Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(1,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, 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("3234.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.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: | \(25.8236200137\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.2700.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 15x - 20 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 462) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.80560\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3234.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.80560 | 1.25470 | 0.627352 | − | 0.778736i | \(-0.284139\pi\) | ||||
0.627352 | + | 0.778736i | \(0.284139\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.80560 | 0.887210 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.80560 | 0.724404 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.96523 | −1.93185 | −0.965926 | − | 0.258820i | \(-0.916666\pi\) | ||||
−0.965926 | + | 0.258820i | \(0.916666\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 6.48261 | 1.48721 | 0.743607 | − | 0.668617i | \(-0.233114\pi\) | ||||
0.743607 | + | 0.668617i | \(0.233114\pi\) | |||||||
\(20\) | 2.80560 | 0.627352 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −5.28822 | −1.10267 | −0.551335 | − | 0.834284i | \(-0.685881\pi\) | ||||
−0.551335 | + | 0.834284i | \(0.685881\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 2.87141 | 0.574281 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.12859 | 0.952356 | 0.476178 | − | 0.879349i | \(-0.342022\pi\) | ||||
0.476178 | + | 0.879349i | \(0.342022\pi\) | |||||||
\(30\) | 2.80560 | 0.512231 | ||||||||
\(31\) | 8.96523 | 1.61020 | 0.805101 | − | 0.593138i | \(-0.202111\pi\) | ||||
0.805101 | + | 0.593138i | \(0.202111\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −7.96523 | −1.36602 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 10.4826 | 1.72333 | 0.861665 | − | 0.507477i | \(-0.169422\pi\) | ||||
0.861665 | + | 0.507477i | \(0.169422\pi\) | |||||||
\(38\) | 6.48261 | 1.05162 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.80560 | 0.443605 | ||||||||
\(41\) | 5.09382 | 0.795521 | 0.397760 | − | 0.917489i | \(-0.369788\pi\) | ||||
0.397760 | + | 0.917489i | \(0.369788\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.4478 | 1.74578 | 0.872890 | − | 0.487918i | \(-0.162243\pi\) | ||||
0.872890 | + | 0.487918i | \(0.162243\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 2.80560 | 0.418235 | ||||||||
\(46\) | −5.28822 | −0.779705 | ||||||||
\(47\) | −0.322990 | −0.0471129 | −0.0235565 | − | 0.999723i | \(-0.507499\pi\) | ||||
−0.0235565 | + | 0.999723i | \(0.507499\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.87141 | 0.406078 | ||||||||
\(51\) | −7.96523 | −1.11535 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.00000 | 1.09888 | 0.549442 | − | 0.835532i | \(-0.314840\pi\) | ||||
0.549442 | + | 0.835532i | \(0.314840\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −2.80560 | −0.378307 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.48261 | 0.858643 | ||||||||
\(58\) | 5.12859 | 0.673417 | ||||||||
\(59\) | 0.871407 | 0.113448 | 0.0567238 | − | 0.998390i | \(-0.481935\pi\) | ||||
0.0567238 | + | 0.998390i | \(0.481935\pi\) | |||||||
\(60\) | 2.80560 | 0.362202 | ||||||||
\(61\) | −2.15962 | −0.276511 | −0.138256 | − | 0.990397i | \(-0.544150\pi\) | ||||
−0.138256 | + | 0.990397i | \(0.544150\pi\) | |||||||
\(62\) | 8.96523 | 1.13858 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | −7.09382 | −0.866648 | −0.433324 | − | 0.901238i | \(-0.642659\pi\) | ||||
−0.433324 | + | 0.901238i | \(0.642659\pi\) | |||||||
\(68\) | −7.96523 | −0.965926 | ||||||||
\(69\) | −5.28822 | −0.636626 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.44784 | −0.883896 | −0.441948 | − | 0.897041i | \(-0.645712\pi\) | ||||
−0.441948 | + | 0.897041i | \(0.645712\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −12.5764 | −1.47196 | −0.735980 | − | 0.677003i | \(-0.763278\pi\) | ||||
−0.735980 | + | 0.677003i | \(0.763278\pi\) | |||||||
\(74\) | 10.4826 | 1.21858 | ||||||||
\(75\) | 2.87141 | 0.331562 | ||||||||
\(76\) | 6.48261 | 0.743607 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.80560 | 0.765690 | 0.382845 | − | 0.923813i | \(-0.374944\pi\) | ||||
0.382845 | + | 0.923813i | \(0.374944\pi\) | |||||||
\(80\) | 2.80560 | 0.313676 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.09382 | 0.562518 | ||||||||
\(83\) | −15.0938 | −1.65676 | −0.828381 | − | 0.560165i | \(-0.810738\pi\) | ||||
−0.828381 | + | 0.560165i | \(0.810738\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −22.3473 | −2.42390 | ||||||||
\(86\) | 11.4478 | 1.23445 | ||||||||
\(87\) | 5.12859 | 0.549843 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −1.61121 | −0.170787 | −0.0853937 | − | 0.996347i | \(-0.527215\pi\) | ||||
−0.0853937 | + | 0.996347i | \(0.527215\pi\) | |||||||
\(90\) | 2.80560 | 0.295737 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.28822 | −0.551335 | ||||||||
\(93\) | 8.96523 | 0.929651 | ||||||||
\(94\) | −0.322990 | −0.0333139 | ||||||||
\(95\) | 18.1876 | 1.86601 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −7.00000 | −0.710742 | −0.355371 | − | 0.934725i | \(-0.615646\pi\) | ||||
−0.355371 | + | 0.934725i | \(0.615646\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 2.87141 | 0.287141 | ||||||||
\(101\) | −10.7398 | −1.06865 | −0.534325 | − | 0.845279i | \(-0.679434\pi\) | ||||
−0.534325 | + | 0.845279i | \(0.679434\pi\) | |||||||
\(102\) | −7.96523 | −0.788675 | ||||||||
\(103\) | −2.96523 | −0.292172 | −0.146086 | − | 0.989272i | \(-0.546668\pi\) | ||||
−0.146086 | + | 0.989272i | \(0.546668\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.00000 | 0.777029 | ||||||||
\(107\) | 4.83663 | 0.467575 | 0.233787 | − | 0.972288i | \(-0.424888\pi\) | ||||
0.233787 | + | 0.972288i | \(0.424888\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −10.1596 | −0.973115 | −0.486558 | − | 0.873648i | \(-0.661748\pi\) | ||||
−0.486558 | + | 0.873648i | \(0.661748\pi\) | |||||||
\(110\) | −2.80560 | −0.267504 | ||||||||
\(111\) | 10.4826 | 0.994966 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.9652 | 1.03152 | 0.515761 | − | 0.856733i | \(-0.327509\pi\) | ||||
0.515761 | + | 0.856733i | \(0.327509\pi\) | |||||||
\(114\) | 6.48261 | 0.607152 | ||||||||
\(115\) | −14.8366 | −1.38352 | ||||||||
\(116\) | 5.12859 | 0.476178 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.871407 | 0.0802195 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.80560 | 0.256115 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.15962 | −0.195523 | ||||||||
