Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9702,2,Mod(1,9702)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9702, 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("9702.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9702.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: | \(77.4708600410\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4352.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 3234) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.27133\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9702.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.79793 | −0.804060 | −0.402030 | − | 0.915627i | \(-0.631695\pi\) | ||||
−0.402030 | + | 0.915627i | \(0.631695\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.79793 | 0.568556 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.63899 | −1.00927 | −0.504637 | − | 0.863331i | \(-0.668374\pi\) | ||||
−0.504637 | + | 0.863331i | \(0.668374\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.11582 | 1.48330 | 0.741652 | − | 0.670785i | \(-0.234043\pi\) | ||||
0.741652 | + | 0.670785i | \(0.234043\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.84106 | −0.422368 | −0.211184 | − | 0.977446i | \(-0.567732\pi\) | ||||
−0.211184 | + | 0.977446i | \(0.567732\pi\) | |||||||
\(20\) | −1.79793 | −0.402030 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 7.37109 | 1.53698 | 0.768489 | − | 0.639863i | \(-0.221009\pi\) | ||||
0.768489 | + | 0.639863i | \(0.221009\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.76744 | −0.353488 | ||||||||
\(26\) | 3.63899 | 0.713665 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.4243 | 1.93574 | 0.967871 | − | 0.251446i | \(-0.0809062\pi\) | ||||
0.967871 | + | 0.251446i | \(0.0809062\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.97958 | −1.43318 | −0.716588 | − | 0.697497i | \(-0.754297\pi\) | ||||
−0.716588 | + | 0.697497i | \(0.754297\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.11582 | −1.04885 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.1995 | 1.67679 | 0.838395 | − | 0.545063i | \(-0.183494\pi\) | ||||
0.838395 | + | 0.545063i | \(0.183494\pi\) | |||||||
\(38\) | 1.84106 | 0.298659 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.79793 | 0.284278 | ||||||||
\(41\) | 8.17680 | 1.27700 | 0.638501 | − | 0.769621i | \(-0.279555\pi\) | ||||
0.638501 | + | 0.769621i | \(0.279555\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.28577 | −0.348576 | −0.174288 | − | 0.984695i | \(-0.555762\pi\) | ||||
−0.174288 | + | 0.984695i | \(0.555762\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.37109 | −1.08681 | ||||||||
\(47\) | −0.669485 | −0.0976545 | −0.0488272 | − | 0.998807i | \(-0.515548\pi\) | ||||
−0.0488272 | + | 0.998807i | \(0.515548\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.76744 | 0.249954 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.63899 | −0.504637 | ||||||||
\(53\) | −11.2848 | −1.55009 | −0.775046 | − | 0.631905i | \(-0.782273\pi\) | ||||
−0.775046 | + | 0.631905i | \(0.782273\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.79793 | 0.242433 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −10.4243 | −1.36878 | ||||||||
\(59\) | −13.5706 | −1.76674 | −0.883371 | − | 0.468674i | \(-0.844732\pi\) | ||||
−0.883371 | + | 0.468674i | \(0.844732\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.274758 | 0.0351791 | 0.0175896 | − | 0.999845i | \(-0.494401\pi\) | ||||
0.0175896 | + | 0.999845i | \(0.494401\pi\) | |||||||
\(62\) | 7.97958 | 1.01341 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.54266 | 0.811517 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.88163 | 0.474217 | 0.237108 | − | 0.971483i | \(-0.423800\pi\) | ||||
0.237108 | + | 0.971483i | \(0.423800\pi\) | |||||||
\(68\) | 6.11582 | 0.741652 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.8738 | −1.29049 | −0.645244 | − | 0.763976i | \(-0.723244\pi\) | ||||
−0.645244 | + | 0.763976i | \(0.723244\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.85892 | −0.451653 | −0.225826 | − | 0.974168i | \(-0.572508\pi\) | ||||
−0.225826 | + | 0.974168i | \(0.572508\pi\) | |||||||
\(74\) | −10.1995 | −1.18567 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.84106 | −0.211184 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.5174 | −1.40832 | −0.704159 | − | 0.710043i | \(-0.748676\pi\) | ||||
−0.704159 | + | 0.710043i | \(0.748676\pi\) | |||||||
\(80\) | −1.79793 | −0.201015 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.17680 | −0.902977 | ||||||||
\(83\) | 5.27314 | 0.578802 | 0.289401 | − | 0.957208i | \(-0.406544\pi\) | ||||
0.289401 | + | 0.957208i | \(0.406544\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.9958 | −1.19266 | ||||||||
\(86\) | 2.28577 | 0.246481 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 1.98214 | 0.210106 | 0.105053 | − | 0.994467i | \(-0.466499\pi\) | ||||
0.105053 | + | 0.994467i | \(0.466499\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.37109 | 0.768489 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.669485 | 0.0690522 | ||||||||
\(95\) | 3.31010 | 0.339609 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.12066 | −0.418390 | −0.209195 | − | 0.977874i | \(-0.567084\pi\) | ||||
−0.209195 | + | 0.977874i | \(0.567084\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.76744 | −0.176744 | ||||||||
\(101\) | 6.90367 | 0.686941 | 0.343470 | − | 0.939163i | \(-0.388397\pi\) | ||||
0.343470 | + | 0.939163i | \(0.388397\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.6154 | −1.24303 | −0.621514 | − | 0.783403i | \(-0.713482\pi\) | ||||
−0.621514 | + | 0.783403i | \(0.713482\pi\) | |||||||
\(104\) | 3.63899 | 0.356832 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.2848 | 1.09608 | ||||||||
\(107\) | −16.9417 | −1.63782 | −0.818908 | − | 0.573925i | \(-0.805420\pi\) | ||||
−0.818908 | + | 0.573925i | \(0.805420\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.76326 | 0.935151 | 0.467576 | − | 0.883953i | \(-0.345128\pi\) | ||||
0.467576 | + | 0.883953i | \(0.345128\pi\) | |||||||
