pi\) | ||||
−0.0233686 | + | 0.999727i | \(0.507439\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.526817 | 0.0463837 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.8745 | 1.56171 | 0.780853 | − | 0.624715i | \(-0.214785\pi\) | ||||
0.780853 | + | 0.624715i | \(0.214785\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.05080 | 0.0911159 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.967741 | −0.0832899 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.58940 | −0.733842 | −0.366921 | − | 0.930252i | \(-0.619588\pi\) | ||||
−0.366921 | + | 0.930252i | \(0.619588\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.68254 | 0.227530 | 0.113765 | − | 0.993508i | \(-0.463709\pi\) | ||||
0.113765 | + | 0.993508i | \(0.463709\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.58992 | 0.133896 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.54250 | 0.294189 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.550583 | 0.0454113 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.22172 | 0.345857 | 0.172929 | − | 0.984934i | \(-0.444677\pi\) | ||||
0.172929 | + | 0.984934i | \(0.444677\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.26015 | 0.590822 | 0.295411 | − | 0.955370i | \(-0.404543\pi\) | ||||
0.295411 | + | 0.955370i | \(0.404543\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −22.9392 | −1.85452 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.01423 | 0.483074 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.7458 | −0.857609 | −0.428805 | − | 0.903397i | \(-0.641065\pi\) | ||||
−0.428805 | + | 0.903397i | \(0.641065\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.43825 | −0.114061 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.97757 | 0.471098 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.75744 | 0.685935 | 0.342968 | − | 0.939347i | \(-0.388568\pi\) | ||||
0.342968 | + | 0.939347i | \(0.388568\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.867873 | −0.0675639 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.29670 | 0.255106 | 0.127553 | − | 0.991832i | \(-0.459288\pi\) | ||||
0.127553 | + | 0.991832i | \(0.459288\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.64663 | 0.125921 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.6617 | 1.57088 | 0.785440 | − | 0.618938i | \(-0.212437\pi\) | ||||
0.785440 | + | 0.618938i | \(0.212437\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.89771 | −0.143454 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.17361 | −0.163378 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.5721 | −1.46289 | −0.731446 | − | 0.681900i | \(-0.761154\pi\) | ||||
−0.731446 | + | 0.681900i | \(0.761154\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.7679 | 0.800369 | 0.400185 | − | 0.916435i | \(-0.368946\pi\) | ||||
0.400185 | + | 0.916435i | \(0.368946\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0893290 | 0.00660339 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.8657 | −0.798863 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −41.3254 | −3.02201 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.83649 | −0.133585 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.3596 | −0.966667 | −0.483334 | − | 0.875436i | \(-0.660574\pi\) | ||||
−0.483334 | + | 0.875436i | \(0.660574\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.69764 | −0.266162 | −0.133081 | − | 0.991105i | \(-0.542487\pi\) | ||||
−0.133081 | + | 0.991105i | \(0.542487\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.5498 | −1.25037 | −0.625187 | − | 0.780475i | \(-0.714977\pi\) | ||||
−0.625187 | + | 0.780475i | \(0.714977\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.2570 | 1.36510 | 0.682548 | − | 0.730841i | \(-0.260872\pi\) | ||||
0.682548 | + | 0.730841i | \(0.260872\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.722597 | 0.0509681 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.72265 | 0.471838 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.74983 | 0.611115 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.36697 | 0.651050 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.96643 | 0.205192 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.0925 | −1.79628 | −0.898142 | − | 0.439705i | \(-0.855083\pi\) | ||||
−0.898142 | + | 0.439705i | \(0.855083\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.32492 | −0.0907824 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.25198 | 0.221783 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.4133 | 0.774784 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.04327 | −0.138071 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.30627 | −0.623194 | −0.311597 | − | 0.950214i | \(-0.600864\pi\) | ||||
−0.311597 | + | 0.950214i | \(0.600864\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.97376 | −0.198250 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.77639 | 0.117903 | 0.0589515 | − | 0.998261i | \(-0.481224\pi\) | ||||
0.0589515 | + | 0.998261i | \(0.481224\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.8216 | −0.847272 | −0.423636 | − | 0.905833i | \(-0.639246\pi\) | ||||
