Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3584,2,Mod(1793,3584)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3584, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3584.1793");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3584 = 2^{9} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3584.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(28.6183840844\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 2 x^{10} + 8 x^{9} + 2 x^{8} + 12 x^{7} + 40 x^{6} + 4 x^{5} + 49 x^{4} - 56 x^{3} + \cdots + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1793.2 | ||
Root | \(2.84980 + 1.18043i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3584.1793 |
Dual form | 3584.2.b.l.1793.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3584\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 2.36086i | − 1.36304i | −0.731799 | − | 0.681520i | \(-0.761319\pi\) | ||||
0.731799 | − | 0.681520i | \(-0.238681\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.711757i | 0.318307i | 0.987254 | + | 0.159154i | \(0.0508765\pi\) | ||||
−0.987254 | + | 0.159154i | \(0.949123\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.57364 | −0.857880 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 2.98785i | − 0.900872i | −0.892809 | − | 0.450436i | \(-0.851269\pi\) | ||||
0.892809 | − | 0.450436i | \(-0.148731\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.85246i | 1.90053i | 0.311442 | + | 0.950265i | \(0.399188\pi\) | ||||
−0.311442 | + | 0.950265i | \(0.600812\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.68036 | 0.433866 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.63038 | 0.880495 | 0.440248 | − | 0.897876i | \(-0.354891\pi\) | ||||
0.440248 | + | 0.897876i | \(0.354891\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.35428i | 0.310693i | 0.987860 | + | 0.155347i | \(0.0496494\pi\) | ||||
−0.987860 | + | 0.155347i | \(0.950351\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 2.36086i | − 0.515181i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.07739 | −0.224651 | −0.112326 | − | 0.993671i | \(-0.535830\pi\) | ||||
−0.112326 | + | 0.993671i | \(0.535830\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.49340 | 0.898680 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 1.00658i | − 0.193716i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.17376i | 1.70352i | 0.523929 | + | 0.851762i | \(0.324466\pi\) | ||||
−0.523929 | + | 0.851762i | \(0.675534\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.57079 | −1.53936 | −0.769680 | − | 0.638430i | \(-0.779584\pi\) | ||||
−0.769680 | + | 0.638430i | \(0.779584\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.05389 | −1.22792 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.711757i | 0.120309i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.30788i | 1.03701i | 0.855075 | + | 0.518505i | \(0.173511\pi\) | ||||
−0.855075 | + | 0.518505i | \(0.826489\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 16.1777 | 2.59050 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.55764 | 0.711784 | 0.355892 | − | 0.934527i | \(-0.384177\pi\) | ||||
0.355892 | + | 0.934527i | \(0.384177\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.12198i | 1.23859i | 0.785158 | + | 0.619295i | \(0.212582\pi\) | ||||
−0.785158 | + | 0.619295i | \(0.787418\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 1.83181i | − 0.273069i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.349902 | −0.0510385 | −0.0255192 | − | 0.999674i | \(-0.508124\pi\) | ||||
−0.0255192 | + | 0.999674i | \(0.508124\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 8.57079i | − 1.20015i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 2.37638i | − 0.326421i | −0.986591 | − | 0.163211i | \(-0.947815\pi\) | ||||
0.986591 | − | 0.163211i | \(-0.0521850\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.12662 | 0.286754 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.19726 | 0.423487 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.30257i | 0.560148i | 0.959978 | + | 0.280074i | \(0.0903589\pi\) | ||||
−0.959978 | + | 0.280074i | \(0.909641\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.92519i | 0.630606i | 0.948991 | + | 0.315303i | \(0.102106\pi\) | ||||
−0.948991 | + | 0.315303i | \(0.897894\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.57364 | −0.324248 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.87728 | −0.604953 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.16618i | 0.264641i | 0.991207 | + | 0.132321i | \(0.0422429\pi\) | ||||
−0.991207 | + | 0.132321i | \(0.957757\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.54356i | 0.306209i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.44999 | 0.409439 | 0.204719 | − | 0.978821i | \(-0.434372\pi\) | ||||
0.204719 | + | 0.978821i | \(0.434372\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.06704 | −0.827135 | −0.413567 | − | 0.910474i | \(-0.635717\pi\) | ||||
−0.413567 | + | 0.910474i | \(0.635717\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 10.6083i | − 1.22494i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 2.98785i | − 0.340497i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.7182 | 1.54342 | 0.771712 | − | 0.635973i | \(-0.219401\pi\) | ||||
0.771712 | + | 0.635973i | \(0.219401\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.0973 | −1.12192 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.7807i | 1.62240i | 0.584772 | + | 0.811198i | \(0.301184\pi\) | ||||
−0.584772 | + | 0.811198i | \(0.698816\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.58394i | 0.280268i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 21.6579 | 2.32197 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.41460 | −0.891946 | −0.445973 | − | 0.895046i | \(-0.647142\pi\) | ||||
−0.445973 | + | 0.895046i | \(0.647142\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.85246i | 0.718333i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 20.2344i | 2.09821i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.963918 | −0.0988959 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.3981 | 1.56344 | 0.781720 | − | 0.623630i | \(-0.214343\pi\) | ||||
0.781720 | + | 0.623630i | \(0.214343\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.68966i | 0.772839i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 11.6052i | − 1.15476i | −0.816475 | − | 0.577381i | \(-0.804075\pi\) | ||||
0.816475 | − | 0.577381i | \(-0.195925\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.0581 | 1.38519 | 0.692594 | − | 0.721327i | \(-0.256468\pi\) | ||||