\(123\) | 5.09382 | 0.459294 | ||||||||
\(124\) | 8.96523 | 0.805101 | ||||||||
\(125\) | −5.97199 | −0.534151 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.28822 | −0.824196 | −0.412098 | − | 0.911140i | \(-0.635204\pi\) | ||||
−0.412098 | + | 0.911140i | \(0.635204\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 11.4478 | 1.00793 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.9652 | −1.13278 | −0.566389 | − | 0.824138i | \(-0.691660\pi\) | ||||
−0.566389 | + | 0.824138i | \(0.691660\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −7.09382 | −0.612813 | ||||||||
\(135\) | 2.80560 | 0.241468 | ||||||||
\(136\) | −7.96523 | −0.683012 | ||||||||
\(137\) | 5.61121 | 0.479398 | 0.239699 | − | 0.970847i | \(-0.422951\pi\) | ||||
0.239699 | + | 0.970847i | \(0.422951\pi\) | |||||||
\(138\) | −5.28822 | −0.450163 | ||||||||
\(139\) | −13.1286 | −1.11355 | −0.556776 | − | 0.830662i | \(-0.687962\pi\) | ||||
−0.556776 | + | 0.830662i | \(0.687962\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.322990 | −0.0272007 | ||||||||
\(142\) | −7.44784 | −0.625009 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 14.3888 | 1.19492 | ||||||||
\(146\) | −12.5764 | −1.04083 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.4826 | 0.861665 | ||||||||
\(149\) | 16.7398 | 1.37138 | 0.685689 | − | 0.727895i | \(-0.259501\pi\) | ||||
0.685689 | + | 0.727895i | \(0.259501\pi\) | |||||||
\(150\) | 2.87141 | 0.234449 | ||||||||
\(151\) | 10.8994 | 0.886982 | 0.443491 | − | 0.896279i | \(-0.353740\pi\) | ||||
0.443491 | + | 0.896279i | \(0.353740\pi\) | |||||||
\(152\) | 6.48261 | 0.525809 | ||||||||
\(153\) | −7.96523 | −0.643950 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.1529 | 2.02033 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.77457 | −0.141626 | −0.0708132 | − | 0.997490i | \(-0.522559\pi\) | ||||
−0.0708132 | + | 0.997490i | \(0.522559\pi\) | |||||||
\(158\) | 6.80560 | 0.541425 | ||||||||
\(159\) | 8.00000 | 0.634441 | ||||||||
\(160\) | 2.80560 | 0.221802 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −4.05904 | −0.317929 | −0.158964 | − | 0.987284i | \(-0.550816\pi\) | ||||
−0.158964 | + | 0.987284i | \(0.550816\pi\) | |||||||
\(164\) | 5.09382 | 0.397760 | ||||||||
\(165\) | −2.80560 | −0.218416 | ||||||||
\(166\) | −15.0938 | −1.17151 | ||||||||
\(167\) | −13.8684 | −1.07317 | −0.536584 | − | 0.843847i | \(-0.680286\pi\) | ||||
−0.536584 | + | 0.843847i | \(0.680286\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | −22.3473 | −1.71396 | ||||||||
\(171\) | 6.48261 | 0.495738 | ||||||||
\(172\) | 11.4478 | 0.872890 | ||||||||
\(173\) | −16.9652 | −1.28984 | −0.644921 | − | 0.764249i | \(-0.723110\pi\) | ||||
−0.644921 | + | 0.764249i | \(0.723110\pi\) | |||||||
\(174\) | 5.12859 | 0.388798 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 0.871407 | 0.0654990 | ||||||||
\(178\) | −1.61121 | −0.120765 | ||||||||
\(179\) | −12.6703 | −0.947019 | −0.473509 | − | 0.880789i | \(-0.657013\pi\) | ||||
−0.473509 | + | 0.880789i | \(0.657013\pi\) | |||||||
\(180\) | 2.80560 | 0.209117 | ||||||||
\(181\) | 2.57643 | 0.191505 | 0.0957523 | − | 0.995405i | \(-0.469474\pi\) | ||||
0.0957523 | + | 0.995405i | \(0.469474\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.15962 | −0.159644 | ||||||||
\(184\) | −5.28822 | −0.389852 | ||||||||
\(185\) | 29.4100 | 2.16227 | ||||||||
\(186\) | 8.96523 | 0.657362 | ||||||||
\(187\) | 7.96523 | 0.582475 | ||||||||
\(188\) | −0.322990 | −0.0235565 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 18.1876 | 1.31947 | ||||||||
\(191\) | −2.38879 | −0.172847 | −0.0864235 | − | 0.996258i | \(-0.527544\pi\) | ||||
−0.0864235 | + | 0.996258i | \(0.527544\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −14.5764 | −1.04923 | −0.524617 | − | 0.851338i | \(-0.675792\pi\) | ||||
−0.524617 | + | 0.851338i | \(0.675792\pi\) | |||||||
\(194\) | −7.00000 | −0.502571 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.4826 | −0.889349 | −0.444675 | − | 0.895692i | \(-0.646681\pi\) | ||||
−0.444675 | + | 0.895692i | \(0.646681\pi\) | |||||||
\(198\) | −1.00000 | −0.0710669 | ||||||||
\(199\) | 14.1876 | 1.00573 | 0.502867 | − | 0.864364i | \(-0.332278\pi\) | ||||
0.502867 | + | 0.864364i | \(0.332278\pi\) | |||||||
\(200\) | 2.87141 | 0.203039 | ||||||||
\(201\) | −7.09382 | −0.500359 | ||||||||
\(202\) | −10.7398 | −0.755650 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −7.96523 | −0.557677 | ||||||||
\(205\) | 14.2912 | 0.998143 | ||||||||
\(206\) | −2.96523 | −0.206597 | ||||||||
\(207\) | −5.28822 | −0.367556 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.48261 | −0.448412 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.8336 | −1.43425 | −0.717123 | − | 0.696947i | \(-0.754541\pi\) | ||||
−0.717123 | + | 0.696947i | \(0.754541\pi\) | |||||||
\(212\) | 8.00000 | 0.549442 | ||||||||
\(213\) | −7.44784 | −0.510318 | ||||||||
\(214\) | 4.83663 | 0.330625 | ||||||||
\(215\) | 32.1181 | 2.19044 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.1596 | −0.688096 | ||||||||
\(219\) | −12.5764 | −0.849836 | ||||||||
\(220\) | −2.80560 | −0.189154 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 10.4826 | 0.703547 | ||||||||
\(223\) | −12.5764 | −0.842180 | −0.421090 | − | 0.907019i | \(-0.638352\pi\) | ||||
−0.421090 | + | 0.907019i | \(0.638352\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.87141 | 0.191427 | ||||||||
\(226\) | 10.9652 | 0.729396 | ||||||||
\(227\) | −20.0590 | −1.33137 | −0.665683 | − | 0.746235i | \(-0.731860\pi\) | ||||
−0.665683 | + | 0.746235i | \(0.731860\pi\) | |||||||
\(228\) | 6.48261 | 0.429322 | ||||||||
\(229\) | 22.5764 | 1.49189 | 0.745946 | − | 0.666006i | \(-0.231998\pi\) | ||||
0.745946 | + | 0.666006i | \(0.231998\pi\) | |||||||
\(230\) | −14.8366 | −0.978299 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.12859 | 0.336709 | ||||||||
\(233\) | −0.742815 | −0.0486634 | −0.0243317 | − | 0.999704i | \(-0.507746\pi\) | ||||
−0.0243317 | + | 0.999704i | \(0.507746\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.906181 | −0.0591128 | ||||||||
\(236\) | 0.871407 | 0.0567238 | ||||||||
\(237\) | 6.80560 | 0.442071 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.31925 | 0.279389 | 0.139694 | − | 0.990195i | \(-0.455388\pi\) | ||||
0.139694 | + | 0.990195i | \(0.455388\pi\) | |||||||
\(240\) | 2.80560 | 0.181101 | ||||||||
\(241\) | 18.1876 | 1.17157 | 0.585784 | − | 0.810467i | \(-0.300787\pi\) | ||||
