Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1120,2,Mod(111,1120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1120, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1120.111");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1120 = 2^{5} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1120.h (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: | \(8.94324502638\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} - 2x^{12} + 6x^{11} - 12x^{9} + 8x^{8} - 24x^{7} + 48x^{5} - 32x^{4} - 128x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 111.10 | ||
Root | \(1.14218 + 0.833926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1120.111 |
Dual form | 1120.2.h.b.111.7 |
$q$-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 \(\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(421\) | \(801\) | \(897\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0.586834i | 0.338809i | 0.985547 | + | 0.169404i | \(0.0541844\pi\) | ||||
−0.985547 | + | 0.169404i | \(0.945816\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.52442 | + | 0.792014i | 0.954142 | + | 0.299353i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.65563 | 0.885209 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.580189 | 0.174934 | 0.0874668 | − | 0.996167i | \(-0.472123\pi\) | ||||
0.0874668 | + | 0.996167i | \(0.472123\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.14766 | 0.318303 | 0.159152 | − | 0.987254i | \(-0.449124\pi\) | ||||
0.159152 | + | 0.987254i | \(0.449124\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.586834i | 0.151520i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.82880i | − | 0.443550i | −0.975098 | − | 0.221775i | \(-0.928815\pi\) | ||
0.975098 | − | 0.221775i | \(-0.0711851\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.72462i | − | 1.08390i | −0.840410 | − | 0.541951i | \(-0.817686\pi\) | ||
0.840410 | − | 0.541951i | \(-0.182314\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.464781 | + | 1.48142i | −0.101423 | + | 0.323272i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.79961i | − | 0.583759i | −0.956455 | − | 0.291879i | \(-0.905719\pi\) | ||
0.956455 | − | 0.291879i | \(-0.0942806\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.31891i | 0.638725i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.40518i | 1.37511i | 0.726133 | + | 0.687554i | \(0.241316\pi\) | ||||
−0.726133 | + | 0.687554i | \(0.758684\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.73007 | −0.849546 | −0.424773 | − | 0.905300i | \(-0.639646\pi\) | ||||
−0.424773 | + | 0.905300i | \(0.639646\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.340475i | 0.0592691i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.52442 | + | 0.792014i | 0.426705 | + | 0.133875i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.35175i | 0.715423i | 0.933832 | + | 0.357712i | \(0.116443\pi\) | ||||
−0.933832 | + | 0.357712i | \(0.883557\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.673485i | 0.107844i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 8.46264i | − | 1.32164i | −0.750544 | − | 0.660821i | \(-0.770208\pi\) | ||
0.750544 | − | 0.660821i | \(-0.229792\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.32314 | 0.659273 | 0.329637 | − | 0.944108i | \(-0.393074\pi\) | ||||
0.329637 | + | 0.944108i | \(0.393074\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.65563 | 0.395877 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.56830 | −0.520490 | −0.260245 | − | 0.965543i | \(-0.583803\pi\) | ||||
−0.260245 | + | 0.965543i | \(0.583803\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.74543 | + | 3.99876i | 0.820775 | + | 0.571251i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.07320 | 0.150279 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.48977i | 0.754079i | 0.926197 | + | 0.377039i | \(0.123058\pi\) | ||||
−0.926197 | + | 0.377039i | \(0.876942\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.580189 | 0.0782327 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.77257 | 0.367235 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 13.2957i | − | 1.73095i | −0.500948 | − | 0.865477i | \(-0.667015\pi\) | ||
0.500948 | − | 0.865477i | \(-0.332985\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.275184 | 0.0352337 | 0.0176168 | − | 0.999845i | \(-0.494392\pi\) | ||||
0.0176168 | + | 0.999845i | \(0.494392\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.70392 | + | 2.10329i | 0.844615 | + | 0.264990i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.14766 | 0.142349 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.71818 | 0.942925 | 0.471463 | − | 0.881886i | \(-0.343726\pi\) | ||||
0.471463 | + | 0.881886i | \(0.343726\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.64291 | 0.197783 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.13454i | 0.134645i | 0.997731 | + | 0.0673224i | \(0.0214456\pi\) | ||||
−0.997731 | + | 0.0673224i | \(0.978554\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.78121i | 0.208474i | 0.994552 | + | 0.104237i | \(0.0332401\pi\) | ||||
−0.994552 | + | 0.104237i | \(0.966760\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.586834i | 0.0677617i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.46464 | + | 0.459518i | 0.166912 | + | 0.0523669i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.0108i | 1.12630i | 0.826355 | + | 0.563149i | \(0.190410\pi\) | ||||
−0.826355 | + | 0.563149i | \(0.809590\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.01923 | 0.668803 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.6230i | 1.71485i | 0.514607 | + | 0.857426i | \(0.327938\pi\) | ||||
−0.514607 | + | 0.857426i | \(0.672062\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1.82880i | − | 0.198362i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.34561 | −0.465899 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.3393i | 1.62596i | 0.582293 | + | 0.812979i | \(0.302156\pi\) | ||||
−0.582293 | + | 0.812979i | \(0.697844\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.89717 | + | 0.908961i | 0.303706 | + | 0.0952850i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 2.77577i | − | 0.287833i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 4.72462i | − | 0.484736i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 14.9759i | − | 1.52058i | −0.649585 | − | 0.760289i | \(-0.725057\pi\) | ||
0.649585 | − | 0.760289i | \(-0.274943\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.54077 | 0.154853 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.7803 | −1.27169 | −0.635845 | − | 0.771817i | \(-0.719348\pi\) | ||||
