Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4650,2,Mod(3349,4650)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4650, 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("4650.3349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4650.d (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: | \(37.1304369399\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 17x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 930) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3349.1 | ||
Root | \(-3.37228i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4650.3349 |
Dual form | 4650.2.d.bh.3349.4 |
$q$-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 \(\left(\mathbb{Z}/4650\mathbb{Z}\right)^\times\).
\(n\) | \(1801\) | \(2977\) | \(3101\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | − 3.37228i | − 1.27460i | −0.770615 | − | 0.637301i | \(-0.780051\pi\) | ||||
0.770615 | − | 0.637301i | \(-0.219949\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.627719 | 0.189264 | 0.0946322 | − | 0.995512i | \(-0.469833\pi\) | ||||
0.0946322 | + | 0.995512i | \(0.469833\pi\) | |||||||
\(12\) | − 1.00000i | − 0.288675i | ||||||||
\(13\) | − 2.00000i | − 0.554700i | −0.960769 | − | 0.277350i | \(-0.910544\pi\) | ||||
0.960769 | − | 0.277350i | \(-0.0894562\pi\) | |||||||
\(14\) | −3.37228 | −0.901280 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.74456i | 1.15073i | 0.817898 | + | 0.575363i | \(0.195139\pi\) | ||||
−0.817898 | + | 0.575363i | \(0.804861\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 0.627719 | 0.144009 | 0.0720043 | − | 0.997404i | \(-0.477060\pi\) | ||||
0.0720043 | + | 0.997404i | \(0.477060\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.37228 | 0.735892 | ||||||||
\(22\) | − 0.627719i | − 0.133830i | ||||||||
\(23\) | 3.37228i | 0.703169i | 0.936156 | + | 0.351585i | \(0.114357\pi\) | ||||
−0.936156 | + | 0.351585i | \(0.885643\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 3.37228i | 0.637301i | ||||||||
\(29\) | 8.74456 | 1.62382 | 0.811912 | − | 0.583779i | \(-0.198427\pi\) | ||||
0.811912 | + | 0.583779i | \(0.198427\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 0.627719i | 0.109272i | ||||||||
\(34\) | 4.74456 | 0.813686 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.744563i | 0.122405i | 0.998125 | + | 0.0612027i | \(0.0194936\pi\) | ||||
−0.998125 | + | 0.0612027i | \(0.980506\pi\) | |||||||
\(38\) | − 0.627719i | − 0.101829i | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.744563 | 0.116281 | 0.0581406 | − | 0.998308i | \(-0.481483\pi\) | ||||
0.0581406 | + | 0.998308i | \(0.481483\pi\) | |||||||
\(42\) | − 3.37228i | − 0.520354i | ||||||||
\(43\) | 0.627719i | 0.0957262i | 0.998854 | + | 0.0478631i | \(0.0152411\pi\) | ||||
−0.998854 | + | 0.0478631i | \(0.984759\pi\) | |||||||
\(44\) | −0.627719 | −0.0946322 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.37228 | 0.497216 | ||||||||
\(47\) | 6.74456i | 0.983796i | 0.870653 | + | 0.491898i | \(0.163697\pi\) | ||||
−0.870653 | + | 0.491898i | \(0.836303\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −4.37228 | −0.624612 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.74456 | −0.664372 | ||||||||
\(52\) | 2.00000i | 0.277350i | ||||||||
\(53\) | 1.37228i | 0.188497i | 0.995549 | + | 0.0942487i | \(0.0300449\pi\) | ||||
−0.995549 | + | 0.0942487i | \(0.969955\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.37228 | 0.450640 | ||||||||
\(57\) | 0.627719i | 0.0831434i | ||||||||
\(58\) | − 8.74456i | − 1.14822i | ||||||||
\(59\) | −2.74456 | −0.357312 | −0.178656 | − | 0.983912i | \(-0.557175\pi\) | ||||
−0.178656 | + | 0.983912i | \(0.557175\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.4891 | 1.47103 | 0.735516 | − | 0.677507i | \(-0.236940\pi\) | ||||
0.735516 | + | 0.677507i | \(0.236940\pi\) | |||||||
\(62\) | 1.00000i | 0.127000i | ||||||||
\(63\) | 3.37228i | 0.424868i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.627719 | 0.0772668 | ||||||||
\(67\) | − 10.7446i | − 1.31266i | −0.754475 | − | 0.656329i | \(-0.772108\pi\) | ||||
0.754475 | − | 0.656329i | \(-0.227892\pi\) | |||||||
\(68\) | − 4.74456i | − 0.575363i | ||||||||
\(69\) | −3.37228 | −0.405975 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.37228 | 0.400216 | 0.200108 | − | 0.979774i | \(-0.435871\pi\) | ||||
0.200108 | + | 0.979774i | \(0.435871\pi\) | |||||||
\(72\) | − 1.00000i | − 0.117851i | ||||||||
\(73\) | − 8.11684i | − 0.950005i | −0.879985 | − | 0.475002i | \(-0.842447\pi\) | ||||
0.879985 | − | 0.475002i | \(-0.157553\pi\) | |||||||
\(74\) | 0.744563 | 0.0865536 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.627719 | −0.0720043 | ||||||||
\(77\) | − 2.11684i | − 0.241237i | ||||||||
\(78\) | − 2.00000i | − 0.226455i | ||||||||
\(79\) | 4.62772 | 0.520659 | 0.260330 | − | 0.965520i | \(-0.416169\pi\) | ||||
0.260330 | + | 0.965520i | \(0.416169\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 0.744563i | − 0.0822232i | ||||||||
\(83\) | − 12.0000i | − 1.31717i | −0.752506 | − | 0.658586i | \(-0.771155\pi\) | ||||
0.752506 | − | 0.658586i | \(-0.228845\pi\) | |||||||
\(84\) | −3.37228 | −0.367946 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.627719 | 0.0676886 | ||||||||
\(87\) | 8.74456i | 0.937516i | ||||||||
\(88\) | 0.627719i | 0.0669150i | ||||||||
\(89\) | 1.37228 | 0.145462 | 0.0727308 | − | 0.997352i | \(-0.476829\pi\) | ||||
0.0727308 | + | 0.997352i | \(0.476829\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.74456 | −0.707022 | ||||||||
\(92\) | − 3.37228i | − 0.351585i | ||||||||
\(93\) | − 1.00000i | − 0.103695i | ||||||||
\(94\) | 6.74456 | 0.695649 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | − 2.00000i | − 0.203069i | −0.994832 | − | 0.101535i | \(-0.967625\pi\) | ||||
0.994832 | − | 0.101535i | \(-0.0323753\pi\) | |||||||
\(98\) | 4.37228i | 0.441667i | ||||||||
\(99\) | −0.627719 | −0.0630881 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.11684 | 0.807656 | 0.403828 | − | 0.914835i | \(-0.367679\pi\) | ||||
0.403828 | + | 0.914835i | \(0.367679\pi\) | |||||||
\(102\) | 4.74456i | 0.469782i | ||||||||
\(103\) | − 8.00000i | − 0.788263i | −0.919054 | − | 0.394132i | \(-0.871045\pi\) | ||||
0.919054 | − | 0.394132i | \(-0.128955\pi\) | |||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.37228 | 0.133288 | ||||||||
\(107\) | − 0.627719i | − 0.0606839i | −0.999540 | − | 0.0303419i | \(-0.990340\pi\) | ||||
0.999540 | − | 0.0303419i | \(-0.00965962\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | −4.74456 | −0.454447 | −0.227223 | − | 0.973843i | \(-0.572965\pi\) | ||||
−0.227223 | + | 0.973843i | \(0.572965\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.744563 | −0.0706708 | ||||||||
\(112\) | − 3.37228i | − 0.318651i | ||||||||
\(113\) | − 2.62772i | − 0.247195i | −0.992332 | − | 0.123597i | \(-0.960557\pi\) | ||||
0.992332 | − | 0.123597i | \(-0.0394432\pi\) | |||||||