0.585784 | + | 0.810467i | \(0.300787\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −2.15962 | −0.138256 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.09382 | 0.324770 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 8.96523 | 0.569292 | ||||||||
\(249\) | −15.0938 | −0.956532 | ||||||||
\(250\) | −5.97199 | −0.377702 | ||||||||
\(251\) | −28.6703 | −1.80965 | −0.904825 | − | 0.425784i | \(-0.859999\pi\) | ||||
−0.904825 | + | 0.425784i | \(0.859999\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.28822 | 0.332467 | ||||||||
\(254\) | −9.28822 | −0.582794 | ||||||||
\(255\) | −22.3473 | −1.39944 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.6112 | 0.849044 | 0.424522 | − | 0.905418i | \(-0.360442\pi\) | ||||
0.424522 | + | 0.905418i | \(0.360442\pi\) | |||||||
\(258\) | 11.4478 | 0.712711 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.12859 | 0.317452 | ||||||||
\(262\) | −12.9652 | −0.800994 | ||||||||
\(263\) | −3.61121 | −0.222676 | −0.111338 | − | 0.993783i | \(-0.535514\pi\) | ||||
−0.111338 | + | 0.993783i | \(0.535514\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | 22.4448 | 1.37877 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.61121 | −0.0986042 | ||||||||
\(268\) | −7.09382 | −0.433324 | ||||||||
\(269\) | 9.38203 | 0.572033 | 0.286016 | − | 0.958225i | \(-0.407669\pi\) | ||||
0.286016 | + | 0.958225i | \(0.407669\pi\) | |||||||
\(270\) | 2.80560 | 0.170744 | ||||||||
\(271\) | −5.61121 | −0.340856 | −0.170428 | − | 0.985370i | \(-0.554515\pi\) | ||||
−0.170428 | + | 0.985370i | \(0.554515\pi\) | |||||||
\(272\) | −7.96523 | −0.482963 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.61121 | 0.338985 | ||||||||
\(275\) | −2.87141 | −0.173152 | ||||||||
\(276\) | −5.28822 | −0.318313 | ||||||||
\(277\) | −16.0000 | −0.961347 | −0.480673 | − | 0.876900i | \(-0.659608\pi\) | ||||
−0.480673 | + | 0.876900i | \(0.659608\pi\) | |||||||
\(278\) | −13.1286 | −0.787401 | ||||||||
\(279\) | 8.96523 | 0.536734 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.1529 | 1.44084 | 0.720420 | − | 0.693539i | \(-0.243949\pi\) | ||||
0.720420 | + | 0.693539i | \(0.243949\pi\) | |||||||
\(282\) | −0.322990 | −0.0192338 | ||||||||
\(283\) | −7.54166 | −0.448305 | −0.224152 | − | 0.974554i | \(-0.571961\pi\) | ||||
−0.224152 | + | 0.974554i | \(0.571961\pi\) | |||||||
\(284\) | −7.44784 | −0.441948 | ||||||||
\(285\) | 18.1876 | 1.07734 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 46.4448 | 2.73205 | ||||||||
\(290\) | 14.3888 | 0.844939 | ||||||||
\(291\) | −7.00000 | −0.410347 | ||||||||
\(292\) | −12.5764 | −0.735980 | ||||||||
\(293\) | −7.90618 | −0.461884 | −0.230942 | − | 0.972968i | \(-0.574181\pi\) | ||||
−0.230942 | + | 0.972968i | \(0.574181\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.44482 | 0.142343 | ||||||||
\(296\) | 10.4826 | 0.609289 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 16.7398 | 0.969710 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 2.87141 | 0.165781 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 10.8994 | 0.627191 | ||||||||
\(303\) | −10.7398 | −0.616985 | ||||||||
\(304\) | 6.48261 | 0.371803 | ||||||||
\(305\) | −6.05904 | −0.346940 | ||||||||
\(306\) | −7.96523 | −0.455342 | ||||||||
\(307\) | −12.8957 | −0.735995 | −0.367998 | − | 0.929827i | \(-0.619957\pi\) | ||||
−0.367998 | + | 0.929827i | \(0.619957\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.96523 | −0.168686 | ||||||||
\(310\) | 25.1529 | 1.42859 | ||||||||
\(311\) | −10.8994 | −0.618049 | −0.309025 | − | 0.951054i | \(-0.600003\pi\) | ||||
−0.309025 | + | 0.951054i | \(0.600003\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.12859 | 0.515979 | 0.257989 | − | 0.966148i | \(-0.416940\pi\) | ||||
0.257989 | + | 0.966148i | \(0.416940\pi\) | |||||||
\(314\) | −1.77457 | −0.100145 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.80560 | 0.382845 | ||||||||
\(317\) | −9.51364 | −0.534339 | −0.267170 | − | 0.963649i | \(-0.586088\pi\) | ||||
−0.267170 | + | 0.963649i | \(0.586088\pi\) | |||||||
\(318\) | 8.00000 | 0.448618 | ||||||||
\(319\) | −5.12859 | −0.287146 | ||||||||
\(320\) | 2.80560 | 0.156838 | ||||||||
\(321\) | 4.83663 | 0.269955 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −51.6355 | −2.87307 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.05904 | −0.224810 | ||||||||
\(327\) | −10.1596 | −0.561828 | ||||||||
\(328\) | 5.09382 | 0.281259 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.80560 | −0.154443 | ||||||||
\(331\) | 1.09382 | 0.0601217 | 0.0300609 | − | 0.999548i | \(-0.490430\pi\) | ||||
0.0300609 | + | 0.999548i | \(0.490430\pi\) | |||||||
\(332\) | −15.0938 | −0.828381 | ||||||||
\(333\) | 10.4826 | 0.574444 | ||||||||
\(334\) | −13.8684 | −0.758845 | ||||||||
\(335\) | −19.9024 | −1.08739 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.7988 | −1.40535 | −0.702676 | − | 0.711510i | \(-0.748012\pi\) | ||||
−0.702676 | + | 0.711510i | \(0.748012\pi\) | |||||||
\(338\) | −13.0000 | −0.707107 | ||||||||
\(339\) | 10.9652 | 0.595549 | ||||||||
\(340\) | −22.3473 | −1.21195 | ||||||||
\(341\) | −8.96523 | −0.485494 | ||||||||
\(342\) | 6.48261 | 0.350540 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 11.4478 | 0.617226 | ||||||||
\(345\) | −14.8366 | −0.798777 | ||||||||
\(346\) | −16.9652 | −0.912056 | ||||||||
\(347\) | 20.7671 | 1.11484 | 0.557418 | − | 0.830232i | \(-0.311792\pi\) | ||||
0.557418 | + | 0.830232i | \(0.311792\pi\) | |||||||
\(348\) | 5.12859 | 0.274921 | ||||||||
\(349\) | 9.51364 | 0.509254 | 0.254627 | − | 0.967039i | \(-0.418047\pi\) | ||||
0.254627 | + | 0.967039i | \(0.418047\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 12.5764 | 0.669376 | 0.334688 | − | 0.942329i | \(-0.391369\pi\) | ||||
0.334688 | + | 0.942329i | \(0.391369\pi\) | |||||||
\(354\) | 0.871407 | 0.0463148 | ||||||||
\(355\) | −20.8957 | −1.10903 | ||||||||
\(356\) | −1.61121 | −0.0853937 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.6703 | −0.669644 | ||||||||
\(359\) | −0.0695483 | −0.00367062 | −0.00183531 | − | 0.999998i | \(-0.500584\pi\) | ||||
−0.00183531 | + | 0.999998i | \(0.500584\pi\) | |||||||
\(360\) | 2.80560 | 0.147868 | ||||||||
\(361\) | 23.0243 | 1.21180 | ||||||||
\(362\) | 2.57643 | 0.135414 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −35.2845 | −1.84687 | ||||||||
\(366\) | −2.15962 | −0.112885 | ||||||||
\(367\) | 31.5417 | 1.64646 | 0.823231 | − | 0.567707i | \(-0.192169\pi\) | ||||
0.823231 | + | 0.567707i | \(0.192169\pi\) | |||||||
\(368\) | −5.28822 | −0.275667 | ||||||||
\(369\) | 5.09382 | 0.265174 | ||||||||
\(370\) | 29.4100 | 1.52896 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 8.96523 | 0.464825 | ||||||||