−0.635845 | + | 0.771817i | \(0.719348\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.1439 | 1.49217 | 0.746085 | − | 0.665851i | \(-0.231931\pi\) | ||||
0.746085 | + | 0.665851i | \(0.231931\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.464781 | + | 1.48142i | −0.0453579 | + | 0.144572i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.70224 | −0.647930 | −0.323965 | − | 0.946069i | \(-0.605016\pi\) | ||||
−0.323965 | + | 0.946069i | \(0.605016\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 11.2152i | − | 1.07422i | −0.843511 | − | 0.537112i | \(-0.819515\pi\) | ||
0.843511 | − | 0.537112i | \(-0.180485\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.55376 | −0.242392 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.41012 | 0.132653 | 0.0663265 | − | 0.997798i | \(-0.478872\pi\) | ||||
0.0663265 | + | 0.997798i | \(0.478872\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2.79961i | − | 0.261065i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.04775 | 0.281765 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.44844 | − | 4.61668i | 0.132778 | − | 0.423210i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6634 | −0.969398 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.96616 | 0.447784 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.7103i | 1.39406i | 0.717041 | + | 0.697031i | \(0.245496\pi\) | ||||
−0.717041 | + | 0.697031i | \(0.754504\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.53697i | 0.223368i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 5.01749i | − | 0.438380i | −0.975682 | − | 0.219190i | \(-0.929658\pi\) | ||
0.975682 | − | 0.219190i | \(-0.0703415\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.74196 | − | 11.9269i | 0.324469 | − | 1.03420i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.31891i | 0.285647i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.8703 | −1.27045 | −0.635226 | − | 0.772326i | \(-0.719093\pi\) | ||||
−0.635226 | + | 0.772326i | \(0.719093\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 0.148572i | − | 0.0126017i | −0.999980 | − | 0.00630086i | \(-0.997994\pi\) | ||
0.999980 | − | 0.00630086i | \(-0.00200564\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 2.09400i | − | 0.176346i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.665859 | 0.0556819 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.40518i | 0.614967i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.34661 | + | 3.37161i | −0.193545 | + | 0.278086i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 8.85493i | − | 0.725424i | −0.931901 | − | 0.362712i | \(-0.881851\pi\) | ||
0.931901 | − | 0.362712i | \(-0.118149\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.3932i | 1.00855i | 0.863544 | + | 0.504273i | \(0.168239\pi\) | ||||
−0.863544 | + | 0.504273i | \(0.831761\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 4.85662i | − | 0.392635i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.73007 | −0.379928 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.6090 | −1.24574 | −0.622869 | − | 0.782326i | \(-0.714033\pi\) | ||||
−0.622869 | + | 0.782326i | \(0.714033\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.22159 | −0.255488 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.21733 | − | 7.06740i | 0.174750 | − | 0.556989i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.60110 | 0.438712 | 0.219356 | − | 0.975645i | \(-0.429604\pi\) | ||||
0.219356 | + | 0.975645i | \(0.429604\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.340475i | 0.0265059i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.34952 | −0.723488 | −0.361744 | − | 0.932278i | \(-0.617819\pi\) | ||||
−0.361744 | + | 0.932278i | \(0.617819\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.6829 | −0.898683 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 12.5468i | − | 0.959479i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.5706 | 1.79204 | 0.896018 | − | 0.444018i | \(-0.146447\pi\) | ||||
0.896018 | + | 0.444018i | \(0.146447\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.52442 | + | 0.792014i | 0.190828 | + | 0.0598706i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.80238 | 0.586463 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.7086 | −1.47309 | −0.736546 | − | 0.676387i | \(-0.763545\pi\) | ||||
−0.736546 | + | 0.676387i | \(0.763545\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.0102 | −1.56168 | −0.780839 | − | 0.624732i | \(-0.785208\pi\) | ||||
−0.780839 | + | 0.624732i | \(0.785208\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.161487i | 0.0119375i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.35175i | 0.319947i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.06105i | − | 0.0775919i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.62862 | + | 8.37834i | −0.191204 | + | 0.609435i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 16.9750i | − | 1.22827i | −0.789201 | − | 0.614135i | \(-0.789505\pi\) | ||
0.789201 | − | 0.614135i | \(-0.210495\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.8445 | 1.06853 | 0.534266 | − | 0.845317i | \(-0.320588\pi\) | ||||
0.534266 | + | 0.845317i | \(0.320588\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.673485i | 0.0482292i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 6.30785i | − | 0.449416i | −0.974426 | − | 0.224708i | \(-0.927857\pi\) | ||
0.974426 | − | 0.224708i | \(-0.0721428\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.9770 | −0.849030 | −0.424515 | − | 0.905421i | \(-0.639555\pi\) | ||||
−0.424515 | + | 0.905421i | \(0.639555\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.52929i | 0.319471i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.86501 | + | 18.6938i | −0.411643 | + | 1.31205i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 8.46264i | − | 0.591056i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 7.43471i | − | 0.516748i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 2.74117i | − | 0.189611i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.8525 | −0.747120 | −0.373560 | − | 0.927606i | \(-0.621863\pi\) | ||||
−0.373560 | + | 0.927606i | \(0.621863\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.665785 | −0.0456189 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.32314 | 0.294836 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.9407 | − | 3.74628i | −0.810588 | − | 0.254314i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.04527 | −0.0706329 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.09884i | − | 0.141183i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.0737 | 0.942445 | 0.471223 | − | 0.882014i | \(-0.343813\pi\) | ||||