\(114\) | 0.627719 | 0.0587912 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.74456 | −0.811912 | ||||||||
\(117\) | 2.00000i | 0.184900i | ||||||||
\(118\) | 2.74456i | 0.252657i | ||||||||
\(119\) | 16.0000 | 1.46672 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6060 | −0.964179 | ||||||||
\(122\) | − 11.4891i | − 1.04018i | ||||||||
\(123\) | 0.744563i | 0.0671350i | ||||||||
\(124\) | 1.00000 | 0.0898027 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.37228 | 0.300427 | ||||||||
\(127\) | − 13.4891i | − 1.19697i | −0.801135 | − | 0.598483i | \(-0.795770\pi\) | ||||
0.801135 | − | 0.598483i | \(-0.204230\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −0.627719 | −0.0552675 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.2337 | −1.41834 | −0.709172 | − | 0.705036i | \(-0.750931\pi\) | ||||
−0.709172 | + | 0.705036i | \(0.750931\pi\) | |||||||
\(132\) | − 0.627719i | − 0.0546359i | ||||||||
\(133\) | − 2.11684i | − 0.183554i | ||||||||
\(134\) | −10.7446 | −0.928189 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.74456 | −0.406843 | ||||||||
\(137\) | 3.48913i | 0.298096i | 0.988830 | + | 0.149048i | \(0.0476209\pi\) | ||||
−0.988830 | + | 0.149048i | \(0.952379\pi\) | |||||||
\(138\) | 3.37228i | 0.287068i | ||||||||
\(139\) | 10.7446 | 0.911342 | 0.455671 | − | 0.890148i | \(-0.349399\pi\) | ||||
0.455671 | + | 0.890148i | \(0.349399\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.74456 | −0.567995 | ||||||||
\(142\) | − 3.37228i | − 0.282996i | ||||||||
\(143\) | − 1.25544i | − 0.104985i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.11684 | −0.671755 | ||||||||
\(147\) | − 4.37228i | − 0.360620i | ||||||||
\(148\) | − 0.744563i | − 0.0612027i | ||||||||
\(149\) | 12.1168 | 0.992651 | 0.496325 | − | 0.868137i | \(-0.334682\pi\) | ||||
0.496325 | + | 0.868137i | \(0.334682\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | 0.627719i | 0.0509147i | ||||||||
\(153\) | − 4.74456i | − 0.383575i | ||||||||
\(154\) | −2.11684 | −0.170580 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.00000 | −0.160128 | ||||||||
\(157\) | − 9.37228i | − 0.747989i | −0.927431 | − | 0.373995i | \(-0.877988\pi\) | ||||
0.927431 | − | 0.373995i | \(-0.122012\pi\) | |||||||
\(158\) | − 4.62772i | − 0.368162i | ||||||||
\(159\) | −1.37228 | −0.108829 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.3723 | 0.896261 | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | 24.2337i | 1.89813i | 0.315082 | + | 0.949064i | \(0.397968\pi\) | ||||
−0.315082 | + | 0.949064i | \(0.602032\pi\) | |||||||
\(164\) | −0.744563 | −0.0581406 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.0000 | −0.931381 | ||||||||
\(167\) | 12.6277i | 0.977162i | 0.872518 | + | 0.488581i | \(0.162485\pi\) | ||||
−0.872518 | + | 0.488581i | \(0.837515\pi\) | |||||||
\(168\) | 3.37228i | 0.260177i | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.627719 | −0.0480028 | ||||||||
\(172\) | − 0.627719i | − 0.0478631i | ||||||||
\(173\) | − 18.0000i | − 1.36851i | −0.729241 | − | 0.684257i | \(-0.760127\pi\) | ||||
0.729241 | − | 0.684257i | \(-0.239873\pi\) | |||||||
\(174\) | 8.74456 | 0.662924 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.627719 | 0.0473161 | ||||||||
\(177\) | − 2.74456i | − 0.206294i | ||||||||
\(178\) | − 1.37228i | − 0.102857i | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.8614 | 1.10464 | 0.552320 | − | 0.833632i | \(-0.313743\pi\) | ||||
0.552320 | + | 0.833632i | \(0.313743\pi\) | |||||||
\(182\) | 6.74456i | 0.499940i | ||||||||
\(183\) | 11.4891i | 0.849301i | ||||||||
\(184\) | −3.37228 | −0.248608 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.00000 | −0.0733236 | ||||||||
\(187\) | 2.97825i | 0.217791i | ||||||||
\(188\) | − 6.74456i | − 0.491898i | ||||||||
\(189\) | −3.37228 | −0.245297 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.0000 | 1.15772 | 0.578860 | − | 0.815427i | \(-0.303498\pi\) | ||||
0.578860 | + | 0.815427i | \(0.303498\pi\) | |||||||
\(192\) | − 1.00000i | − 0.0721688i | ||||||||
\(193\) | 15.4891i | 1.11493i | 0.830200 | + | 0.557466i | \(0.188226\pi\) | ||||
−0.830200 | + | 0.557466i | \(0.811774\pi\) | |||||||
\(194\) | −2.00000 | −0.143592 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.37228 | 0.312306 | ||||||||
\(197\) | − 19.4891i | − 1.38854i | −0.719713 | − | 0.694271i | \(-0.755727\pi\) | ||||
0.719713 | − | 0.694271i | \(-0.244273\pi\) | |||||||
\(198\) | 0.627719i | 0.0446100i | ||||||||
\(199\) | 12.6277 | 0.895155 | 0.447578 | − | 0.894245i | \(-0.352287\pi\) | ||||
0.447578 | + | 0.894245i | \(0.352287\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.7446 | 0.757863 | ||||||||
\(202\) | − 8.11684i | − 0.571099i | ||||||||
\(203\) | − 29.4891i | − 2.06973i | ||||||||
\(204\) | 4.74456 | 0.332186 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.00000 | −0.557386 | ||||||||
\(207\) | − 3.37228i | − 0.234390i | ||||||||
\(208\) | − 2.00000i | − 0.138675i | ||||||||
\(209\) | 0.394031 | 0.0272557 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.627719 | −0.0432139 | −0.0216070 | − | 0.999767i | \(-0.506878\pi\) | ||||
−0.0216070 | + | 0.999767i | \(0.506878\pi\) | |||||||
\(212\) | − 1.37228i | − 0.0942487i | ||||||||
\(213\) | 3.37228i | 0.231065i | ||||||||
\(214\) | −0.627719 | −0.0429100 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 3.37228i | 0.228925i | ||||||||
\(218\) | 4.74456i | 0.321342i | ||||||||
\(219\) | 8.11684 | 0.548485 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.48913 | 0.638308 | ||||||||
\(222\) | 0.744563i | 0.0499718i | ||||||||
\(223\) | 9.25544i | 0.619790i | 0.950771 | + | 0.309895i | \(0.100294\pi\) | ||||
−0.950771 | + | 0.309895i | \(0.899706\pi\) | |||||||
\(224\) | −3.37228 | −0.225320 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.62772 | −0.174793 | ||||||||
\(227\) | − 6.11684i | − 0.405989i | −0.979180 | − | 0.202995i | \(-0.934933\pi\) | ||||
0.979180 | − | 0.202995i | \(-0.0650674\pi\) | |||||||
\(228\) | − 0.627719i | − 0.0415717i | ||||||||
\(229\) | −3.88316 | −0.256606 | −0.128303 | − | 0.991735i | \(-0.540953\pi\) | ||||
−0.128303 | + | 0.991735i | \(0.540953\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.11684 | 0.139278 | ||||||||
\(232\) | 8.74456i | 0.574109i | ||||||||
\(233\) | − 14.8614i | − 0.973603i | −0.873513 | − | 0.486802i | \(-0.838163\pi\) | ||||
0.873513 | − | 0.486802i | \(-0.161837\pi\) | |||||||
\(234\) | 2.00000 | 0.130744 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.74456 | 0.178656 | ||||||||
\(237\) | 4.62772i | 0.300603i | ||||||||
\(238\) | − 16.0000i | − 1.03713i | ||||||||
\(239\) | 29.4891 | 1.90749 | 0.953746 | − | 0.300612i | \(-0.0971910\pi\) | ||||
0.953746 | + | 0.300612i | \(0.0971910\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.51087 | 0.290571 | 0.145285 | − | 0.989390i | \(-0.453590\pi\) | ||||