\(373\) | 15.3125 | 0.792850 | 0.396425 | − | 0.918067i | \(-0.370251\pi\) | ||||
0.396425 | + | 0.918067i | \(0.370251\pi\) | |||||||
\(374\) | 7.96523 | 0.411872 | ||||||||
\(375\) | −5.97199 | −0.308392 | ||||||||
\(376\) | −0.322990 | −0.0166569 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0590 | 0.824898 | 0.412449 | − | 0.910981i | \(-0.364674\pi\) | ||||
0.412449 | + | 0.910981i | \(0.364674\pi\) | |||||||
\(380\) | 18.1876 | 0.933006 | ||||||||
\(381\) | −9.28822 | −0.475850 | ||||||||
\(382\) | −2.38879 | −0.122221 | ||||||||
\(383\) | 0.739798 | 0.0378019 | 0.0189010 | − | 0.999821i | \(-0.493983\pi\) | ||||
0.0189010 | + | 0.999821i | \(0.493983\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.5764 | −0.741921 | ||||||||
\(387\) | 11.4478 | 0.581926 | ||||||||
\(388\) | −7.00000 | −0.355371 | ||||||||
\(389\) | 3.58319 | 0.181675 | 0.0908375 | − | 0.995866i | \(-0.471046\pi\) | ||||
0.0908375 | + | 0.995866i | \(0.471046\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 42.1218 | 2.13019 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.9652 | −0.654009 | ||||||||
\(394\) | −12.4826 | −0.628865 | ||||||||
\(395\) | 19.0938 | 0.960714 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | 25.1286 | 1.26117 | 0.630584 | − | 0.776121i | \(-0.282815\pi\) | ||||
0.630584 | + | 0.776121i | \(0.282815\pi\) | |||||||
\(398\) | 14.1876 | 0.711162 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.87141 | 0.143570 | ||||||||
\(401\) | −3.86839 | −0.193178 | −0.0965891 | − | 0.995324i | \(-0.530793\pi\) | ||||
−0.0965891 | + | 0.995324i | \(0.530793\pi\) | |||||||
\(402\) | −7.09382 | −0.353808 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −10.7398 | −0.534325 | ||||||||
\(405\) | 2.80560 | 0.139412 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.4826 | −0.519604 | ||||||||
\(408\) | −7.96523 | −0.394337 | ||||||||
\(409\) | −4.64598 | −0.229729 | −0.114864 | − | 0.993381i | \(-0.536643\pi\) | ||||
−0.114864 | + | 0.993381i | \(0.536643\pi\) | |||||||
\(410\) | 14.2912 | 0.705794 | ||||||||
\(411\) | 5.61121 | 0.276780 | ||||||||
\(412\) | −2.96523 | −0.146086 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −5.28822 | −0.259902 | ||||||||
\(415\) | −42.3473 | −2.07875 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.1286 | −0.642910 | ||||||||
\(418\) | −6.48261 | −0.317075 | ||||||||
\(419\) | 19.5174 | 0.953487 | 0.476743 | − | 0.879043i | \(-0.341817\pi\) | ||||
0.476743 | + | 0.879043i | \(0.341817\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.5174 | 0.756271 | 0.378136 | − | 0.925750i | \(-0.376565\pi\) | ||||
0.378136 | + | 0.925750i | \(0.376565\pi\) | |||||||
\(422\) | −20.8336 | −1.01416 | ||||||||
\(423\) | −0.322990 | −0.0157043 | ||||||||
\(424\) | 8.00000 | 0.388514 | ||||||||
\(425\) | −22.8714 | −1.10943 | ||||||||
\(426\) | −7.44784 | −0.360849 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.83663 | 0.233787 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 32.1181 | 1.54887 | ||||||||
\(431\) | −14.3888 | −0.693084 | −0.346542 | − | 0.938034i | \(-0.612644\pi\) | ||||
−0.346542 | + | 0.938034i | \(0.612644\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −2.03477 | −0.0977850 | −0.0488925 | − | 0.998804i | \(-0.515569\pi\) | ||||
−0.0488925 | + | 0.998804i | \(0.515569\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.3888 | 0.689890 | ||||||||
\(436\) | −10.1596 | −0.486558 | ||||||||
\(437\) | −34.2815 | −1.63990 | ||||||||
\(438\) | −12.5764 | −0.600925 | ||||||||
\(439\) | −3.22616 | −0.153976 | −0.0769880 | − | 0.997032i | \(-0.524530\pi\) | ||||
−0.0769880 | + | 0.997032i | \(0.524530\pi\) | |||||||
\(440\) | −2.80560 | −0.133752 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.0938 | −1.04971 | −0.524854 | − | 0.851192i | \(-0.675880\pi\) | ||||
−0.524854 | + | 0.851192i | \(0.675880\pi\) | |||||||
\(444\) | 10.4826 | 0.497483 | ||||||||
\(445\) | −4.52040 | −0.214288 | ||||||||
\(446\) | −12.5764 | −0.595511 | ||||||||
\(447\) | 16.7398 | 0.791765 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.2497 | 1.05003 | 0.525014 | − | 0.851094i | \(-0.324060\pi\) | ||||
0.525014 | + | 0.851094i | \(0.324060\pi\) | |||||||
\(450\) | 2.87141 | 0.135359 | ||||||||
\(451\) | −5.09382 | −0.239859 | ||||||||
\(452\) | 10.9652 | 0.515761 | ||||||||
\(453\) | 10.8994 | 0.512099 | ||||||||
\(454\) | −20.0590 | −0.941418 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.48261 | 0.303576 | ||||||||
\(457\) | −18.6385 | −0.871872 | −0.435936 | − | 0.899978i | \(-0.643583\pi\) | ||||
−0.435936 | + | 0.899978i | \(0.643583\pi\) | |||||||
\(458\) | 22.5764 | 1.05493 | ||||||||
\(459\) | −7.96523 | −0.371785 | ||||||||
\(460\) | −14.8366 | −0.691762 | ||||||||
\(461\) | 20.9895 | 0.977578 | 0.488789 | − | 0.872402i | \(-0.337439\pi\) | ||||
0.488789 | + | 0.872402i | \(0.337439\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.35402 | −0.248822 | −0.124411 | − | 0.992231i | \(-0.539704\pi\) | ||||
−0.124411 | + | 0.992231i | \(0.539704\pi\) | |||||||
\(464\) | 5.12859 | 0.238089 | ||||||||
\(465\) | 25.1529 | 1.16644 | ||||||||
\(466\) | −0.742815 | −0.0344102 | ||||||||
\(467\) | −26.0243 | −1.20426 | −0.602130 | − | 0.798398i | \(-0.705681\pi\) | ||||
−0.602130 | + | 0.798398i | \(0.705681\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.906181 | −0.0417990 | ||||||||
\(471\) | −1.77457 | −0.0817680 | ||||||||
\(472\) | 0.871407 | 0.0401098 | ||||||||
\(473\) | −11.4478 | −0.526372 | ||||||||
\(474\) | 6.80560 | 0.312592 | ||||||||
\(475\) | 18.6142 | 0.854079 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.00000 | 0.366295 | ||||||||
\(478\) | 4.31925 | 0.197558 | ||||||||
\(479\) | 3.61121 | 0.165000 | 0.0825001 | − | 0.996591i | \(-0.473710\pi\) | ||||
0.0825001 | + | 0.996591i | \(0.473710\pi\) | |||||||
\(480\) | 2.80560 | 0.128058 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 18.1876 | 0.828424 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −19.6392 | −0.891771 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −8.06206 | −0.365327 | −0.182663 | − | 0.983176i | \(-0.558472\pi\) | ||||
−0.182663 | + | 0.983176i | \(0.558472\pi\) | |||||||
\(488\) | −2.15962 | −0.0977615 | ||||||||
\(489\) | −4.05904 | −0.183556 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.9062 | 0.943483 | 0.471741 | − | 0.881737i | \(-0.343626\pi\) | ||||
0.471741 | + | 0.881737i | \(0.343626\pi\) | |||||||
\(492\) | 5.09382 | 0.229647 | ||||||||
\(493\) | −40.8504 | −1.83981 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.80560 | −0.126102 | ||||||||
\(496\) | 8.96523 | 0.402551 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −15.0938 | −0.676370 | ||||||||