−0.423636 | + | 0.905833i | \(0.639246\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.64697 | −0.108363 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.8823 | −1.10599 | −0.552997 | − | 0.833183i | \(-0.686516\pi\) | ||||
−0.552997 | + | 0.833183i | \(0.686516\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.81442 | 0.640222 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.17289 | −0.141144 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.5027 | 1.32621 | 0.663106 | − | 0.748526i | \(-0.269238\pi\) | ||||
0.663106 | + | 0.748526i | \(0.269238\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.0766 | 0.713504 | 0.356752 | − | 0.934199i | \(-0.383884\pi\) | ||||
0.356752 | + | 0.934199i | \(0.383884\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.32306 | −0.277324 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.39868 | 0.217134 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.878548 | 0.0556757 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.61833 | −0.102148 | −0.0510740 | − | 0.998695i | \(-0.516264\pi\) | ||||
−0.0510740 | + | 0.998695i | \(0.516264\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.8748 | 1.06091 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.24964 | 0.0782554 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.6190 | 0.849532 | 0.424766 | − | 0.905303i | \(-0.360356\pi\) | ||||
0.424766 | + | 0.905303i | \(0.360356\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.6200 | −1.28127 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.5345 | 0.652071 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.1385 | 0.686828 | 0.343414 | − | 0.939184i | \(-0.388417\pi\) | ||||
0.343414 | + | 0.939184i | \(0.388417\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.87818 | −0.545382 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.237743 | −0.0145496 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.2455 | 1.11245 | 0.556223 | − | 0.831033i | \(-0.312250\pi\) | ||||
0.556223 | + | 0.831033i | \(0.312250\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.2410 | 1.04732 | 0.523658 | − | 0.851929i | \(-0.324567\pi\) | ||||
0.523658 | + | 0.851929i | \(0.324567\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.35728 | −0.323056 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.7759 | −1.00797 | −0.503983 | − | 0.863713i | \(-0.668133\pi\) | ||||
−0.503983 | + | 0.863713i | \(0.668133\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.8849 | 1.07074 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.71383 | 0.221549 | 0.110774 | − | 0.993846i | \(-0.464667\pi\) | ||||
0.110774 | + | 0.993846i | \(0.464667\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.2742 | 1.74017 | 0.870086 | − | 0.492900i | \(-0.164063\pi\) | ||||
0.870086 | + | 0.492900i | \(0.164063\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.0897018 | −0.00531348 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.6047 | 0.980143 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 42.5039 | 2.50023 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.921845 | −0.0540395 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.58006 | −0.442832 | −0.221416 | − | 0.975179i | \(-0.571068\pi\) | ||||
−0.221416 | + | 0.975179i | \(0.571068\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.4174 | −0.781194 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.18446 | −0.300833 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.17133 | 0.355710 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.10164 | −0.0632875 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.551418 | 0.0315741 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.94812 | 0.168258 | 0.0841292 | − | 0.996455i | \(-0.473189\pi\) | ||||
0.0841292 | + | 0.996455i | \(0.473189\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.09110 | −0.118958 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.64858 | −0.320302 | −0.160151 | − | 0.987093i | \(-0.551198\pi\) | ||||
−0.160151 | + | 0.987093i | \(0.551198\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.4132 | 0.927726 | 0.463863 | − | 0.885907i | \(-0.346463\pi\) | ||||
0.463863 | + | 0.885907i | \(0.346463\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.64334 | −0.317966 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.3498 | −1.42378 | −0.711892 | − | 0.702289i | \(-0.752162\pi\) | ||||
−0.711892 | + | 0.702289i | \(0.752162\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.9782 | 1.06257 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.686822 | 0.0383347 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.27132 | −0.237663 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.13413 | 0.0627178 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.6250 | 1.02683 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.8750 | −0.927534 | −0.463767 | − | 0.885957i | \(-0.653503\pi\) | ||||
−0.463767 | + | 0.885957i | \(0.653503\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −32.3120 | −1.77069 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.46051 | 0.243704 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.2141 | 1.80929 | 0.904643 | − | 0.426170i | \(-0.140138\pi\) | ||||