0.692594 | + | 0.721327i | \(0.256468\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.68036 | 0.163986 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 2.39821i | − 0.231844i | −0.993258 | − | 0.115922i | \(-0.963018\pi\) | ||||
0.993258 | − | 0.115922i | \(-0.0369823\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1.28723i | − 0.123294i | −0.998098 | − | 0.0616471i | \(-0.980365\pi\) | ||||
0.998098 | − | 0.0616471i | \(-0.0196353\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.8920 | 1.41349 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.85411 | −0.456636 | −0.228318 | − | 0.973587i | \(-0.573323\pi\) | ||||
−0.228318 | + | 0.973587i | \(0.573323\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 0.766840i | − 0.0715082i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 17.6358i | − 1.63043i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.63038 | 0.332796 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.07274 | 0.188431 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 10.7599i | − 0.970190i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.75699i | 0.604364i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.92442 | −0.348236 | −0.174118 | − | 0.984725i | \(-0.555707\pi\) | ||||
−0.174118 | + | 0.984725i | \(0.555707\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 19.1748 | 1.68825 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 13.4518i | − 1.17529i | −0.809118 | − | 0.587646i | \(-0.800055\pi\) | ||||
0.809118 | − | 0.587646i | \(-0.199945\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.35428i | 0.117431i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.716437 | 0.0616611 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.6239 | 1.59115 | 0.795575 | − | 0.605855i | \(-0.207169\pi\) | ||||
0.795575 | + | 0.605855i | \(0.207169\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.14960i | 0.606421i | 0.952924 | + | 0.303211i | \(0.0980586\pi\) | ||||
−0.952924 | + | 0.303211i | \(0.901941\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.826069i | 0.0695675i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 20.4741 | 1.71213 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.52948 | −0.542244 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 2.36086i | − 0.194720i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 0.489493i | − 0.0401008i | −0.999799 | − | 0.0200504i | \(-0.993617\pi\) | ||||
0.999799 | − | 0.0200504i | \(-0.00638267\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.4722 | −1.82876 | −0.914382 | − | 0.404853i | \(-0.867323\pi\) | ||||
−0.914382 | + | 0.404853i | \(0.867323\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.34328 | −0.755359 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 6.10032i | − 0.489989i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.2478i | 1.29672i | 0.761335 | + | 0.648359i | \(0.224544\pi\) | ||||
−0.761335 | + | 0.648359i | \(0.775456\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.61029 | −0.444925 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.07739 | −0.0849102 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 4.84263i | − 0.379304i | −0.981851 | − | 0.189652i | \(-0.939264\pi\) | ||||
0.981851 | − | 0.189652i | \(-0.0607360\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 5.02065i | − 0.390857i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.49149 | −0.734473 | −0.367237 | − | 0.930128i | \(-0.619696\pi\) | ||||
−0.367237 | + | 0.930128i | \(0.619696\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −33.9562 | −2.61202 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 3.48543i | − 0.266537i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 7.89792i | − 0.600467i | −0.953866 | − | 0.300234i | \(-0.902935\pi\) | ||||
0.953866 | − | 0.300234i | \(-0.0970647\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.49340 | 0.339669 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.1578 | 0.763504 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 22.5817i | − 1.68783i | −0.536475 | − | 0.843916i | \(-0.680244\pi\) | ||||
0.536475 | − | 0.843916i | \(-0.319756\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 13.7043i | − 1.01863i | −0.860580 | − | 0.509315i | \(-0.829899\pi\) | ||||
0.860580 | − | 0.509315i | \(-0.170101\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.6277 | 0.859541 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.48968 | −0.330088 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 10.8470i | − 0.793213i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 1.00658i | − 0.0732176i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.1266 | 1.38395 | 0.691975 | − | 0.721921i | \(-0.256741\pi\) | ||||
0.691975 | + | 0.721921i | \(0.256741\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.35271 | −0.601241 | −0.300620 | − | 0.953744i | \(-0.597194\pi\) | ||||
−0.300620 | + | 0.953744i | \(0.597194\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 11.5146i | 0.824575i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.38203i | 0.0984657i | 0.998787 | + | 0.0492328i | \(0.0156776\pi\) | ||||
−0.998787 | + | 0.0492328i | \(0.984322\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.47653 | −0.175556 | −0.0877782 | − | 0.996140i | \(-0.527977\pi\) | ||||
−0.0877782 | + | 0.996140i | \(0.527977\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.11404 | 0.360717 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.17376i | 0.643872i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.24393i | 0.226566i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.77281 | 0.192724 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.04639 | 0.279894 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.71501i | 0.668809i | 0.942430 | + | 0.334405i | \(0.108535\pi\) | ||||
−0.942430 | + | 0.334405i | \(0.891465\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 8.14493i | − 0.558082i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.78087 | −0.394252 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.57079 | −0.581823 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.6843i | 1.12742i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24.8770i | 1.67341i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.70540 | 0.181167 | 0.0905835 | − | 0.995889i | \(-0.471127\pi\) | ||||
0.0905835 | + | 0.995889i | \(0.471127\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.5644 | −0.770960 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.4716i | 1.09326i | 0.837375 | + | 0.546628i | \(0.184089\pi\) | ||||
−0.837375 | + | 0.546628i | \(0.815911\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 22.0757i | − 1.45880i | −0.684086 | − | 0.729401i | \(-0.739799\pi\) | ||||