0.471223 | + | 0.882014i | \(0.343813\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.65563 | 0.177042 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 14.9683i | − | 0.993478i | −0.867900 | − | 0.496739i | \(-0.834531\pi\) | ||
0.867900 | − | 0.496739i | \(-0.165469\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.5684 | 1.42528 | 0.712641 | − | 0.701529i | \(-0.247499\pi\) | ||||
0.712641 | + | 0.701529i | \(0.247499\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.269661 | + | 0.859503i | −0.0177424 | + | 0.0565511i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.5888 | −1.28331 | −0.641653 | − | 0.766995i | \(-0.721751\pi\) | ||||
−0.641653 | + | 0.766995i | \(0.721751\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.56830 | −0.232770 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.87465 | −0.381600 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 23.2562i | − | 1.50432i | −0.658981 | − | 0.752160i | \(-0.729012\pi\) | ||
0.658981 | − | 0.752160i | \(-0.270988\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 20.9056i | − | 1.34665i | −0.739347 | − | 0.673324i | \(-0.764866\pi\) | ||
0.739347 | − | 0.673324i | \(-0.235134\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.4890i | 0.865321i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.74543 | + | 3.99876i | 0.367062 | + | 0.255471i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 5.42225i | − | 0.345009i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.16813 | −0.581007 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.33668i | 0.210610i | 0.994440 | + | 0.105305i | \(0.0335818\pi\) | ||||
−0.994440 | + | 0.105305i | \(0.966418\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 1.62430i | − | 0.102119i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.07320 | 0.0672067 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.4200i | 1.52328i | 0.648002 | + | 0.761639i | \(0.275605\pi\) | ||||
−0.648002 | + | 0.761639i | \(0.724395\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.44665 | + | 10.9857i | −0.214164 | + | 0.682616i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 19.6654i | 1.21726i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 27.1113i | − | 1.67176i | −0.548915 | − | 0.835878i | \(-0.684959\pi\) | ||
0.548915 | − | 0.835878i | \(-0.315041\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.48977i | 0.337234i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.00160 | −0.550889 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.5701 | −1.13224 | −0.566121 | − | 0.824322i | \(-0.691556\pi\) | ||||
−0.566121 | + | 0.824322i | \(0.691556\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.9119 | −0.784344 | −0.392172 | − | 0.919892i | \(-0.628276\pi\) | ||||
−0.392172 | + | 0.919892i | \(0.628276\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.533409 | + | 1.70016i | −0.0322834 | + | 0.102898i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.580189 | 0.0349867 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 0.557017i | − | 0.0334679i | −0.999860 | − | 0.0167340i | \(-0.994673\pi\) | ||
0.999860 | − | 0.0167340i | \(-0.00532683\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.5613 | −0.752025 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.3862 | −1.63372 | −0.816860 | − | 0.576835i | \(-0.804287\pi\) | ||||
−0.816860 | + | 0.576835i | \(0.804287\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.24149i | 0.311574i | 0.987791 | + | 0.155787i | \(0.0497914\pi\) | ||||
−0.987791 | + | 0.155787i | \(0.950209\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.77257 | 0.164233 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.70253 | − | 21.3633i | 0.395638 | − | 1.26103i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.6555 | 0.803263 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.78840 | 0.515185 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.66098 | 0.389138 | 0.194569 | − | 0.980889i | \(-0.437669\pi\) | ||||
0.194569 | + | 0.980889i | \(0.437669\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 13.2957i | − | 0.774107i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.92560i | 0.111735i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 3.21299i | − | 0.185812i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.9134 | + | 3.42399i | 0.629041 | + | 0.197355i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 7.49993i | − | 0.430860i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.275184 | 0.0157570 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 17.0826i | − | 0.974957i | −0.873135 | − | 0.487479i | \(-0.837917\pi\) | ||
0.873135 | − | 0.487479i | \(-0.162083\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.88694i | 0.505560i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.4721 | −1.67121 | −0.835604 | − | 0.549332i | \(-0.814882\pi\) | ||||
−0.835604 | + | 0.549332i | \(0.814882\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.1624i | 1.47879i | 0.673275 | + | 0.739393i | \(0.264887\pi\) | ||||
−0.673275 | + | 0.739393i | \(0.735113\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.70392 | + | 2.10329i | 0.377723 | + | 0.118507i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.72675i | 0.321646i | 0.986983 | + | 0.160823i | \(0.0514149\pi\) | ||||
−0.986983 | + | 0.160823i | \(0.948585\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.29641i | 0.240553i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 3.93310i | − | 0.219524i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.64040 | −0.480765 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.14766 | 0.0636606 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.58148 | 0.363957 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.00789 | − | 2.82614i | −0.496621 | − | 0.155810i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.6047 | −0.967641 | −0.483820 | − | 0.875167i | \(-0.660751\pi\) | ||||
−0.483820 | + | 0.875167i | \(0.660751\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.5566i | 0.633299i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.71818 | 0.421689 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.3443 | 1.32612 | 0.663059 | − | 0.748567i | \(-0.269258\pi\) | ||||