\(499\) | 4.96523 | 0.222274 | 0.111137 | − | 0.993805i | \(-0.464551\pi\) | ||||
0.111137 | + | 0.993805i | \(0.464551\pi\) | |||||||
\(500\) | −5.97199 | −0.267075 | ||||||||
\(501\) | −13.8684 | −0.619594 | ||||||||
\(502\) | −28.6703 | −1.27962 | ||||||||
\(503\) | 17.7988 | 0.793611 | 0.396806 | − | 0.917903i | \(-0.370119\pi\) | ||||
0.396806 | + | 0.917903i | \(0.370119\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −30.1316 | −1.34084 | ||||||||
\(506\) | 5.28822 | 0.235090 | ||||||||
\(507\) | −13.0000 | −0.577350 | ||||||||
\(508\) | −9.28822 | −0.412098 | ||||||||
\(509\) | −4.51437 | −0.200096 | −0.100048 | − | 0.994983i | \(-0.531900\pi\) | ||||
−0.100048 | + | 0.994983i | \(0.531900\pi\) | |||||||
\(510\) | −22.3473 | −0.989553 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 6.48261 | 0.286214 | ||||||||
\(514\) | 13.6112 | 0.600365 | ||||||||
\(515\) | −8.31925 | −0.366590 | ||||||||
\(516\) | 11.4478 | 0.503963 | ||||||||
\(517\) | 0.322990 | 0.0142051 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.9652 | −0.744691 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | 5.12859 | 0.224472 | ||||||||
\(523\) | −6.90317 | −0.301854 | −0.150927 | − | 0.988545i | \(-0.548226\pi\) | ||||
−0.150927 | + | 0.988545i | \(0.548226\pi\) | |||||||
\(524\) | −12.9652 | −0.566389 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.61121 | −0.157456 | ||||||||
\(527\) | −71.4100 | −3.11067 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | 4.96523 | 0.215879 | ||||||||
\(530\) | 22.4448 | 0.974941 | ||||||||
\(531\) | 0.871407 | 0.0378159 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1.61121 | −0.0697237 | ||||||||
\(535\) | 13.5697 | 0.586668 | ||||||||
\(536\) | −7.09382 | −0.306406 | ||||||||
\(537\) | −12.6703 | −0.546762 | ||||||||
\(538\) | 9.38203 | 0.404488 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.80560 | 0.120734 | ||||||||
\(541\) | 2.80560 | 0.120622 | 0.0603111 | − | 0.998180i | \(-0.480791\pi\) | ||||
0.0603111 | + | 0.998180i | \(0.480791\pi\) | |||||||
\(542\) | −5.61121 | −0.241022 | ||||||||
\(543\) | 2.57643 | 0.110565 | ||||||||
\(544\) | −7.96523 | −0.341506 | ||||||||
\(545\) | −28.5039 | −1.22097 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.9274 | 1.40788 | 0.703938 | − | 0.710262i | \(-0.251423\pi\) | ||||
0.703938 | + | 0.710262i | \(0.251423\pi\) | |||||||
\(548\) | 5.61121 | 0.239699 | ||||||||
\(549\) | −2.15962 | −0.0921705 | ||||||||
\(550\) | −2.87141 | −0.122437 | ||||||||
\(551\) | 33.2467 | 1.41636 | ||||||||
\(552\) | −5.28822 | −0.225081 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −16.0000 | −0.679775 | ||||||||
\(555\) | 29.4100 | 1.24839 | ||||||||
\(556\) | −13.1286 | −0.556776 | ||||||||
\(557\) | 23.7050 | 1.00441 | 0.502207 | − | 0.864747i | \(-0.332522\pi\) | ||||
0.502207 | + | 0.864747i | \(0.332522\pi\) | |||||||
\(558\) | 8.96523 | 0.379528 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.96523 | 0.336292 | ||||||||
\(562\) | 24.1529 | 1.01883 | ||||||||
\(563\) | −30.4448 | −1.28310 | −0.641548 | − | 0.767083i | \(-0.721708\pi\) | ||||
−0.641548 | + | 0.767083i | \(0.721708\pi\) | |||||||
\(564\) | −0.322990 | −0.0136003 | ||||||||
\(565\) | 30.7641 | 1.29425 | ||||||||
\(566\) | −7.54166 | −0.317000 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.44784 | −0.312504 | ||||||||
\(569\) | 22.2815 | 0.934087 | 0.467044 | − | 0.884234i | \(-0.345319\pi\) | ||||
0.467044 | + | 0.884234i | \(0.345319\pi\) | |||||||
\(570\) | 18.1876 | 0.761796 | ||||||||
\(571\) | −2.87141 | −0.120165 | −0.0600823 | − | 0.998193i | \(-0.519136\pi\) | ||||
−0.0600823 | + | 0.998193i | \(0.519136\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.38879 | −0.0997933 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.1846 | −0.633242 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 15.0243 | 0.625469 | 0.312734 | − | 0.949841i | \(-0.398755\pi\) | ||||
0.312734 | + | 0.949841i | \(0.398755\pi\) | |||||||
\(578\) | 46.4448 | 1.93185 | ||||||||
\(579\) | −14.5764 | −0.605776 | ||||||||
\(580\) | 14.3888 | 0.597462 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −7.00000 | −0.290159 | ||||||||
\(583\) | −8.00000 | −0.331326 | ||||||||
\(584\) | −12.5764 | −0.520416 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.90618 | −0.326601 | ||||||||
\(587\) | 42.5069 | 1.75445 | 0.877223 | − | 0.480082i | \(-0.159393\pi\) | ||||
0.877223 | + | 0.480082i | \(0.159393\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 58.1181 | 2.39471 | ||||||||
\(590\) | 2.44482 | 0.100652 | ||||||||
\(591\) | −12.4826 | −0.513466 | ||||||||
\(592\) | 10.4826 | 0.430833 | ||||||||
\(593\) | −15.3858 | −0.631818 | −0.315909 | − | 0.948789i | \(-0.602309\pi\) | ||||
−0.315909 | + | 0.948789i | \(0.602309\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.7398 | 0.685689 | ||||||||
\(597\) | 14.1876 | 0.580661 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −39.6392 | −1.61961 | −0.809807 | − | 0.586696i | \(-0.800428\pi\) | ||||
−0.809807 | + | 0.586696i | \(0.800428\pi\) | |||||||
\(600\) | 2.87141 | 0.117225 | ||||||||
\(601\) | −33.3405 | −1.35999 | −0.679994 | − | 0.733218i | \(-0.738017\pi\) | ||||
−0.679994 | + | 0.733218i | \(0.738017\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.09382 | −0.288883 | ||||||||
\(604\) | 10.8994 | 0.443491 | ||||||||
\(605\) | 2.80560 | 0.114064 | ||||||||
\(606\) | −10.7398 | −0.436274 | ||||||||
\(607\) | −15.9585 | −0.647734 | −0.323867 | − | 0.946103i | \(-0.604983\pi\) | ||||
−0.323867 | + | 0.946103i | \(0.604983\pi\) | |||||||
\(608\) | 6.48261 | 0.262905 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.05904 | −0.245324 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −7.96523 | −0.321975 | ||||||||
\(613\) | 46.6665 | 1.88484 | 0.942421 | − | 0.334428i | \(-0.108543\pi\) | ||||
0.942421 | + | 0.334428i | \(0.108543\pi\) | |||||||
\(614\) | −12.8957 | −0.520427 | ||||||||
\(615\) | 14.2912 | 0.576278 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.28447 | −0.373779 | −0.186889 | − | 0.982381i | \(-0.559841\pi\) | ||||
−0.186889 | + | 0.982381i | \(0.559841\pi\) | |||||||
\(618\) | −2.96523 | −0.119279 | ||||||||
\(619\) | −33.9895 | −1.36615 | −0.683077 | − | 0.730347i | \(-0.739358\pi\) | ||||
−0.683077 | + | 0.730347i | \(0.739358\pi\) | |||||||
\(620\) | 25.1529 | 1.01016 | ||||||||
\(621\) | −5.28822 | −0.212209 | ||||||||
\(622\) | −10.8994 | −0.437027 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1121 | −1.24448 | ||||||||
\(626\) | 9.12859 | 0.364852 | ||||||||
\(627\) | −6.48261 | −0.258891 | ||||||||