\(110\) | −1.79793 | −0.171426 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.9348 | 1.21681 | 0.608404 | − | 0.793628i | \(-0.291810\pi\) | ||||
0.608404 | + | 0.793628i | \(0.291810\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.2527 | −1.23582 | ||||||||
\(116\) | 10.4243 | 0.967871 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.5706 | 1.24928 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −0.274758 | −0.0248754 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.97958 | −0.716588 | ||||||||
\(125\) | 12.1674 | 1.08829 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.43208 | −0.659490 | −0.329745 | − | 0.944070i | \(-0.606963\pi\) | ||||
−0.329745 | + | 0.944070i | \(0.606963\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.54266 | −0.573829 | ||||||||
\(131\) | 1.64154 | 0.143422 | 0.0717112 | − | 0.997425i | \(-0.477154\pi\) | ||||
0.0717112 | + | 0.997425i | \(0.477154\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.88163 | −0.335322 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.11582 | −0.524427 | ||||||||
\(137\) | −14.5307 | −1.24144 | −0.620721 | − | 0.784032i | \(-0.713160\pi\) | ||||
−0.620721 | + | 0.784032i | \(0.713160\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.26535 | 0.701058 | 0.350529 | − | 0.936552i | \(-0.386002\pi\) | ||||
0.350529 | + | 0.936552i | \(0.386002\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.8738 | 0.912513 | ||||||||
\(143\) | 3.63899 | 0.304308 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.7422 | −1.55645 | ||||||||
\(146\) | 3.85892 | 0.319367 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.1995 | 0.838395 | ||||||||
\(149\) | 7.55045 | 0.618557 | 0.309278 | − | 0.950972i | \(-0.399913\pi\) | ||||
0.309278 | + | 0.950972i | \(0.399913\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.3990 | 1.00902 | 0.504509 | − | 0.863406i | \(-0.331673\pi\) | ||||
0.504509 | + | 0.863406i | \(0.331673\pi\) | |||||||
\(152\) | 1.84106 | 0.149330 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.3468 | 1.15236 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.54011 | −0.362340 | −0.181170 | − | 0.983452i | \(-0.557988\pi\) | ||||
−0.181170 | + | 0.983452i | \(0.557988\pi\) | |||||||
\(158\) | 12.5174 | 0.995831 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.79793 | 0.142139 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.8275 | 1.23971 | 0.619853 | − | 0.784718i | \(-0.287192\pi\) | ||||
0.619853 | + | 0.784718i | \(0.287192\pi\) | |||||||
\(164\) | 8.17680 | 0.638501 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.27314 | −0.409275 | ||||||||
\(167\) | −22.0844 | −1.70894 | −0.854471 | − | 0.519499i | \(-0.826118\pi\) | ||||
−0.854471 | + | 0.519499i | \(0.826118\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.242256 | 0.0186350 | ||||||||
\(170\) | 10.9958 | 0.843341 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.28577 | −0.174288 | ||||||||
\(173\) | −10.2628 | −0.780266 | −0.390133 | − | 0.920758i | \(-0.627571\pi\) | ||||
−0.390133 | + | 0.920758i | \(0.627571\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.98214 | −0.148567 | ||||||||
\(179\) | 12.3954 | 0.926477 | 0.463239 | − | 0.886234i | \(-0.346687\pi\) | ||||
0.463239 | + | 0.886234i | \(0.346687\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.4506 | 1.66874 | 0.834370 | − | 0.551204i | \(-0.185831\pi\) | ||||
0.834370 | + | 0.551204i | \(0.185831\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.37109 | −0.543404 | ||||||||
\(185\) | −18.3380 | −1.34824 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.11582 | −0.447233 | ||||||||
\(188\) | −0.669485 | −0.0488272 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.31010 | −0.240140 | ||||||||
\(191\) | 13.7142 | 0.992327 | 0.496164 | − | 0.868229i | \(-0.334742\pi\) | ||||
0.496164 | + | 0.868229i | \(0.334742\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.77883 | 0.272006 | 0.136003 | − | 0.990708i | \(-0.456574\pi\) | ||||
0.136003 | + | 0.990708i | \(0.456574\pi\) | |||||||
\(194\) | 4.12066 | 0.295846 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.6316 | 1.54119 | 0.770594 | − | 0.637327i | \(-0.219960\pi\) | ||||
0.770594 | + | 0.637327i | \(0.219960\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.8323 | 1.26410 | 0.632051 | − | 0.774927i | \(-0.282213\pi\) | ||||
0.632051 | + | 0.774927i | \(0.282213\pi\) | |||||||
\(200\) | 1.76744 | 0.124977 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.90367 | −0.485741 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.7013 | −1.02679 | ||||||||
\(206\) | 12.6154 | 0.878953 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.63899 | −0.252319 | ||||||||
\(209\) | 1.84106 | 0.127349 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.27020 | −0.569344 | −0.284672 | − | 0.958625i | \(-0.591885\pi\) | ||||
−0.284672 | + | 0.958625i | \(0.591885\pi\) | |||||||
\(212\) | −11.2848 | −0.775046 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 16.9417 | 1.15811 | ||||||||
\(215\) | 4.10965 | 0.280276 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −9.76326 | −0.661252 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.79793 | 0.121217 | ||||||||
\(221\) | −22.2554 | −1.49706 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.10574 | 0.609765 | 0.304883 | − | 0.952390i | \(-0.401383\pi\) | ||||
0.304883 | + | 0.952390i | \(0.401383\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.9348 | −0.860413 | ||||||||
\(227\) | −0.620456 | −0.0411811 | −0.0205905 | − | 0.999788i | \(-0.506555\pi\) | ||||
−0.0205905 | + | 0.999788i | \(0.506555\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.0011 | −1.18954 | −0.594772 | − | 0.803895i | \(-0.702758\pi\) | ||||
−0.594772 | + | 0.803895i | \(0.702758\pi\) | |||||||
\(230\) | 13.2527 | 0.873858 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.4243 | −0.684388 | ||||||||
\(233\) | 19.8697 | 1.30171 | 0.650853 | − | 0.759204i | \(-0.274412\pi\) | ||||
0.650853 | + | 0.759204i | \(0.274412\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.20369 | 0.0785201 | ||||||||