0.663059 | + | 0.748567i | \(0.269258\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.827507i | 0.0449440i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.74434 | −0.148614 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.3368 | + | 14.6450i | 0.612131 | + | 0.790756i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.64291 | 0.0884510 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.7400 | −0.898650 | −0.449325 | − | 0.893368i | \(-0.648336\pi\) | ||||
−0.449325 | + | 0.893368i | \(0.648336\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.2317 | −0.761807 | −0.380903 | − | 0.924615i | \(-0.624387\pi\) | ||||
−0.380903 | + | 0.924615i | \(0.624387\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.80898i | 0.203308i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 6.08004i | − | 0.323608i | −0.986823 | − | 0.161804i | \(-0.948269\pi\) | ||
0.986823 | − | 0.161804i | \(-0.0517312\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.13454i | 0.0602150i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.70922 | + | 0.849993i | 0.143387 | + | 0.0449864i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.3854i | 0.864787i | 0.901685 | + | 0.432394i | \(0.142331\pi\) | ||||
−0.901685 | + | 0.432394i | \(0.857669\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.32202 | −0.174843 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 6.25763i | − | 0.328441i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.78121i | 0.0932326i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.1245 | −0.685092 | −0.342546 | − | 0.939501i | \(-0.611289\pi\) | ||||
−0.342546 | + | 0.939501i | \(0.611289\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 22.4736i | − | 1.16993i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.34798 | + | 13.8585i | −0.225736 | + | 0.719498i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 0.552362i | − | 0.0286002i | −0.999898 | − | 0.0143001i | \(-0.995448\pi\) | ||
0.999898 | − | 0.0143001i | \(-0.00455202\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.586834i | 0.0303040i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.49862i | 0.437701i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.1600 | 1.49785 | 0.748925 | − | 0.662655i | \(-0.230570\pi\) | ||||
0.748925 | + | 0.662655i | \(0.230570\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.21933 | −0.472320 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.89451 | 0.301195 | 0.150598 | − | 0.988595i | \(-0.451880\pi\) | ||||
0.150598 | + | 0.988595i | \(0.451880\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.46464 | + | 0.459518i | 0.0746451 | + | 0.0234192i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.4807 | 0.583594 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 13.5376i | − | 0.686385i | −0.939265 | − | 0.343192i | \(-0.888492\pi\) | ||
0.939265 | − | 0.343192i | \(-0.111508\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.11994 | −0.258926 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.94444 | 0.148527 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.0108i | 0.503696i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.22501 | −0.212047 | −0.106024 | − | 0.994364i | \(-0.533812\pi\) | ||||
−0.106024 | + | 0.994364i | \(0.533812\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.99913 | + | 2.19591i | 0.350395 | + | 0.109933i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.09225 | 0.404108 | 0.202054 | − | 0.979374i | \(-0.435238\pi\) | ||||
0.202054 | + | 0.979374i | \(0.435238\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.42850 | −0.270413 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.01923 | 0.299098 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.52484i | 0.125152i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 27.6608i | − | 1.36774i | −0.729605 | − | 0.683868i | \(-0.760296\pi\) | ||
0.729605 | − | 0.683868i | \(-0.239704\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 8.72637i | − | 0.430440i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.5304 | − | 33.5640i | 0.518167 | − | 1.65158i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.6230i | 0.766905i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.0871872 | 0.00426957 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.5982i | 0.517755i | 0.965910 | + | 0.258877i | \(0.0833526\pi\) | ||||
−0.965910 | + | 0.258877i | \(0.916647\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 25.5951i | − | 1.24743i | −0.781652 | − | 0.623715i | \(-0.785623\pi\) | ||
0.781652 | − | 0.623715i | \(-0.214377\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.47606 | −0.460742 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1.82880i | − | 0.0887101i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.694680 | + | 0.217949i | 0.0336179 | + | 0.0105473i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.390749i | 0.0188655i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.7406i | 1.57706i | 0.614997 | + | 0.788529i | \(0.289157\pi\) | ||||
−0.614997 | + | 0.788529i | \(0.710843\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.8933i | 0.811840i | 0.913909 | + | 0.405920i | \(0.133049\pi\) | ||||
−0.913909 | + | 0.405920i | \(0.866951\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.34561 | −0.208356 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.2271 | −0.632737 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.6749 | 1.51176 | 0.755881 | − | 0.654709i | \(-0.227209\pi\) | ||||
0.755881 | + | 0.654709i | \(0.227209\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.2577 | + | 10.6192i | 0.726558 | + | 0.505676i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.8303 | 0.609587 | 0.304794 | − | 0.952418i | \(-0.401413\pi\) | ||||
0.304794 | + | 0.952418i | \(0.401413\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.3393i | 0.727151i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.19637 | 0.245780 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.10148 | 0.429525 | 0.214763 | − | 0.976666i | \(-0.431102\pi\) | ||||
0.214763 | + | 0.976666i | \(0.431102\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 4.90993i | − | 0.231200i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.27276 | −0.341704 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.89717 | + | 0.908961i | 0.135822 | + | 0.0426127i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.29969 | −0.247909 | −0.123954 | − | 0.992288i | \(-0.539558\pi\) | ||||
−0.123954 | + | 0.992288i | \(0.539558\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.06964 | 0.283307 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.755725 | 0.0351976 | 0.0175988 | − | 0.999845i | \(-0.494398\pi\) | ||||