\(628\) | −1.77457 | −0.0708132 | ||||||||
\(629\) | −83.4964 | −3.32922 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.6460 | −0.583047 | −0.291524 | − | 0.956564i | \(-0.594162\pi\) | ||||
−0.291524 | + | 0.956564i | \(0.594162\pi\) | |||||||
\(632\) | 6.80560 | 0.270712 | ||||||||
\(633\) | −20.8336 | −0.828062 | ||||||||
\(634\) | −9.51364 | −0.377835 | ||||||||
\(635\) | −26.0590 | −1.03412 | ||||||||
\(636\) | 8.00000 | 0.317221 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.12859 | −0.203043 | ||||||||
\(639\) | −7.44784 | −0.294632 | ||||||||
\(640\) | 2.80560 | 0.110901 | ||||||||
\(641\) | 20.9652 | 0.828077 | 0.414038 | − | 0.910259i | \(-0.364118\pi\) | ||||
0.414038 | + | 0.910259i | \(0.364118\pi\) | |||||||
\(642\) | 4.83663 | 0.190887 | ||||||||
\(643\) | 23.6733 | 0.933582 | 0.466791 | − | 0.884368i | \(-0.345410\pi\) | ||||
0.466791 | + | 0.884368i | \(0.345410\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 32.1181 | 1.26465 | ||||||||
\(646\) | −51.6355 | −2.03157 | ||||||||
\(647\) | 12.4168 | 0.488155 | 0.244078 | − | 0.969756i | \(-0.421515\pi\) | ||||
0.244078 | + | 0.969756i | \(0.421515\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −0.871407 | −0.0342057 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.05904 | −0.158964 | ||||||||
\(653\) | −0.0975625 | −0.00381792 | −0.00190896 | − | 0.999998i | \(-0.500608\pi\) | ||||
−0.00190896 | + | 0.999998i | \(0.500608\pi\) | |||||||
\(654\) | −10.1596 | −0.397273 | ||||||||
\(655\) | −36.3753 | −1.42130 | ||||||||
\(656\) | 5.09382 | 0.198880 | ||||||||
\(657\) | −12.5764 | −0.490653 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.0243 | −1.36435 | −0.682176 | − | 0.731188i | \(-0.738966\pi\) | ||||
−0.682176 | + | 0.731188i | \(0.738966\pi\) | |||||||
\(660\) | −2.80560 | −0.109208 | ||||||||
\(661\) | −29.6355 | −1.15269 | −0.576343 | − | 0.817208i | \(-0.695521\pi\) | ||||
−0.576343 | + | 0.817208i | \(0.695521\pi\) | |||||||
\(662\) | 1.09382 | 0.0425125 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.0938 | −0.585754 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.4826 | 0.406193 | ||||||||
\(667\) | −27.1211 | −1.05013 | ||||||||
\(668\) | −13.8684 | −0.536584 | ||||||||
\(669\) | −12.5764 | −0.486233 | ||||||||
\(670\) | −19.9024 | −0.768898 | ||||||||
\(671\) | 2.15962 | 0.0833713 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.8957 | 0.651281 | 0.325640 | − | 0.945494i | \(-0.394420\pi\) | ||||
0.325640 | + | 0.945494i | \(0.394420\pi\) | |||||||
\(674\) | −25.7988 | −0.993734 | ||||||||
\(675\) | 2.87141 | 0.110521 | ||||||||
\(676\) | −13.0000 | −0.500000 | ||||||||
\(677\) | −13.1907 | −0.506958 | −0.253479 | − | 0.967341i | \(-0.581575\pi\) | ||||
−0.253479 | + | 0.967341i | \(0.581575\pi\) | |||||||
\(678\) | 10.9652 | 0.421117 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −22.3473 | −0.856978 | ||||||||
\(681\) | −20.0590 | −0.768664 | ||||||||
\(682\) | −8.96523 | −0.343296 | ||||||||
\(683\) | 9.83663 | 0.376388 | 0.188194 | − | 0.982132i | \(-0.439737\pi\) | ||||
0.188194 | + | 0.982132i | \(0.439737\pi\) | |||||||
\(684\) | 6.48261 | 0.247869 | ||||||||
\(685\) | 15.7428 | 0.601502 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.5764 | 0.861345 | ||||||||
\(688\) | 11.4478 | 0.436445 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −14.8366 | −0.564821 | ||||||||
\(691\) | 49.9895 | 1.90169 | 0.950845 | − | 0.309667i | \(-0.100218\pi\) | ||||
0.950845 | + | 0.309667i | \(0.100218\pi\) | |||||||
\(692\) | −16.9652 | −0.644921 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.7671 | 0.788308 | ||||||||
\(695\) | −36.8336 | −1.39718 | ||||||||
\(696\) | 5.12859 | 0.194399 | ||||||||
\(697\) | −40.5734 | −1.53683 | ||||||||
\(698\) | 9.51364 | 0.360097 | ||||||||
\(699\) | −0.742815 | −0.0280958 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.7050 | −0.668710 | −0.334355 | − | 0.942447i | \(-0.608518\pi\) | ||||
−0.334355 | + | 0.942447i | \(0.608518\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 67.9547 | 2.56296 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −0.906181 | −0.0341288 | ||||||||
\(706\) | 12.5764 | 0.473320 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.871407 | 0.0327495 | ||||||||
\(709\) | −31.9547 | −1.20008 | −0.600042 | − | 0.799968i | \(-0.704850\pi\) | ||||
−0.600042 | + | 0.799968i | \(0.704850\pi\) | |||||||
\(710\) | −20.8957 | −0.784201 | ||||||||
\(711\) | 6.80560 | 0.255230 | ||||||||
\(712\) | −1.61121 | −0.0603825 | ||||||||
\(713\) | −47.4100 | −1.77552 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.6703 | −0.473509 | ||||||||
\(717\) | 4.31925 | 0.161305 | ||||||||
\(718\) | −0.0695483 | −0.00259552 | ||||||||
\(719\) | −21.7951 | −0.812820 | −0.406410 | − | 0.913691i | \(-0.633220\pi\) | ||||
−0.406410 | + | 0.913691i | \(0.633220\pi\) | |||||||
\(720\) | 2.80560 | 0.104559 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 23.0243 | 0.856875 | ||||||||
\(723\) | 18.1876 | 0.676406 | ||||||||
\(724\) | 2.57643 | 0.0957523 | ||||||||
\(725\) | 14.7263 | 0.546920 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | 4.84714 | 0.179770 | 0.0898852 | − | 0.995952i | \(-0.471350\pi\) | ||||
0.0898852 | + | 0.995952i | \(0.471350\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −35.2845 | −1.30594 | ||||||||
\(731\) | −91.1846 | −3.37259 | ||||||||
\(732\) | −2.15962 | −0.0798220 | ||||||||
\(733\) | −12.2292 | −0.451695 | −0.225847 | − | 0.974163i | \(-0.572515\pi\) | ||||
−0.225847 | + | 0.974163i | \(0.572515\pi\) | |||||||
\(734\) | 31.5417 | 1.16422 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.28822 | −0.194926 | ||||||||
\(737\) | 7.09382 | 0.261304 | ||||||||
\(738\) | 5.09382 | 0.187506 | ||||||||
\(739\) | −1.03477 | −0.0380648 | −0.0190324 | − | 0.999819i | \(-0.506059\pi\) | ||||
−0.0190324 | + | 0.999819i | \(0.506059\pi\) | |||||||
\(740\) | 29.4100 | 1.08113 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.9925 | −0.880200 | −0.440100 | − | 0.897949i | \(-0.645057\pi\) | ||||
−0.440100 | + | 0.897949i | \(0.645057\pi\) | |||||||
\(744\) | 8.96523 | 0.328681 | ||||||||
\(745\) | 46.9652 | 1.72067 | ||||||||
\(746\) | 15.3125 | 0.560630 | ||||||||
\(747\) | −15.0938 | −0.552254 | ||||||||
\(748\) | 7.96523 | 0.291238 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −5.97199 | −0.218066 | ||||||||
\(751\) | 20.5069 | 0.748307 | 0.374153 | − | 0.927367i | \(-0.377933\pi\) | ||||
0.374153 | + | 0.927367i | \(0.377933\pi\) | |||||||
\(752\) | −0.322990 | −0.0117782 | ||||||||