\(236\) | −13.5706 | −0.883371 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.4201 | 1.12681 | 0.563407 | − | 0.826180i | \(-0.309490\pi\) | ||||
0.563407 | + | 0.826180i | \(0.309490\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.4149 | −1.18621 | −0.593104 | − | 0.805126i | \(-0.702098\pi\) | ||||
−0.593104 | + | 0.805126i | \(0.702098\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.274758 | 0.0175896 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.69959 | 0.426285 | ||||||||
\(248\) | 7.97958 | 0.506704 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.1674 | −0.769534 | ||||||||
\(251\) | 21.8022 | 1.37614 | 0.688072 | − | 0.725642i | \(-0.258457\pi\) | ||||
0.688072 | + | 0.725642i | \(0.258457\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.37109 | −0.463416 | ||||||||
\(254\) | 7.43208 | 0.466330 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.00229 | −0.249656 | −0.124828 | − | 0.992178i | \(-0.539838\pi\) | ||||
−0.124828 | + | 0.992178i | \(0.539838\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.54266 | 0.405759 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.64154 | −0.101415 | ||||||||
\(263\) | 1.13946 | 0.0702619 | 0.0351309 | − | 0.999383i | \(-0.488815\pi\) | ||||
0.0351309 | + | 0.999383i | \(0.488815\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.2894 | 1.24637 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.88163 | 0.237108 | ||||||||
\(269\) | 3.85892 | 0.235283 | 0.117641 | − | 0.993056i | \(-0.462467\pi\) | ||||
0.117641 | + | 0.993056i | \(0.462467\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.0202 | 1.33763 | 0.668815 | − | 0.743429i | \(-0.266802\pi\) | ||||
0.668815 | + | 0.743429i | \(0.266802\pi\) | |||||||
\(272\) | 6.11582 | 0.370826 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.5307 | 0.877832 | ||||||||
\(275\) | 1.76744 | 0.106581 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.1307 | −0.788950 | −0.394475 | − | 0.918907i | \(-0.629073\pi\) | ||||
−0.394475 | + | 0.918907i | \(0.629073\pi\) | |||||||
\(278\) | −8.26535 | −0.495723 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.1064 | 0.960828 | 0.480414 | − | 0.877042i | \(-0.340486\pi\) | ||||
0.480414 | + | 0.877042i | \(0.340486\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.6085 | 0.630610 | 0.315305 | − | 0.948990i | \(-0.397893\pi\) | ||||
0.315305 | + | 0.948990i | \(0.397893\pi\) | |||||||
\(284\) | −10.8738 | −0.645244 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.63899 | −0.215178 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 20.4032 | 1.20019 | ||||||||
\(290\) | 18.7422 | 1.10058 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.85892 | −0.225826 | ||||||||
\(293\) | −3.69313 | −0.215755 | −0.107877 | − | 0.994164i | \(-0.534405\pi\) | ||||
−0.107877 | + | 0.994164i | \(0.534405\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.3990 | 1.42057 | ||||||||
\(296\) | −10.1995 | −0.592835 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.55045 | −0.437386 | ||||||||
\(299\) | −26.8233 | −1.55123 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −12.3990 | −0.713484 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.84106 | −0.105592 | ||||||||
\(305\) | −0.493996 | −0.0282861 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.1223 | −1.09137 | −0.545683 | − | 0.837992i | \(-0.683730\pi\) | ||||
−0.545683 | + | 0.837992i | \(0.683730\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −14.3468 | −0.814841 | ||||||||
\(311\) | −13.1190 | −0.743913 | −0.371956 | − | 0.928250i | \(-0.621313\pi\) | ||||
−0.371956 | + | 0.928250i | \(0.621313\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.6248 | 0.713594 | 0.356797 | − | 0.934182i | \(-0.383869\pi\) | ||||
0.356797 | + | 0.934182i | \(0.383869\pi\) | |||||||
\(314\) | 4.54011 | 0.256213 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.5174 | −0.704159 | ||||||||
\(317\) | 29.4555 | 1.65438 | 0.827192 | − | 0.561919i | \(-0.189937\pi\) | ||||
0.827192 | + | 0.561919i | \(0.189937\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.4243 | −0.583648 | ||||||||
\(320\) | −1.79793 | −0.100507 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.2596 | −0.626499 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.43169 | 0.356766 | ||||||||
\(326\) | −15.8275 | −0.876604 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.17680 | −0.451489 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.28901 | 0.125815 | 0.0629077 | − | 0.998019i | \(-0.479963\pi\) | ||||
0.0629077 | + | 0.998019i | \(0.479963\pi\) | |||||||
\(332\) | 5.27314 | 0.289401 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 22.0844 | 1.20840 | ||||||||
\(335\) | −6.97891 | −0.381299 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.35093 | 0.291484 | 0.145742 | − | 0.989323i | \(-0.453443\pi\) | ||||
0.145742 | + | 0.989323i | \(0.453443\pi\) | |||||||
\(338\) | −0.242256 | −0.0131770 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −10.9958 | −0.596332 | ||||||||
\(341\) | 7.97958 | 0.432119 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.28577 | 0.123240 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.2628 | 0.551731 | ||||||||
\(347\) | −20.8197 | −1.11766 | −0.558830 | − | 0.829282i | \(-0.688750\pi\) | ||||
−0.558830 | + | 0.829282i | \(0.688750\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.1843 | 1.24103 | 0.620514 | − | 0.784195i | \(-0.286924\pi\) | ||||
0.620514 | + | 0.784195i | \(0.286924\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 12.1243 | 0.645310 | 0.322655 | − | 0.946517i | \(-0.395425\pi\) | ||||
0.322655 | + | 0.946517i | \(0.395425\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.5504 | 1.03763 | ||||||||
\(356\) | 1.98214 | 0.105053 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.3954 | −0.655118 | ||||||||
\(359\) | −12.3312 | −0.650815 | −0.325408 | − | 0.945574i | \(-0.605501\pi\) | ||||
−0.325408 | + | 0.945574i | \(0.605501\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.6105 | −0.821605 | ||||||||
