Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4225,2,Mod(1,4225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4225 = 5^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4225.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: | \(33.7367948540\) |
Analytic rank: | \(1\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 26x^{16} + 281x^{14} - 1632x^{12} + 5482x^{10} - 10620x^{8} + 11052x^{6} - 5165x^{4} + 760x^{2} - 29 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 845) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-0.242854\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.242854 | −0.171724 | −0.0858619 | − | 0.996307i | \(-0.527364\pi\) | ||||
−0.0858619 | + | 0.996307i | \(0.527364\pi\) | |||||||
\(3\) | 1.19348 | 0.689053 | 0.344527 | − | 0.938777i | \(-0.388039\pi\) | ||||
0.344527 | + | 0.938777i | \(0.388039\pi\) | |||||||
\(4\) | −1.94102 | −0.970511 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.289840 | −0.118327 | ||||||||
\(7\) | 4.78046 | 1.80684 | 0.903422 | − | 0.428753i | \(-0.141047\pi\) | ||||
0.903422 | + | 0.428753i | \(0.141047\pi\) | |||||||
\(8\) | 0.957093 | 0.338383 | ||||||||
\(9\) | −1.57562 | −0.525205 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.30170 | 0.392479 | 0.196239 | − | 0.980556i | \(-0.437127\pi\) | ||||
0.196239 | + | 0.980556i | \(0.437127\pi\) | |||||||
\(12\) | −2.31656 | −0.668734 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.16095 | −0.310278 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.64961 | 0.912402 | ||||||||
\(17\) | −5.83916 | −1.41620 | −0.708102 | − | 0.706110i | \(-0.750448\pi\) | ||||
−0.708102 | + | 0.706110i | \(0.750448\pi\) | |||||||
\(18\) | 0.382645 | 0.0901902 | ||||||||
\(19\) | −4.27490 | −0.980729 | −0.490365 | − | 0.871517i | \(-0.663136\pi\) | ||||
−0.490365 | + | 0.871517i | \(0.663136\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.70536 | 1.24501 | ||||||||
\(22\) | −0.316124 | −0.0673979 | ||||||||
\(23\) | −4.13523 | −0.862255 | −0.431127 | − | 0.902291i | \(-0.641884\pi\) | ||||
−0.431127 | + | 0.902291i | \(0.641884\pi\) | |||||||
\(24\) | 1.14227 | 0.233164 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.46089 | −1.05095 | ||||||||
\(28\) | −9.27898 | −1.75356 | ||||||||
\(29\) | −3.08654 | −0.573156 | −0.286578 | − | 0.958057i | \(-0.592518\pi\) | ||||
−0.286578 | + | 0.958057i | \(0.592518\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.43011 | 0.975277 | 0.487639 | − | 0.873046i | \(-0.337858\pi\) | ||||
0.487639 | + | 0.873046i | \(0.337858\pi\) | |||||||
\(32\) | −2.80051 | −0.495065 | ||||||||
\(33\) | 1.55355 | 0.270439 | ||||||||
\(34\) | 1.41806 | 0.243196 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.05831 | 0.509718 | ||||||||
\(37\) | −4.84188 | −0.796000 | −0.398000 | − | 0.917385i | \(-0.630296\pi\) | ||||
−0.398000 | + | 0.917385i | \(0.630296\pi\) | |||||||
\(38\) | 1.03818 | 0.168414 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.00178 | −1.24967 | −0.624834 | − | 0.780757i | \(-0.714833\pi\) | ||||
−0.624834 | + | 0.780757i | \(0.714833\pi\) | |||||||
\(42\) | −1.38557 | −0.213798 | ||||||||
\(43\) | −2.70433 | −0.412406 | −0.206203 | − | 0.978509i | \(-0.566111\pi\) | ||||
−0.206203 | + | 0.978509i | \(0.566111\pi\) | |||||||
\(44\) | −2.52664 | −0.380905 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00426 | 0.148070 | ||||||||
\(47\) | −6.31797 | −0.921570 | −0.460785 | − | 0.887512i | \(-0.652432\pi\) | ||||
−0.460785 | + | 0.887512i | \(0.652432\pi\) | |||||||
\(48\) | 4.35572 | 0.628694 | ||||||||
\(49\) | 15.8528 | 2.26468 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.96890 | −0.975841 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.506686 | 0.0695986 | 0.0347993 | − | 0.999394i | \(-0.488921\pi\) | ||||
0.0347993 | + | 0.999394i | \(0.488921\pi\) | |||||||
\(54\) | 1.32620 | 0.180473 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.57534 | 0.611406 | ||||||||
\(57\) | −5.10199 | −0.675775 | ||||||||
\(58\) | 0.749578 | 0.0984244 | ||||||||
\(59\) | −3.12373 | −0.406675 | −0.203337 | − | 0.979109i | \(-0.565179\pi\) | ||||
−0.203337 | + | 0.979109i | \(0.565179\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.79253 | −0.357547 | −0.178773 | − | 0.983890i | \(-0.557213\pi\) | ||||
−0.178773 | + | 0.983890i | \(0.557213\pi\) | |||||||
\(62\) | −1.31872 | −0.167478 | ||||||||
\(63\) | −7.53217 | −0.948964 | ||||||||
\(64\) | −6.61911 | −0.827388 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.377287 | −0.0464408 | ||||||||
\(67\) | 4.07096 | 0.497347 | 0.248673 | − | 0.968587i | \(-0.420005\pi\) | ||||
0.248673 | + | 0.968587i | \(0.420005\pi\) | |||||||
\(68\) | 11.3339 | 1.37444 | ||||||||
\(69\) | −4.93529 | −0.594140 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.18916 | −0.853196 | −0.426598 | − | 0.904441i | \(-0.640288\pi\) | ||||
−0.426598 | + | 0.904441i | \(0.640288\pi\) | |||||||
\(72\) | −1.50801 | −0.177721 | ||||||||
\(73\) | 5.23396 | 0.612589 | 0.306294 | − | 0.951937i | \(-0.400911\pi\) | ||||
0.306294 | + | 0.951937i | \(0.400911\pi\) | |||||||
\(74\) | 1.17587 | 0.136692 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.29767 | 0.951808 | ||||||||
\(77\) | 6.22275 | 0.709148 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.18371 | −0.808231 | −0.404116 | − | 0.914708i | \(-0.632421\pi\) | ||||
−0.404116 | + | 0.914708i | \(0.632421\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.79058 | −0.198954 | ||||||||
\(82\) | 1.94327 | 0.214598 | ||||||||
\(83\) | −9.99869 | −1.09750 | −0.548749 | − | 0.835987i | \(-0.684896\pi\) | ||||
−0.548749 | + | 0.835987i | \(0.684896\pi\) | |||||||
\(84\) | −11.0742 | −1.20830 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.656757 | 0.0708199 | ||||||||
\(87\) | −3.68371 | −0.394935 | ||||||||
\(88\) | 1.24585 | 0.132808 | ||||||||
\(89\) | 12.3735 | 1.31159 | 0.655794 | − | 0.754940i | \(-0.272334\pi\) | ||||
0.655794 | + | 0.754940i | \(0.272334\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.02657 | 0.836828 | ||||||||
\(93\) | 6.48071 | 0.672018 | ||||||||
\(94\) | 1.53434 | 0.158256 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.34234 | −0.341126 | ||||||||
\(97\) | 2.82773 | 0.287112 | 0.143556 | − | 0.989642i | \(-0.454146\pi\) | ||||
0.143556 | + | 0.989642i | \(0.454146\pi\) | |||||||
\(98\) | −3.84991 | −0.388900 | ||||||||
\(99\) | −2.05099 | −0.206132 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.36950 | 0.733293 | 0.366646 | − | 0.930360i | \(-0.380506\pi\) | ||||
0.366646 | + | 0.930360i | \(0.380506\pi\) | |||||||
\(102\) | 1.69242 | 0.167575 | ||||||||
\(103\) | 9.50730 | 0.936783 | 0.468391 | − | 0.883521i | \(-0.344834\pi\) | ||||
0.468391 | + | 0.883521i | \(0.344834\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.123051 | −0.0119517 | ||||||||
\(107\) | 5.15118 | 0.497984 | 0.248992 | − | 0.968506i | \(-0.419901\pi\) | ||||
0.248992 | + | 0.968506i | \(0.419901\pi\) | |||||||
\(108\) | 10.5997 | 1.01996 | ||||||||
\(109\) | −8.78837 | −0.841773 | −0.420887 | − | 0.907113i | \(-0.638281\pi\) | ||||