0.684086 | − | 0.729401i | \(-0.260201\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.05389 | −0.464112 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.2673 | 1.19673 | 0.598365 | − | 0.801224i | \(-0.295817\pi\) | ||||
0.598365 | + | 0.801224i | \(0.295817\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 0.249045i | − 0.0162459i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 32.3868i | − 2.10375i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.4441 | 0.869627 | 0.434814 | − | 0.900520i | \(-0.356814\pi\) | ||||
0.434814 | + | 0.900520i | \(0.356814\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.34893 | 0.537802 | 0.268901 | − | 0.963168i | \(-0.413340\pi\) | ||||
0.268901 | + | 0.963168i | \(0.413340\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20.8185i | 1.33551i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.711757i | 0.0454725i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.28014 | −0.590481 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 34.8952 | 2.21139 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.33731i | 0.336888i | 0.985711 | + | 0.168444i | \(0.0538742\pi\) | ||||
−0.985711 | + | 0.168444i | \(0.946126\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.21908i | 0.202382i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.10032 | 0.382017 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −25.4346 | −1.58657 | −0.793285 | − | 0.608851i | \(-0.791631\pi\) | ||||
−0.793285 | + | 0.608851i | \(0.791631\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.30788i | 0.391953i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 23.6099i | − 1.46142i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.2187 | 0.815102 | 0.407551 | − | 0.913182i | \(-0.366383\pi\) | ||||
0.407551 | + | 0.913182i | \(0.366383\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.69141 | 0.103902 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 19.8657i | 1.21576i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 17.5765i | − 1.07166i | −0.844326 | − | 0.535830i | \(-0.819999\pi\) | ||||
0.844326 | − | 0.535830i | \(-0.180001\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.5468 | 1.24813 | 0.624064 | − | 0.781373i | \(-0.285480\pi\) | ||||
0.624064 | + | 0.781373i | \(0.285480\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 16.1777 | 0.979117 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 13.4256i | − 0.809596i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 22.0715i | − 1.32615i | −0.748555 | − | 0.663073i | \(-0.769252\pi\) | ||||
0.748555 | − | 0.663073i | \(-0.230748\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 22.0581 | 1.32059 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.0269 | 1.01574 | 0.507869 | − | 0.861434i | \(-0.330433\pi\) | ||||
0.507869 | + | 0.861434i | \(0.330433\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.0782i | 0.896304i | 0.893957 | + | 0.448152i | \(0.147918\pi\) | ||||
−0.893957 | + | 0.448152i | \(0.852082\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.27567i | 0.134799i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.55764 | 0.269029 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.82037 | −0.224728 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 36.3527i | − 2.13103i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 7.28162i | − 0.425397i | −0.977118 | − | 0.212699i | \(-0.931775\pi\) | ||||
0.977118 | − | 0.212699i | \(-0.0682252\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.06239 | −0.178299 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.00750 | −0.174513 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 7.38277i | − 0.426957i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.12198i | 0.468143i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −27.3983 | −1.57399 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.50554 | −0.200726 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.84254i | 0.504670i | 0.967640 | + | 0.252335i | \(0.0811986\pi\) | ||||
−0.967640 | + | 0.252335i | \(0.918801\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 33.1892i | − 1.88807i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.9075 | −1.80931 | −0.904654 | − | 0.426147i | \(-0.859871\pi\) | ||||
−0.904654 | + | 0.426147i | \(0.859871\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.06377 | −0.512314 | −0.256157 | − | 0.966635i | \(-0.582456\pi\) | ||||
−0.256157 | + | 0.966635i | \(0.582456\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 1.83181i | − 0.103211i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 29.5991i | − 1.66245i | −0.555936 | − | 0.831225i | \(-0.687640\pi\) | ||||
0.555936 | − | 0.831225i | \(-0.312360\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.4098 | 1.53466 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.66184 | −0.316013 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.91654i | 0.273564i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 30.7909i | 1.70797i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.03896 | −0.168055 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.349902 | −0.0192907 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 15.4620i | − 0.849868i | −0.905224 | − | 0.424934i | \(-0.860297\pi\) | ||||
0.905224 | − | 0.424934i | \(-0.139703\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 16.2342i | − 0.889630i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.54179 | −0.0842373 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.21951 | 0.120904 | 0.0604522 | − | 0.998171i | \(-0.480746\pi\) | ||||
0.0604522 | + | 0.998171i | \(0.480746\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.4599i | 0.622414i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.6083i | 1.38677i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.81040 | −0.0974685 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 13.5674i | − 0.728336i | −0.931333 | − | 0.364168i | \(-0.881353\pi\) | ||||
0.931333 | − | 0.364168i | \(-0.118647\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.4963i | 1.73949i | 0.493504 | + | 0.869743i | \(0.335716\pi\) | ||||
−0.493504 | + | 0.869743i | \(0.664284\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.89752 | 0.368162 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.1266 | 0.645435 | 0.322718 | − | 0.946495i | \(-0.395404\pi\) | ||||
0.322718 | + | 0.946495i | \(0.395404\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.45556i | 0.130327i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 8.57079i | − 0.453614i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.1927 | 0.749060 | 0.374530 | − | 0.927215i | \(-0.377804\pi\) | ||||