0.145285 | + | 0.989390i | \(0.453590\pi\) | |||||||
\(242\) | 10.6060i | 0.681778i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −11.4891 | −0.735516 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.744563 | 0.0474716 | ||||||||
\(247\) | − 1.25544i | − 0.0798816i | ||||||||
\(248\) | − 1.00000i | − 0.0635001i | ||||||||
\(249\) | 12.0000 | 0.760469 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.00000 | −0.252478 | −0.126239 | − | 0.992000i | \(-0.540291\pi\) | ||||
−0.126239 | + | 0.992000i | \(0.540291\pi\) | |||||||
\(252\) | − 3.37228i | − 0.212434i | ||||||||
\(253\) | 2.11684i | 0.133085i | ||||||||
\(254\) | −13.4891 | −0.846383 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 13.3723i | − 0.834140i | −0.908874 | − | 0.417070i | \(-0.863057\pi\) | ||||
0.908874 | − | 0.417070i | \(-0.136943\pi\) | |||||||
\(258\) | 0.627719i | 0.0390801i | ||||||||
\(259\) | 2.51087 | 0.156018 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.74456 | −0.541275 | ||||||||
\(262\) | 16.2337i | 1.00292i | ||||||||
\(263\) | − 18.9783i | − 1.17025i | −0.810943 | − | 0.585125i | \(-0.801046\pi\) | ||||
0.810943 | − | 0.585125i | \(-0.198954\pi\) | |||||||
\(264\) | −0.627719 | −0.0386334 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.11684 | −0.129792 | ||||||||
\(267\) | 1.37228i | 0.0839823i | ||||||||
\(268\) | 10.7446i | 0.656329i | ||||||||
\(269\) | 2.00000 | 0.121942 | 0.0609711 | − | 0.998140i | \(-0.480580\pi\) | ||||
0.0609711 | + | 0.998140i | \(0.480580\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.8832 | −0.843342 | −0.421671 | − | 0.906749i | \(-0.638556\pi\) | ||||
−0.421671 | + | 0.906749i | \(0.638556\pi\) | |||||||
\(272\) | 4.74456i | 0.287681i | ||||||||
\(273\) | − 6.74456i | − 0.408200i | ||||||||
\(274\) | 3.48913 | 0.210786 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.37228 | 0.202987 | ||||||||
\(277\) | − 15.2554i | − 0.916610i | −0.888795 | − | 0.458305i | \(-0.848457\pi\) | ||||
0.888795 | − | 0.458305i | \(-0.151543\pi\) | |||||||
\(278\) | − 10.7446i | − 0.644416i | ||||||||
\(279\) | 1.00000 | 0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.7446 | 0.998897 | 0.499448 | − | 0.866344i | \(-0.333536\pi\) | ||||
0.499448 | + | 0.866344i | \(0.333536\pi\) | |||||||
\(282\) | 6.74456i | 0.401633i | ||||||||
\(283\) | 12.0000i | 0.713326i | 0.934233 | + | 0.356663i | \(0.116086\pi\) | ||||
−0.934233 | + | 0.356663i | \(0.883914\pi\) | |||||||
\(284\) | −3.37228 | −0.200108 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.25544 | −0.0742356 | ||||||||
\(287\) | − 2.51087i | − 0.148212i | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −5.51087 | −0.324169 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.00000 | 0.117242 | ||||||||
\(292\) | 8.11684i | 0.475002i | ||||||||
\(293\) | − 7.48913i | − 0.437519i | −0.975779 | − | 0.218760i | \(-0.929799\pi\) | ||||
0.975779 | − | 0.218760i | \(-0.0702011\pi\) | |||||||
\(294\) | −4.37228 | −0.254997 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.744563 | −0.0432768 | ||||||||
\(297\) | − 0.627719i | − 0.0364239i | ||||||||
\(298\) | − 12.1168i | − 0.701910i | ||||||||
\(299\) | 6.74456 | 0.390048 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.11684 | 0.122013 | ||||||||
\(302\) | 8.00000i | 0.460348i | ||||||||
\(303\) | 8.11684i | 0.466301i | ||||||||
\(304\) | 0.627719 | 0.0360021 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.74456 | −0.271229 | ||||||||
\(307\) | − 30.9783i | − 1.76802i | −0.467466 | − | 0.884011i | \(-0.654833\pi\) | ||||
0.467466 | − | 0.884011i | \(-0.345167\pi\) | |||||||
\(308\) | 2.11684i | 0.120618i | ||||||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.00000 | 0.453638 | 0.226819 | − | 0.973937i | \(-0.427167\pi\) | ||||
0.226819 | + | 0.973937i | \(0.427167\pi\) | |||||||
\(312\) | 2.00000i | 0.113228i | ||||||||
\(313\) | 10.0000i | 0.565233i | 0.959233 | + | 0.282617i | \(0.0912024\pi\) | ||||
−0.959233 | + | 0.282617i | \(0.908798\pi\) | |||||||
\(314\) | −9.37228 | −0.528908 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.62772 | −0.260330 | ||||||||
\(317\) | 24.7446i | 1.38979i | 0.719110 | + | 0.694897i | \(0.244550\pi\) | ||||
−0.719110 | + | 0.694897i | \(0.755450\pi\) | |||||||
\(318\) | 1.37228i | 0.0769537i | ||||||||
\(319\) | 5.48913 | 0.307332 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.627719 | 0.0350358 | ||||||||
\(322\) | − 11.3723i | − 0.633752i | ||||||||
\(323\) | 2.97825i | 0.165714i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 24.2337 | 1.34218 | ||||||||
\(327\) | − 4.74456i | − 0.262375i | ||||||||
\(328\) | 0.744563i | 0.0411116i | ||||||||
\(329\) | 22.7446 | 1.25395 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.48913 | −0.0818497 | −0.0409249 | − | 0.999162i | \(-0.513030\pi\) | ||||
−0.0409249 | + | 0.999162i | \(0.513030\pi\) | |||||||
\(332\) | 12.0000i | 0.658586i | ||||||||
\(333\) | − 0.744563i | − 0.0408018i | ||||||||
\(334\) | 12.6277 | 0.690958 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.37228 | 0.183973 | ||||||||
\(337\) | − 28.9783i | − 1.57855i | −0.614043 | − | 0.789273i | \(-0.710458\pi\) | ||||
0.614043 | − | 0.789273i | \(-0.289542\pi\) | |||||||
\(338\) | − 9.00000i | − 0.489535i | ||||||||
\(339\) | 2.62772 | 0.142718 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.627719 | −0.0339929 | ||||||||
\(342\) | 0.627719i | 0.0339431i | ||||||||
\(343\) | − 8.86141i | − 0.478471i | ||||||||
\(344\) | −0.627719 | −0.0338443 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.0000 | −0.967686 | ||||||||
\(347\) | − 36.4674i | − 1.95767i | −0.204648 | − | 0.978836i | \(-0.565605\pi\) | ||||
0.204648 | − | 0.978836i | \(-0.434395\pi\) | |||||||
\(348\) | − 8.74456i | − 0.468758i | ||||||||
\(349\) | −7.25544 | −0.388375 | −0.194187 | − | 0.980964i | \(-0.562207\pi\) | ||||
−0.194187 | + | 0.980964i | \(0.562207\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | − 0.627719i | − 0.0334575i | ||||||||
\(353\) | 15.4891i | 0.824403i | 0.911093 | + | 0.412201i | \(0.135240\pi\) | ||||
−0.911093 | + | 0.412201i | \(0.864760\pi\) | |||||||
\(354\) | −2.74456 | −0.145872 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.37228 | −0.0727308 | ||||||||
\(357\) | 16.0000i | 0.846810i | ||||||||
\(358\) | − 12.0000i | − 0.634220i | ||||||||
\(359\) | −3.37228 | −0.177982 | −0.0889911 | − | 0.996032i | \(-0.528364\pi\) | ||||
−0.0889911 | + | 0.996032i | \(0.528364\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6060 | −0.979262 | ||||||||
\(362\) | − 14.8614i | − 0.781098i | ||||||||
\(363\) | − 10.6060i | − 0.556669i | ||||||||
\(364\) | 6.74456 | 0.353511 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 11.4891 | 0.600546 | ||||||||
\(367\) | 20.2337i | 1.05619i | 0.849185 | + | 0.528095i | \(0.177093\pi\) | ||||
−0.849185 | + | 0.528095i | \(0.822907\pi\) | |||||||
\(368\) | 3.37228i | 0.175792i | ||||||||