−0.420887 | + | 0.907113i | \(0.638281\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.77866 | −0.548486 | ||||||||
\(112\) | 17.4468 | 1.64857 | ||||||||
\(113\) | −12.2753 | −1.15477 | −0.577383 | − | 0.816473i | \(-0.695926\pi\) | ||||
−0.577383 | + | 0.816473i | \(0.695926\pi\) | |||||||
\(114\) | 1.23904 | 0.116047 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.99104 | 0.556254 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.758610 | 0.0698357 | ||||||||
\(119\) | −27.9139 | −2.55886 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.30556 | −0.845960 | ||||||||
\(122\) | 0.678177 | 0.0613992 | ||||||||
\(123\) | −9.54993 | −0.861088 | ||||||||
\(124\) | −10.5400 | −0.946517 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.82922 | 0.162960 | ||||||||
\(127\) | 12.5953 | 1.11766 | 0.558828 | − | 0.829284i | \(-0.311251\pi\) | ||||
0.558828 | + | 0.829284i | \(0.311251\pi\) | |||||||
\(128\) | 7.20849 | 0.637147 | ||||||||
\(129\) | −3.22755 | −0.284170 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.91530 | 0.342082 | 0.171041 | − | 0.985264i | \(-0.445287\pi\) | ||||
0.171041 | + | 0.985264i | \(0.445287\pi\) | |||||||
\(132\) | −3.01548 | −0.262464 | ||||||||
\(133\) | −20.4360 | −1.77202 | ||||||||
\(134\) | −0.988649 | −0.0854062 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.58862 | −0.479220 | ||||||||
\(137\) | −14.4959 | −1.23847 | −0.619233 | − | 0.785207i | \(-0.712556\pi\) | ||||
−0.619233 | + | 0.785207i | \(0.712556\pi\) | |||||||
\(138\) | 1.19856 | 0.102028 | ||||||||
\(139\) | 13.6934 | 1.16146 | 0.580730 | − | 0.814096i | \(-0.302767\pi\) | ||||
0.580730 | + | 0.814096i | \(0.302767\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.54034 | −0.635011 | ||||||||
\(142\) | 1.74592 | 0.146514 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −5.75038 | −0.479199 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.27109 | −0.105196 | ||||||||
\(147\) | 18.9199 | 1.56049 | ||||||||
\(148\) | 9.39819 | 0.772527 | ||||||||
\(149\) | −9.45832 | −0.774856 | −0.387428 | − | 0.921900i | \(-0.626636\pi\) | ||||
−0.387428 | + | 0.921900i | \(0.626636\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.59276 | −0.780648 | −0.390324 | − | 0.920678i | \(-0.627637\pi\) | ||||
−0.390324 | + | 0.920678i | \(0.627637\pi\) | |||||||
\(152\) | −4.09148 | −0.331863 | ||||||||
\(153\) | 9.20028 | 0.743798 | ||||||||
\(154\) | −1.51122 | −0.121778 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.8447 | 1.18473 | 0.592366 | − | 0.805669i | \(-0.298194\pi\) | ||||
0.592366 | + | 0.805669i | \(0.298194\pi\) | |||||||
\(158\) | 1.74459 | 0.138792 | ||||||||
\(159\) | 0.604717 | 0.0479572 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.7683 | −1.55796 | ||||||||
\(162\) | 0.434851 | 0.0341651 | ||||||||
\(163\) | 1.68754 | 0.132178 | 0.0660891 | − | 0.997814i | \(-0.478948\pi\) | ||||
0.0660891 | + | 0.997814i | \(0.478948\pi\) | |||||||
\(164\) | 15.5316 | 1.21282 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.42822 | 0.188467 | ||||||||
\(167\) | 10.4585 | 0.809305 | 0.404652 | − | 0.914471i | \(-0.367393\pi\) | ||||
0.404652 | + | 0.914471i | \(0.367393\pi\) | |||||||
\(168\) | 5.46056 | 0.421291 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.73560 | 0.515084 | ||||||||
\(172\) | 5.24916 | 0.400244 | ||||||||
\(173\) | −20.5699 | −1.56390 | −0.781950 | − | 0.623342i | \(-0.785775\pi\) | ||||
−0.781950 | + | 0.623342i | \(0.785775\pi\) | |||||||
\(174\) | 0.894603 | 0.0678197 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.75072 | 0.358099 | ||||||||
\(177\) | −3.72809 | −0.280221 | ||||||||
\(178\) | −3.00495 | −0.225231 | ||||||||
\(179\) | 19.8999 | 1.48739 | 0.743694 | − | 0.668520i | \(-0.233072\pi\) | ||||
0.743694 | + | 0.668520i | \(0.233072\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.55507 | −0.412905 | −0.206453 | − | 0.978457i | \(-0.566192\pi\) | ||||
−0.206453 | + | 0.978457i | \(0.566192\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.33281 | −0.246369 | ||||||||
\(184\) | −3.95780 | −0.291773 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.57387 | −0.115401 | ||||||||
\(187\) | −7.60087 | −0.555830 | ||||||||
\(188\) | 12.2633 | 0.894394 | ||||||||
\(189\) | −26.1055 | −1.89890 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.20413 | 0.521272 | 0.260636 | − | 0.965437i | \(-0.416068\pi\) | ||||
0.260636 | + | 0.965437i | \(0.416068\pi\) | |||||||
\(192\) | −7.89974 | −0.570115 | ||||||||
\(193\) | −4.46771 | −0.321593 | −0.160796 | − | 0.986988i | \(-0.551406\pi\) | ||||
−0.160796 | + | 0.986988i | \(0.551406\pi\) | |||||||
\(194\) | −0.686725 | −0.0493040 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −30.7706 | −2.19790 | ||||||||
\(197\) | −6.17342 | −0.439838 | −0.219919 | − | 0.975518i | \(-0.570579\pi\) | ||||
−0.219919 | + | 0.975518i | \(0.570579\pi\) | |||||||
\(198\) | 0.498091 | 0.0353978 | ||||||||
\(199\) | −0.734601 | −0.0520745 | −0.0260372 | − | 0.999661i | \(-0.508289\pi\) | ||||
−0.0260372 | + | 0.999661i | \(0.508289\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.85859 | 0.342698 | ||||||||
\(202\) | −1.78971 | −0.125924 | ||||||||
\(203\) | −14.7551 | −1.03560 | ||||||||
\(204\) | 13.5268 | 0.947064 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.30889 | −0.160868 | ||||||||
\(207\) | 6.51553 | 0.452861 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.56466 | −0.384915 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.6319 | −1.62689 | −0.813443 | − | 0.581644i | \(-0.802410\pi\) | ||||
−0.813443 | + | 0.581644i | \(0.802410\pi\) | |||||||
\(212\) | −0.983488 | −0.0675462 | ||||||||
\(213\) | −8.58008 | −0.587898 | ||||||||
\(214\) | −1.25099 | −0.0855156 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.22658 | −0.355623 | ||||||||
\(217\) | 25.9584 | 1.76217 | ||||||||
\(218\) | 2.13429 | 0.144552 | ||||||||
\(219\) | 6.24660 | 0.422106 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.40337 | 0.0941881 | ||||||||
\(223\) | 18.7656 | 1.25664 | 0.628320 | − | 0.777955i | \(-0.283743\pi\) | ||||
0.628320 | + | 0.777955i | \(0.283743\pi\) | |||||||
\(224\) | −13.3877 | −0.894504 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.98111 | 0.198301 | ||||||||
\(227\) | 18.2444 | 1.21092 | 0.605461 | − | 0.795875i | \(-0.292989\pi\) | ||||
0.605461 | + | 0.795875i | \(0.292989\pi\) | |||||||
\(228\) | 9.90307 | 0.655847 | ||||||||
\(229\) | −5.07143 | −0.335130 | −0.167565 | − | 0.985861i | \(-0.553590\pi\) | ||||
−0.167565 | + | 0.985861i | \(0.553590\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.42670 | 0.488641 | ||||||||
\(232\) | −2.95410 | −0.193946 | ||||||||
\(233\) | −30.1285 | −1.97379 | −0.986893 | − | 0.161374i | \(-0.948408\pi\) | ||||
−0.986893 | + | 0.161374i | \(0.948408\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.06323 | 0.394682 | ||||||||
\(237\) | −8.57359 | −0.556914 | ||||||||
\(238\) | 6.77900 | 0.439417 | ||||||||
\(239\) | −7.85492 | −0.508092 | −0.254046 | − | 0.967192i | \(-0.581762\pi\) | ||||