0.904643 | + | 0.426170i | \(0.140138\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.371261 | −0.0201642 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 32.2199 | 1.74481 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.7337 | 1.06552 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.510276 | −0.0274724 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −32.1558 | −1.72621 | −0.863107 | − | 0.505021i | \(-0.831485\pi\) | ||||
−0.863107 | + | 0.505021i | \(0.831485\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.18315 | 0.116861 | 0.0584307 | − | 0.998291i | \(-0.481390\pi\) | ||||
0.0584307 | + | 0.998291i | \(0.481390\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.8132 | −0.575529 | −0.287764 | − | 0.957701i | \(-0.592912\pi\) | ||||
−0.287764 | + | 0.957701i | \(0.592912\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.17861 | −0.434076 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.37145 | 0.125511 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.4897 | 1.08140 | 0.540702 | − | 0.841214i | \(-0.318159\pi\) | ||||
0.540702 | + | 0.841214i | \(0.318159\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6934 | −0.983863 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.86746 | −0.150503 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.6129 | −0.660188 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.5527 | −1.69924 | −0.849619 | − | 0.527398i | \(-0.823168\pi\) | ||||
−0.849619 | + | 0.527398i | \(0.823168\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 26.0199 | 1.35454 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.8482 | −0.874717 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.8558 | 0.976317 | 0.488159 | − | 0.872755i | \(-0.337669\pi\) | ||||
0.488159 | + | 0.872755i | \(0.337669\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.161999 | 0.00836558 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.3031 | 0.683332 | 0.341666 | − | 0.939821i | \(-0.389009\pi\) | ||||
0.341666 | + | 0.939821i | \(0.389009\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.0853250 | 0.00437133 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.3902 | −1.45067 | −0.725336 | − | 0.688395i | \(-0.758315\pi\) | ||||
−0.725336 | + | 0.688395i | \(0.758315\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.1666 | −0.518137 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.67061 | 0.491585 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.38713 | −0.374543 | −0.187271 | − | 0.982308i | \(-0.559964\pi\) | ||||
−0.187271 | + | 0.982308i | \(0.559964\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.2978 | −1.22879 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.89565 | −0.146066 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.4130 | −0.674881 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.1613 | −0.811114 | −0.405557 | − | 0.914070i | \(-0.632922\pi\) | ||||
−0.405557 | + | 0.914070i | \(0.632922\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.170228 | −0.00852208 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.05887 | 0.402441 | 0.201220 | − | 0.979546i | \(-0.435509\pi\) | ||||
0.201220 | + | 0.979546i | \(0.435509\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.76450 | −0.435511 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −58.2107 | −2.88540 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.9429 | −1.23335 | −0.616674 | − | 0.787219i | \(-0.711520\pi\) | ||||
−0.616674 | + | 0.787219i | \(0.711520\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.39147 | 0.0686363 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −25.4625 | −1.25293 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.42318 | 0.266213 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.434568 | −0.0212809 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.758173 | −0.0370392 | −0.0185196 | − | 0.999828i | \(-0.505895\pi\) | ||||
−0.0185196 | + | 0.999828i | \(0.505895\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.20278 | −0.0586199 | −0.0293099 | − | 0.999570i | \(-0.509331\pi\) | ||||
−0.0293099 | + | 0.999570i | \(0.509331\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 29.1857 | 1.41906 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.71387 | 0.374178 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.04643 | 0.0506404 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.55978 | 0.171469 | 0.0857344 | − | 0.996318i | \(-0.472676\pi\) | ||||
0.0857344 | + | 0.996318i | \(0.472676\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.2920 | 1.79214 | 0.896070 | − | 0.443913i | \(-0.146410\pi\) | ||||
0.896070 | + | 0.443913i | \(0.146410\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.573881 | −0.0275155 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.74415 | 0.0834339 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.0813 | −0.624336 | −0.312168 | − | 0.950027i | \(-0.601055\pi\) | ||||
−0.312168 | + | 0.950027i | \(0.601055\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.1069 | 0.481279 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.1758 | −1.05360 | −0.526802 | − | 0.849988i | \(-0.676609\pi\) | ||||
−0.526802 | + | 0.849988i | \(0.676609\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.46756 | −0.0695689 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.683914 | −0.0323480 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.92762 | 0.185356 | 0.0926778 | − | 0.995696i | \(-0.470457\pi\) | ||||