\(369\) | −0.744563 | −0.0387604 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.62772 | 0.240259 | ||||||||
\(372\) | 1.00000i | 0.0518476i | ||||||||
\(373\) | 14.8614i | 0.769494i | 0.923022 | + | 0.384747i | \(0.125711\pi\) | ||||
−0.923022 | + | 0.384747i | \(0.874289\pi\) | |||||||
\(374\) | 2.97825 | 0.154002 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.74456 | −0.347824 | ||||||||
\(377\) | − 17.4891i | − 0.900736i | ||||||||
\(378\) | 3.37228i | 0.173451i | ||||||||
\(379\) | 28.8614 | 1.48251 | 0.741255 | − | 0.671223i | \(-0.234231\pi\) | ||||
0.741255 | + | 0.671223i | \(0.234231\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.4891 | 0.691069 | ||||||||
\(382\) | − 16.0000i | − 0.818631i | ||||||||
\(383\) | 13.4891i | 0.689262i | 0.938738 | + | 0.344631i | \(0.111996\pi\) | ||||
−0.938738 | + | 0.344631i | \(0.888004\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 15.4891 | 0.788376 | ||||||||
\(387\) | − 0.627719i | − 0.0319087i | ||||||||
\(388\) | 2.00000i | 0.101535i | ||||||||
\(389\) | −16.9783 | −0.860831 | −0.430416 | − | 0.902631i | \(-0.641633\pi\) | ||||
−0.430416 | + | 0.902631i | \(0.641633\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0000 | −0.809155 | ||||||||
\(392\) | − 4.37228i | − 0.220834i | ||||||||
\(393\) | − 16.2337i | − 0.818881i | ||||||||
\(394\) | −19.4891 | −0.981848 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.627719 | 0.0315441 | ||||||||
\(397\) | 1.60597i | 0.0806013i | 0.999188 | + | 0.0403006i | \(0.0128316\pi\) | ||||
−0.999188 | + | 0.0403006i | \(0.987168\pi\) | |||||||
\(398\) | − 12.6277i | − 0.632970i | ||||||||
\(399\) | 2.11684 | 0.105975 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.6277 | 1.12997 | 0.564987 | − | 0.825100i | \(-0.308881\pi\) | ||||
0.564987 | + | 0.825100i | \(0.308881\pi\) | |||||||
\(402\) | − 10.7446i | − 0.535890i | ||||||||
\(403\) | 2.00000i | 0.0996271i | ||||||||
\(404\) | −8.11684 | −0.403828 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −29.4891 | −1.46352 | ||||||||
\(407\) | 0.467376i | 0.0231670i | ||||||||
\(408\) | − 4.74456i | − 0.234891i | ||||||||
\(409\) | 10.2337 | 0.506023 | 0.253012 | − | 0.967463i | \(-0.418579\pi\) | ||||
0.253012 | + | 0.967463i | \(0.418579\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.48913 | −0.172106 | ||||||||
\(412\) | 8.00000i | 0.394132i | ||||||||
\(413\) | 9.25544i | 0.455430i | ||||||||
\(414\) | −3.37228 | −0.165739 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.00000 | −0.0980581 | ||||||||
\(417\) | 10.7446i | 0.526163i | ||||||||
\(418\) | − 0.394031i | − 0.0192727i | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.4891 | 0.949842 | 0.474921 | − | 0.880028i | \(-0.342477\pi\) | ||||
0.474921 | + | 0.880028i | \(0.342477\pi\) | |||||||
\(422\) | 0.627719i | 0.0305569i | ||||||||
\(423\) | − 6.74456i | − 0.327932i | ||||||||
\(424\) | −1.37228 | −0.0666439 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.37228 | 0.163388 | ||||||||
\(427\) | − 38.7446i | − 1.87498i | ||||||||
\(428\) | 0.627719i | 0.0303419i | ||||||||
\(429\) | 1.25544 | 0.0606131 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.9783 | −1.29950 | −0.649748 | − | 0.760149i | \(-0.725126\pi\) | ||||
−0.649748 | + | 0.760149i | \(0.725126\pi\) | |||||||
\(432\) | − 1.00000i | − 0.0481125i | ||||||||
\(433\) | 36.1168i | 1.73566i | 0.496857 | + | 0.867832i | \(0.334487\pi\) | ||||
−0.496857 | + | 0.867832i | \(0.665513\pi\) | |||||||
\(434\) | 3.37228 | 0.161875 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.74456 | 0.227223 | ||||||||
\(437\) | 2.11684i | 0.101262i | ||||||||
\(438\) | − 8.11684i | − 0.387838i | ||||||||
\(439\) | −14.7446 | −0.703720 | −0.351860 | − | 0.936053i | \(-0.614451\pi\) | ||||
−0.351860 | + | 0.936053i | \(0.614451\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.37228 | 0.208204 | ||||||||
\(442\) | − 9.48913i | − 0.451352i | ||||||||
\(443\) | 34.3505i | 1.63204i | 0.578022 | + | 0.816022i | \(0.303825\pi\) | ||||
−0.578022 | + | 0.816022i | \(0.696175\pi\) | |||||||
\(444\) | 0.744563 | 0.0353354 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.25544 | 0.438258 | ||||||||
\(447\) | 12.1168i | 0.573107i | ||||||||
\(448\) | 3.37228i | 0.159325i | ||||||||
\(449\) | 8.97825 | 0.423710 | 0.211855 | − | 0.977301i | \(-0.432050\pi\) | ||||
0.211855 | + | 0.977301i | \(0.432050\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.467376 | 0.0220079 | ||||||||
\(452\) | 2.62772i | 0.123597i | ||||||||
\(453\) | − 8.00000i | − 0.375873i | ||||||||
\(454\) | −6.11684 | −0.287078 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.627719 | −0.0293956 | ||||||||
\(457\) | − 34.4674i | − 1.61232i | −0.591700 | − | 0.806158i | \(-0.701543\pi\) | ||||
0.591700 | − | 0.806158i | \(-0.298457\pi\) | |||||||
\(458\) | 3.88316i | 0.181448i | ||||||||
\(459\) | 4.74456 | 0.221457 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.7228 | −0.918583 | −0.459291 | − | 0.888286i | \(-0.651897\pi\) | ||||
−0.459291 | + | 0.888286i | \(0.651897\pi\) | |||||||
\(462\) | − 2.11684i | − 0.0984845i | ||||||||
\(463\) | 2.51087i | 0.116690i | 0.998296 | + | 0.0583451i | \(0.0185824\pi\) | ||||
−0.998296 | + | 0.0583451i | \(0.981418\pi\) | |||||||
\(464\) | 8.74456 | 0.405956 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.8614 | −0.688441 | ||||||||
\(467\) | − 6.51087i | − 0.301287i | −0.988588 | − | 0.150644i | \(-0.951865\pi\) | ||||
0.988588 | − | 0.150644i | \(-0.0481346\pi\) | |||||||
\(468\) | − 2.00000i | − 0.0924500i | ||||||||
\(469\) | −36.2337 | −1.67312 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.37228 | 0.431852 | ||||||||
\(472\) | − 2.74456i | − 0.126329i | ||||||||
\(473\) | 0.394031i | 0.0181176i | ||||||||
\(474\) | 4.62772 | 0.212558 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −16.0000 | −0.733359 | ||||||||
\(477\) | − 1.37228i | − 0.0628324i | ||||||||
\(478\) | − 29.4891i | − 1.34880i | ||||||||
\(479\) | −8.86141 | −0.404888 | −0.202444 | − | 0.979294i | \(-0.564888\pi\) | ||||
−0.202444 | + | 0.979294i | \(0.564888\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.48913 | 0.0678983 | ||||||||
\(482\) | − 4.51087i | − 0.205465i | ||||||||
\(483\) | 11.3723i | 0.517457i | ||||||||
\(484\) | 10.6060 | 0.482090 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 37.4891i | 1.69879i | 0.527754 | + | 0.849397i | \(0.323034\pi\) | ||||
−0.527754 | + | 0.849397i | \(0.676966\pi\) | |||||||
\(488\) | 11.4891i | 0.520088i | ||||||||
\(489\) | −24.2337 | −1.09589 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.6060 | 1.24584 | 0.622920 | − | 0.782286i | \(-0.285946\pi\) | ||||
0.622920 | + | 0.782286i | \(0.285946\pi\) | |||||||
\(492\) | − 0.744563i | − 0.0335675i | ||||||||
\(493\) | 41.4891i | 1.86858i | ||||||||
\(494\) | −1.25544 | −0.0564848 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | − 11.3723i | − 0.510117i | ||||||||