0.0175988 | + | 0.999845i | \(0.494398\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.99447i | 0.185639i | 0.995683 | + | 0.0928193i | \(0.0295879\pi\) | ||||
−0.995683 | + | 0.0928193i | \(0.970412\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 2.77577i | − | 0.128723i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.90589i | 0.180743i | 0.995908 | + | 0.0903716i | \(0.0288055\pi\) | ||||
−0.995908 | + | 0.0903716i | \(0.971195\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.4839 | + | 6.11290i | 0.899685 | + | 0.282268i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 9.15992i | − | 0.422067i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.50824 | 0.115329 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 4.72462i | − | 0.216780i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.5788i | 0.667517i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.21055 | −0.420841 | −0.210420 | − | 0.977611i | \(-0.567483\pi\) | ||||
−0.210420 | + | 0.977611i | \(0.567483\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.99432i | 0.227721i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.14739 | + | 1.30120i | 0.188713 | + | 0.0592068i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 14.9759i | − | 0.680023i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.4403i | 0.971552i | 0.874083 | + | 0.485776i | \(0.161463\pi\) | ||||
−0.874083 | + | 0.485776i | \(0.838537\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.28692i | 0.148640i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.6672 | −0.887570 | −0.443785 | − | 0.896133i | \(-0.646365\pi\) | ||||
−0.443785 | + | 0.896133i | \(0.646365\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.5426 | 0.609930 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.54077 | 0.0692523 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.898570 | + | 2.86405i | −0.0403064 | + | 0.128470i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.2344 | 0.547686 | 0.273843 | − | 0.961774i | \(-0.411705\pi\) | ||||
0.273843 | + | 0.961774i | \(0.411705\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 5.48662i | − | 0.245124i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.42742 | −0.241997 | −0.120998 | − | 0.992653i | \(-0.538610\pi\) | ||||
−0.120998 | + | 0.992653i | \(0.538610\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.7803 | −0.568717 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 6.85591i | − | 0.304482i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.3838 | −0.770522 | −0.385261 | − | 0.922808i | \(-0.625889\pi\) | ||||
−0.385261 | + | 0.922808i | \(0.625889\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.41074 | + | 4.49652i | −0.0624074 | + | 0.198914i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 15.6806 | 0.692315 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.1439 | 0.667319 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.07029 | −0.0910511 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.8320i | 0.607157i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 12.8139i | − | 0.561388i | −0.959797 | − | 0.280694i | \(-0.909435\pi\) | ||
0.959797 | − | 0.280694i | \(-0.0905646\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 8.05393i | − | 0.352174i | −0.984375 | − | 0.176087i | \(-0.943656\pi\) | ||
0.984375 | − | 0.176087i | \(-0.0563439\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.464781 | + | 1.48142i | −0.0202847 | + | 0.0646544i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.65037i | 0.376816i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.1622 | 0.659226 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 35.3085i | − | 1.53226i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 9.71221i | − | 0.420683i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.70224 | −0.289763 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 11.5657i | − | 0.499096i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.33344 | + | 2.32004i | 0.143581 | + | 0.0999310i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.9099i | 0.684018i | 0.939697 | + | 0.342009i | \(0.111107\pi\) | ||||
−0.939697 | + | 0.342009i | \(0.888893\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 12.3295i | − | 0.529110i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 11.2152i | − | 0.480408i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.6893 | 1.22667 | 0.613333 | − | 0.789825i | \(-0.289828\pi\) | ||||
0.613333 | + | 0.789825i | \(0.289828\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.730785 | 0.0311891 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.9867 | 1.49048 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.92866 | + | 25.2714i | −0.337161 | + | 1.07465i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.55376 | −0.108401 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 29.6910i | − | 1.25805i | −0.777386 | − | 0.629024i | \(-0.783455\pi\) | ||
0.777386 | − | 0.629024i | \(-0.216545\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.96149 | 0.209849 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.622662 | 0.0262888 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 25.7978i | − | 1.08725i | −0.839329 | − | 0.543624i | \(-0.817052\pi\) | ||
0.839329 | − | 0.543624i | \(-0.182948\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.41012 | 0.0593242 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.1951 | + | 4.76731i | 0.638133 | + | 0.200208i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.17604 | −0.258913 | −0.129457 | − | 0.991585i | \(-0.541323\pi\) | ||||
−0.129457 | + | 0.991585i | \(0.541323\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 44.7626 | 1.87326 | 0.936628 | − | 0.350325i | \(-0.113929\pi\) | ||||
0.936628 | + | 0.350325i | \(0.113929\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.96153 | 0.416149 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 2.79961i | − | 0.116752i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 45.0609i | − | 1.87591i | −0.346760 | − | 0.937954i | \(-0.612718\pi\) | ||
0.346760 | − | 0.937954i | \(-0.387282\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.71126i | 0.362028i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.3737 | + | 39.4392i | −0.513346 | + | 1.63621i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.18511i | 0.131914i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.04775 | 0.126009 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 0.738708i | − | 0.0304897i | −0.999884 | − | 0.0152449i | \(-0.995147\pi\) | ||