0.0926778 | + | 0.995696i | \(0.470457\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 46.8753 | 2.20727 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.17613 | −0.0552596 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.1786 | 1.36492 | 0.682458 | − | 0.730925i | \(-0.260911\pi\) | ||||
0.682458 | + | 0.730925i | \(0.260911\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.46503 | 0.348438 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.8570 | 0.645384 | 0.322692 | − | 0.946504i | \(-0.395412\pi\) | ||||
0.322692 | + | 0.946504i | \(0.395412\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.0020 | 1.30136 | 0.650682 | − | 0.759351i | \(-0.274483\pi\) | ||||
0.650682 | + | 0.759351i | \(0.274483\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.974297 | −0.0451820 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.17194 | 0.331878 | 0.165939 | − | 0.986136i | \(-0.446935\pi\) | ||||
0.165939 | + | 0.986136i | \(0.446935\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.46477 | 0.390867 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.74081 | 0.0802122 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.4218 | 0.801056 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.553719 | −0.0254064 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −26.4015 | −1.20884 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.4839 | −0.707478 | −0.353739 | − | 0.935344i | \(-0.615090\pi\) | ||||
−0.353739 | + | 0.935344i | \(0.615090\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.968358 | −0.0440618 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.69045 | −0.258390 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.4727 | −1.56211 | −0.781054 | − | 0.624464i | \(-0.785317\pi\) | ||||
−0.781054 | + | 0.624464i | \(0.785317\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.41869 | −0.0641555 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.8837 | −1.43889 | −0.719446 | − | 0.694548i | \(-0.755604\pi\) | ||||
−0.719446 | + | 0.694548i | \(0.755604\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.3264 | −1.23072 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −15.9313 | −0.716057 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.5207 | −0.696197 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.94343 | 0.221298 | 0.110649 | − | 0.993860i | \(-0.464707\pi\) | ||||
0.110649 | + | 0.993860i | \(0.464707\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.534061 | −0.0238601 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.1426 | −1.34399 | −0.671996 | − | 0.740555i | \(-0.734563\pi\) | ||||
−0.671996 | + | 0.740555i | \(0.734563\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.80029 | −0.302609 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.3768 | 1.25778 | 0.628889 | − | 0.777495i | \(-0.283510\pi\) | ||||
0.628889 | + | 0.777495i | \(0.283510\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.9356 | −1.05885 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.535857 | −0.0236587 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.9081 | −0.568799 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 52.5787 | 2.31241 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.34717 | −0.146924 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.8552 | −1.08893 | −0.544463 | − | 0.838785i | \(-0.683267\pi\) | ||||
−0.544463 | + | 0.838785i | \(0.683267\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.95417 | 0.172904 | 0.0864520 | − | 0.996256i | \(-0.472447\pi\) | ||||
0.0864520 | + | 0.996256i | \(0.472447\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.307427 | 0.0134172 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −46.3930 | −2.02091 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0783 | −0.568620 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −39.9002 | −1.73152 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.23968 | 0.183297 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.17066 | 0.136824 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.2077 | 0.784262 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.8032 | −0.507461 | −0.253731 | − | 0.967275i | \(-0.581658\pi\) | ||||
−0.253731 | + | 0.967275i | \(0.581658\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.74438 | −0.0748585 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.00088 | 0.299885 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.2805 | −0.952644 | −0.476322 | − | 0.879271i | \(-0.658030\pi\) | ||||
−0.476322 | + | 0.879271i | \(0.658030\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.63978 | 0.0699842 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.96155 | 0.0835649 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −25.4540 | −1.08241 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.76023 | 0.0747177 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 34.7144 | 1.47090 | 0.735448 | − | 0.677581i | \(-0.236972\pi\) | ||||
0.735448 | + | 0.677581i | \(0.236972\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.69467 | 0.282649 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.0781 | −0.846191 | −0.423095 | − | 0.906085i | \(-0.639056\pi\) | ||||