\(362\) | −22.4506 | −1.17998 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.93808 | 0.363156 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.0860 | 0.944081 | 0.472041 | − | 0.881577i | \(-0.343518\pi\) | ||||
0.472041 | + | 0.881577i | \(0.343518\pi\) | |||||||
\(368\) | 7.37109 | 0.384245 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 18.3380 | 0.953349 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.95365 | 0.360046 | 0.180023 | − | 0.983662i | \(-0.442383\pi\) | ||||
0.180023 | + | 0.983662i | \(0.442383\pi\) | |||||||
\(374\) | 6.11582 | 0.316241 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.669485 | 0.0345261 | ||||||||
\(377\) | −37.9339 | −1.95370 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.14307 | 0.264182 | 0.132091 | − | 0.991238i | \(-0.457831\pi\) | ||||
0.132091 | + | 0.991238i | \(0.457831\pi\) | |||||||
\(380\) | 3.31010 | 0.169804 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −13.7142 | −0.701681 | ||||||||
\(383\) | −18.8810 | −0.964772 | −0.482386 | − | 0.875959i | \(-0.660230\pi\) | ||||
−0.482386 | + | 0.875959i | \(0.660230\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.77883 | −0.192337 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.12066 | −0.209195 | ||||||||
\(389\) | 30.3990 | 1.54129 | 0.770646 | − | 0.637263i | \(-0.219934\pi\) | ||||
0.770646 | + | 0.637263i | \(0.219934\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 45.0802 | 2.27980 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −21.6316 | −1.08978 | ||||||||
\(395\) | 22.5054 | 1.13237 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.08009 | 0.104397 | 0.0521983 | − | 0.998637i | \(-0.483377\pi\) | ||||
0.0521983 | + | 0.998637i | \(0.483377\pi\) | |||||||
\(398\) | −17.8323 | −0.893855 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.76744 | −0.0883719 | ||||||||
\(401\) | 21.8444 | 1.09086 | 0.545429 | − | 0.838157i | \(-0.316367\pi\) | ||||
0.545429 | + | 0.838157i | \(0.316367\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.0376 | 1.44647 | ||||||||
\(404\) | 6.90367 | 0.343470 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.1995 | −0.505571 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.7571 | −1.66918 | −0.834591 | − | 0.550871i | \(-0.814296\pi\) | ||||
−0.834591 | + | 0.550871i | \(0.814296\pi\) | |||||||
\(410\) | 14.7013 | 0.726048 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −12.6154 | −0.621514 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.48074 | −0.465391 | ||||||||
\(416\) | 3.63899 | 0.178416 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.84106 | −0.0900491 | ||||||||
\(419\) | 22.7371 | 1.11078 | 0.555389 | − | 0.831590i | \(-0.312569\pi\) | ||||
0.555389 | + | 0.831590i | \(0.312569\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.0192 | −1.02441 | −0.512207 | − | 0.858862i | \(-0.671172\pi\) | ||||
−0.512207 | + | 0.858862i | \(0.671172\pi\) | |||||||
\(422\) | 8.27020 | 0.402587 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.2848 | 0.548040 | ||||||||
\(425\) | −10.8093 | −0.524329 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −16.9417 | −0.818908 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.10965 | −0.198185 | ||||||||
\(431\) | −7.03305 | −0.338770 | −0.169385 | − | 0.985550i | \(-0.554178\pi\) | ||||
−0.169385 | + | 0.985550i | \(0.554178\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.77293 | −0.277429 | −0.138715 | − | 0.990332i | \(-0.544297\pi\) | ||||
−0.138715 | + | 0.990332i | \(0.544297\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.76326 | 0.467576 | ||||||||
\(437\) | −13.5706 | −0.649170 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.2275 | −1.49041 | −0.745203 | − | 0.666838i | \(-0.767647\pi\) | ||||
−0.745203 | + | 0.666838i | \(0.767647\pi\) | |||||||
\(440\) | −1.79793 | −0.0857131 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 22.2554 | 1.05858 | ||||||||
\(443\) | 35.8953 | 1.70544 | 0.852720 | − | 0.522369i | \(-0.174952\pi\) | ||||
0.852720 | + | 0.522369i | \(0.174952\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.56375 | −0.168938 | ||||||||
\(446\) | −9.10574 | −0.431169 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.5495 | 1.15856 | 0.579282 | − | 0.815127i | \(-0.303333\pi\) | ||||
0.579282 | + | 0.815127i | \(0.303333\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.17680 | −0.385031 | ||||||||
\(452\) | 12.9348 | 0.608404 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.620456 | 0.0291194 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.2771 | 1.22919 | 0.614594 | − | 0.788843i | \(-0.289320\pi\) | ||||
0.614594 | + | 0.788843i | \(0.289320\pi\) | |||||||
\(458\) | 18.0011 | 0.841134 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −13.2527 | −0.617911 | ||||||||
\(461\) | 20.8330 | 0.970289 | 0.485144 | − | 0.874434i | \(-0.338767\pi\) | ||||
0.485144 | + | 0.874434i | \(0.338767\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.8697 | 0.830474 | 0.415237 | − | 0.909713i | \(-0.363699\pi\) | ||||
0.415237 | + | 0.909713i | \(0.363699\pi\) | |||||||
\(464\) | 10.4243 | 0.483936 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −19.8697 | −0.920445 | ||||||||
\(467\) | −26.8642 | −1.24312 | −0.621562 | − | 0.783365i | \(-0.713502\pi\) | ||||
−0.621562 | + | 0.783365i | \(0.713502\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.20369 | −0.0555221 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.5706 | 0.624638 | ||||||||
\(473\) | 2.28577 | 0.105100 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.25396 | 0.149302 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −17.4201 | −0.796778 | ||||||||
\(479\) | −15.5050 | −0.708443 | −0.354221 | − | 0.935162i | \(-0.615254\pi\) | ||||
−0.354221 | + | 0.935162i | \(0.615254\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.1159 | −1.69234 | ||||||||
\(482\) | 18.4149 | 0.838775 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 7.40867 | 0.336411 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.8858 | 0.493283 | 0.246641 | − | 0.969107i | \(-0.420673\pi\) | ||||
0.246641 | + | 0.969107i | \(0.420673\pi\) | |||||||