0.999884 | − | 0.0152449i | \(-0.00485278\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.3478i | 0.920824i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.70166 | 0.152266 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.51961i | 0.226663i | 0.993557 | + | 0.113332i | \(0.0361522\pi\) | ||||
−0.993557 | + | 0.113332i | \(0.963848\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.44844 | − | 4.61668i | 0.0593802 | − | 0.189265i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 7.02853i | − | 0.287659i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.145815i | 0.00595785i | 0.999996 | + | 0.00297893i | \(0.000948223\pi\) | ||||
−0.999996 | + | 0.00297893i | \(0.999052\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.7269i | 0.886257i | 0.896458 | + | 0.443128i | \(0.146131\pi\) | ||||
−0.896458 | + | 0.443128i | \(0.853869\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.4966 | 0.834686 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.6634 | −0.433528 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.6456 | −0.756804 | −0.378402 | − | 0.925641i | \(-0.623526\pi\) | ||||
−0.378402 | + | 0.925641i | \(0.623526\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.9702 | − | 3.44179i | −0.444534 | − | 0.139468i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.09518 | −0.165673 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 47.1735i | 1.90532i | 0.304041 | + | 0.952659i | \(0.401664\pi\) | ||||
−0.304041 | + | 0.952659i | \(0.598336\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.96616 | 0.200255 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.2076 | 0.652493 | 0.326246 | − | 0.945285i | \(-0.394216\pi\) | ||||
0.326246 | + | 0.945285i | \(0.394216\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.2319i | 1.21512i | 0.794273 | + | 0.607561i | \(0.207852\pi\) | ||||
−0.794273 | + | 0.607561i | \(0.792148\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.29166 | 0.372861 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.1489 | + | 38.7228i | −0.486736 | + | 1.55140i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.60861 | 0.0642418 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.95850 | 0.317326 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 6.27504i | − | 0.249806i | −0.992169 | − | 0.124903i | \(-0.960138\pi\) | ||
0.992169 | − | 0.124903i | \(-0.0398619\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 6.36864i | − | 0.253131i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.7103i | 0.623443i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.59379 | + | 4.58920i | 0.261255 | + | 0.181831i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.01291i | 0.119189i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.954180 | −0.0376878 | −0.0188439 | − | 0.999822i | \(-0.505999\pi\) | ||||
−0.0188439 | + | 0.999822i | \(0.505999\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 29.7150i | − | 1.17184i | −0.810367 | − | 0.585922i | \(-0.800732\pi\) | ||
0.810367 | − | 0.585922i | \(-0.199268\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.53697i | 0.0998930i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.3760 | −0.879693 | −0.439846 | − | 0.898073i | \(-0.644967\pi\) | ||||
−0.439846 | + | 0.898073i | \(0.644967\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 7.71403i | − | 0.302802i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.19844 | − | 7.00721i | 0.0861638 | − | 0.274634i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.18538i | 0.124653i | 0.998056 | + | 0.0623267i | \(0.0198521\pi\) | ||||
−0.998056 | + | 0.0623267i | \(0.980148\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 5.01749i | − | 0.196050i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.73022i | 0.184543i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.50751 | 0.0587242 | 0.0293621 | − | 0.999569i | \(-0.490652\pi\) | ||||
0.0293621 | + | 0.999569i | \(0.490652\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.0607 | 0.430210 | 0.215105 | − | 0.976591i | \(-0.430991\pi\) | ||||
0.215105 | + | 0.976591i | \(0.430991\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.23167 | 0.0478342 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.74196 | − | 11.9269i | 0.145107 | − | 0.462507i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.7316 | 0.802731 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.25893i | 0.319309i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.159659 | 0.00616355 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.5781 | 1.21725 | 0.608624 | − | 0.793459i | \(-0.291722\pi\) | ||||
0.608624 | + | 0.793459i | \(0.291722\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.31891i | 0.127745i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.96254 | 0.229159 | 0.114580 | − | 0.993414i | \(-0.463448\pi\) | ||||
0.114580 | + | 0.993414i | \(0.463448\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.8612 | − | 37.8056i | 0.455189 | − | 1.45085i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.78388 | 0.336599 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.0466 | −1.22623 | −0.613114 | − | 0.789994i | \(-0.710084\pi\) | ||||
−0.613114 | + | 0.789994i | \(0.710084\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.8703 | −0.568163 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.6571i | 0.482898i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.30038i | 0.240026i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.0740i | 0.649526i | 0.945795 | + | 0.324763i | \(0.105285\pi\) | ||||
−0.945795 | + | 0.324763i | \(0.894715\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.88955 | + | 1.22031i | 0.147752 | + | 0.0463557i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 0.148572i | − | 0.00563566i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.4765 | −0.586215 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 11.4954i | − | 0.434796i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 32.7289i | − | 1.23615i | −0.786118 | − | 0.618076i | \(-0.787912\pi\) | ||
0.786118 | − | 0.618076i | \(-0.212088\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.5604 | 0.775449 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 2.09400i | − | 0.0788645i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −32.2629 | − | 10.1222i | −1.21337 | − | 0.380684i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 20.9447i | − | 0.786594i | −0.919412 | − | 0.393297i | \(-0.871334\pi\) | ||