0.374530 | + | 0.927215i | \(0.377804\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.1659 | 0.903470 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 4.89343i | − 0.256838i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 5.03002i | − 0.263283i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.2817 | −1.31969 | −0.659847 | − | 0.751400i | \(-0.729379\pi\) | ||||
−0.659847 | + | 0.751400i | \(0.729379\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.7297 | −0.610625 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 2.37638i | − 0.123376i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 25.1188i | − 1.30060i | −0.759677 | − | 0.650300i | \(-0.774643\pi\) | ||||
0.759677 | − | 0.650300i | \(-0.225357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15.9523 | 0.823773 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −62.8628 | −3.23760 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 19.4994i | − 1.00162i | −0.865558 | − | 0.500809i | \(-0.833036\pi\) | ||||
0.865558 | − | 0.500809i | \(-0.166964\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.26498i | 0.474659i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.8525 | 1.72978 | 0.864891 | − | 0.501960i | \(-0.167387\pi\) | ||||
0.864891 | + | 0.501960i | \(0.167387\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.12662 | 0.108383 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 20.9030i | − 1.06256i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.2154i | 1.53198i | 0.642852 | + | 0.765990i | \(0.277751\pi\) | ||||
−0.642852 | + | 0.765990i | \(0.722249\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.91133 | −0.197804 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −31.7579 | −1.60197 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.76405i | 0.491283i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 9.05698i | − 0.454557i | −0.973830 | − | 0.227278i | \(-0.927017\pi\) | ||||
0.973830 | − | 0.227278i | \(-0.0729828\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.19726 | 0.160063 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.78707 | 0.189117 | 0.0945587 | − | 0.995519i | \(-0.469856\pi\) | ||||
0.0945587 | + | 0.995519i | \(0.469856\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 58.7310i | − 2.92560i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 7.18682i | − 0.357116i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.8470 | 0.934212 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.7532 | 1.17452 | 0.587260 | − | 0.809398i | \(-0.300207\pi\) | ||||
0.587260 | + | 0.809398i | \(0.300207\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 43.9684i | − 2.16880i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.30257i | 0.211716i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.5203 | −0.516420 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.8792 | 0.826577 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.9658i | 1.51278i | 0.654123 | + | 0.756388i | \(0.273038\pi\) | ||||
−0.654123 | + | 0.756388i | \(0.726962\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.9523i | 0.777467i | 0.921350 | + | 0.388733i | \(0.127087\pi\) | ||||
−0.921350 | + | 0.388733i | \(0.872913\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.900522 | 0.0437849 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16.3127 | 0.791284 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.92519i | 0.238347i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 48.3365i | − 2.33371i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.50425 | −0.457804 | −0.228902 | − | 0.973449i | \(-0.573514\pi\) | ||||
−0.228902 | + | 0.973449i | \(0.573514\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.41658 | 0.260304 | 0.130152 | − | 0.991494i | \(-0.458453\pi\) | ||||
0.130152 | + | 0.991494i | \(0.458453\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 15.4152i | 0.739101i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 1.45909i | − 0.0697976i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.7082 | −1.41790 | −0.708948 | − | 0.705261i | \(-0.750830\pi\) | ||||
−0.708948 | + | 0.705261i | \(0.750830\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.57364 | −0.122554 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.0290i | 0.809071i | 0.914522 | + | 0.404535i | \(0.132567\pi\) | ||||
−0.914522 | + | 0.404535i | \(0.867433\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 5.98915i | − 0.283913i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.15562 | −0.0546590 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 41.6242 | 1.96437 | 0.982183 | − | 0.187929i | \(-0.0601773\pi\) | ||||
0.982183 | + | 0.187929i | \(0.0601773\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 13.6176i | − 0.641226i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 53.0537i | 2.49268i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.87728 | −0.228651 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.5834 | 1.38385 | 0.691925 | − | 0.721969i | \(-0.256763\pi\) | ||||
0.691925 | + | 0.721969i | \(0.256763\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 3.65425i | − 0.170566i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 0.815920i | − 0.0380012i | −0.999819 | − | 0.0190006i | \(-0.993952\pi\) | ||||
0.999819 | − | 0.0190006i | \(-0.00604844\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.9633 | −1.06719 | −0.533597 | − | 0.845739i | \(-0.679160\pi\) | ||||
−0.533597 | + | 0.845739i | \(0.679160\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.4020 | −0.667876 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.5170i | 0.532945i | 0.963842 | + | 0.266473i | \(0.0858582\pi\) | ||||
−0.963842 | + | 0.266473i | \(0.914142\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.16618i | 0.100025i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 38.3588 | 1.76748 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.2673 | 1.11581 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.08532i | 0.279214i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.11595i | 0.280030i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.9202 | 0.681719 | 0.340860 | − | 0.940114i | \(-0.389282\pi\) | ||||
0.340860 | + | 0.940114i | \(0.389282\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −43.2245 | −1.97087 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.54356i | 0.115736i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.9597i | 0.497654i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −36.1278 | −1.63711 | −0.818554 | − | 0.574429i | \(-0.805224\pi\) | ||||