\(498\) | − 12.0000i | − 0.537733i | ||||||||
\(499\) | −33.4891 | −1.49918 | −0.749590 | − | 0.661903i | \(-0.769749\pi\) | ||||
−0.749590 | + | 0.661903i | \(0.769749\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.6277 | −0.564165 | ||||||||
\(502\) | 4.00000i | 0.178529i | ||||||||
\(503\) | 5.48913i | 0.244748i | 0.992484 | + | 0.122374i | \(0.0390507\pi\) | ||||
−0.992484 | + | 0.122374i | \(0.960949\pi\) | |||||||
\(504\) | −3.37228 | −0.150213 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.11684 | 0.0941052 | ||||||||
\(507\) | 9.00000i | 0.399704i | ||||||||
\(508\) | 13.4891i | 0.598483i | ||||||||
\(509\) | 27.2554 | 1.20808 | 0.604038 | − | 0.796956i | \(-0.293558\pi\) | ||||
0.604038 | + | 0.796956i | \(0.293558\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.3723 | −1.21088 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | − 0.627719i | − 0.0277145i | ||||||||
\(514\) | −13.3723 | −0.589826 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.627719 | 0.0276338 | ||||||||
\(517\) | 4.23369i | 0.186197i | ||||||||
\(518\) | − 2.51087i | − 0.110322i | ||||||||
\(519\) | 18.0000 | 0.790112 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.9783 | 1.62005 | 0.810023 | − | 0.586398i | \(-0.199454\pi\) | ||||
0.810023 | + | 0.586398i | \(0.199454\pi\) | |||||||
\(522\) | 8.74456i | 0.382739i | ||||||||
\(523\) | − 12.8614i | − 0.562390i | −0.959651 | − | 0.281195i | \(-0.909269\pi\) | ||||
0.959651 | − | 0.281195i | \(-0.0907308\pi\) | |||||||
\(524\) | 16.2337 | 0.709172 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.9783 | −0.827491 | ||||||||
\(527\) | − 4.74456i | − 0.206676i | ||||||||
\(528\) | 0.627719i | 0.0273179i | ||||||||
\(529\) | 11.6277 | 0.505553 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.74456 | 0.119104 | ||||||||
\(532\) | 2.11684i | 0.0917768i | ||||||||
\(533\) | − 1.48913i | − 0.0645012i | ||||||||
\(534\) | 1.37228 | 0.0593844 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 10.7446 | 0.464094 | ||||||||
\(537\) | 12.0000i | 0.517838i | ||||||||
\(538\) | − 2.00000i | − 0.0862261i | ||||||||
\(539\) | −2.74456 | −0.118217 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.4891 | −0.665930 | −0.332965 | − | 0.942939i | \(-0.608049\pi\) | ||||
−0.332965 | + | 0.942939i | \(0.608049\pi\) | |||||||
\(542\) | 13.8832i | 0.596333i | ||||||||
\(543\) | 14.8614i | 0.637764i | ||||||||
\(544\) | 4.74456 | 0.203421 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −6.74456 | −0.288641 | ||||||||
\(547\) | 2.74456i | 0.117349i | 0.998277 | + | 0.0586745i | \(0.0186874\pi\) | ||||
−0.998277 | + | 0.0586745i | \(0.981313\pi\) | |||||||
\(548\) | − 3.48913i | − 0.149048i | ||||||||
\(549\) | −11.4891 | −0.490344 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.48913 | 0.233845 | ||||||||
\(552\) | − 3.37228i | − 0.143534i | ||||||||
\(553\) | − 15.6060i | − 0.663633i | ||||||||
\(554\) | −15.2554 | −0.648141 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.7446 | −0.455671 | ||||||||
\(557\) | − 11.8832i | − 0.503505i | −0.967792 | − | 0.251753i | \(-0.918993\pi\) | ||||
0.967792 | − | 0.251753i | \(-0.0810070\pi\) | |||||||
\(558\) | − 1.00000i | − 0.0423334i | ||||||||
\(559\) | 1.25544 | 0.0530993 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.97825 | −0.125742 | ||||||||
\(562\) | − 16.7446i | − 0.706327i | ||||||||
\(563\) | − 6.97825i | − 0.294098i | −0.989129 | − | 0.147049i | \(-0.953022\pi\) | ||||
0.989129 | − | 0.147049i | \(-0.0469775\pi\) | |||||||
\(564\) | 6.74456 | 0.283997 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 12.0000 | 0.504398 | ||||||||
\(567\) | − 3.37228i | − 0.141623i | ||||||||
\(568\) | 3.37228i | 0.141498i | ||||||||
\(569\) | 1.37228 | 0.0575290 | 0.0287645 | − | 0.999586i | \(-0.490843\pi\) | ||||
0.0287645 | + | 0.999586i | \(0.490843\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.7446 | −1.11923 | −0.559613 | − | 0.828754i | \(-0.689050\pi\) | ||||
−0.559613 | + | 0.828754i | \(0.689050\pi\) | |||||||
\(572\) | 1.25544i | 0.0524925i | ||||||||
\(573\) | 16.0000i | 0.668410i | ||||||||
\(574\) | −2.51087 | −0.104802 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 2.23369i | 0.0929896i | 0.998919 | + | 0.0464948i | \(0.0148051\pi\) | ||||
−0.998919 | + | 0.0464948i | \(0.985195\pi\) | |||||||
\(578\) | 5.51087i | 0.229222i | ||||||||
\(579\) | −15.4891 | −0.643706 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −40.4674 | −1.67887 | ||||||||
\(582\) | − 2.00000i | − 0.0829027i | ||||||||
\(583\) | 0.861407i | 0.0356758i | ||||||||
\(584\) | 8.11684 | 0.335877 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.48913 | −0.309373 | ||||||||
\(587\) | − 12.0000i | − 0.495293i | −0.968850 | − | 0.247647i | \(-0.920343\pi\) | ||||
0.968850 | − | 0.247647i | \(-0.0796572\pi\) | |||||||
\(588\) | 4.37228i | 0.180310i | ||||||||
\(589\) | −0.627719 | −0.0258647 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.4891 | 0.801675 | ||||||||
\(592\) | 0.744563i | 0.0306013i | ||||||||
\(593\) | 44.9783i | 1.84704i | 0.383556 | + | 0.923518i | \(0.374699\pi\) | ||||
−0.383556 | + | 0.923518i | \(0.625301\pi\) | |||||||
\(594\) | −0.627719 | −0.0257556 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.1168 | −0.496325 | ||||||||
\(597\) | 12.6277i | 0.516818i | ||||||||
\(598\) | − 6.74456i | − 0.275806i | ||||||||
\(599\) | −10.1168 | −0.413363 | −0.206682 | − | 0.978408i | \(-0.566266\pi\) | ||||
−0.206682 | + | 0.978408i | \(0.566266\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.5109 | 0.510329 | 0.255165 | − | 0.966898i | \(-0.417870\pi\) | ||||
0.255165 | + | 0.966898i | \(0.417870\pi\) | |||||||
\(602\) | − 2.11684i | − 0.0862761i | ||||||||
\(603\) | 10.7446i | 0.437552i | ||||||||
\(604\) | 8.00000 | 0.325515 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 8.11684 | 0.329724 | ||||||||
\(607\) | 4.62772i | 0.187833i | 0.995580 | + | 0.0939167i | \(0.0299387\pi\) | ||||
−0.995580 | + | 0.0939167i | \(0.970061\pi\) | |||||||
\(608\) | − 0.627719i | − 0.0254574i | ||||||||
\(609\) | 29.4891 | 1.19496 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.4891 | 0.545712 | ||||||||
\(612\) | 4.74456i | 0.191788i | ||||||||
\(613\) | 35.4891i | 1.43339i | 0.697386 | + | 0.716696i | \(0.254347\pi\) | ||||
−0.697386 | + | 0.716696i | \(0.745653\pi\) | |||||||
\(614\) | −30.9783 | −1.25018 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.11684 | 0.0852901 | ||||||||
\(617\) | − 7.88316i | − 0.317364i | −0.987330 | − | 0.158682i | \(-0.949276\pi\) | ||||
0.987330 | − | 0.158682i | \(-0.0507244\pi\) | |||||||
\(618\) | − 8.00000i | − 0.321807i | ||||||||
\(619\) | −16.2337 | −0.652487 | −0.326244 | − | 0.945286i | \(-0.605783\pi\) | ||||
−0.326244 | + | 0.945286i | \(0.605783\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.37228 | 0.135325 | ||||||||
\(622\) | − 8.00000i | − 0.320771i | ||||||||
\(623\) | − 4.62772i | − 0.185406i | ||||||||