−0.423095 | + | 0.906085i | \(0.639056\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.29176 | −0.0964149 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16.6325 | −0.698499 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.2353 | −0.471010 | −0.235505 | − | 0.971873i | \(-0.575674\pi\) | ||||
−0.235505 | + | 0.971873i | \(0.575674\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.7673 | −1.07833 | −0.539164 | − | 0.842201i | \(-0.681260\pi\) | ||||
−0.539164 | + | 0.842201i | \(0.681260\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.16424 | 0.0904124 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.14988 | −0.131359 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.07927 | −0.0449307 | −0.0224654 | − | 0.999748i | \(-0.507152\pi\) | ||||
−0.0224654 | + | 0.999748i | \(0.507152\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.599014 | 0.0248942 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.2916 | 0.426969 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −47.5629 | −1.96985 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.9803 | 1.23742 | 0.618710 | − | 0.785620i | \(-0.287656\pi\) | ||||
0.618710 | + | 0.785620i | \(0.287656\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.33019 | 0.137218 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.84305 | 0.116947 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.87304 | −0.323307 | −0.161653 | − | 0.986848i | \(-0.551683\pi\) | ||||
−0.161653 | + | 0.986848i | \(0.551683\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.6387 | 0.600129 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.11962 | −0.127677 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.7409 | 0.806590 | 0.403295 | − | 0.915070i | \(-0.367865\pi\) | ||||
0.403295 | + | 0.915070i | \(0.367865\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.33925 | −0.136211 | −0.0681054 | − | 0.997678i | \(-0.521695\pi\) | ||||
−0.0681054 | + | 0.997678i | \(0.521695\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.2645 | 0.540171 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.7005 | −0.719628 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.2968 | 0.904998 | 0.452499 | − | 0.891765i | \(-0.350533\pi\) | ||||
0.452499 | + | 0.891765i | \(0.350533\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.08906 | −0.0441310 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.6710 | 0.875285 | 0.437643 | − | 0.899149i | \(-0.355814\pi\) | ||||
0.437643 | + | 0.899149i | \(0.355814\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.41746 | −0.0571576 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.1369 | 1.17301 | 0.586504 | − | 0.809946i | \(-0.300504\pi\) | ||||
0.586504 | + | 0.809946i | \(0.300504\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.1986 | 1.33437 | 0.667183 | − | 0.744894i | \(-0.267500\pi\) | ||||
0.667183 | + | 0.744894i | \(0.267500\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.04827 | −0.122323 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.78500 | −0.111579 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.480558 | −0.0191916 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 83.8168 | 3.34199 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.5904 | 1.85473 | 0.927366 | − | 0.374155i | \(-0.122067\pi\) | ||||
0.927366 | + | 0.374155i | \(0.122067\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.22696 | 0.168006 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.526702 | 0.0209015 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.3212 | −0.962132 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.9608 | −1.22288 | −0.611438 | − | 0.791292i | \(-0.709409\pi\) | ||||
−0.611438 | + | 0.791292i | \(0.709409\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.0391 | 0.948010 | 0.474005 | − | 0.880522i | \(-0.342808\pi\) | ||||
0.474005 | + | 0.880522i | \(0.342808\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.526817 | −0.0207434 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.9606 | 1.64964 | 0.824822 | − | 0.565393i | \(-0.191275\pi\) | ||||
0.824822 | + | 0.565393i | \(0.191275\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −71.8811 | −2.82158 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.84894 | −0.0724656 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.92478 | −0.0753223 | −0.0376612 | − | 0.999291i | \(-0.511991\pi\) | ||||
−0.0376612 | + | 0.999291i | \(0.511991\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.8745 | −0.698416 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −37.5076 | −1.46331 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.78444 | 0.108466 | 0.0542332 | − | 0.998528i | \(-0.482729\pi\) | ||||
0.0542332 | + | 0.998528i | \(0.482729\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.5553 | 0.488346 | 0.244173 | − | 0.969732i | \(-0.421484\pi\) | ||||
0.244173 | + | 0.969732i | \(0.421484\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.05080 | −0.0407483 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.1584 | 0.432057 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.50760 | 0.0582874 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.95410 | 0.114042 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 46.3999 | 1.78859 | 0.894293 | − | 0.447481i | \(-0.147679\pi\) | ||||