\(488\) | −0.274758 | −0.0124377 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.06975 | −0.319053 | −0.159527 | − | 0.987194i | \(-0.550997\pi\) | ||||
−0.159527 | + | 0.987194i | \(0.550997\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 63.7531 | 2.87129 | ||||||||
\(494\) | −6.69959 | −0.301429 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.97958 | −0.358294 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.8678 | 0.844637 | 0.422319 | − | 0.906447i | \(-0.361216\pi\) | ||||
0.422319 | + | 0.906447i | \(0.361216\pi\) | |||||||
\(500\) | 12.1674 | 0.544143 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −21.8022 | −0.973081 | ||||||||
\(503\) | 28.9752 | 1.29194 | 0.645969 | − | 0.763364i | \(-0.276453\pi\) | ||||
0.645969 | + | 0.763364i | \(0.276453\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.4123 | −0.552342 | ||||||||
\(506\) | 7.37109 | 0.327685 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.43208 | −0.329745 | ||||||||
\(509\) | −16.3539 | −0.724874 | −0.362437 | − | 0.932008i | \(-0.618055\pi\) | ||||
−0.362437 | + | 0.932008i | \(0.618055\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.00229 | 0.176534 | ||||||||
\(515\) | 22.6816 | 0.999469 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.669485 | 0.0294439 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.54266 | −0.286915 | ||||||||
\(521\) | −21.6949 | −0.950470 | −0.475235 | − | 0.879859i | \(-0.657637\pi\) | ||||
−0.475235 | + | 0.879859i | \(0.657637\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.8171 | 1.65363 | 0.826814 | − | 0.562475i | \(-0.190151\pi\) | ||||
0.826814 | + | 0.562475i | \(0.190151\pi\) | |||||||
\(524\) | 1.64154 | 0.0717112 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.13946 | −0.0496826 | ||||||||
\(527\) | −48.8017 | −2.12583 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 31.3329 | 1.36230 | ||||||||
\(530\) | −20.2894 | −0.881314 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −29.7553 | −1.28885 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 30.4600 | 1.31690 | ||||||||
\(536\) | −3.88163 | −0.167661 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.85892 | −0.166370 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.68212 | 0.0723198 | 0.0361599 | − | 0.999346i | \(-0.488487\pi\) | ||||
0.0361599 | + | 0.999346i | \(0.488487\pi\) | |||||||
\(542\) | −22.0202 | −0.945847 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.11582 | −0.262213 | ||||||||
\(545\) | −17.5537 | −0.751917 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.6665 | 0.584339 | 0.292170 | − | 0.956366i | \(-0.405623\pi\) | ||||
0.292170 | + | 0.956366i | \(0.405623\pi\) | |||||||
\(548\) | −14.5307 | −0.620721 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.76744 | −0.0753638 | ||||||||
\(551\) | −19.1917 | −0.817595 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 13.1307 | 0.557872 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.26535 | 0.350529 | ||||||||
\(557\) | 8.99583 | 0.381165 | 0.190583 | − | 0.981671i | \(-0.438962\pi\) | ||||
0.190583 | + | 0.981671i | \(0.438962\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.31788 | 0.351809 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.1064 | −0.679408 | ||||||||
\(563\) | 21.7461 | 0.916489 | 0.458244 | − | 0.888826i | \(-0.348478\pi\) | ||||
0.458244 | + | 0.888826i | \(0.348478\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −23.2560 | −0.978386 | ||||||||
\(566\) | −10.6085 | −0.445908 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.8738 | 0.456256 | ||||||||
\(569\) | −32.4549 | −1.36058 | −0.680290 | − | 0.732943i | \(-0.738146\pi\) | ||||
−0.680290 | + | 0.732943i | \(0.738146\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.2031 | −0.845474 | −0.422737 | − | 0.906252i | \(-0.638931\pi\) | ||||
−0.422737 | + | 0.906252i | \(0.638931\pi\) | |||||||
\(572\) | 3.63899 | 0.152154 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.0279 | −0.543303 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.4458 | −1.01769 | −0.508845 | − | 0.860858i | \(-0.669927\pi\) | ||||
−0.508845 | + | 0.860858i | \(0.669927\pi\) | |||||||
\(578\) | −20.4032 | −0.848661 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −18.7422 | −0.778226 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.2848 | 0.467370 | ||||||||
\(584\) | 3.85892 | 0.159683 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.69313 | 0.152562 | ||||||||
\(587\) | 16.8894 | 0.697101 | 0.348550 | − | 0.937290i | \(-0.386674\pi\) | ||||
0.348550 | + | 0.937290i | \(0.386674\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.6909 | 0.605327 | ||||||||
\(590\) | −24.3990 | −1.00449 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.1995 | 0.419197 | ||||||||
\(593\) | −22.2781 | −0.914852 | −0.457426 | − | 0.889248i | \(-0.651229\pi\) | ||||
−0.457426 | + | 0.889248i | \(0.651229\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.55045 | 0.309278 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 26.8233 | 1.09689 | ||||||||
\(599\) | 6.25179 | 0.255441 | 0.127721 | − | 0.991810i | \(-0.459234\pi\) | ||||
0.127721 | + | 0.991810i | \(0.459234\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.3043 | −1.27693 | −0.638465 | − | 0.769651i | \(-0.720430\pi\) | ||||
−0.638465 | + | 0.769651i | \(0.720430\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.3990 | 0.504509 | ||||||||
\(605\) | −1.79793 | −0.0730964 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.0348 | 1.01613 | 0.508066 | − | 0.861318i | \(-0.330361\pi\) | ||||
0.508066 | + | 0.861318i | \(0.330361\pi\) | |||||||
\(608\) | 1.84106 | 0.0746648 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.493996 | 0.0200013 | ||||||||
\(611\) | 2.43625 | 0.0985602 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.17157 | 0.0473194 | 0.0236597 | − | 0.999720i | \(-0.492468\pi\) | ||||
0.0236597 | + | 0.999720i | \(0.492468\pi\) | |||||||
\(614\) | 19.1223 | 0.771713 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.06651 | −0.203970 | −0.101985 | − | 0.994786i | \(-0.532519\pi\) | ||||