\(624\) | 2.00000 | 0.0800641 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10.0000 | 0.399680 | ||||||||
\(627\) | 0.394031i | 0.0157361i | ||||||||
\(628\) | 9.37228i | 0.373995i | ||||||||
\(629\) | −3.53262 | −0.140855 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −46.3505 | −1.84519 | −0.922593 | − | 0.385775i | \(-0.873934\pi\) | ||||
−0.922593 | + | 0.385775i | \(0.873934\pi\) | |||||||
\(632\) | 4.62772i | 0.184081i | ||||||||
\(633\) | − 0.627719i | − 0.0249496i | ||||||||
\(634\) | 24.7446 | 0.982732 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.37228 | 0.0544145 | ||||||||
\(637\) | 8.74456i | 0.346472i | ||||||||
\(638\) | − 5.48913i | − 0.217317i | ||||||||
\(639\) | −3.37228 | −0.133405 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.0000 | 0.710957 | 0.355479 | − | 0.934684i | \(-0.384318\pi\) | ||||
0.355479 | + | 0.934684i | \(0.384318\pi\) | |||||||
\(642\) | − 0.627719i | − 0.0247741i | ||||||||
\(643\) | − 25.0951i | − 0.989654i | −0.868992 | − | 0.494827i | \(-0.835231\pi\) | ||||
0.868992 | − | 0.494827i | \(-0.164769\pi\) | |||||||
\(644\) | −11.3723 | −0.448131 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.97825 | 0.117178 | ||||||||
\(647\) | − 50.5842i | − 1.98867i | −0.106287 | − | 0.994335i | \(-0.533896\pi\) | ||||
0.106287 | − | 0.994335i | \(-0.466104\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −1.72281 | −0.0676263 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.37228 | −0.132170 | ||||||||
\(652\) | − 24.2337i | − 0.949064i | ||||||||
\(653\) | 40.9783i | 1.60360i | 0.597591 | + | 0.801801i | \(0.296125\pi\) | ||||
−0.597591 | + | 0.801801i | \(0.703875\pi\) | |||||||
\(654\) | −4.74456 | −0.185527 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.744563 | 0.0290703 | ||||||||
\(657\) | 8.11684i | 0.316668i | ||||||||
\(658\) | − 22.7446i | − 0.886675i | ||||||||
\(659\) | −36.0000 | −1.40236 | −0.701180 | − | 0.712984i | \(-0.747343\pi\) | ||||
−0.701180 | + | 0.712984i | \(0.747343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.97825 | −0.193632 | −0.0968158 | − | 0.995302i | \(-0.530866\pi\) | ||||
−0.0968158 | + | 0.995302i | \(0.530866\pi\) | |||||||
\(662\) | 1.48913i | 0.0578765i | ||||||||
\(663\) | 9.48913i | 0.368527i | ||||||||
\(664\) | 12.0000 | 0.465690 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.744563 | −0.0288512 | ||||||||
\(667\) | 29.4891i | 1.14182i | ||||||||
\(668\) | − 12.6277i | − 0.488581i | ||||||||
\(669\) | −9.25544 | −0.357836 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.21194 | 0.278414 | ||||||||
\(672\) | − 3.37228i | − 0.130089i | ||||||||
\(673\) | − 0.510875i | − 0.0196928i | −0.999952 | − | 0.00984639i | \(-0.996866\pi\) | ||||
0.999952 | − | 0.00984639i | \(-0.00313425\pi\) | |||||||
\(674\) | −28.9783 | −1.11620 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | 41.6060i | 1.59905i | 0.600635 | + | 0.799524i | \(0.294915\pi\) | ||||
−0.600635 | + | 0.799524i | \(0.705085\pi\) | |||||||
\(678\) | − 2.62772i | − 0.100917i | ||||||||
\(679\) | −6.74456 | −0.258833 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.11684 | 0.234398 | ||||||||
\(682\) | 0.627719i | 0.0240366i | ||||||||
\(683\) | − 12.8614i | − 0.492128i | −0.969254 | − | 0.246064i | \(-0.920863\pi\) | ||||
0.969254 | − | 0.246064i | \(-0.0791373\pi\) | |||||||
\(684\) | 0.627719 | 0.0240014 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.86141 | −0.338330 | ||||||||
\(687\) | − 3.88316i | − 0.148152i | ||||||||
\(688\) | 0.627719i | 0.0239316i | ||||||||
\(689\) | 2.74456 | 0.104560 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.1386 | −0.728066 | −0.364033 | − | 0.931386i | \(-0.618601\pi\) | ||||
−0.364033 | + | 0.931386i | \(0.618601\pi\) | |||||||
\(692\) | 18.0000i | 0.684257i | ||||||||
\(693\) | 2.11684i | 0.0804123i | ||||||||
\(694\) | −36.4674 | −1.38428 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8.74456 | −0.331462 | ||||||||
\(697\) | 3.53262i | 0.133808i | ||||||||
\(698\) | 7.25544i | 0.274622i | ||||||||
\(699\) | 14.8614 | 0.562110 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.6060 | 1.72251 | 0.861257 | − | 0.508170i | \(-0.169678\pi\) | ||||
0.861257 | + | 0.508170i | \(0.169678\pi\) | |||||||
\(702\) | 2.00000i | 0.0754851i | ||||||||
\(703\) | 0.467376i | 0.0176274i | ||||||||
\(704\) | −0.627719 | −0.0236580 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.4891 | 0.582941 | ||||||||
\(707\) | − 27.3723i | − 1.02944i | ||||||||
\(708\) | 2.74456i | 0.103147i | ||||||||
\(709\) | −40.1168 | −1.50662 | −0.753310 | − | 0.657666i | \(-0.771544\pi\) | ||||
−0.753310 | + | 0.657666i | \(0.771544\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.62772 | −0.173553 | ||||||||
\(712\) | 1.37228i | 0.0514284i | ||||||||
\(713\) | − 3.37228i | − 0.126293i | ||||||||
\(714\) | 16.0000 | 0.598785 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | 29.4891i | 1.10129i | ||||||||
\(718\) | 3.37228i | 0.125852i | ||||||||
\(719\) | −38.7446 | −1.44493 | −0.722464 | − | 0.691408i | \(-0.756991\pi\) | ||||
−0.722464 | + | 0.691408i | \(0.756991\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.9783 | −1.00472 | ||||||||
\(722\) | 18.6060i | 0.692442i | ||||||||
\(723\) | 4.51087i | 0.167761i | ||||||||
\(724\) | −14.8614 | −0.552320 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −10.6060 | −0.393624 | ||||||||
\(727\) | − 19.3723i | − 0.718478i | −0.933246 | − | 0.359239i | \(-0.883036\pi\) | ||||
0.933246 | − | 0.359239i | \(-0.116964\pi\) | |||||||
\(728\) | − 6.74456i | − 0.249970i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.97825 | −0.110155 | ||||||||
\(732\) | − 11.4891i | − 0.424650i | ||||||||
\(733\) | − 34.0000i | − 1.25582i | −0.778287 | − | 0.627909i | \(-0.783911\pi\) | ||||
0.778287 | − | 0.627909i | \(-0.216089\pi\) | |||||||
\(734\) | 20.2337 | 0.746839 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.37228 | 0.124304 | ||||||||
\(737\) | − 6.74456i | − 0.248439i | ||||||||
\(738\) | 0.744563i | 0.0274077i | ||||||||
\(739\) | 22.9783 | 0.845269 | 0.422634 | − | 0.906300i | \(-0.361105\pi\) | ||||
0.422634 | + | 0.906300i | \(0.361105\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.25544 | 0.0461196 | ||||||||
\(742\) | − 4.62772i | − 0.169889i | ||||||||
\(743\) | − 35.3723i | − 1.29768i | −0.760924 | − | 0.648842i | \(-0.775254\pi\) | ||||
0.760924 | − | 0.648842i | \(-0.224746\pi\) | |||||||
\(744\) | 1.00000 | 0.0366618 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 14.8614 | 0.544115 | ||||||||
\(747\) | 12.0000i | 0.439057i | ||||||||
\(748\) | − 2.97825i | − 0.108896i | ||||||||
\(749\) | −2.11684 | −0.0773478 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.7446 | −1.41381 | −0.706905 | − | 0.707309i | \(-0.749909\pi\) | ||||
−0.706905 | + | 0.707309i | \(0.749909\pi\) | |||||||
\(752\) | 6.74456i | 0.245949i | ||||||||
\(753\) | − 4.00000i | − 0.145768i | ||||||||