0.894293 | + | 0.447481i | \(0.147679\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.967741 | 0.0372484 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −45.7333 | −1.75767 | −0.878837 | − | 0.477123i | \(-0.841680\pi\) | ||||
−0.878837 | + | 0.477123i | \(0.841680\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.7988 | −0.414421 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.287773 | −0.0110275 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 40.5600 | 1.55198 | 0.775992 | − | 0.630743i | \(-0.217250\pi\) | ||||
0.775992 | + | 0.630743i | \(0.217250\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.58940 | 0.328184 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.07708 | 0.0792454 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.9242 | −0.681868 | −0.340934 | − | 0.940087i | \(-0.610743\pi\) | ||||
−0.340934 | + | 0.940087i | \(0.610743\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −30.2330 | −1.14846 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.68254 | −0.101755 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −67.4951 | −2.55656 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.73491 | 0.103444 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.5457 | −0.738230 | −0.369115 | − | 0.929384i | \(-0.620339\pi\) | ||||
−0.369115 | + | 0.929384i | \(0.620339\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.01656 | −0.226919 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.58992 | −0.0598800 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.9050 | −0.485343 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 46.6490 | 1.75194 | 0.875970 | − | 0.482366i | \(-0.160222\pi\) | ||||
0.875970 | + | 0.482366i | \(0.160222\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −39.8870 | −1.49588 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.9441 | 0.709462 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.32142 | −0.124041 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.4882 | −1.50995 | −0.754977 | − | 0.655751i | \(-0.772352\pi\) | ||||
−0.754977 | + | 0.655751i | \(0.772352\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.4959 | −0.912274 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.79439 | −0.0667341 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.54250 | −0.131565 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.9582 | 0.851471 | 0.425736 | − | 0.904848i | \(-0.360015\pi\) | ||||
0.425736 | + | 0.904848i | \(0.360015\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.5932 | −0.947895 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.0854 | −0.927817 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.3753 | 0.789513 | 0.394757 | − | 0.918786i | \(-0.370829\pi\) | ||||
0.394757 | + | 0.918786i | \(0.370829\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.550583 | −0.0203085 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.8962 | 0.880229 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.1671 | −1.29364 | −0.646821 | − | 0.762642i | \(-0.723902\pi\) | ||||
−0.646821 | + | 0.762642i | \(0.723902\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.9324 | 0.731249 | 0.365625 | − | 0.930762i | \(-0.380855\pi\) | ||||
0.365625 | + | 0.930762i | \(0.380855\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.22172 | −0.154672 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.1272 | 0.590064 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.04569 | 0.293983 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.7277 | 1.23074 | 0.615370 | − | 0.788238i | \(-0.289006\pi\) | ||||
0.615370 | + | 0.788238i | \(0.289006\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.262167 | 0.00955390 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.26015 | −0.264224 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.3007 | 0.846877 | 0.423439 | − | 0.905925i | \(-0.360823\pi\) | ||||
0.423439 | + | 0.905925i | \(0.360823\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.73370 | −0.0992269 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.72440 | 0.280009 | 0.140005 | − | 0.990151i | \(-0.455288\pi\) | ||||
0.140005 | + | 0.990151i | \(0.455288\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.2857 | 0.480973 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 22.9392 | 0.829368 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.44221 | 0.232312 | 0.116156 | − | 0.993231i | \(-0.462943\pi\) | ||||
0.116156 | + | 0.993231i | \(0.462943\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.20627 | −0.0794568 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −39.1922 | −1.40964 | −0.704822 | − | 0.709384i | \(-0.748973\pi\) | ||||
−0.704822 | + | 0.709384i | \(0.748973\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.01423 | −0.216037 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.34042 | 0.119837 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.84495 | 0.173588 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −43.8152 | −1.56783 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.42822 | −0.122515 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.7458 | 0.383535 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.0865 | −0.965529 | −0.482765 | − | 0.875750i | \(-0.660367\pi\) | ||||