0.919412 | − | 0.393297i | \(-0.128666\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 26.5848i | 0.997009i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.2423i | 0.495930i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.665859 | 0.0249017 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.6475 | 0.509677 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.417030 | 0.0155526 | 0.00777630 | − | 0.999970i | \(-0.497525\pi\) | ||||
0.00777630 | + | 0.999970i | \(0.497525\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 38.2295 | + | 11.9942i | 1.42374 | + | 0.446686i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.2681 | 0.456256 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.40518i | 0.275022i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.48987 | −0.166520 | −0.0832601 | − | 0.996528i | \(-0.526533\pi\) | ||||
−0.0832601 | + | 0.996528i | \(0.526533\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.1419 | 0.375624 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 7.90619i | − | 0.292421i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.8948 | 0.845640 | 0.422820 | − | 0.906214i | \(-0.361040\pi\) | ||||
0.422820 | + | 0.906214i | \(0.361040\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.34661 | + | 3.37161i | −0.0865559 | + | 0.124364i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.47800 | 0.164949 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.354985 | 0.0130583 | 0.00652917 | − | 0.999979i | \(-0.497922\pi\) | ||||
0.00652917 | + | 0.999979i | \(0.497922\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.18196 | 0.116892 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.75171i | 0.247696i | 0.992301 | + | 0.123848i | \(0.0395235\pi\) | ||||
−0.992301 | + | 0.123848i | \(0.960476\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 8.85493i | − | 0.324419i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 41.4890i | 1.51800i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.9193 | − | 5.30827i | −0.618218 | − | 0.193960i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 27.4120i | − | 1.00028i | −0.865945 | − | 0.500139i | \(-0.833282\pi\) | ||
0.865945 | − | 0.500139i | \(-0.166718\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.95808 | −0.0713564 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.3932i | 0.451035i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.6550i | 1.00514i | 0.864537 | + | 0.502570i | \(0.167612\pi\) | ||||
−0.864537 | + | 0.502570i | \(0.832388\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.953196 | 0.0345988 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 14.1083i | − | 0.511424i | −0.966753 | − | 0.255712i | \(-0.917690\pi\) | ||
0.966753 | − | 0.255712i | \(-0.0823099\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.88262 | − | 28.3120i | 0.321572 | − | 1.02496i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 4.85662i | − | 0.175592i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 15.2589i | − | 0.550968i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 2.82610i | − | 0.101912i | −0.998701 | − | 0.0509558i | \(-0.983773\pi\) | ||
0.998701 | − | 0.0509558i | \(-0.0162268\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.3305 | −0.516100 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −44.5587 | −1.60266 | −0.801332 | − | 0.598220i | \(-0.795875\pi\) | ||||
−0.801332 | + | 0.598220i | \(0.795875\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.73007 | −0.169909 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.44676 | − | 2.02261i | −0.231276 | − | 0.0725607i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −39.9827 | −1.43253 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.658247i | 0.0235539i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −24.5772 | −0.878316 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.6090 | −0.557111 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.3744i | 1.08273i | 0.840788 | + | 0.541365i | \(0.182092\pi\) | ||||
−0.840788 | + | 0.541365i | \(0.817908\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.9098 | 0.566406 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.55974 | + | 1.11684i | 0.126570 | + | 0.0397101i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.315817 | 0.0112150 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.22159 | −0.114258 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 43.5064 | 1.54108 | 0.770538 | − | 0.637394i | \(-0.219988\pi\) | ||||
0.770538 | + | 0.637394i | \(0.219988\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.52572i | 0.230863i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 40.7353i | 1.43931i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.03344i | 0.0364692i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.21733 | − | 7.06740i | 0.0781506 | − | 0.249093i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 10.8976i | − | 0.383613i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.7818 | −0.625176 | −0.312588 | − | 0.949889i | \(-0.601196\pi\) | ||||
−0.312588 | + | 0.949889i | \(0.601196\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.03219i | 0.246934i | 0.992349 | + | 0.123467i | \(0.0394012\pi\) | ||||
−0.992349 | + | 0.123467i | \(0.960599\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 7.57716i | − | 0.265743i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.60110 | 0.196198 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 20.4252i | − | 0.714588i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.69381 | + | 2.41386i | 0.268844 | + | 0.0843471i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.24453i | 0.252836i | 0.991977 | + | 0.126418i | \(0.0403481\pi\) | ||||
−0.991977 | + | 0.126418i | \(0.959652\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 46.4665i | − | 1.61972i | −0.586624 | − | 0.809860i | \(-0.699543\pi\) | ||
0.586624 | − | 0.809860i | \(-0.300457\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.340475i | 0.0118538i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 51.0385 | 1.77478 | 0.887392 | − | 0.461016i | \(-0.152515\pi\) | ||||
0.887392 | + | 0.461016i | \(0.152515\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.8970 | −0.517393 | −0.258696 | − | 0.965959i | \(-0.583293\pi\) | ||||
−0.258696 | + | 0.965959i | \(0.583293\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.326876 | 0.0113392 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.31294 | − | 10.5073i | 0.253379 | − | 0.364055i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.34952 | −0.323554 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 15.6987i | − | 0.542626i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.53355 | −0.156516 | −0.0782578 | − | 0.996933i | \(-0.524936\pi\) | ||||