−0.254046 | + | 0.967192i | \(0.581762\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.1490 | −1.81324 | −0.906619 | − | 0.421949i | \(-0.861346\pi\) | ||||
−0.906619 | + | 0.421949i | \(0.861346\pi\) | |||||||
\(242\) | 2.25989 | 0.145271 | ||||||||
\(243\) | 14.2456 | 0.913858 | ||||||||
\(244\) | 5.42036 | 0.347003 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.31924 | 0.147869 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 5.19712 | 0.330018 | ||||||||
\(249\) | −11.9332 | −0.756235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.9594 | −1.44918 | −0.724592 | − | 0.689178i | \(-0.757972\pi\) | ||||
−0.724592 | + | 0.689178i | \(0.757972\pi\) | |||||||
\(252\) | 14.6201 | 0.920980 | ||||||||
\(253\) | −5.38285 | −0.338417 | ||||||||
\(254\) | −3.05883 | −0.191928 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.4876 | 0.717975 | ||||||||
\(257\) | −18.1164 | −1.13007 | −0.565034 | − | 0.825068i | \(-0.691137\pi\) | ||||
−0.565034 | + | 0.825068i | \(0.691137\pi\) | |||||||
\(258\) | 0.783823 | 0.0487987 | ||||||||
\(259\) | −23.1464 | −1.43825 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.86320 | 0.301024 | ||||||||
\(262\) | −0.950847 | −0.0587435 | ||||||||
\(263\) | 6.49275 | 0.400360 | 0.200180 | − | 0.979759i | \(-0.435847\pi\) | ||||
0.200180 | + | 0.979759i | \(0.435847\pi\) | |||||||
\(264\) | 1.48689 | 0.0915120 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.96296 | 0.304299 | ||||||||
\(267\) | 14.7675 | 0.903754 | ||||||||
\(268\) | −7.90182 | −0.482680 | ||||||||
\(269\) | 13.5473 | 0.825995 | 0.412998 | − | 0.910732i | \(-0.364482\pi\) | ||||
0.412998 | + | 0.910732i | \(0.364482\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.147908 | 0.00898478 | 0.00449239 | − | 0.999990i | \(-0.498570\pi\) | ||||
0.00449239 | + | 0.999990i | \(0.498570\pi\) | |||||||
\(272\) | −21.3107 | −1.29215 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.52038 | 0.212674 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 9.57952 | 0.576619 | ||||||||
\(277\) | −21.1703 | −1.27200 | −0.636000 | − | 0.771689i | \(-0.719412\pi\) | ||||
−0.636000 | + | 0.771689i | \(0.719412\pi\) | |||||||
\(278\) | −3.32550 | −0.199450 | ||||||||
\(279\) | −8.55577 | −0.512221 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.918162 | −0.0547729 | −0.0273865 | − | 0.999625i | \(-0.508718\pi\) | ||||
−0.0273865 | + | 0.999625i | \(0.508718\pi\) | |||||||
\(282\) | 1.83120 | 0.109046 | ||||||||
\(283\) | −7.38223 | −0.438828 | −0.219414 | − | 0.975632i | \(-0.570415\pi\) | ||||
−0.219414 | + | 0.975632i | \(0.570415\pi\) | |||||||
\(284\) | 13.9543 | 0.828036 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −38.2522 | −2.25796 | ||||||||
\(288\) | 4.41253 | 0.260011 | ||||||||
\(289\) | 17.0958 | 1.00564 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.37482 | 0.197836 | ||||||||
\(292\) | −10.1592 | −0.594524 | ||||||||
\(293\) | −8.29377 | −0.484527 | −0.242264 | − | 0.970210i | \(-0.577890\pi\) | ||||
−0.242264 | + | 0.970210i | \(0.577890\pi\) | |||||||
\(294\) | −4.59478 | −0.267973 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.63413 | −0.269353 | ||||||||
\(297\) | −7.10846 | −0.412475 | ||||||||
\(298\) | 2.29699 | 0.133061 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.9279 | −0.745153 | ||||||||
\(302\) | 2.32964 | 0.134056 | ||||||||
\(303\) | 8.79532 | 0.505278 | ||||||||
\(304\) | −15.6017 | −0.894820 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.23432 | −0.127728 | ||||||||
\(307\) | −21.1166 | −1.20519 | −0.602595 | − | 0.798047i | \(-0.705867\pi\) | ||||
−0.602595 | + | 0.798047i | \(0.705867\pi\) | |||||||
\(308\) | −12.0785 | −0.688236 | ||||||||
\(309\) | 11.3467 | 0.645493 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.7664 | 0.780623 | 0.390311 | − | 0.920683i | \(-0.372367\pi\) | ||||
0.390311 | + | 0.920683i | \(0.372367\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.5602 | −0.766469 | −0.383234 | − | 0.923651i | \(-0.625190\pi\) | ||||
−0.383234 | + | 0.923651i | \(0.625190\pi\) | |||||||
\(314\) | −3.60509 | −0.203447 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.9437 | 0.784397 | ||||||||
\(317\) | 18.9348 | 1.06348 | 0.531741 | − | 0.846907i | \(-0.321538\pi\) | ||||
0.531741 | + | 0.846907i | \(0.321538\pi\) | |||||||
\(318\) | −0.146858 | −0.00823538 | ||||||||
\(319\) | −4.01776 | −0.224951 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.14781 | 0.343137 | ||||||||
\(322\) | 4.80081 | 0.267539 | ||||||||
\(323\) | 24.9618 | 1.38891 | ||||||||
\(324\) | 3.47556 | 0.193087 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.409825 | −0.0226981 | ||||||||
\(327\) | −10.4887 | −0.580027 | ||||||||
\(328\) | −7.65845 | −0.422867 | ||||||||
\(329\) | −30.2028 | −1.66513 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.6678 | −0.916144 | −0.458072 | − | 0.888915i | \(-0.651460\pi\) | ||||
−0.458072 | + | 0.888915i | \(0.651460\pi\) | |||||||
\(332\) | 19.4077 | 1.06513 | ||||||||
\(333\) | 7.62894 | 0.418063 | ||||||||
\(334\) | −2.53989 | −0.138977 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 20.8223 | 1.13595 | ||||||||
\(337\) | −26.1775 | −1.42598 | −0.712990 | − | 0.701174i | \(-0.752659\pi\) | ||||
−0.712990 | + | 0.701174i | \(0.752659\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.6503 | −0.795696 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.06840 | 0.382776 | ||||||||
\(342\) | −1.63577 | −0.0884522 | ||||||||
\(343\) | 42.3204 | 2.28509 | ||||||||
\(344\) | −2.58829 | −0.139551 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.99548 | 0.268559 | ||||||||
\(347\) | −12.5193 | −0.672074 | −0.336037 | − | 0.941849i | \(-0.609087\pi\) | ||||
−0.336037 | + | 0.941849i | \(0.609087\pi\) | |||||||
\(348\) | 7.15015 | 0.383289 | ||||||||
\(349\) | −4.30934 | −0.230674 | −0.115337 | − | 0.993326i | \(-0.536795\pi\) | ||||
−0.115337 | + | 0.993326i | \(0.536795\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.64544 | −0.194302 | ||||||||
\(353\) | −20.5555 | −1.09406 | −0.547031 | − | 0.837113i | \(-0.684242\pi\) | ||||
−0.547031 | + | 0.837113i | \(0.684242\pi\) | |||||||
\(354\) | 0.905383 | 0.0481205 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −24.0172 | −1.27291 | ||||||||
\(357\) | −33.3145 | −1.76319 | ||||||||
\(358\) | −4.83277 | −0.255420 | ||||||||
\(359\) | −4.73134 | −0.249710 | −0.124855 | − | 0.992175i | \(-0.539847\pi\) | ||||
−0.124855 | + | 0.992175i | \(0.539847\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.725234 | −0.0381702 | ||||||||
\(362\) | 1.34907 | 0.0709056 | ||||||||
\(363\) | −11.1060 | −0.582912 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.809387 | 0.0423073 | ||||||||
\(367\) | 13.7595 | 0.718240 | 0.359120 | − | 0.933291i | \(-0.383077\pi\) | ||||
0.359120 | + | 0.933291i | \(0.383077\pi\) | |||||||
\(368\) | −15.0920 | −0.786724 | ||||||||
\(369\) | 12.6077 | 0.656333 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.42219 | 0.125754 | ||||||||
\(372\) | −12.5792 | −0.652201 | ||||||||