\(754\) | −17.4891 | −0.636916 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.37228 | 0.122649 | ||||||||
\(757\) | 26.0000i | 0.944986i | 0.881334 | + | 0.472493i | \(0.156646\pi\) | ||||
−0.881334 | + | 0.472493i | \(0.843354\pi\) | |||||||
\(758\) | − 28.8614i | − 1.04829i | ||||||||
\(759\) | −2.11684 | −0.0768366 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −46.8614 | −1.69872 | −0.849362 | − | 0.527810i | \(-0.823013\pi\) | ||||
−0.849362 | + | 0.527810i | \(0.823013\pi\) | |||||||
\(762\) | − 13.4891i | − 0.488659i | ||||||||
\(763\) | 16.0000i | 0.579239i | ||||||||
\(764\) | −16.0000 | −0.578860 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.4891 | 0.487382 | ||||||||
\(767\) | 5.48913i | 0.198201i | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 9.37228 | 0.337973 | 0.168987 | − | 0.985618i | \(-0.445951\pi\) | ||||
0.168987 | + | 0.985618i | \(0.445951\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.3723 | 0.481591 | ||||||||
\(772\) | − 15.4891i | − 0.557466i | ||||||||
\(773\) | 21.6060i | 0.777113i | 0.921425 | + | 0.388556i | \(0.127026\pi\) | ||||
−0.921425 | + | 0.388556i | \(0.872974\pi\) | |||||||
\(774\) | −0.627719 | −0.0225629 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.00000 | 0.0717958 | ||||||||
\(777\) | 2.51087i | 0.0900771i | ||||||||
\(778\) | 16.9783i | 0.608700i | ||||||||
\(779\) | 0.467376 | 0.0167455 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.11684 | 0.0757466 | ||||||||
\(782\) | 16.0000i | 0.572159i | ||||||||
\(783\) | − 8.74456i | − 0.312505i | ||||||||
\(784\) | −4.37228 | −0.156153 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −16.2337 | −0.579036 | ||||||||
\(787\) | 9.88316i | 0.352296i | 0.984364 | + | 0.176148i | \(0.0563638\pi\) | ||||
−0.984364 | + | 0.176148i | \(0.943636\pi\) | |||||||
\(788\) | 19.4891i | 0.694271i | ||||||||
\(789\) | 18.9783 | 0.675644 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.86141 | −0.315075 | ||||||||
\(792\) | − 0.627719i | − 0.0223050i | ||||||||
\(793\) | − 22.9783i | − 0.815982i | ||||||||
\(794\) | 1.60597 | 0.0569937 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.6277 | −0.447578 | ||||||||
\(797\) | 20.5109i | 0.726532i | 0.931685 | + | 0.363266i | \(0.118338\pi\) | ||||
−0.931685 | + | 0.363266i | \(0.881662\pi\) | |||||||
\(798\) | − 2.11684i | − 0.0749355i | ||||||||
\(799\) | −32.0000 | −1.13208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.37228 | −0.0484872 | ||||||||
\(802\) | − 22.6277i | − 0.799013i | ||||||||
\(803\) | − 5.09509i | − 0.179802i | ||||||||
\(804\) | −10.7446 | −0.378932 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.00000 | 0.0704470 | ||||||||
\(807\) | 2.00000i | 0.0704033i | ||||||||
\(808\) | 8.11684i | 0.285550i | ||||||||
\(809\) | −9.60597 | −0.337728 | −0.168864 | − | 0.985639i | \(-0.554010\pi\) | ||||
−0.168864 | + | 0.985639i | \(0.554010\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.6277 | −1.42663 | −0.713316 | − | 0.700842i | \(-0.752808\pi\) | ||||
−0.713316 | + | 0.700842i | \(0.752808\pi\) | |||||||
\(812\) | 29.4891i | 1.03487i | ||||||||
\(813\) | − 13.8832i | − 0.486904i | ||||||||
\(814\) | 0.467376 | 0.0163815 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.74456 | −0.166093 | ||||||||
\(817\) | 0.394031i | 0.0137854i | ||||||||
\(818\) | − 10.2337i | − 0.357813i | ||||||||
\(819\) | 6.74456 | 0.235674 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.2554 | 0.532418 | 0.266209 | − | 0.963915i | \(-0.414229\pi\) | ||||
0.266209 | + | 0.963915i | \(0.414229\pi\) | |||||||
\(822\) | 3.48913i | 0.121697i | ||||||||
\(823\) | − 17.2554i | − 0.601487i | −0.953705 | − | 0.300743i | \(-0.902765\pi\) | ||||
0.953705 | − | 0.300743i | \(-0.0972348\pi\) | |||||||
\(824\) | 8.00000 | 0.278693 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.25544 | 0.322038 | ||||||||
\(827\) | 17.4891i | 0.608156i | 0.952647 | + | 0.304078i | \(0.0983484\pi\) | ||||
−0.952647 | + | 0.304078i | \(0.901652\pi\) | |||||||
\(828\) | 3.37228i | 0.117195i | ||||||||
\(829\) | 31.0951 | 1.07998 | 0.539989 | − | 0.841672i | \(-0.318429\pi\) | ||||
0.539989 | + | 0.841672i | \(0.318429\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.2554 | 0.529205 | ||||||||
\(832\) | 2.00000i | 0.0693375i | ||||||||
\(833\) | − 20.7446i | − 0.718756i | ||||||||
\(834\) | 10.7446 | 0.372054 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.394031 | −0.0136278 | ||||||||
\(837\) | 1.00000i | 0.0345651i | ||||||||
\(838\) | − 12.0000i | − 0.414533i | ||||||||
\(839\) | −16.8614 | −0.582120 | −0.291060 | − | 0.956705i | \(-0.594008\pi\) | ||||
−0.291060 | + | 0.956705i | \(0.594008\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47.4674 | 1.63681 | ||||||||
\(842\) | − 19.4891i | − 0.671640i | ||||||||
\(843\) | 16.7446i | 0.576713i | ||||||||
\(844\) | 0.627719 | 0.0216070 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.74456 | −0.231883 | ||||||||
\(847\) | 35.7663i | 1.22895i | ||||||||
\(848\) | 1.37228i | 0.0471243i | ||||||||
\(849\) | −12.0000 | −0.411839 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.51087 | −0.0860717 | ||||||||
\(852\) | − 3.37228i | − 0.115532i | ||||||||
\(853\) | − 39.0951i | − 1.33859i | −0.742997 | − | 0.669295i | \(-0.766596\pi\) | ||||
0.742997 | − | 0.669295i | \(-0.233404\pi\) | |||||||
\(854\) | −38.7446 | −1.32581 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.627719 | 0.0214550 | ||||||||
\(857\) | − 7.48913i | − 0.255824i | −0.991786 | − | 0.127912i | \(-0.959173\pi\) | ||||
0.991786 | − | 0.127912i | \(-0.0408275\pi\) | |||||||
\(858\) | − 1.25544i | − 0.0428599i | ||||||||
\(859\) | 17.4891 | 0.596721 | 0.298361 | − | 0.954453i | \(-0.403560\pi\) | ||||
0.298361 | + | 0.954453i | \(0.403560\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.51087 | 0.0855704 | ||||||||
\(862\) | 26.9783i | 0.918883i | ||||||||
\(863\) | − 6.35053i | − 0.216175i | −0.994141 | − | 0.108087i | \(-0.965527\pi\) | ||||
0.994141 | − | 0.108087i | \(-0.0344726\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 36.1168 | 1.22730 | ||||||||
\(867\) | − 5.51087i | − 0.187159i | ||||||||
\(868\) | − 3.37228i | − 0.114463i | ||||||||
\(869\) | 2.90491 | 0.0985422 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.4891 | −0.728131 | ||||||||
\(872\) | − 4.74456i | − 0.160671i | ||||||||
\(873\) | 2.00000i | 0.0676897i | ||||||||
\(874\) | 2.11684 | 0.0716033 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.11684 | −0.274243 | ||||||||
\(877\) | 44.9783i | 1.51881i | 0.650620 | + | 0.759404i | \(0.274509\pi\) | ||||
−0.650620 | + | 0.759404i | \(0.725491\pi\) | |||||||
\(878\) | 14.7446i | 0.497605i | ||||||||
\(879\) | 7.48913 | 0.252602 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.02175 | −0.101805 | −0.0509027 | − | 0.998704i | \(-0.516210\pi\) | ||||
−0.0509027 | + | 0.998704i | \(0.516210\pi\) | |||||||