\(753\) | −28.6703 | −1.04480 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30.5794 | 1.11290 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.8019 | −0.610674 | −0.305337 | − | 0.952244i | \(-0.598769\pi\) | ||||
−0.305337 | + | 0.952244i | \(0.598769\pi\) | |||||||
\(758\) | 16.0590 | 0.583291 | ||||||||
\(759\) | 5.28822 | 0.191950 | ||||||||
\(760\) | 18.1876 | 0.659735 | ||||||||
\(761\) | 14.5099 | 0.525983 | 0.262992 | − | 0.964798i | \(-0.415291\pi\) | ||||
0.262992 | + | 0.964798i | \(0.415291\pi\) | |||||||
\(762\) | −9.28822 | −0.336477 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.38879 | −0.0864235 | ||||||||
\(765\) | −22.3473 | −0.807967 | ||||||||
\(766\) | 0.739798 | 0.0267300 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −3.35402 | −0.120949 | −0.0604745 | − | 0.998170i | \(-0.519261\pi\) | ||||
−0.0604745 | + | 0.998170i | \(0.519261\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.6112 | 0.490196 | ||||||||
\(772\) | −14.5764 | −0.524617 | ||||||||
\(773\) | −1.84038 | −0.0661938 | −0.0330969 | − | 0.999452i | \(-0.510537\pi\) | ||||
−0.0330969 | + | 0.999452i | \(0.510537\pi\) | |||||||
\(774\) | 11.4478 | 0.411484 | ||||||||
\(775\) | 25.7428 | 0.924709 | ||||||||
\(776\) | −7.00000 | −0.251285 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.58319 | 0.128464 | ||||||||
\(779\) | 33.0213 | 1.18311 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.44784 | 0.266505 | ||||||||
\(782\) | 42.1218 | 1.50627 | ||||||||
\(783\) | 5.12859 | 0.183281 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.97875 | −0.177699 | ||||||||
\(786\) | −12.9652 | −0.462454 | ||||||||
\(787\) | −11.5869 | −0.413030 | −0.206515 | − | 0.978443i | \(-0.566212\pi\) | ||||
−0.206515 | + | 0.978443i | \(0.566212\pi\) | |||||||
\(788\) | −12.4826 | −0.444675 | ||||||||
\(789\) | −3.61121 | −0.128562 | ||||||||
\(790\) | 19.0938 | 0.679328 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 25.1286 | 0.891780 | ||||||||
\(795\) | 22.4448 | 0.796036 | ||||||||
\(796\) | 14.1876 | 0.502867 | ||||||||
\(797\) | 48.4653 | 1.71673 | 0.858365 | − | 0.513039i | \(-0.171480\pi\) | ||||
0.858365 | + | 0.513039i | \(0.171480\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.57269 | 0.0910151 | ||||||||
\(800\) | 2.87141 | 0.101520 | ||||||||
\(801\) | −1.61121 | −0.0569292 | ||||||||
\(802\) | −3.86839 | −0.136598 | ||||||||
\(803\) | 12.5764 | 0.443813 | ||||||||
\(804\) | −7.09382 | −0.250180 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.38203 | 0.330263 | ||||||||
\(808\) | −10.7398 | −0.377825 | ||||||||
\(809\) | −2.76708 | −0.0972855 | −0.0486428 | − | 0.998816i | \(-0.515490\pi\) | ||||
−0.0486428 | + | 0.998816i | \(0.515490\pi\) | |||||||
\(810\) | 2.80560 | 0.0985788 | ||||||||
\(811\) | −4.89568 | −0.171910 | −0.0859552 | − | 0.996299i | \(-0.527394\pi\) | ||||
−0.0859552 | + | 0.996299i | \(0.527394\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.61121 | −0.196794 | ||||||||
\(814\) | −10.4826 | −0.367415 | ||||||||
\(815\) | −11.3881 | −0.398907 | ||||||||
\(816\) | −7.96523 | −0.278839 | ||||||||
\(817\) | 74.2119 | 2.59635 | ||||||||
\(818\) | −4.64598 | −0.162443 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14.2912 | 0.499071 | ||||||||
\(821\) | 3.54915 | 0.123866 | 0.0619330 | − | 0.998080i | \(-0.480273\pi\) | ||||
0.0619330 | + | 0.998080i | \(0.480273\pi\) | |||||||
\(822\) | 5.61121 | 0.195713 | ||||||||
\(823\) | 32.5069 | 1.13312 | 0.566559 | − | 0.824021i | \(-0.308274\pi\) | ||||
0.566559 | + | 0.824021i | \(0.308274\pi\) | |||||||
\(824\) | −2.96523 | −0.103299 | ||||||||
\(825\) | −2.87141 | −0.0999696 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.5447 | 0.679635 | 0.339817 | − | 0.940491i | \(-0.389635\pi\) | ||||
0.339817 | + | 0.940491i | \(0.389635\pi\) | |||||||
\(828\) | −5.28822 | −0.183778 | ||||||||
\(829\) | −25.1907 | −0.874908 | −0.437454 | − | 0.899241i | \(-0.644120\pi\) | ||||
−0.437454 | + | 0.899241i | \(0.644120\pi\) | |||||||
\(830\) | −42.3473 | −1.46989 | ||||||||
\(831\) | −16.0000 | −0.555034 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −13.1286 | −0.454606 | ||||||||
\(835\) | −38.9092 | −1.34651 | ||||||||
\(836\) | −6.48261 | −0.224206 | ||||||||
\(837\) | 8.96523 | 0.309884 | ||||||||
\(838\) | 19.5174 | 0.674217 | ||||||||
\(839\) | 50.4033 | 1.74011 | 0.870057 | − | 0.492950i | \(-0.164082\pi\) | ||||
0.870057 | + | 0.492950i | \(0.164082\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.69754 | −0.0930185 | ||||||||
\(842\) | 15.5174 | 0.534764 | ||||||||
\(843\) | 24.1529 | 0.831869 | ||||||||
\(844\) | −20.8336 | −0.717123 | ||||||||
\(845\) | −36.4728 | −1.25470 | ||||||||
\(846\) | −0.322990 | −0.0111046 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.00000 | 0.274721 | ||||||||
\(849\) | −7.54166 | −0.258829 | ||||||||
\(850\) | −22.8714 | −0.784483 | ||||||||
\(851\) | −55.4343 | −1.90026 | ||||||||
\(852\) | −7.44784 | −0.255159 | ||||||||
\(853\) | 16.8752 | 0.577794 | 0.288897 | − | 0.957360i | \(-0.406711\pi\) | ||||
0.288897 | + | 0.957360i | \(0.406711\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.1876 | 0.622004 | ||||||||
\(856\) | 4.83663 | 0.165313 | ||||||||
\(857\) | −43.3057 | −1.47930 | −0.739648 | − | 0.672994i | \(-0.765008\pi\) | ||||
−0.739648 | + | 0.672994i | \(0.765008\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.61422 | −0.123316 | −0.0616578 | − | 0.998097i | \(-0.519639\pi\) | ||||
−0.0616578 | + | 0.998097i | \(0.519639\pi\) | |||||||
\(860\) | 32.1181 | 1.09522 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14.3888 | −0.490084 | ||||||||
\(863\) | 4.41681 | 0.150350 | 0.0751750 | − | 0.997170i | \(-0.476048\pi\) | ||||
0.0751750 | + | 0.997170i | \(0.476048\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −47.5977 | −1.61837 | ||||||||
\(866\) | −2.03477 | −0.0691444 | ||||||||
\(867\) | 46.4448 | 1.57735 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.80560 | −0.230864 | ||||||||
\(870\) | 14.3888 | 0.487826 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −10.1596 | −0.344048 | ||||||||
\(873\) | −7.00000 | −0.236914 | ||||||||
\(874\) | −34.2815 | −1.15959 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.5764 | −0.424918 | ||||||||
\(877\) | 44.2777 | 1.49515 | 0.747576 | − | 0.664176i | \(-0.231218\pi\) | ||||
0.747576 | + | 0.664176i | \(0.231218\pi\) | |||||||
\(878\) | −3.22616 | −0.108877 | ||||||||
\(879\) | −7.90618 | −0.266669 | ||||||||
\(880\) | −2.80560 | −0.0945769 | ||||||||
\(881\) | 18.1876 | 0.612757 | 0.306379 | − | 0.951910i | \(-0.400883\pi\) | ||||
0.306379 | + | 0.951910i | \(0.400883\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.57945 | −0.154111 | −0.0770553 | − | 0.997027i | \(-0.524552\pi\) | ||||