\(373\) | 27.5451 | 1.42623 | 0.713117 | − | 0.701045i | \(-0.247283\pi\) | ||||
0.713117 | + | 0.701045i | \(0.247283\pi\) | |||||||
\(374\) | 1.84590 | 0.0954492 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.04688 | −0.311844 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 6.33984 | 0.326086 | ||||||||
\(379\) | 8.61694 | 0.442623 | 0.221311 | − | 0.975203i | \(-0.428966\pi\) | ||||
0.221311 | + | 0.975203i | \(0.428966\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.0322 | 0.770124 | ||||||||
\(382\) | −1.74955 | −0.0895149 | ||||||||
\(383\) | 26.2816 | 1.34292 | 0.671462 | − | 0.741039i | \(-0.265666\pi\) | ||||
0.671462 | + | 0.741039i | \(0.265666\pi\) | |||||||
\(384\) | 8.60316 | 0.439028 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.08500 | 0.0552251 | ||||||||
\(387\) | 4.26098 | 0.216598 | ||||||||
\(388\) | −5.48868 | −0.278646 | ||||||||
\(389\) | 32.3511 | 1.64027 | 0.820133 | − | 0.572173i | \(-0.193899\pi\) | ||||
0.820133 | + | 0.572173i | \(0.193899\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.1463 | 1.22113 | ||||||||
\(392\) | 15.1726 | 0.766332 | ||||||||
\(393\) | 4.67282 | 0.235713 | ||||||||
\(394\) | 1.49924 | 0.0755306 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.98101 | 0.200053 | ||||||||
\(397\) | −0.377739 | −0.0189582 | −0.00947909 | − | 0.999955i | \(-0.503017\pi\) | ||||
−0.00947909 | + | 0.999955i | \(0.503017\pi\) | |||||||
\(398\) | 0.178401 | 0.00894242 | ||||||||
\(399\) | −24.3898 | −1.22102 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.2378 | −1.11050 | −0.555252 | − | 0.831682i | \(-0.687378\pi\) | ||||
−0.555252 | + | 0.831682i | \(0.687378\pi\) | |||||||
\(402\) | −1.17993 | −0.0588495 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −14.3044 | −0.711669 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.58333 | 0.177838 | ||||||||
\(407\) | −6.30270 | −0.312413 | ||||||||
\(408\) | −6.66988 | −0.330208 | ||||||||
\(409\) | −22.6239 | −1.11868 | −0.559341 | − | 0.828938i | \(-0.688946\pi\) | ||||
−0.559341 | + | 0.828938i | \(0.688946\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.3005 | −0.853369 | ||||||||
\(412\) | −18.4539 | −0.909158 | ||||||||
\(413\) | −14.9329 | −0.734798 | ||||||||
\(414\) | −1.58232 | −0.0777670 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.3428 | 0.800308 | ||||||||
\(418\) | 1.35140 | 0.0660991 | ||||||||
\(419\) | −40.2612 | −1.96689 | −0.983444 | − | 0.181212i | \(-0.941998\pi\) | ||||
−0.983444 | + | 0.181212i | \(0.941998\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.3027 | 1.76929 | 0.884644 | − | 0.466268i | \(-0.154402\pi\) | ||||
0.884644 | + | 0.466268i | \(0.154402\pi\) | |||||||
\(422\) | 5.73910 | 0.279375 | ||||||||
\(423\) | 9.95469 | 0.484014 | ||||||||
\(424\) | 0.484945 | 0.0235510 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.08371 | 0.100956 | ||||||||
\(427\) | −13.3496 | −0.646031 | ||||||||
\(428\) | −9.99856 | −0.483299 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37.0989 | −1.78699 | −0.893495 | − | 0.449073i | \(-0.851754\pi\) | ||||
−0.893495 | + | 0.449073i | \(0.851754\pi\) | |||||||
\(432\) | −19.9301 | −0.958888 | ||||||||
\(433\) | 33.0641 | 1.58896 | 0.794480 | − | 0.607290i | \(-0.207744\pi\) | ||||
0.794480 | + | 0.607290i | \(0.207744\pi\) | |||||||
\(434\) | −6.30411 | −0.302607 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.0584 | 0.816950 | ||||||||
\(437\) | 17.6777 | 0.845639 | ||||||||
\(438\) | −1.51701 | −0.0724857 | ||||||||
\(439\) | 9.86163 | 0.470670 | 0.235335 | − | 0.971914i | \(-0.424381\pi\) | ||||
0.235335 | + | 0.971914i | \(0.424381\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −24.9779 | −1.18942 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.9028 | 1.13566 | 0.567828 | − | 0.823147i | \(-0.307784\pi\) | ||||
0.567828 | + | 0.823147i | \(0.307784\pi\) | |||||||
\(444\) | 11.2165 | 0.532312 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.55731 | −0.215795 | ||||||||
\(447\) | −11.2883 | −0.533917 | ||||||||
\(448\) | −31.6424 | −1.49496 | ||||||||
\(449\) | 15.5735 | 0.734957 | 0.367479 | − | 0.930032i | \(-0.380221\pi\) | ||||
0.367479 | + | 0.930032i | \(0.380221\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.4160 | −0.490468 | ||||||||
\(452\) | 23.8267 | 1.12071 | ||||||||
\(453\) | −11.4487 | −0.537908 | ||||||||
\(454\) | −4.43072 | −0.207944 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.88308 | −0.228671 | ||||||||
\(457\) | 32.5970 | 1.52483 | 0.762413 | − | 0.647091i | \(-0.224015\pi\) | ||||
0.762413 | + | 0.647091i | \(0.224015\pi\) | |||||||
\(458\) | 1.23162 | 0.0575497 | ||||||||
\(459\) | 31.8870 | 1.48836 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.2984 | 0.479644 | 0.239822 | − | 0.970817i | \(-0.422911\pi\) | ||||
0.239822 | + | 0.970817i | \(0.422911\pi\) | |||||||
\(462\) | −1.80360 | −0.0839112 | ||||||||
\(463\) | 2.97479 | 0.138250 | 0.0691251 | − | 0.997608i | \(-0.477979\pi\) | ||||
0.0691251 | + | 0.997608i | \(0.477979\pi\) | |||||||
\(464\) | −11.2647 | −0.522949 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.31684 | 0.338946 | ||||||||
\(467\) | 34.9628 | 1.61789 | 0.808943 | − | 0.587887i | \(-0.200040\pi\) | ||||
0.808943 | + | 0.587887i | \(0.200040\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.4611 | 0.898628 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.7167 | 0.816344 | ||||||||
\(472\) | −2.98970 | −0.137612 | ||||||||
\(473\) | −3.52024 | −0.161861 | ||||||||
\(474\) | 2.08213 | 0.0956354 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 54.1814 | 2.48340 | ||||||||
\(477\) | −0.798342 | −0.0365536 | ||||||||
\(478\) | 1.90760 | 0.0872515 | ||||||||
\(479\) | −13.7338 | −0.627511 | −0.313756 | − | 0.949504i | \(-0.601587\pi\) | ||||
−0.313756 | + | 0.949504i | \(0.601587\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 6.83611 | 0.311376 | ||||||||
\(483\) | −23.5930 | −1.07352 | ||||||||
\(484\) | 18.0623 | 0.821014 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −3.45961 | −0.156931 | ||||||||
\(487\) | 39.4097 | 1.78582 | 0.892911 | − | 0.450233i | \(-0.148659\pi\) | ||||
0.892911 | + | 0.450233i | \(0.148659\pi\) | |||||||
\(488\) | −2.67271 | −0.120988 | ||||||||
\(489\) | 2.01404 | 0.0910778 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.97696 | 0.179477 | 0.0897387 | − | 0.995965i | \(-0.471397\pi\) | ||||
0.0897387 | + | 0.995965i | \(0.471397\pi\) | |||||||
\(492\) | 18.5366 | 0.835696 | ||||||||
\(493\) | 18.0228 | 0.811706 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 19.8178 | 0.889845 | ||||||||
\(497\) | −34.3675 | −1.54159 | ||||||||
\(498\) | 2.89802 | 0.129864 | ||||||||
\(499\) | −4.86965 | −0.217996 | −0.108998 | − | 0.994042i | \(-0.534764\pi\) | ||||
−0.108998 | + | 0.994042i | \(0.534764\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.4820 | 0.557654 | ||||||||
\(502\) | 5.57578 | 0.248859 | ||||||||
\(503\) | 12.6904 | 0.565836 | 0.282918 | − | 0.959144i | \(-0.408698\pi\) | ||||
0.282918 | + | 0.959144i | \(0.408698\pi\) | |||||||