−0.101985 | + | 0.994786i | \(0.532519\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.6812 | 0.992021 | 0.496010 | − | 0.868317i | \(-0.334798\pi\) | ||||
0.496010 | + | 0.868317i | \(0.334798\pi\) | |||||||
\(620\) | 14.3468 | 0.576180 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 13.1190 | 0.526026 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.0390 | −0.521559 | ||||||||
\(626\) | −12.6248 | −0.504587 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.54011 | −0.181170 | ||||||||
\(629\) | 62.3784 | 2.48719 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.8408 | −1.02871 | −0.514353 | − | 0.857579i | \(-0.671968\pi\) | ||||
−0.514353 | + | 0.857579i | \(0.671968\pi\) | |||||||
\(632\) | 12.5174 | 0.497915 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −29.4555 | −1.16983 | ||||||||
\(635\) | 13.3624 | 0.530270 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 10.4243 | 0.412702 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.79793 | 0.0710695 | ||||||||
\(641\) | 3.19684 | 0.126267 | 0.0631337 | − | 0.998005i | \(-0.479891\pi\) | ||||
0.0631337 | + | 0.998005i | \(0.479891\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.7623 | −0.818787 | −0.409393 | − | 0.912358i | \(-0.634260\pi\) | ||||
−0.409393 | + | 0.912358i | \(0.634260\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.2596 | 0.443002 | ||||||||
\(647\) | 28.4056 | 1.11674 | 0.558370 | − | 0.829592i | \(-0.311427\pi\) | ||||
0.558370 | + | 0.829592i | \(0.311427\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.5706 | 0.532693 | ||||||||
\(650\) | −6.43169 | −0.252272 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15.8275 | 0.619853 | ||||||||
\(653\) | −16.7825 | −0.656750 | −0.328375 | − | 0.944548i | \(-0.606501\pi\) | ||||
−0.328375 | + | 0.944548i | \(0.606501\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.95138 | −0.115320 | ||||||||
\(656\) | 8.17680 | 0.319251 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.3426 | 0.597662 | 0.298831 | − | 0.954306i | \(-0.403403\pi\) | ||||
0.298831 | + | 0.954306i | \(0.403403\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.68735 | 0.260108 | 0.130054 | − | 0.991507i | \(-0.458485\pi\) | ||||
0.130054 | + | 0.991507i | \(0.458485\pi\) | |||||||
\(662\) | −2.28901 | −0.0889649 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.27314 | −0.204637 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 76.8384 | 2.97519 | ||||||||
\(668\) | −22.0844 | −0.854471 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.97891 | 0.269619 | ||||||||
\(671\) | −0.274758 | −0.0106069 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.4921 | 0.481536 | 0.240768 | − | 0.970583i | \(-0.422601\pi\) | ||||
0.240768 | + | 0.970583i | \(0.422601\pi\) | |||||||
\(674\) | −5.35093 | −0.206110 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.242256 | 0.00931752 | ||||||||
\(677\) | 16.8830 | 0.648866 | 0.324433 | − | 0.945909i | \(-0.394826\pi\) | ||||
0.324433 | + | 0.945909i | \(0.394826\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 10.9958 | 0.421671 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.97958 | −0.305554 | ||||||||
\(683\) | 6.76970 | 0.259036 | 0.129518 | − | 0.991577i | \(-0.458657\pi\) | ||||
0.129518 | + | 0.991577i | \(0.458657\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.1252 | 0.998193 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.28577 | −0.0871440 | ||||||||
\(689\) | 41.0654 | 1.56447 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 42.8876 | 1.63152 | 0.815760 | − | 0.578391i | \(-0.196319\pi\) | ||||
0.815760 | + | 0.578391i | \(0.196319\pi\) | |||||||
\(692\) | −10.2628 | −0.390133 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.8197 | 0.790305 | ||||||||
\(695\) | −14.8605 | −0.563693 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 50.0078 | 1.89418 | ||||||||
\(698\) | −23.1843 | −0.877540 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.8990 | 1.28035 | 0.640173 | − | 0.768231i | \(-0.278863\pi\) | ||||
0.640173 | + | 0.768231i | \(0.278863\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.7779 | −0.708222 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.1243 | −0.456303 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.6407 | −1.07562 | −0.537812 | − | 0.843065i | \(-0.680749\pi\) | ||||
−0.537812 | + | 0.843065i | \(0.680749\pi\) | |||||||
\(710\) | −19.5504 | −0.733715 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.98214 | −0.0742837 | ||||||||
\(713\) | −58.8182 | −2.20276 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.54266 | −0.244682 | ||||||||
\(716\) | 12.3954 | 0.463239 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12.3312 | 0.460196 | ||||||||
\(719\) | 2.52225 | 0.0940639 | 0.0470319 | − | 0.998893i | \(-0.485024\pi\) | ||||
0.0470319 | + | 0.998893i | \(0.485024\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 15.6105 | 0.580963 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 22.4506 | 0.834370 | ||||||||
\(725\) | −18.4243 | −0.684261 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.0452 | 1.11431 | 0.557157 | − | 0.830407i | \(-0.311892\pi\) | ||||
0.557157 | + | 0.830407i | \(0.311892\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.93808 | −0.256790 | ||||||||
\(731\) | −13.9793 | −0.517044 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.5866 | 1.24055 | 0.620275 | − | 0.784385i | \(-0.287021\pi\) | ||||
0.620275 | + | 0.784385i | \(0.287021\pi\) | |||||||
\(734\) | −18.0860 | −0.667566 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.37109 | −0.271702 | ||||||||
\(737\) | −3.88163 | −0.142982 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.7380 | −1.09393 | −0.546965 | − | 0.837155i | \(-0.684217\pi\) | ||||
−0.546965 | + | 0.837155i | \(0.684217\pi\) | |||||||
\(740\) | −18.3380 | −0.674120 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.59262 | −0.0584276 | −0.0292138 | − | 0.999573i | \(-0.509300\pi\) | ||||
−0.0292138 | + | 0.999573i | \(0.509300\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.5752 | −0.497357 | ||||||||