−0.482765 | + | 0.875750i | \(0.660367\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.80442 | −0.0642390 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.34909 | −0.154636 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.43825 | 0.0510096 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.49750 | 0.123888 | 0.0619440 | − | 0.998080i | \(-0.480270\pi\) | ||||
0.0619440 | + | 0.998080i | \(0.480270\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −75.7072 | −2.67833 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.36416 | −0.154200 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −67.5708 | −2.38452 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.97757 | −0.210682 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.95574 | −0.104047 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.6258 | 0.443898 | 0.221949 | − | 0.975058i | \(-0.428758\pi\) | ||||
0.221949 | + | 0.975058i | \(0.428758\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.7350 | 1.43040 | 0.715200 | − | 0.698920i | \(-0.246336\pi\) | ||||
0.715200 | + | 0.698920i | \(0.246336\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.79302 | −0.0979554 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.75744 | −0.306760 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.80069 | 0.0629980 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.0805 | 0.910214 | 0.455107 | − | 0.890437i | \(-0.349601\pi\) | ||||
0.455107 | + | 0.890437i | \(0.349601\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.24240 | −0.147881 | −0.0739404 | − | 0.997263i | \(-0.523557\pi\) | ||||
−0.0739404 | + | 0.997263i | \(0.523557\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.867873 | 0.0302155 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −41.1905 | −1.43234 | −0.716168 | − | 0.697928i | \(-0.754105\pi\) | ||||
−0.716168 | + | 0.697928i | \(0.754105\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.2757 | −0.912591 | −0.456296 | − | 0.889828i | \(-0.650824\pi\) | ||||
−0.456296 | + | 0.889828i | \(0.650824\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.71768 | 0.0942752 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26.2170 | −0.908366 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.29670 | −0.114087 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.82022 | −0.201176 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.6372 | 1.02319 | 0.511594 | − | 0.859227i | \(-0.329055\pi\) | ||||
0.511594 | + | 0.859227i | \(0.329055\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.4507 | −0.567265 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.601637 | −0.0207215 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −33.5905 | −1.15418 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.74239 | −0.162758 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34.2257 | −1.17324 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.5743 | 1.28652 | 0.643259 | − | 0.765648i | \(-0.277582\pi\) | ||||
0.643259 | + | 0.765648i | \(0.277582\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.64663 | −0.0563134 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.4208 | 1.41491 | 0.707453 | − | 0.706760i | \(-0.249844\pi\) | ||||
0.707453 | + | 0.706760i | \(0.249844\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.17985 | −0.210854 | −0.105427 | − | 0.994427i | \(-0.533621\pi\) | ||||
−0.105427 | + | 0.994427i | \(0.533621\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.68994 | −0.0916728 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.0410 | 0.614124 | 0.307062 | − | 0.951690i | \(-0.400654\pi\) | ||||
0.307062 | + | 0.951690i | \(0.400654\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.6617 | −0.702519 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.88557 | −0.233846 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −71.8572 | −2.43759 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.9220 | −0.572723 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.89771 | 0.0641544 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.3180 | −0.517251 | −0.258625 | − | 0.965978i | \(-0.583270\pi\) | ||||
−0.258625 | + | 0.965978i | \(0.583270\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.22796 | 0.0414181 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.9448 | 1.31208 | 0.656042 | − | 0.754725i | \(-0.272230\pi\) | ||||
0.656042 | + | 0.754725i | \(0.272230\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −53.4157 | −1.79758 | −0.898791 | − | 0.438376i | \(-0.855554\pi\) | ||||
−0.898791 | + | 0.438376i | \(0.855554\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.17361 | 0.0730651 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.9682 | 0.536161 | 0.268080 | − | 0.963397i | \(-0.413611\pi\) | ||||