\(504\) | −7.20899 | −0.321114 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.30725 | 0.0581142 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −24.4478 | −1.08470 | ||||||||
\(509\) | 14.6745 | 0.650434 | 0.325217 | − | 0.945639i | \(-0.394563\pi\) | ||||
0.325217 | + | 0.945639i | \(0.394563\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.0207 | 1.10685 | ||||||||
\(512\) | −17.2068 | −0.760440 | ||||||||
\(513\) | 23.3447 | 1.03070 | ||||||||
\(514\) | 4.39963 | 0.194059 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6.26474 | 0.275790 | ||||||||
\(517\) | −8.22413 | −0.361697 | ||||||||
\(518\) | 5.62120 | 0.246981 | ||||||||
\(519\) | −24.5496 | −1.07761 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.04993 | 0.265052 | 0.132526 | − | 0.991180i | \(-0.457691\pi\) | ||||
0.132526 | + | 0.991180i | \(0.457691\pi\) | |||||||
\(522\) | −1.18105 | −0.0516930 | ||||||||
\(523\) | 28.2967 | 1.23733 | 0.618664 | − | 0.785655i | \(-0.287674\pi\) | ||||
0.618664 | + | 0.785655i | \(0.287674\pi\) | |||||||
\(524\) | −7.59969 | −0.331994 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.57679 | −0.0687514 | ||||||||
\(527\) | −31.7073 | −1.38119 | ||||||||
\(528\) | 5.66986 | 0.246749 | ||||||||
\(529\) | −5.89988 | −0.256516 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.92180 | 0.213588 | ||||||||
\(532\) | 39.6667 | 1.71977 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3.58634 | −0.155196 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.89629 | 0.168294 | ||||||||
\(537\) | 23.7501 | 1.02489 | ||||||||
\(538\) | −3.29002 | −0.141843 | ||||||||
\(539\) | 20.6357 | 0.888841 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.32246 | −0.271824 | −0.135912 | − | 0.990721i | \(-0.543396\pi\) | ||||
−0.135912 | + | 0.990721i | \(0.543396\pi\) | |||||||
\(542\) | −0.0359201 | −0.00154290 | ||||||||
\(543\) | −6.62984 | −0.284514 | ||||||||
\(544\) | 16.3526 | 0.701113 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.21492 | 0.180217 | 0.0901084 | − | 0.995932i | \(-0.471279\pi\) | ||||
0.0901084 | + | 0.995932i | \(0.471279\pi\) | |||||||
\(548\) | 28.1368 | 1.20195 | ||||||||
\(549\) | 4.39995 | 0.187785 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.1946 | 0.562110 | ||||||||
\(552\) | −4.72354 | −0.201047 | ||||||||
\(553\) | −34.3415 | −1.46035 | ||||||||
\(554\) | 5.14129 | 0.218433 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −26.5792 | −1.12721 | ||||||||
\(557\) | 18.3347 | 0.776867 | 0.388434 | − | 0.921477i | \(-0.373016\pi\) | ||||
0.388434 | + | 0.921477i | \(0.373016\pi\) | |||||||
\(558\) | 2.07780 | 0.0879605 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.07145 | −0.382997 | ||||||||
\(562\) | 0.222979 | 0.00940581 | ||||||||
\(563\) | 13.2135 | 0.556884 | 0.278442 | − | 0.960453i | \(-0.410182\pi\) | ||||
0.278442 | + | 0.960453i | \(0.410182\pi\) | |||||||
\(564\) | 14.6360 | 0.616285 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.79280 | 0.0753571 | ||||||||
\(567\) | −8.55982 | −0.359478 | ||||||||
\(568\) | −6.88069 | −0.288707 | ||||||||
\(569\) | −25.3262 | −1.06173 | −0.530865 | − | 0.847457i | \(-0.678133\pi\) | ||||
−0.530865 | + | 0.847457i | \(0.678133\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.47261 | −0.145324 | −0.0726621 | − | 0.997357i | \(-0.523149\pi\) | ||||
−0.0726621 | + | 0.997357i | \(0.523149\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.59795 | 0.359185 | ||||||||
\(574\) | 9.28970 | 0.387745 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 10.4292 | 0.434549 | ||||||||
\(577\) | −9.33439 | −0.388596 | −0.194298 | − | 0.980943i | \(-0.562243\pi\) | ||||
−0.194298 | + | 0.980943i | \(0.562243\pi\) | |||||||
\(578\) | −4.15178 | −0.172691 | ||||||||
\(579\) | −5.33210 | −0.221595 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −47.7983 | −1.98301 | ||||||||
\(582\) | −0.819590 | −0.0339731 | ||||||||
\(583\) | 0.659555 | 0.0273160 | ||||||||
\(584\) | 5.00939 | 0.207290 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.01418 | 0.0832048 | ||||||||
\(587\) | −14.4210 | −0.595218 | −0.297609 | − | 0.954688i | \(-0.596189\pi\) | ||||
−0.297609 | + | 0.954688i | \(0.596189\pi\) | |||||||
\(588\) | −36.7240 | −1.51447 | ||||||||
\(589\) | −23.2132 | −0.956483 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.36783 | −0.303072 | ||||||||
\(592\) | −17.6710 | −0.726272 | ||||||||
\(593\) | 19.2593 | 0.790883 | 0.395441 | − | 0.918491i | \(-0.370592\pi\) | ||||
0.395441 | + | 0.918491i | \(0.370592\pi\) | |||||||
\(594\) | 1.72632 | 0.0708317 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 18.3588 | 0.752006 | ||||||||
\(597\) | −0.876728 | −0.0358821 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.3956 | 1.44623 | 0.723113 | − | 0.690730i | \(-0.242711\pi\) | ||||
0.723113 | + | 0.690730i | \(0.242711\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.2161 | −0.498305 | −0.249152 | − | 0.968464i | \(-0.580152\pi\) | ||||
−0.249152 | + | 0.968464i | \(0.580152\pi\) | |||||||
\(602\) | 3.13960 | 0.127960 | ||||||||
\(603\) | −6.41427 | −0.261209 | ||||||||
\(604\) | 18.6198 | 0.757628 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.13598 | −0.0867682 | ||||||||
\(607\) | −0.852469 | −0.0346007 | −0.0173003 | − | 0.999850i | \(-0.505507\pi\) | ||||
−0.0173003 | + | 0.999850i | \(0.505507\pi\) | |||||||
\(608\) | 11.9719 | 0.485524 | ||||||||
\(609\) | −17.6098 | −0.713585 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −17.8579 | −0.721864 | ||||||||
\(613\) | −23.2544 | −0.939234 | −0.469617 | − | 0.882870i | \(-0.655608\pi\) | ||||
−0.469617 | + | 0.882870i | \(0.655608\pi\) | |||||||
\(614\) | 5.12826 | 0.206960 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.95575 | 0.239964 | ||||||||
\(617\) | −35.4404 | −1.42678 | −0.713388 | − | 0.700770i | \(-0.752840\pi\) | ||||
−0.713388 | + | 0.700770i | \(0.752840\pi\) | |||||||
\(618\) | −2.75560 | −0.110846 | ||||||||
\(619\) | −1.77450 | −0.0713232 | −0.0356616 | − | 0.999364i | \(-0.511354\pi\) | ||||
−0.0356616 | + | 0.999364i | \(0.511354\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22.5820 | 0.906185 | ||||||||
\(622\) | −3.34323 | −0.134051 | ||||||||
\(623\) | 59.1510 | 2.36984 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.29315 | 0.131621 | ||||||||
\(627\) | −6.64128 | −0.265227 | ||||||||
\(628\) | −28.8138 | −1.14980 | ||||||||
\(629\) | 28.2725 | 1.12730 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.678894 | −0.0270263 | −0.0135132 | − | 0.999909i | \(-0.504302\pi\) | ||||
−0.0135132 | + | 0.999909i | \(0.504302\pi\) | |||||||
\(632\) | −6.87548 | −0.273492 | ||||||||
\(633\) | −28.2041 | −1.12101 | ||||||||
\(634\) | −4.59839 | −0.182625 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.17377 | −0.0465430 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.975729 | 0.0386295 | ||||||||
\(639\) | 11.3274 | 0.448103 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.5481 | −1.36457 | −0.682283 | − | 0.731088i | \(-0.739013\pi\) | ||||