−0.818554 | + | 0.574429i | \(0.805224\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.4327 | −0.517007 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 33.6926i | − 1.52052i | −0.649616 | − | 0.760262i | \(-0.725070\pi\) | ||||
0.649616 | − | 0.760262i | \(-0.274930\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.3042i | 1.49994i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.47316 | −0.246000 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.44999 | 0.154753 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.1230i | 0.721766i | 0.932611 | + | 0.360883i | \(0.117525\pi\) | ||||
−0.932611 | + | 0.360883i | \(0.882475\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.4080i | 1.00112i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.3607 | −0.506549 | −0.253275 | − | 0.967394i | \(-0.581508\pi\) | ||||
−0.253275 | + | 0.967394i | \(0.581508\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.26010 | 0.367569 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 80.1657i | 3.56028i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 36.1459i | 1.60214i | 0.598572 | + | 0.801069i | \(0.295735\pi\) | ||||
−0.598572 | + | 0.801069i | \(0.704265\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.06704 | −0.312628 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.36319 | 0.0601861 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.0060i | 0.440916i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.04546i | 0.0459791i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.6458 | −0.818461 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.6860 | −1.60724 | −0.803622 | − | 0.595140i | \(-0.797097\pi\) | ||||
−0.803622 | + | 0.595140i | \(0.797097\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 32.5558i | − 1.42357i | −0.702399 | − | 0.711783i | \(-0.747888\pi\) | ||||
0.702399 | − | 0.711783i | \(-0.252112\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 10.6083i | − 0.462983i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −31.1152 | −1.35540 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.8392 | −0.949532 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 11.0733i | − 0.480539i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31.2310i | 1.35277i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.70695 | 0.0737977 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −53.3120 | −2.30058 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 2.98785i | − 0.128696i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.9654i | 1.46029i | 0.683293 | + | 0.730144i | \(0.260547\pi\) | ||||
−0.683293 | + | 0.730144i | \(0.739453\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −32.3538 | −1.38843 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.916195 | 0.0392455 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.41390i | 0.103211i | 0.998668 | + | 0.0516055i | \(0.0164338\pi\) | ||||
−0.998668 | + | 0.0516055i | \(0.983566\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 12.6757i | − 0.540984i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.4238 | −0.529273 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.7182 | 0.583359 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.5995i | 0.449923i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.0466i | 0.468060i | 0.972229 | + | 0.234030i | \(0.0751914\pi\) | ||||
−0.972229 | + | 0.234030i | \(0.924809\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −55.6555 | −2.35398 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −25.6083 | −1.08118 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.5465i | 0.528773i | 0.964417 | + | 0.264387i | \(0.0851695\pi\) | ||||
−0.964417 | + | 0.264387i | \(0.914830\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 3.45495i | − 0.145351i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.0973 | −0.424047 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.7545 | 1.16353 | 0.581764 | − | 0.813358i | \(-0.302363\pi\) | ||||
0.581764 | + | 0.813358i | \(0.302363\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 4.50930i | − 0.188708i | −0.995539 | − | 0.0943541i | \(-0.969921\pi\) | ||||
0.995539 | − | 0.0943541i | \(-0.0300786\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 45.1551i | − 1.88638i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.84115 | −0.201890 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.11497 | −0.0880475 | −0.0440238 | − | 0.999030i | \(-0.514018\pi\) | ||||
−0.0440238 | + | 0.999030i | \(0.514018\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.7195i | 0.819516i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.7807i | 0.613208i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.10028 | −0.294063 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.5524 | 0.518977 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 44.9688i | 1.85606i | 0.372505 | + | 0.928030i | \(0.378499\pi\) | ||||
−0.372505 | + | 0.928030i | \(0.621501\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 11.6072i | − 0.478268i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.26278 | 0.134213 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.5463 | −1.00800 | −0.503998 | − | 0.863705i | \(-0.668138\pi\) | ||||
−0.503998 | + | 0.863705i | \(0.668138\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.58394i | 0.105931i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.84672i | 0.239290i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.0946 | 1.22963 | 0.614817 | − | 0.788670i | \(-0.289230\pi\) | ||||
0.614817 | + | 0.788670i | \(0.289230\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.02003 | −0.0416078 | −0.0208039 | − | 0.999784i | \(-0.506623\pi\) | ||||
−0.0208039 | + | 0.999784i | \(0.506623\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 5.57497i | − 0.227030i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.47528i | 0.0599788i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.1251 | −0.776263 | −0.388132 | − | 0.921604i | \(-0.626879\pi\) | ||||
−0.388132 | + | 0.921604i | \(0.626879\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 21.6579 | 0.877623 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 2.39769i | − 0.0970002i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 25.0418i | − 1.01143i | −0.862701 | − | 0.505715i | \(-0.831229\pi\) | ||||
0.862701 | − | 0.505715i | \(-0.168771\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.65845 | 0.308819 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.1687 | −1.73790 | −0.868952 | − | 0.494896i | \(-0.835206\pi\) | ||||