\(746\) | −6.95365 | −0.254591 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.11582 | −0.223616 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.305924 | 0.0111633 | 0.00558166 | − | 0.999984i | \(-0.498223\pi\) | ||||
0.00558166 | + | 0.999984i | \(0.498223\pi\) | |||||||
\(752\) | −0.669485 | −0.0244136 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 37.9339 | 1.38147 | ||||||||
\(755\) | −22.2926 | −0.811312 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.4921 | 1.47171 | 0.735856 | − | 0.677138i | \(-0.236780\pi\) | ||||
0.735856 | + | 0.677138i | \(0.236780\pi\) | |||||||
\(758\) | −5.14307 | −0.186805 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.31010 | −0.120070 | ||||||||
\(761\) | 48.6887 | 1.76496 | 0.882482 | − | 0.470346i | \(-0.155871\pi\) | ||||
0.882482 | + | 0.470346i | \(0.155871\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 13.7142 | 0.496164 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.8810 | 0.682197 | ||||||||
\(767\) | 49.3833 | 1.78313 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.7255 | −0.531017 | −0.265508 | − | 0.964109i | \(-0.585540\pi\) | ||||
−0.265508 | + | 0.964109i | \(0.585540\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.77883 | 0.136003 | ||||||||
\(773\) | 28.9612 | 1.04166 | 0.520830 | − | 0.853660i | \(-0.325622\pi\) | ||||
0.520830 | + | 0.853660i | \(0.325622\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.1034 | 0.506610 | ||||||||
\(776\) | 4.12066 | 0.147923 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −30.3990 | −1.08986 | ||||||||
\(779\) | −15.0540 | −0.539365 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.8738 | 0.389097 | ||||||||
\(782\) | −45.0802 | −1.61207 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.16281 | 0.291343 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.14203 | 0.0763551 | 0.0381775 | − | 0.999271i | \(-0.487845\pi\) | ||||
0.0381775 | + | 0.999271i | \(0.487845\pi\) | |||||||
\(788\) | 21.6316 | 0.770594 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −22.5054 | −0.800708 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.999840 | −0.0355054 | ||||||||
\(794\) | −2.08009 | −0.0738196 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.8323 | 0.632051 | ||||||||
\(797\) | 7.38735 | 0.261673 | 0.130837 | − | 0.991404i | \(-0.458234\pi\) | ||||
0.130837 | + | 0.991404i | \(0.458234\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.09445 | −0.144851 | ||||||||
\(800\) | 1.76744 | 0.0624884 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −21.8444 | −0.771353 | ||||||||
\(803\) | 3.85892 | 0.136178 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −29.0376 | −1.02281 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.90367 | −0.242870 | ||||||||
\(809\) | −8.49214 | −0.298568 | −0.149284 | − | 0.988794i | \(-0.547697\pi\) | ||||
−0.149284 | + | 0.988794i | \(0.547697\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.97995 | 0.209984 | 0.104992 | − | 0.994473i | \(-0.466518\pi\) | ||||
0.104992 | + | 0.994473i | \(0.466518\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10.1995 | 0.357493 | ||||||||
\(815\) | −28.4568 | −0.996797 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.20823 | 0.147227 | ||||||||
\(818\) | 33.7571 | 1.18029 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14.7013 | −0.513393 | ||||||||
\(821\) | −20.6430 | −0.720445 | −0.360223 | − | 0.932866i | \(-0.617299\pi\) | ||||
−0.360223 | + | 0.932866i | \(0.617299\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.8269 | −1.14427 | −0.572137 | − | 0.820158i | \(-0.693886\pi\) | ||||
−0.572137 | + | 0.820158i | \(0.693886\pi\) | |||||||
\(824\) | 12.6154 | 0.439477 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.22287 | −0.251164 | −0.125582 | − | 0.992083i | \(-0.540080\pi\) | ||||
−0.125582 | + | 0.992083i | \(0.540080\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −52.2625 | −1.81515 | −0.907577 | − | 0.419887i | \(-0.862070\pi\) | ||||
−0.907577 | + | 0.419887i | \(0.862070\pi\) | |||||||
\(830\) | 9.48074 | 0.329081 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.63899 | −0.126159 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 39.7062 | 1.37409 | ||||||||
\(836\) | 1.84106 | 0.0636743 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −22.7371 | −0.785439 | ||||||||
\(839\) | −20.5644 | −0.709963 | −0.354981 | − | 0.934873i | \(-0.615513\pi\) | ||||
−0.354981 | + | 0.934873i | \(0.615513\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 79.6659 | 2.74710 | ||||||||
\(842\) | 21.0192 | 0.724370 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8.27020 | −0.284672 | ||||||||
\(845\) | −0.435559 | −0.0149837 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −11.2848 | −0.387523 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 10.8093 | 0.370757 | ||||||||
\(851\) | 75.1815 | 2.57719 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.8004 | −0.849148 | −0.424574 | − | 0.905393i | \(-0.639576\pi\) | ||||
−0.424574 | + | 0.905393i | \(0.639576\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16.9417 | 0.579055 | ||||||||
\(857\) | −30.1658 | −1.03044 | −0.515222 | − | 0.857056i | \(-0.672291\pi\) | ||||
−0.515222 | + | 0.857056i | \(0.672291\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.3550 | −0.899219 | −0.449610 | − | 0.893225i | \(-0.648437\pi\) | ||||
−0.449610 | + | 0.893225i | \(0.648437\pi\) | |||||||
\(860\) | 4.10965 | 0.140138 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.03305 | 0.239547 | ||||||||
\(863\) | 16.8489 | 0.573545 | 0.286772 | − | 0.957999i | \(-0.407418\pi\) | ||||
0.286772 | + | 0.957999i | \(0.407418\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.4518 | 0.627381 | ||||||||
\(866\) | 5.77293 | 0.196172 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.5174 | 0.424624 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.1252 | −0.478615 | ||||||||
\(872\) | −9.76326 | −0.330626 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13.5706 | 0.459032 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39.3054 | 1.32725 | 0.663624 | − | 0.748066i | \(-0.269018\pi\) | ||||
0.663624 | + | 0.748066i | \(0.269018\pi\) | |||||||