−0.682283 | + | 0.731088i | \(0.739013\pi\) | |||||||
\(642\) | −1.49302 | −0.0589248 | ||||||||
\(643\) | −11.3200 | −0.446418 | −0.223209 | − | 0.974771i | \(-0.571653\pi\) | ||||
−0.223209 | + | 0.974771i | \(0.571653\pi\) | |||||||
\(644\) | 38.3707 | 1.51202 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.06208 | −0.238509 | ||||||||
\(647\) | −8.22475 | −0.323348 | −0.161674 | − | 0.986844i | \(-0.551689\pi\) | ||||
−0.161674 | + | 0.986844i | \(0.551689\pi\) | |||||||
\(648\) | −1.71376 | −0.0673227 | ||||||||
\(649\) | −4.06617 | −0.159611 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 30.9808 | 1.21423 | ||||||||
\(652\) | −3.27555 | −0.128280 | ||||||||
\(653\) | 5.22441 | 0.204447 | 0.102223 | − | 0.994761i | \(-0.467404\pi\) | ||||
0.102223 | + | 0.994761i | \(0.467404\pi\) | |||||||
\(654\) | 2.54722 | 0.0996043 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −29.2034 | −1.14020 | ||||||||
\(657\) | −8.24671 | −0.321735 | ||||||||
\(658\) | 7.33487 | 0.285943 | ||||||||
\(659\) | −21.1150 | −0.822525 | −0.411263 | − | 0.911517i | \(-0.634912\pi\) | ||||
−0.411263 | + | 0.911517i | \(0.634912\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.52692 | −0.0593904 | −0.0296952 | − | 0.999559i | \(-0.509454\pi\) | ||||
−0.0296952 | + | 0.999559i | \(0.509454\pi\) | |||||||
\(662\) | 4.04784 | 0.157324 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.56968 | −0.371375 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.85272 | −0.0717914 | ||||||||
\(667\) | 12.7635 | 0.494206 | ||||||||
\(668\) | −20.3002 | −0.785439 | ||||||||
\(669\) | 22.3963 | 0.865892 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.63505 | −0.140329 | ||||||||
\(672\) | −15.9779 | −0.616361 | ||||||||
\(673\) | 7.81728 | 0.301334 | 0.150667 | − | 0.988585i | \(-0.451858\pi\) | ||||
0.150667 | + | 0.988585i | \(0.451858\pi\) | |||||||
\(674\) | 6.35731 | 0.244875 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.8535 | 0.878332 | 0.439166 | − | 0.898406i | \(-0.355274\pi\) | ||||
0.439166 | + | 0.898406i | \(0.355274\pi\) | |||||||
\(678\) | 3.55789 | 0.136640 | ||||||||
\(679\) | 13.5178 | 0.518767 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.7742 | 0.834391 | ||||||||
\(682\) | −1.71659 | −0.0657316 | ||||||||
\(683\) | 30.7945 | 1.17832 | 0.589160 | − | 0.808016i | \(-0.299459\pi\) | ||||
0.589160 | + | 0.808016i | \(0.299459\pi\) | |||||||
\(684\) | −13.0740 | −0.499895 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10.2777 | −0.392404 | ||||||||
\(687\) | −6.05263 | −0.230922 | ||||||||
\(688\) | −9.86974 | −0.376280 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.1778 | 1.18606 | 0.593030 | − | 0.805180i | \(-0.297931\pi\) | ||||
0.593030 | + | 0.805180i | \(0.297931\pi\) | |||||||
\(692\) | 39.9266 | 1.51778 | ||||||||
\(693\) | −9.80466 | −0.372448 | ||||||||
\(694\) | 3.04037 | 0.115411 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.52565 | −0.133639 | ||||||||
\(697\) | 46.7237 | 1.76979 | ||||||||
\(698\) | 1.04654 | 0.0396121 | ||||||||
\(699\) | −35.9577 | −1.36004 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.7533 | 1.61477 | 0.807385 | − | 0.590025i | \(-0.200882\pi\) | ||||
0.807385 | + | 0.590025i | \(0.200882\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.6985 | 0.780660 | ||||||||
\(704\) | −8.61612 | −0.324732 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.99200 | 0.187876 | ||||||||
\(707\) | 35.2296 | 1.32495 | ||||||||
\(708\) | 7.23631 | 0.271957 | ||||||||
\(709\) | 7.54090 | 0.283204 | 0.141602 | − | 0.989924i | \(-0.454775\pi\) | ||||
0.141602 | + | 0.989924i | \(0.454775\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.3188 | 0.424487 | ||||||||
\(712\) | 11.8426 | 0.443820 | ||||||||
\(713\) | −22.4548 | −0.840937 | ||||||||
\(714\) | 8.09057 | 0.302782 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −38.6262 | −1.44353 | ||||||||
\(717\) | −9.37465 | −0.350103 | ||||||||
\(718\) | 1.14902 | 0.0428812 | ||||||||
\(719\) | 32.9984 | 1.23063 | 0.615316 | − | 0.788281i | \(-0.289029\pi\) | ||||
0.615316 | + | 0.788281i | \(0.289029\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 45.4493 | 1.69262 | ||||||||
\(722\) | 0.176126 | 0.00655473 | ||||||||
\(723\) | −33.5952 | −1.24942 | ||||||||
\(724\) | 10.7825 | 0.400729 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.69713 | 0.100100 | ||||||||
\(727\) | −31.2676 | −1.15965 | −0.579826 | − | 0.814741i | \(-0.696879\pi\) | ||||
−0.579826 | + | 0.814741i | \(0.696879\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.3736 | 0.828651 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.7910 | 0.584051 | ||||||||
\(732\) | 6.46906 | 0.239103 | ||||||||
\(733\) | −28.2677 | −1.04409 | −0.522046 | − | 0.852917i | \(-0.674831\pi\) | ||||
−0.522046 | + | 0.852917i | \(0.674831\pi\) | |||||||
\(734\) | −3.34155 | −0.123339 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11.5807 | 0.426872 | ||||||||
\(737\) | 5.29919 | 0.195198 | ||||||||
\(738\) | −3.06184 | −0.112708 | ||||||||
\(739\) | −38.1632 | −1.40385 | −0.701927 | − | 0.712249i | \(-0.747677\pi\) | ||||
−0.701927 | + | 0.712249i | \(0.747677\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.588239 | −0.0215949 | ||||||||
\(743\) | 5.93960 | 0.217903 | 0.108951 | − | 0.994047i | \(-0.465251\pi\) | ||||
0.108951 | + | 0.994047i | \(0.465251\pi\) | |||||||
\(744\) | 6.20264 | 0.227400 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −6.68945 | −0.244918 | ||||||||
\(747\) | 15.7541 | 0.576412 | ||||||||
\(748\) | 14.7534 | 0.539439 | ||||||||
\(749\) | 24.6250 | 0.899779 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.6332 | 0.825897 | 0.412948 | − | 0.910754i | \(-0.364499\pi\) | ||||
0.412948 | + | 0.910754i | \(0.364499\pi\) | |||||||
\(752\) | −23.0581 | −0.840843 | ||||||||
\(753\) | −27.4015 | −0.998565 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 50.6714 | 1.84290 | ||||||||
\(757\) | 40.2878 | 1.46429 | 0.732143 | − | 0.681151i | \(-0.238520\pi\) | ||||
0.732143 | + | 0.681151i | \(0.238520\pi\) | |||||||
\(758\) | −2.09266 | −0.0760088 | ||||||||
\(759\) | −6.42430 | −0.233187 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.7739 | 1.26055 | 0.630277 | − | 0.776371i | \(-0.282941\pi\) | ||||
0.630277 | + | 0.776371i | \(0.282941\pi\) | |||||||
\(762\) | −3.65064 | −0.132249 | ||||||||
\(763\) | −42.0124 | −1.52095 | ||||||||
\(764\) | −13.9834 | −0.505901 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.38258 | −0.230612 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 13.7102 | 0.494723 | ||||||||
\(769\) | 10.2840 | 0.370851 | 0.185425 | − | 0.982658i | \(-0.440634\pi\) | ||||
0.185425 | + | 0.982658i | \(0.440634\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.6214 | −0.778677 | ||||||||
\(772\) | 8.67192 | 0.312109 | ||||||||
\(773\) | −39.0773 | −1.40551 | −0.702757 | − | 0.711430i | \(-0.748048\pi\) | ||||
−0.702757 | + | 0.711430i | \(0.748048\pi\) | |||||||
\(774\) | −1.03480 | −0.0371950 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.70640 | 0.0971541 | ||||||||