\(882\) | − 4.37228i | − 0.147222i | ||||||||
\(883\) | 44.8614i | 1.50971i | 0.655894 | + | 0.754853i | \(0.272292\pi\) | ||||
−0.655894 | + | 0.754853i | \(0.727708\pi\) | |||||||
\(884\) | −9.48913 | −0.319154 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 34.3505 | 1.15403 | ||||||||
\(887\) | 30.7446i | 1.03230i | 0.856498 | + | 0.516151i | \(0.172636\pi\) | ||||
−0.856498 | + | 0.516151i | \(0.827364\pi\) | |||||||
\(888\) | − 0.744563i | − 0.0249859i | ||||||||
\(889\) | −45.4891 | −1.52566 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.627719 | 0.0210294 | ||||||||
\(892\) | − 9.25544i | − 0.309895i | ||||||||
\(893\) | 4.23369i | 0.141675i | ||||||||
\(894\) | 12.1168 | 0.405248 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.37228 | 0.112660 | ||||||||
\(897\) | 6.74456i | 0.225194i | ||||||||
\(898\) | − 8.97825i | − 0.299608i | ||||||||
\(899\) | −8.74456 | −0.291647 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.51087 | −0.216909 | ||||||||
\(902\) | − 0.467376i | − 0.0155619i | ||||||||
\(903\) | 2.11684i | 0.0704442i | ||||||||
\(904\) | 2.62772 | 0.0873966 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −8.00000 | −0.265782 | ||||||||
\(907\) | 17.4891i | 0.580717i | 0.956918 | + | 0.290358i | \(0.0937745\pi\) | ||||
−0.956918 | + | 0.290358i | \(0.906225\pi\) | |||||||
\(908\) | 6.11684i | 0.202995i | ||||||||
\(909\) | −8.11684 | −0.269219 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.51087 | −0.0831890 | −0.0415945 | − | 0.999135i | \(-0.513244\pi\) | ||||
−0.0415945 | + | 0.999135i | \(0.513244\pi\) | |||||||
\(912\) | 0.627719i | 0.0207858i | ||||||||
\(913\) | − 7.53262i | − 0.249293i | ||||||||
\(914\) | −34.4674 | −1.14008 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.88316 | 0.128303 | ||||||||
\(917\) | 54.7446i | 1.80782i | ||||||||
\(918\) | − 4.74456i | − 0.156594i | ||||||||
\(919\) | 12.2337 | 0.403552 | 0.201776 | − | 0.979432i | \(-0.435329\pi\) | ||||
0.201776 | + | 0.979432i | \(0.435329\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30.9783 | 1.02077 | ||||||||
\(922\) | 19.7228i | 0.649536i | ||||||||
\(923\) | − 6.74456i | − 0.222000i | ||||||||
\(924\) | −2.11684 | −0.0696391 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.51087 | 0.0825125 | ||||||||
\(927\) | 8.00000i | 0.262754i | ||||||||
\(928\) | − 8.74456i | − 0.287054i | ||||||||
\(929\) | 16.1168 | 0.528776 | 0.264388 | − | 0.964416i | \(-0.414830\pi\) | ||||
0.264388 | + | 0.964416i | \(0.414830\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.74456 | −0.0899494 | ||||||||
\(932\) | 14.8614i | 0.486802i | ||||||||
\(933\) | 8.00000i | 0.261908i | ||||||||
\(934\) | −6.51087 | −0.213042 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.00000 | −0.0653720 | ||||||||
\(937\) | 31.2554i | 1.02107i | 0.859857 | + | 0.510535i | \(0.170553\pi\) | ||||
−0.859857 | + | 0.510535i | \(0.829447\pi\) | |||||||
\(938\) | 36.2337i | 1.18307i | ||||||||
\(939\) | −10.0000 | −0.326338 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.7228 | −0.642945 | −0.321473 | − | 0.946919i | \(-0.604178\pi\) | ||||
−0.321473 | + | 0.946919i | \(0.604178\pi\) | |||||||
\(942\) | − 9.37228i | − 0.305365i | ||||||||
\(943\) | 2.51087i | 0.0817653i | ||||||||
\(944\) | −2.74456 | −0.0893279 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.394031 | 0.0128110 | ||||||||
\(947\) | 2.74456i | 0.0891863i | 0.999005 | + | 0.0445932i | \(0.0141991\pi\) | ||||
−0.999005 | + | 0.0445932i | \(0.985801\pi\) | |||||||
\(948\) | − 4.62772i | − 0.150301i | ||||||||
\(949\) | −16.2337 | −0.526968 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.7446 | −0.802397 | ||||||||
\(952\) | 16.0000i | 0.518563i | ||||||||
\(953\) | 11.7228i | 0.379739i | 0.981809 | + | 0.189870i | \(0.0608065\pi\) | ||||
−0.981809 | + | 0.189870i | \(0.939193\pi\) | |||||||
\(954\) | −1.37228 | −0.0444292 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −29.4891 | −0.953746 | ||||||||
\(957\) | 5.48913i | 0.177438i | ||||||||
\(958\) | 8.86141i | 0.286299i | ||||||||
\(959\) | 11.7663 | 0.379954 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | − 1.48913i | − 0.0480113i | ||||||||
\(963\) | 0.627719i | 0.0202280i | ||||||||
\(964\) | −4.51087 | −0.145285 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 11.3723 | 0.365897 | ||||||||
\(967\) | − 8.00000i | − 0.257263i | −0.991692 | − | 0.128631i | \(-0.958942\pi\) | ||||
0.991692 | − | 0.128631i | \(-0.0410584\pi\) | |||||||
\(968\) | − 10.6060i | − 0.340889i | ||||||||
\(969\) | −2.97825 | −0.0956752 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48.7011 | −1.56289 | −0.781446 | − | 0.623973i | \(-0.785517\pi\) | ||||
−0.781446 | + | 0.623973i | \(0.785517\pi\) | |||||||
\(972\) | − 1.00000i | − 0.0320750i | ||||||||
\(973\) | − 36.2337i | − 1.16160i | ||||||||
\(974\) | 37.4891 | 1.20123 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.4891 | 0.367758 | ||||||||
\(977\) | 46.0000i | 1.47167i | 0.677161 | + | 0.735835i | \(0.263210\pi\) | ||||
−0.677161 | + | 0.735835i | \(0.736790\pi\) | |||||||
\(978\) | 24.2337i | 0.774908i | ||||||||
\(979\) | 0.861407 | 0.0275307 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.74456 | 0.151482 | ||||||||
\(982\) | − 27.6060i | − 0.880942i | ||||||||
\(983\) | − 2.97825i | − 0.0949914i | −0.998871 | − | 0.0474957i | \(-0.984876\pi\) | ||||
0.998871 | − | 0.0474957i | \(-0.0151240\pi\) | |||||||
\(984\) | −0.744563 | −0.0237358 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 41.4891 | 1.32128 | ||||||||
\(987\) | 22.7446i | 0.723967i | ||||||||
\(988\) | 1.25544i | 0.0399408i | ||||||||
\(989\) | −2.11684 | −0.0673117 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.6060 | −1.51225 | −0.756127 | − | 0.654425i | \(-0.772911\pi\) | ||||
−0.756127 | + | 0.654425i | \(0.772911\pi\) | |||||||
\(992\) | 1.00000i | 0.0317500i | ||||||||
\(993\) | − 1.48913i | − 0.0472560i | ||||||||
\(994\) | −11.3723 | −0.360707 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −12.0000 | −0.380235 | ||||||||
\(997\) | − 6.00000i | − 0.190022i | −0.995476 | − | 0.0950110i | \(-0.969711\pi\) | ||||
0.995476 | − | 0.0950110i | \(-0.0302886\pi\) | |||||||
\(998\) | 33.4891i | 1.06008i | ||||||||
\(999\) | 0.744563 | 0.0235569 |
(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 | 4650.2.d.bh.3349.1 | 4 | ||
5.2 | odd | 4 | 930.2.a.r.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 4650.2.a.by.1.1 | 2 | |||
5.4 | even | 2 | inner | 4650.2.d.bh.3349.4 | 4 | ||
15.2 | even | 4 | 2790.2.a.bd.1.2 | 2 | |||
20.7 | even | 4 | 7440.2.a.bg.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.a.r.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
2790.2.a.bd.1.2 | 2 | 15.2 | even | 4 | |||
4650.2.a.by.1.1 | 2 | 5.3 | odd | 4 | |||
4650.2.d.bh.3349.1 | 4 | 1.1 | even | 1 | trivial | ||
4650.2.d.bh.3349.4 | 4 | 5.4 | even | 2 | inner | ||
7440.2.a.bg.1.1 | 2 | 20.7 | even | 4 |