0.268080 | + | 0.963397i | \(0.413611\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.999529 | 0.0335231 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −46.9539 | −1.57302 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.43444 | 0.181856 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.5721 | 0.654225 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.3054 | 0.710575 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 68.4851 | 2.28157 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.999748 | −0.0332695 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.7679 | −0.357936 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.85604 | 0.327265 | 0.163632 | − | 0.986521i | \(-0.447679\pi\) | ||||
0.163632 | + | 0.986521i | \(0.447679\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −20.2224 | −0.670735 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.1345 | 1.52850 | 0.764252 | − | 0.644918i | \(-0.223109\pi\) | ||||
0.764252 | + | 0.644918i | \(0.223109\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29.0535 | 0.961531 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.0893290 | −0.00295312 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −33.9208 | −1.12016 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.6260 | 0.515455 | 0.257727 | − | 0.966218i | \(-0.417026\pi\) | ||||
0.257727 | + | 0.966218i | \(0.417026\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.477592 | −0.0157372 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.8657 | 0.357263 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −38.3855 | −1.26075 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.2052 | 0.597294 | 0.298647 | − | 0.954364i | \(-0.403465\pi\) | ||||
0.298647 | + | 0.954364i | \(0.403465\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.88192 | 0.0616773 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.915063 | 0.0299578 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 41.3254 | 1.35149 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.4735 | −1.35488 | −0.677440 | − | 0.735578i | \(-0.736911\pi\) | ||||
−0.677440 | + | 0.735578i | \(0.736911\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.65891 | −0.0867702 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.1745 | 0.820665 | 0.410333 | − | 0.911936i | \(-0.365413\pi\) | ||||
0.410333 | + | 0.911936i | \(0.365413\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.5609 | 0.897507 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.83649 | 0.0597412 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.6232 | −0.897634 | −0.448817 | − | 0.893624i | \(-0.648155\pi\) | ||||
−0.448817 | + | 0.893624i | \(0.648155\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.10663 | 0.133167 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.7517 | −1.15811 | −0.579055 | − | 0.815289i | \(-0.696578\pi\) | ||||
−0.579055 | + | 0.815289i | \(0.696578\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.3596 | 0.432307 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.07444 | −0.0993826 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.3002 | 0.526362 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.17095 | 0.166805 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.6078 | 0.406280 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.69764 | 0.119031 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47.4240 | −1.52505 | −0.762527 | − | 0.646957i | \(-0.776041\pi\) | ||||
−0.762527 | + | 0.646957i | \(0.776041\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.691949 | 0.0222286 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.7029 | −0.632295 | −0.316147 | − | 0.948710i | \(-0.602389\pi\) | ||||
−0.316147 | + | 0.948710i | \(0.602389\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.09069 | −0.163200 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.0105702 | 0.000338172 0 | 0.000169086 | − | 1.00000i | \(-0.499946\pi\) | ||||
0.000169086 | 1.00000i | \(0.499946\pi\) | ||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.86213 | −0.251275 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.8189 | 0.664697 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.7240 | 0.565306 | 0.282653 | − | 0.959222i | \(-0.408785\pi\) | ||||
0.282653 | + | 0.959222i | \(0.408785\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.5498 | 0.559184 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.01722 | −0.0960392 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.2434 | 0.325720 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.89901 | 0.219154 | 0.109577 | − | 0.993978i | \(-0.465050\pi\) | ||||
0.109577 | + | 0.993978i | \(0.465050\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.73373 | 0.0867523 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.2570 | −0.610489 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.36107 | −0.138117 | −0.0690583 | − | 0.997613i | \(-0.521999\pi\) | ||||
−0.0690583 | + | 0.997613i | \(0.521999\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.5152 | 0.332686 |
(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 | 3380.2.a.r.1.5 | ✓ | 9 | |
13.5 | odd | 4 | 3380.2.f.j.3041.10 | 18 | |||
13.8 | odd | 4 | 3380.2.f.j.3041.9 | 18 | |||
13.12 | even | 2 | 3380.2.a.s.1.5 | yes | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3380.2.a.r.1.5 | ✓ | 9 | 1.1 | even | 1 | trivial | |
3380.2.a.s.1.5 | yes | 9 | 13.12 | even | 2 | ||
3380.2.f.j.3041.9 | 18 | 13.8 | odd | 4 | |||
3380.2.f.j.3041.10 | 18 | 13.5 | odd | 4 |