\(777\) | −27.6247 | −0.991029 | ||||||||
\(778\) | −7.85660 | −0.281673 | ||||||||
\(779\) | 34.2068 | 1.22559 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.35816 | −0.334861 | ||||||||
\(782\) | −5.86402 | −0.209697 | ||||||||
\(783\) | 16.8552 | 0.602357 | ||||||||
\(784\) | 57.8565 | 2.06630 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.13481 | −0.0404774 | ||||||||
\(787\) | 31.9154 | 1.13766 | 0.568831 | − | 0.822454i | \(-0.307396\pi\) | ||||
0.568831 | + | 0.822454i | \(0.307396\pi\) | |||||||
\(788\) | 11.9827 | 0.426868 | ||||||||
\(789\) | 7.74894 | 0.275870 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −58.6817 | −2.08648 | ||||||||
\(792\) | −1.96299 | −0.0697517 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0.0917354 | 0.00325557 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.42588 | 0.0505388 | ||||||||
\(797\) | −23.7632 | −0.841737 | −0.420869 | − | 0.907122i | \(-0.638275\pi\) | ||||
−0.420869 | + | 0.907122i | \(0.638275\pi\) | |||||||
\(798\) | 5.92317 | 0.209678 | ||||||||
\(799\) | 36.8916 | 1.30513 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.4959 | −0.688853 | ||||||||
\(802\) | 5.40055 | 0.190700 | ||||||||
\(803\) | 6.81307 | 0.240428 | ||||||||
\(804\) | −9.43063 | −0.332593 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.1684 | 0.569155 | ||||||||
\(808\) | 7.05330 | 0.248134 | ||||||||
\(809\) | 22.9840 | 0.808076 | 0.404038 | − | 0.914742i | \(-0.367606\pi\) | ||||
0.404038 | + | 0.914742i | \(0.367606\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.1171 | −0.741520 | −0.370760 | − | 0.928729i | \(-0.620903\pi\) | ||||
−0.370760 | + | 0.928729i | \(0.620903\pi\) | |||||||
\(812\) | 28.6399 | 1.00506 | ||||||||
\(813\) | 0.176525 | 0.00619099 | ||||||||
\(814\) | 1.53064 | 0.0536487 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −25.4338 | −0.890359 | ||||||||
\(817\) | 11.5607 | 0.404459 | ||||||||
\(818\) | 5.49432 | 0.192104 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.7584 | −0.829175 | −0.414587 | − | 0.910010i | \(-0.636074\pi\) | ||||
−0.414587 | + | 0.910010i | \(0.636074\pi\) | |||||||
\(822\) | 4.20149 | 0.146544 | ||||||||
\(823\) | −41.8058 | −1.45726 | −0.728629 | − | 0.684908i | \(-0.759842\pi\) | ||||
−0.728629 | + | 0.684908i | \(0.759842\pi\) | |||||||
\(824\) | 9.09937 | 0.316992 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.62651 | 0.126182 | ||||||||
\(827\) | 4.92854 | 0.171382 | 0.0856910 | − | 0.996322i | \(-0.472690\pi\) | ||||
0.0856910 | + | 0.996322i | \(0.472690\pi\) | |||||||
\(828\) | −12.6468 | −0.439507 | ||||||||
\(829\) | −46.6538 | −1.62035 | −0.810177 | − | 0.586186i | \(-0.800629\pi\) | ||||
−0.810177 | + | 0.586186i | \(0.800629\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.2662 | −0.876476 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −92.5670 | −3.20726 | ||||||||
\(834\) | −3.96891 | −0.137432 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 10.8011 | 0.373565 | ||||||||
\(837\) | −29.6532 | −1.02497 | ||||||||
\(838\) | 9.77759 | 0.337761 | ||||||||
\(839\) | 9.95523 | 0.343693 | 0.171846 | − | 0.985124i | \(-0.445027\pi\) | ||||
0.171846 | + | 0.985124i | \(0.445027\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.4733 | −0.671493 | ||||||||
\(842\) | −8.81627 | −0.303829 | ||||||||
\(843\) | −1.09580 | −0.0377415 | ||||||||
\(844\) | 45.8700 | 1.57891 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.41754 | −0.0831167 | ||||||||
\(847\) | −44.4849 | −1.52852 | ||||||||
\(848\) | 1.84921 | 0.0635020 | ||||||||
\(849\) | −8.81051 | −0.302376 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.0223 | 0.686355 | ||||||||
\(852\) | 16.6541 | 0.570561 | ||||||||
\(853\) | −12.8126 | −0.438695 | −0.219348 | − | 0.975647i | \(-0.570393\pi\) | ||||
−0.219348 | + | 0.975647i | \(0.570393\pi\) | |||||||
\(854\) | 3.24200 | 0.110939 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.93016 | 0.168509 | ||||||||
\(857\) | −13.1145 | −0.447984 | −0.223992 | − | 0.974591i | \(-0.571909\pi\) | ||||
−0.223992 | + | 0.974591i | \(0.571909\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.9112 | 0.952317 | 0.476158 | − | 0.879359i | \(-0.342029\pi\) | ||||
0.476158 | + | 0.879359i | \(0.342029\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −45.6531 | −1.55585 | ||||||||
\(862\) | 9.00961 | 0.306869 | ||||||||
\(863\) | 17.9152 | 0.609842 | 0.304921 | − | 0.952378i | \(-0.401370\pi\) | ||||
0.304921 | + | 0.952378i | \(0.401370\pi\) | |||||||
\(864\) | 15.2933 | 0.520287 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −8.02975 | −0.272862 | ||||||||
\(867\) | 20.4034 | 0.692936 | ||||||||
\(868\) | −50.3859 | −1.71021 | ||||||||
\(869\) | −9.35108 | −0.317214 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −8.41129 | −0.284842 | ||||||||
\(873\) | −4.45541 | −0.150793 | ||||||||
\(874\) | −4.29310 | −0.145216 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.1248 | −0.409659 | ||||||||
\(877\) | −24.7957 | −0.837292 | −0.418646 | − | 0.908149i | \(-0.637495\pi\) | ||||
−0.418646 | + | 0.908149i | \(0.637495\pi\) | |||||||
\(878\) | −2.39494 | −0.0808252 | ||||||||
\(879\) | −9.89841 | −0.333865 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.5986 | −0.896130 | −0.448065 | − | 0.894001i | \(-0.647887\pi\) | ||||
−0.448065 | + | 0.894001i | \(0.647887\pi\) | |||||||
\(882\) | 6.06599 | 0.204252 | ||||||||
\(883\) | 11.1078 | 0.373808 | 0.186904 | − | 0.982378i | \(-0.440155\pi\) | ||||
0.186904 | + | 0.982378i | \(0.440155\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.80489 | −0.195019 | ||||||||
\(887\) | −4.20024 | −0.141030 | −0.0705152 | − | 0.997511i | \(-0.522464\pi\) | ||||
−0.0705152 | + | 0.997511i | \(0.522464\pi\) | |||||||
\(888\) | −5.53072 | −0.185599 | ||||||||
\(889\) | 60.2115 | 2.01943 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.33081 | −0.0780852 | ||||||||
\(892\) | −36.4245 | −1.21958 | ||||||||
\(893\) | 27.0087 | 0.903811 | ||||||||
\(894\) | 2.74140 | 0.0916862 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 34.4599 | 1.15122 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.78208 | −0.126210 | ||||||||
\(899\) | −16.7602 | −0.558985 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.95862 | −0.0985659 | ||||||||
\(902\) | 2.52956 | 0.0842251 | ||||||||
\(903\) | −15.4292 | −0.513450 | ||||||||
\(904\) | −11.7486 | −0.390754 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.78037 | 0.0923716 | ||||||||
\(907\) | 2.73644 | 0.0908621 | 0.0454311 | − | 0.998967i | \(-0.485534\pi\) | ||||
0.0454311 | + | 0.998967i | \(0.485534\pi\) | |||||||
\(908\) | −35.4128 | −1.17521 | ||||||||
\(909\) | −11.6115 | −0.385129 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.0840 | 1.09612 | 0.548061 | − | 0.836438i | \(-0.315366\pi\) | ||||
0.548061 | + | 0.836438i | \(0.315366\pi\) | |||||||
\(912\) | −18.6203 | −0.616579 | ||||||||
\(913\) | −13.0153 | −0.430745 | ||||||||
\(914\) | −7.91632 | −0.261849 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.84376 | 0.325247 | ||||||||