−0.0770553 | + | 0.997027i | \(0.524552\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.44482 | 0.0821818 | ||||||||
\(886\) | −22.0938 | −0.742256 | ||||||||
\(887\) | 0.576432 | 0.0193547 | 0.00967734 | − | 0.999953i | \(-0.496920\pi\) | ||||
0.00967734 | + | 0.999953i | \(0.496920\pi\) | |||||||
\(888\) | 10.4826 | 0.351773 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4.52040 | −0.151524 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −12.5764 | −0.421090 | ||||||||
\(893\) | −2.09382 | −0.0700670 | ||||||||
\(894\) | 16.7398 | 0.559863 | ||||||||
\(895\) | −35.5477 | −1.18823 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22.2497 | 0.742482 | ||||||||
\(899\) | 45.9790 | 1.53349 | ||||||||
\(900\) | 2.87141 | 0.0957136 | ||||||||
\(901\) | −63.7218 | −2.12288 | ||||||||
\(902\) | −5.09382 | −0.169606 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.9652 | 0.364698 | ||||||||
\(905\) | 7.22844 | 0.240282 | ||||||||
\(906\) | 10.8994 | 0.362109 | ||||||||
\(907\) | −22.0590 | −0.732459 | −0.366229 | − | 0.930525i | \(-0.619351\pi\) | ||||
−0.366229 | + | 0.930525i | \(0.619351\pi\) | |||||||
\(908\) | −20.0590 | −0.665683 | ||||||||
\(909\) | −10.7398 | −0.356217 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.93420 | 0.329135 | 0.164567 | − | 0.986366i | \(-0.447377\pi\) | ||||
0.164567 | + | 0.986366i | \(0.447377\pi\) | |||||||
\(912\) | 6.48261 | 0.214661 | ||||||||
\(913\) | 15.0938 | 0.499532 | ||||||||
\(914\) | −18.6385 | −0.616507 | ||||||||
\(915\) | −6.05904 | −0.200306 | ||||||||
\(916\) | 22.5764 | 0.745946 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −7.96523 | −0.262892 | ||||||||
\(919\) | 44.6347 | 1.47236 | 0.736182 | − | 0.676783i | \(-0.236627\pi\) | ||||
0.736182 | + | 0.676783i | \(0.236627\pi\) | |||||||
\(920\) | −14.8366 | −0.489149 | ||||||||
\(921\) | −12.8957 | −0.424927 | ||||||||
\(922\) | 20.9895 | 0.691252 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.0999 | 0.989677 | ||||||||
\(926\) | −5.35402 | −0.175944 | ||||||||
\(927\) | −2.96523 | −0.0973908 | ||||||||
\(928\) | 5.12859 | 0.168354 | ||||||||
\(929\) | 42.5764 | 1.39689 | 0.698444 | − | 0.715665i | \(-0.253876\pi\) | ||||
0.698444 | + | 0.715665i | \(0.253876\pi\) | |||||||
\(930\) | 25.1529 | 0.824795 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.742815 | −0.0243317 | ||||||||
\(933\) | −10.8994 | −0.356831 | ||||||||
\(934\) | −26.0243 | −0.851540 | ||||||||
\(935\) | 22.3473 | 0.730834 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.2572 | 1.18447 | 0.592235 | − | 0.805765i | \(-0.298246\pi\) | ||||
0.592235 | + | 0.805765i | \(0.298246\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.12859 | 0.297900 | ||||||||
\(940\) | −0.906181 | −0.0295564 | ||||||||
\(941\) | −2.68377 | −0.0874884 | −0.0437442 | − | 0.999043i | \(-0.513929\pi\) | ||||
−0.0437442 | + | 0.999043i | \(0.513929\pi\) | |||||||
\(942\) | −1.77457 | −0.0578187 | ||||||||
\(943\) | −26.9372 | −0.877196 | ||||||||
\(944\) | 0.871407 | 0.0283619 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.4478 | −0.372201 | ||||||||
\(947\) | 49.5039 | 1.60866 | 0.804330 | − | 0.594183i | \(-0.202525\pi\) | ||||
0.804330 | + | 0.594183i | \(0.202525\pi\) | |||||||
\(948\) | 6.80560 | 0.221036 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 18.6142 | 0.603925 | ||||||||
\(951\) | −9.51364 | −0.308501 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.8019 | 0.511872 | 0.255936 | − | 0.966694i | \(-0.417616\pi\) | ||||
0.255936 | + | 0.966694i | \(0.417616\pi\) | |||||||
\(954\) | 8.00000 | 0.259010 | ||||||||
\(955\) | −6.70201 | −0.216872 | ||||||||
\(956\) | 4.31925 | 0.139694 | ||||||||
\(957\) | −5.12859 | −0.165784 | ||||||||
\(958\) | 3.61121 | 0.116673 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.80560 | 0.0905504 | ||||||||
\(961\) | 49.3753 | 1.59275 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.83663 | 0.155858 | ||||||||
\(964\) | 18.1876 | 0.585784 | ||||||||
\(965\) | −40.8957 | −1.31648 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.6497 | −0.406788 | −0.203394 | − | 0.979097i | \(-0.565197\pi\) | ||||
−0.203394 | + | 0.979097i | \(0.565197\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | −51.6355 | −1.65877 | ||||||||
\(970\) | −19.6392 | −0.630577 | ||||||||
\(971\) | −49.5342 | −1.58963 | −0.794814 | − | 0.606854i | \(-0.792431\pi\) | ||||
−0.794814 | + | 0.606854i | \(0.792431\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −8.06206 | −0.258325 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.15962 | −0.0691278 | ||||||||
\(977\) | 34.4448 | 1.10199 | 0.550994 | − | 0.834509i | \(-0.314249\pi\) | ||||
0.550994 | + | 0.834509i | \(0.314249\pi\) | |||||||
\(978\) | −4.05904 | −0.129794 | ||||||||
\(979\) | 1.61121 | 0.0514944 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.1596 | −0.324372 | ||||||||
\(982\) | 20.9062 | 0.667143 | ||||||||
\(983\) | 3.35776 | 0.107096 | 0.0535480 | − | 0.998565i | \(-0.482947\pi\) | ||||
0.0535480 | + | 0.998565i | \(0.482947\pi\) | |||||||
\(984\) | 5.09382 | 0.162385 | ||||||||
\(985\) | −35.0213 | −1.11587 | ||||||||
\(986\) | −40.8504 | −1.30094 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −60.5386 | −1.92502 | ||||||||
\(990\) | −2.80560 | −0.0891679 | ||||||||
\(991\) | −45.8474 | −1.45639 | −0.728195 | − | 0.685370i | \(-0.759641\pi\) | ||||
−0.728195 | + | 0.685370i | \(0.759641\pi\) | |||||||
\(992\) | 8.96523 | 0.284646 | ||||||||
\(993\) | 1.09382 | 0.0347113 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 39.8049 | 1.26190 | ||||||||
\(996\) | −15.0938 | −0.478266 | ||||||||
\(997\) | 43.8609 | 1.38909 | 0.694544 | − | 0.719450i | \(-0.255606\pi\) | ||||
0.694544 | + | 0.719450i | \(0.255606\pi\) | |||||||
\(998\) | 4.96523 | 0.157171 | ||||||||
\(999\) | 10.4826 | 0.331655 |
(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 | 3234.2.a.bh.1.3 | 3 | ||
3.2 | odd | 2 | 9702.2.a.dw.1.1 | 3 | |||
7.3 | odd | 6 | 462.2.i.g.331.3 | yes | 6 | ||
7.5 | odd | 6 | 462.2.i.g.67.3 | ✓ | 6 | ||
7.6 | odd | 2 | 3234.2.a.bf.1.1 | 3 | |||
21.5 | even | 6 | 1386.2.k.v.991.1 | 6 | |||
21.17 | even | 6 | 1386.2.k.v.793.1 | 6 | |||
21.20 | even | 2 | 9702.2.a.dv.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.i.g.67.3 | ✓ | 6 | 7.5 | odd | 6 | ||
462.2.i.g.331.3 | yes | 6 | 7.3 | odd | 6 | ||
1386.2.k.v.793.1 | 6 | 21.17 | even | 6 | |||
1386.2.k.v.991.1 | 6 | 21.5 | even | 6 | |||
3234.2.a.bf.1.1 | 3 | 7.6 | odd | 2 | |||
3234.2.a.bh.1.3 | 3 | 1.1 | even | 1 | trivial | ||
9702.2.a.dv.1.3 | 3 | 21.20 | even | 2 | |||
9702.2.a.dw.1.1 | 3 | 3.2 | odd | 2 |