−0.868952 | + | 0.494896i | \(0.835206\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 12.7180i | − 0.511180i | −0.966785 | − | 0.255590i | \(-0.917730\pi\) | ||||
0.966785 | − | 0.255590i | \(-0.0822697\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.08448i | 0.0435185i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.41460 | −0.337124 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.6577 | 0.706307 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 9.55294i | − 0.381508i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.9000i | 0.913082i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.4744 | −1.33260 | −0.666298 | − | 0.745685i | \(-0.732122\pi\) | ||||
−0.666298 | + | 0.745685i | \(0.732122\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.9357 | 0.911614 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 2.79323i | − 0.110846i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.85246i | 0.271504i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.87904 | −0.351249 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.3148 | −0.407408 | −0.203704 | − | 0.979033i | \(-0.565298\pi\) | ||||
−0.203704 | + | 0.979033i | \(0.565298\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 20.7404i | − 0.817920i | −0.912552 | − | 0.408960i | \(-0.865892\pi\) | ||||
0.912552 | − | 0.408960i | \(-0.134108\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.6478i | 0.537382i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.0656 | 0.592291 | 0.296146 | − | 0.955143i | \(-0.404299\pi\) | ||||
0.296146 | + | 0.955143i | \(0.404299\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.8555 | 0.504621 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.2344i | 0.793049i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.9568i | 0.859236i | 0.903011 | + | 0.429618i | \(0.141352\pi\) | ||||
−0.903011 | + | 0.429618i | \(0.858648\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.57444 | 0.374104 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18.1880 | 0.709582 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.8657i | 1.16340i | 0.813403 | + | 0.581700i | \(0.197612\pi\) | ||||
−0.813403 | + | 0.581700i | \(0.802388\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.5152i | 0.564575i | 0.959330 | + | 0.282287i | \(0.0910932\pi\) | ||||
−0.959330 | + | 0.282287i | \(0.908907\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 58.7310 | 2.28092 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.963918 | −0.0373791 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 9.88371i | − 0.382699i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 6.38706i | − 0.246938i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.7157 | 0.568095 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.1998 | 0.624456 | 0.312228 | − | 0.950007i | \(-0.398925\pi\) | ||||
0.312228 | + | 0.950007i | \(0.398925\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 4.52295i | − 0.174088i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 10.7247i | − 0.412185i | −0.978533 | − | 0.206092i | \(-0.933925\pi\) | ||||
0.978533 | − | 0.206092i | \(-0.0660748\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.3981 | 0.590925 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 38.8870 | 1.49015 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.7354i | 0.869946i | 0.900443 | + | 0.434973i | \(0.143242\pi\) | ||||
−0.900443 | + | 0.434973i | \(0.856758\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.2557i | 0.506475i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −52.1175 | −1.98841 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.2841 | 0.620373 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.6241i | 0.898705i | 0.893355 | + | 0.449352i | \(0.148345\pi\) | ||||
−0.893355 | + | 0.449352i | \(0.851655\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.68966i | 0.292106i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.08878 | −0.193028 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.5459 | 0.626722 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 43.1264i | − 1.63119i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 1.12363i | − 0.0424387i | −0.999775 | − | 0.0212194i | \(-0.993245\pi\) | ||||
0.999775 | − | 0.0212194i | \(-0.00675484\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.54264 | −0.322192 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.587960 | −0.0221439 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 11.6052i | − 0.436459i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.1324i | 0.605865i | 0.953012 | + | 0.302933i | \(0.0979657\pi\) | ||||
−0.953012 | + | 0.302933i | \(0.902034\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −35.3058 | −1.32407 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.23409 | 0.345819 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.5726i | 0.544985i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 31.7396i | − 1.18534i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −46.6686 | −1.74044 | −0.870222 | − | 0.492660i | \(-0.836025\pi\) | ||||
−0.870222 | + | 0.492660i | \(0.836025\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.0581 | 0.523552 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 19.7106i | − 0.733046i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 41.2214i | 1.53092i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.4515 | −0.387625 | −0.193812 | − | 0.981039i | \(-0.562085\pi\) | ||||
−0.193812 | + | 0.981039i | \(0.562085\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18.8577 | 0.698432 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 29.4858i | 1.09057i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 15.5723i | − 0.575176i | −0.957754 | − | 0.287588i | \(-0.907147\pi\) | ||||
0.957754 | − | 0.287588i | \(-0.0928534\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.68036 | 0.0619808 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.47223 | 0.238408 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 44.0571i | − 1.62067i | −0.585969 | − | 0.810334i | \(-0.699286\pi\) | ||||
0.585969 | − | 0.810334i | \(-0.300714\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.9091i | 0.804850i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.0389 | 0.991960 | 0.495980 | − | 0.868334i | \(-0.334809\pi\) | ||||
0.495980 | + | 0.868334i | \(0.334809\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.348400 | 0.0127644 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 38.0403i | − 1.39182i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 2.39821i | − 0.0876288i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.0575811 | 0.00210116 | 0.00105058 | − | 0.999999i | \(-0.499666\pi\) | ||||