\(878\) | 31.2275 | 1.05388 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.79793 | 0.0606083 | ||||||||
\(881\) | 12.1055 | 0.407843 | 0.203922 | − | 0.978987i | \(-0.434631\pi\) | ||||
0.203922 | + | 0.978987i | \(0.434631\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.0614 | 0.708773 | 0.354386 | − | 0.935099i | \(-0.384690\pi\) | ||||
0.354386 | + | 0.935099i | \(0.384690\pi\) | |||||||
\(884\) | −22.2554 | −0.748530 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −35.8953 | −1.20593 | ||||||||
\(887\) | −45.1762 | −1.51687 | −0.758434 | − | 0.651750i | \(-0.774035\pi\) | ||||
−0.758434 | + | 0.651750i | \(0.774035\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.56375 | 0.119457 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.10574 | 0.304883 | ||||||||
\(893\) | 1.23256 | 0.0412461 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.2861 | −0.744943 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −24.5495 | −0.819228 | ||||||||
\(899\) | −83.1815 | −2.77426 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −69.0160 | −2.29926 | ||||||||
\(902\) | 8.17680 | 0.272258 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.9348 | −0.430206 | ||||||||
\(905\) | −40.3647 | −1.34177 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.5283 | −1.11329 | −0.556644 | − | 0.830751i | \(-0.687911\pi\) | ||||
−0.556644 | + | 0.830751i | \(0.687911\pi\) | |||||||
\(908\) | −0.620456 | −0.0205905 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.3400 | 0.905813 | 0.452906 | − | 0.891558i | \(-0.350387\pi\) | ||||
0.452906 | + | 0.891558i | \(0.350387\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.27314 | −0.174515 | ||||||||
\(914\) | −26.2771 | −0.869168 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18.0011 | −0.594772 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.6118 | −0.416026 | −0.208013 | − | 0.978126i | \(-0.566700\pi\) | ||||
−0.208013 | + | 0.978126i | \(0.566700\pi\) | |||||||
\(920\) | 13.2527 | 0.436929 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −20.8330 | −0.686098 | ||||||||
\(923\) | 39.5698 | 1.30246 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.0270 | −0.592725 | ||||||||
\(926\) | −17.8697 | −0.587234 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −10.4243 | −0.342194 | ||||||||
\(929\) | −53.3407 | −1.75005 | −0.875027 | − | 0.484075i | \(-0.839156\pi\) | ||||
−0.875027 | + | 0.484075i | \(0.839156\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 19.8697 | 0.650853 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 26.8642 | 0.879022 | ||||||||
\(935\) | 10.9958 | 0.359602 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.5927 | 0.672736 | 0.336368 | − | 0.941731i | \(-0.390801\pi\) | ||||
0.336368 | + | 0.941731i | \(0.390801\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.20369 | 0.0392600 | ||||||||
\(941\) | −27.9554 | −0.911319 | −0.455660 | − | 0.890154i | \(-0.650597\pi\) | ||||
−0.455660 | + | 0.890154i | \(0.650597\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 60.2719 | 1.96272 | ||||||||
\(944\) | −13.5706 | −0.441686 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.28577 | −0.0743167 | ||||||||
\(947\) | 44.7266 | 1.45342 | 0.726710 | − | 0.686945i | \(-0.241049\pi\) | ||||
0.726710 | + | 0.686945i | \(0.241049\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.0426 | 0.455841 | ||||||||
\(950\) | −3.25396 | −0.105572 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.6527 | 1.67320 | 0.836598 | − | 0.547817i | \(-0.184541\pi\) | ||||
0.836598 | + | 0.547817i | \(0.184541\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.6573 | −0.797890 | ||||||||
\(956\) | 17.4201 | 0.563407 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15.5050 | 0.500945 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 32.6738 | 1.05399 | ||||||||
\(962\) | 37.1159 | 1.19667 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −18.4149 | −0.593104 | ||||||||
\(965\) | −6.79409 | −0.218709 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −50.7320 | −1.63143 | −0.815715 | − | 0.578454i | \(-0.803656\pi\) | ||||
−0.815715 | + | 0.578454i | \(0.803656\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.40867 | −0.237878 | ||||||||
\(971\) | −22.7299 | −0.729436 | −0.364718 | − | 0.931118i | \(-0.618835\pi\) | ||||
−0.364718 | + | 0.931118i | \(0.618835\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −10.8858 | −0.348804 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.274758 | 0.00879478 | ||||||||
\(977\) | 27.4811 | 0.879198 | 0.439599 | − | 0.898194i | \(-0.355120\pi\) | ||||
0.439599 | + | 0.898194i | \(0.355120\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.98214 | −0.0633494 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.06975 | 0.225605 | ||||||||
\(983\) | 34.2044 | 1.09095 | 0.545475 | − | 0.838127i | \(-0.316349\pi\) | ||||
0.545475 | + | 0.838127i | \(0.316349\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −38.8921 | −1.23921 | ||||||||
\(986\) | −63.7531 | −2.03031 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.69959 | 0.213143 | ||||||||
\(989\) | −16.8486 | −0.535754 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.3890 | −1.06064 | −0.530318 | − | 0.847799i | \(-0.677927\pi\) | ||||
−0.530318 | + | 0.847799i | \(0.677927\pi\) | |||||||
\(992\) | 7.97958 | 0.253352 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −32.0614 | −1.01641 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.74406 | −0.245257 | −0.122628 | − | 0.992453i | \(-0.539132\pi\) | ||||
−0.122628 | + | 0.992453i | \(0.539132\pi\) | |||||||
\(998\) | −18.8678 | −0.597249 | ||||||||
\(999\) | 0 | 0 |
(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 | 9702.2.a.ea.1.1 | 4 | ||
3.2 | odd | 2 | 3234.2.a.bl.1.4 | ✓ | 4 | ||
7.6 | odd | 2 | 9702.2.a.dz.1.4 | 4 | |||
21.20 | even | 2 | 3234.2.a.bm.1.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3234.2.a.bl.1.4 | ✓ | 4 | 3.2 | odd | 2 | ||
3234.2.a.bm.1.1 | yes | 4 | 21.20 | even | 2 | ||
9702.2.a.dz.1.4 | 4 | 7.6 | odd | 2 | |||
9702.2.a.ea.1.1 | 4 | 1.1 | even | 1 | trivial |