\(917\) | 18.7170 | 0.618088 | ||||||||
\(918\) | −7.74388 | −0.255586 | ||||||||
\(919\) | −25.5915 | −0.844185 | −0.422092 | − | 0.906553i | \(-0.638704\pi\) | ||||
−0.422092 | + | 0.906553i | \(0.638704\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.2022 | −0.830441 | ||||||||
\(922\) | −2.50100 | −0.0823662 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −14.4154 | −0.474231 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.722440 | −0.0237409 | ||||||||
\(927\) | −14.9799 | −0.492003 | ||||||||
\(928\) | 8.64387 | 0.283749 | ||||||||
\(929\) | 54.8425 | 1.79932 | 0.899661 | − | 0.436589i | \(-0.143813\pi\) | ||||
0.899661 | + | 0.436589i | \(0.143813\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −67.7691 | −2.22104 | ||||||||
\(932\) | 58.4802 | 1.91558 | ||||||||
\(933\) | 16.4299 | 0.537891 | ||||||||
\(934\) | −8.49086 | −0.277830 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −48.7703 | −1.59326 | −0.796629 | − | 0.604469i | \(-0.793385\pi\) | ||||
−0.796629 | + | 0.604469i | \(0.793385\pi\) | |||||||
\(938\) | −4.72619 | −0.154316 | ||||||||
\(939\) | −16.1838 | −0.528138 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.7281 | −0.936510 | −0.468255 | − | 0.883593i | \(-0.655117\pi\) | ||||
−0.468255 | + | 0.883593i | \(0.655117\pi\) | |||||||
\(942\) | −4.30258 | −0.140186 | ||||||||
\(943\) | 33.0892 | 1.07753 | ||||||||
\(944\) | −11.4004 | −0.371051 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.854903 | 0.0277953 | ||||||||
\(947\) | −44.2195 | −1.43694 | −0.718470 | − | 0.695558i | \(-0.755157\pi\) | ||||
−0.718470 | + | 0.695558i | \(0.755157\pi\) | |||||||
\(948\) | 16.6415 | 0.540491 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.5982 | 0.732796 | ||||||||
\(952\) | −26.7162 | −0.865876 | ||||||||
\(953\) | 10.9105 | 0.353426 | 0.176713 | − | 0.984262i | \(-0.443454\pi\) | ||||
0.176713 | + | 0.984262i | \(0.443454\pi\) | |||||||
\(954\) | 0.193881 | 0.00627712 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 15.2466 | 0.493109 | ||||||||
\(957\) | −4.79510 | −0.155004 | ||||||||
\(958\) | 3.33530 | 0.107759 | ||||||||
\(959\) | −69.2970 | −2.23772 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.51387 | −0.0488347 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.11629 | −0.261544 | ||||||||
\(964\) | 54.6379 | 1.75977 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 5.72965 | 0.184348 | ||||||||
\(967\) | 14.1899 | 0.456317 | 0.228159 | − | 0.973624i | \(-0.426729\pi\) | ||||
0.228159 | + | 0.973624i | \(0.426729\pi\) | |||||||
\(968\) | −8.90629 | −0.286259 | ||||||||
\(969\) | 29.7913 | 0.957035 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.308213 | 0.00989102 | 0.00494551 | − | 0.999988i | \(-0.498426\pi\) | ||||
0.00494551 | + | 0.999988i | \(0.498426\pi\) | |||||||
\(972\) | −27.6511 | −0.886909 | ||||||||
\(973\) | 65.4608 | 2.09858 | ||||||||
\(974\) | −9.57079 | −0.306668 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.1916 | −0.326226 | ||||||||
\(977\) | 5.50140 | 0.176005 | 0.0880027 | − | 0.996120i | \(-0.471952\pi\) | ||||
0.0880027 | + | 0.996120i | \(0.471952\pi\) | |||||||
\(978\) | −0.489117 | −0.0156402 | ||||||||
\(979\) | 16.1066 | 0.514771 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.8471 | 0.442104 | ||||||||
\(982\) | −0.965820 | −0.0308205 | ||||||||
\(983\) | 13.0306 | 0.415611 | 0.207805 | − | 0.978170i | \(-0.433368\pi\) | ||||
0.207805 | + | 0.978170i | \(0.433368\pi\) | |||||||
\(984\) | −9.14017 | −0.291378 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.37691 | −0.139389 | ||||||||
\(987\) | −36.0463 | −1.14737 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.1830 | 0.355599 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.85779 | 0.186079 | 0.0930393 | − | 0.995662i | \(-0.470342\pi\) | ||||
0.0930393 | + | 0.995662i | \(0.470342\pi\) | |||||||
\(992\) | −15.2071 | −0.482825 | ||||||||
\(993\) | −19.8926 | −0.631272 | ||||||||
\(994\) | 8.34628 | 0.264728 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 23.1626 | 0.733935 | ||||||||
\(997\) | 11.4851 | 0.363738 | 0.181869 | − | 0.983323i | \(-0.441785\pi\) | ||||
0.181869 | + | 0.983323i | \(0.441785\pi\) | |||||||
\(998\) | 1.18261 | 0.0374350 | ||||||||
\(999\) | 26.4409 | 0.836554 |
(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 | 4225.2.a.ca.1.9 | 18 | ||
5.2 | odd | 4 | 845.2.b.g.339.9 | ✓ | 18 | ||
5.3 | odd | 4 | 845.2.b.g.339.10 | yes | 18 | ||
5.4 | even | 2 | inner | 4225.2.a.ca.1.10 | 18 | ||
13.12 | even | 2 | 4225.2.a.cb.1.10 | 18 | |||
65.2 | even | 12 | 845.2.l.g.654.20 | 72 | |||
65.3 | odd | 12 | 845.2.n.i.529.9 | 36 | |||
65.7 | even | 12 | 845.2.l.g.699.17 | 72 | |||
65.8 | even | 4 | 845.2.d.e.844.18 | 36 | |||
65.12 | odd | 4 | 845.2.b.h.339.10 | yes | 18 | ||
65.17 | odd | 12 | 845.2.n.h.484.10 | 36 | |||
65.18 | even | 4 | 845.2.d.e.844.20 | 36 | |||
65.22 | odd | 12 | 845.2.n.i.484.9 | 36 | |||
65.23 | odd | 12 | 845.2.n.h.529.10 | 36 | |||
65.28 | even | 12 | 845.2.l.g.654.17 | 72 | |||
65.32 | even | 12 | 845.2.l.g.699.19 | 72 | |||
65.33 | even | 12 | 845.2.l.g.699.20 | 72 | |||
65.37 | even | 12 | 845.2.l.g.654.18 | 72 | |||
65.38 | odd | 4 | 845.2.b.h.339.9 | yes | 18 | ||
65.42 | odd | 12 | 845.2.n.i.529.10 | 36 | |||
65.43 | odd | 12 | 845.2.n.h.484.9 | 36 | |||
65.47 | even | 4 | 845.2.d.e.844.19 | 36 | |||
65.48 | odd | 12 | 845.2.n.i.484.10 | 36 | |||
65.57 | even | 4 | 845.2.d.e.844.17 | 36 | |||
65.58 | even | 12 | 845.2.l.g.699.18 | 72 | |||
65.62 | odd | 12 | 845.2.n.h.529.9 | 36 | |||
65.63 | even | 12 | 845.2.l.g.654.19 | 72 | |||
65.64 | even | 2 | 4225.2.a.cb.1.9 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
845.2.b.g.339.9 | ✓ | 18 | 5.2 | odd | 4 | ||
845.2.b.g.339.10 | yes | 18 | 5.3 | odd | 4 | ||
845.2.b.h.339.9 | yes | 18 | 65.38 | odd | 4 | ||
845.2.b.h.339.10 | yes | 18 | 65.12 | odd | 4 | ||
845.2.d.e.844.17 | 36 | 65.57 | even | 4 | |||
845.2.d.e.844.18 | 36 | 65.8 | even | 4 | |||
845.2.d.e.844.19 | 36 | 65.47 | even | 4 | |||
845.2.d.e.844.20 | 36 | 65.18 | even | 4 | |||
845.2.l.g.654.17 | 72 | 65.28 | even | 12 | |||
845.2.l.g.654.18 | 72 | 65.37 | even | 12 | |||
845.2.l.g.654.19 | 72 | 65.63 | even | 12 | |||
845.2.l.g.654.20 | 72 | 65.2 | even | 12 | |||
845.2.l.g.699.17 | 72 | 65.7 | even | 12 | |||
845.2.l.g.699.18 | 72 | 65.58 | even | 12 | |||
845.2.l.g.699.19 | 72 | 65.32 | even | 12 | |||
845.2.l.g.699.20 | 72 | 65.33 | even | 12 | |||
845.2.n.h.484.9 | 36 | 65.43 | odd | 12 | |||
845.2.n.h.484.10 | 36 | 65.17 | odd | 12 | |||
845.2.n.h.529.9 | 36 | 65.62 | odd | 12 | |||
845.2.n.h.529.10 | 36 | 65.23 | odd | 12 | |||
845.2.n.i.484.9 | 36 | 65.22 | odd | 12 | |||
845.2.n.i.484.10 | 36 | 65.48 | odd | 12 | |||
845.2.n.i.529.9 | 36 | 65.3 | odd | 12 | |||
845.2.n.i.529.10 | 36 | 65.42 | odd | 12 | |||
4225.2.a.ca.1.9 | 18 | 1.1 | even | 1 | trivial | ||
4225.2.a.ca.1.10 | 18 | 5.4 | even | 2 | inner | ||
4225.2.a.cb.1.9 | 18 | 65.64 | even | 2 | |||
4225.2.a.cb.1.10 | 18 | 13.12 | even | 2 |