0.00105058 | + | 0.999999i | \(0.499666\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.6006 | 0.459192 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 15.9948i | − 0.582109i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.1685i | 0.660345i | 0.943921 | + | 0.330172i | \(0.107107\pi\) | ||||
−0.943921 | + | 0.330172i | \(0.892893\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.59979 | 0.275855 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.8713 | −0.792835 | −0.396418 | − | 0.918070i | \(-0.629747\pi\) | ||||
−0.396418 | + | 0.918070i | \(0.629747\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1.28723i | − 0.0466008i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 6.65014i | − 0.240436i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −29.4832 | −1.06458 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.3141 | −1.48982 | −0.744912 | − | 0.667163i | \(-0.767508\pi\) | ||||
−0.744912 | + | 0.667163i | \(0.767508\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 60.0475i | 2.16256i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.2428i | 1.08776i | 0.839164 | + | 0.543879i | \(0.183045\pi\) | ||||
−0.839164 | + | 0.543879i | \(0.816955\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −38.5120 | −1.38339 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.8920 | 0.534248 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.17232i | 0.221146i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 10.3081i | − 0.368852i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.23409 | 0.329999 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.5645 | −0.412755 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.3754i | 0.583721i | 0.956461 | + | 0.291861i | \(0.0942744\pi\) | ||||
−0.956461 | + | 0.291861i | \(0.905726\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 31.2075i | − 1.11102i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.85411 | −0.172592 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.7497 | −1.19849 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 3.99316i | − 0.141623i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 17.9392i | − 0.635440i | −0.948185 | − | 0.317720i | \(-0.897083\pi\) | ||||
0.948185 | − | 0.317720i | \(-0.102917\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.27028 | −0.0449391 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.6561 | 0.765182 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 21.1153i | 0.745142i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 0.766840i | − 0.0270275i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −41.4956 | −1.46072 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −33.9919 | −1.19509 | −0.597545 | − | 0.801835i | \(-0.703857\pi\) | ||||
−0.597545 | + | 0.801835i | \(0.703857\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.5862i | 0.617534i | 0.951138 | + | 0.308767i | \(0.0999163\pi\) | ||||
−0.951138 | + | 0.308767i | \(0.900084\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 48.5080i | − 1.70125i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.44677 | 0.120735 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.9994 | −0.384821 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 17.6358i | − 0.616243i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.7270i | 1.28178i | 0.767632 | + | 0.640891i | \(0.221435\pi\) | ||||
−0.767632 | + | 0.640891i | \(0.778565\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.5706 | −1.30963 | −0.654814 | − | 0.755790i | \(-0.727253\pi\) | ||||
−0.654814 | + | 0.755790i | \(0.727253\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −31.6960 | −1.10351 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 32.4315i | − 1.12775i | −0.825859 | − | 0.563877i | \(-0.809309\pi\) | ||||
0.825859 | − | 0.563877i | \(-0.190691\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 20.3050i | − 0.705222i | −0.935770 | − | 0.352611i | \(-0.885294\pi\) | ||||
0.935770 | − | 0.352611i | \(-0.114706\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −52.1075 | −1.80759 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.63038 | 0.125785 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 6.75563i | − 0.233788i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.62716i | 0.298198i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.6124 | 0.849713 | 0.424857 | − | 0.905261i | \(-0.360325\pi\) | ||||
0.424857 | + | 0.905261i | \(0.360325\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −55.1578 | −1.90199 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 40.1980i | − 1.38449i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 24.1686i | − 0.831424i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.07274 | 0.0712200 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 35.5974 | 1.22170 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 6.79605i | − 0.232966i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.0447i | 1.09719i | 0.836088 | + | 0.548595i | \(0.184837\pi\) | ||||
−0.836088 | + | 0.548595i | \(0.815163\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.48078 | 0.0848408 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.0599 | 0.992668 | 0.496334 | − | 0.868132i | \(-0.334679\pi\) | ||||
0.496334 | + | 0.868132i | \(0.334679\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.261668i | 0.00892799i | 0.999990 | + | 0.00446399i | \(0.00142094\pi\) | ||||
−0.999990 | + | 0.00446399i | \(0.998579\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 10.7599i | − 0.366697i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.9690 | 0.611673 | 0.305836 | − | 0.952084i | \(-0.401064\pi\) | ||||
0.305836 | + | 0.952084i | \(0.401064\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.62140 | 0.191133 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.01935i | 0.306313i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 40.9881i | − 1.39043i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.8437 | −0.502959 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −39.6291 | −1.34124 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.75699i | 0.228428i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 4.35104i | − 0.146924i | −0.997298 | − | 0.0734621i | \(-0.976595\pi\) | ||||
0.997298 | − | 0.0734621i | \(-0.0234048\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.1909 | −0.579833 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.2303 | 0.378357 | 0.189178 | − | 0.981943i | \(-0.439418\pi\) | ||||
0.189178 | + | 0.981943i | \(0.439418\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 39.7974i | − 1.33929i | −0.742681 | − | 0.669645i | \(-0.766446\pi\) | ||||
0.742681 | − | 0.669645i | \(-0.233554\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.22985i | 0.243029i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.8390 | 0.397515 | 0.198757 | − | 0.980049i | \(-0.436309\pi\) | ||||
0.198757 | + | 0.980049i | \(0.436309\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.92442 | −0.131621 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 30.1692i | 1.01071i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 0.473865i | − 0.0158573i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.0726 | 0.537249 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17.4297 | −0.581959 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 78.6264i | − 2.62234i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 8.62716i | − 0.287412i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 19.1748 | 0.638098 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.75410 | 0.324237 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.14412i | 0.0711943i | 0.999366 | + | 0.0355972i | \(0.0113333\pi\) | ||||
−0.999366 | + | 0.0355972i | \(0.988667\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 29.8677i | 0.990648i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.1211 | 1.79311 | 0.896557 | − | 0.442929i | \(-0.146061\pi\) | ||||
0.896557 | + | 0.442929i | \(0.146061\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 44.1626 | 1.46157 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.27607i | 0.273598i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 13.4518i | − 0.444219i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.0290 | −1.55134 | −0.775672 | − | 0.631136i | \(-0.782589\pi\) | ||||
−0.775672 | + | 0.631136i | \(0.782589\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.8760 | 0.687886 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 23.6409i | 0.778151i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.3439i | 0.931940i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −36.1805 | −1.18833 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −53.9999 | −1.77168 | −0.885839 | − | 0.463993i | \(-0.846416\pi\) | ||||
−0.885839 | + | 0.463993i | \(0.846416\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.35428i | 0.0443847i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 75.3290i | 2.46616i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.72045 | 0.252486 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.4089 | 0.340044 | 0.170022 | − | 0.985440i | \(-0.445616\pi\) | ||||
0.170022 | + | 0.985440i | \(0.445616\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.3982i | 0.698305i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 32.6610i | − 1.06472i | −0.846518 | − | 0.532359i | \(-0.821306\pi\) | ||||
0.846518 | − | 0.532359i | \(-0.178694\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.91036 | −0.159903 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.716437 | 0.0233057 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 25.1457i | − 0.817126i | −0.912730 | − | 0.408563i | \(-0.866030\pi\) | ||||
0.912730 | − | 0.408563i | \(-0.133970\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 48.4266i | − 1.57199i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −69.8792 | −2.26599 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.5674 | 1.41129 | 0.705643 | − | 0.708567i | \(-0.250658\pi\) | ||||
0.705643 | + | 0.708567i | \(0.250658\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.6135i | 0.440522i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 64.7107i | − 2.09180i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.6239 | 0.601398 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 42.4585 | 1.36963 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.17214i | 0.198894i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 5.94510i | − 0.191379i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.97147 | 0.288503 | 0.144252 | − | 0.989541i | \(-0.453923\pi\) | ||||
0.144252 | + | 0.989541i | \(0.453923\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.6072 | 0.372879 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 53.5414i | − 1.71822i | −0.511787 | − | 0.859112i | \(-0.671016\pi\) | ||||
0.511787 | − | 0.859112i | \(-0.328984\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.14960i | 0.229206i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 72.6928 | 2.32803 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.3412 | 1.19465 | 0.597326 | − | 0.801998i | \(-0.296230\pi\) | ||||
0.597326 | + | 0.801998i | \(0.296230\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25.1416i | 0.803529i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.31286i | 0.105772i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36.2225 | −1.15532 | −0.577659 | − | 0.816278i | \(-0.696034\pi\) | ||||
−0.577659 | + | 0.816278i | \(0.696034\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.983671 | −0.0313424 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.826069i | 0.0262941i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 8.75054i | − 0.278251i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.4960 | 0.365182 | 0.182591 | − | 0.983189i | \(-0.441552\pi\) | ||||
0.182591 | + | 0.983189i | \(0.441552\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −36.5035 | −1.15840 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 1.76268i | − 0.0558809i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 20.5111i | − 0.649594i | −0.945784 | − | 0.324797i | \(-0.894704\pi\) | ||||
0.945784 | − | 0.324797i | \(-0.105296\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.34937 | 0.200885 |
(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 | 3584.2.b.l.1793.2 | 12 | ||
4.3 | odd | 2 | 3584.2.b.j.1793.11 | 12 | |||
8.3 | odd | 2 | 3584.2.b.j.1793.2 | 12 | |||
8.5 | even | 2 | inner | 3584.2.b.l.1793.11 | 12 | ||
16.3 | odd | 4 | 3584.2.a.h.1.1 | yes | 6 | ||
16.5 | even | 4 | 3584.2.a.i.1.1 | yes | 6 | ||
16.11 | odd | 4 | 3584.2.a.j.1.6 | yes | 6 | ||
16.13 | even | 4 | 3584.2.a.g.1.6 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3584.2.a.g.1.6 | ✓ | 6 | 16.13 | even | 4 | ||
3584.2.a.h.1.1 | yes | 6 | 16.3 | odd | 4 | ||
3584.2.a.i.1.1 | yes | 6 | 16.5 | even | 4 | ||
3584.2.a.j.1.6 | yes | 6 | 16.11 | odd | 4 | ||
3584.2.b.j.1793.2 | 12 | 8.3 | odd | 2 | |||
3584.2.b.j.1793.11 | 12 | 4.3 | odd | 2 | |||
3584.2.b.l.1793.2 | 12 | 1.1 | even | 1 | trivial | ||
3584.2.b.l.1793.11 | 12 | 8.5 | even | 2 | inner |