−0.0782578 | + | 0.996933i | \(0.524936\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.8367 | −0.890922 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 16.0711i | − | 0.553519i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.6829 | −0.401903 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26.9189 | − | 8.44554i | −0.924944 | − | 0.290192i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.07588 | −0.105564 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.1832 | 0.417635 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.0584 | −1.33734 | −0.668668 | − | 0.743561i | \(-0.733135\pi\) | ||||
−0.668668 | + | 0.743561i | \(0.733135\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 12.5468i | − | 0.429092i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 52.9271i | 1.80795i | 0.427580 | + | 0.903977i | \(0.359366\pi\) | ||||
−0.427580 | + | 0.903977i | \(0.640634\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.8556i | 0.882182i | 0.897462 | + | 0.441091i | \(0.145408\pi\) | ||||
−0.897462 | + | 0.441091i | \(0.854592\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.5367 | + | 3.93327i | 0.427250 | + | 0.134045i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.9510i | 1.08762i | 0.839207 | + | 0.543812i | \(0.183020\pi\) | ||||
−0.839207 | + | 0.543812i | \(0.816980\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.5706 | 0.801423 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.01350i | 0.272153i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.80813i | 0.197027i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.85783 | 0.300136 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 39.7705i | − | 1.34603i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.52442 | + | 0.792014i | 0.0853411 | + | 0.0267750i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.3185i | 1.36146i | 0.732534 | + | 0.680730i | \(0.238337\pi\) | ||||
−0.732534 | + | 0.680730i | \(0.761663\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.90889i | 0.131843i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.03841i | − | 0.0349848i | −0.999847 | − | 0.0174924i | \(-0.994432\pi\) | ||
0.999847 | − | 0.0174924i | \(-0.00556829\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.1810 | −1.04932 | −0.524662 | − | 0.851310i | \(-0.675808\pi\) | ||||
−0.524662 | + | 0.851310i | \(0.675808\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.80238 | 0.262274 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.4273 | 1.08880 | 0.544402 | − | 0.838825i | \(-0.316757\pi\) | ||||
0.544402 | + | 0.838825i | \(0.316757\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.4428 | + | 39.6594i | −0.417317 | + | 1.33013i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.49229 | 0.116996 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.8588i | 0.564160i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.7086 | −0.658787 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.88549 | 0.0629548 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 35.0270i | − | 1.16822i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.0397 | 0.334472 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.00931 | + | 6.40438i | −0.0668658 | + | 0.213124i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21.0102 | −0.698404 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −48.3550 | −1.60560 | −0.802801 | − | 0.596248i | \(-0.796658\pi\) | ||||
−0.802801 | + | 0.596248i | \(0.796658\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −33.9398 | −1.12571 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 48.2821i | − | 1.59966i | −0.600229 | − | 0.799828i | \(-0.704924\pi\) | ||
0.600229 | − | 0.799828i | \(-0.295076\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.06432i | 0.299985i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.161487i | 0.00533860i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.97392 | − | 12.6663i | 0.131231 | − | 0.418277i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 6.72784i | − | 0.221931i | −0.993824 | − | 0.110965i | \(-0.964606\pi\) | ||
0.993824 | − | 0.110965i | \(-0.0353943\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.0247 | 0.330324 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.30206i | 0.0428579i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.35175i | 0.143085i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 40.2165 | 1.32088 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 15.7311i | − | 0.516120i | −0.966129 | − | 0.258060i | \(-0.916917\pi\) | ||
0.966129 | − | 0.258060i | \(-0.0830832\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.8926 | − | 27.1450i | 0.619180 | − | 0.889640i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 17.2952i | − | 0.566220i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 1.06105i | − | 0.0347001i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 32.8060i | − | 1.07172i | −0.844306 | − | 0.535862i | \(-0.819987\pi\) | ||
0.844306 | − | 0.535862i | \(-0.180013\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.3530 | −0.501025 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.5674 | 0.344488 | 0.172244 | − | 0.985054i | \(-0.444898\pi\) | ||||
0.172244 | + | 0.985054i | \(0.444898\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.6921 | −0.771520 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.62862 | + | 8.37834i | −0.0855092 | + | 0.272548i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.2414 | −1.11269 | −0.556347 | − | 0.830950i | \(-0.687798\pi\) | ||||
−0.556347 | + | 0.830950i | \(0.687798\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.04421i | 0.0663580i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.36065 | −0.108977 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.54692 | −0.114896 | −0.0574480 | − | 0.998348i | \(-0.518296\pi\) | ||||
−0.0574480 | + | 0.998348i | \(0.518296\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 16.9750i | − | 0.549299i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.52128 | −0.0815013 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −37.5388 | − | 11.7775i | −1.21219 | − | 0.380314i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.62644 | −0.278272 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17.7986 | −0.573553 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.8445 | 0.477862 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.7899i | 0.443454i | 0.975109 | + | 0.221727i | \(0.0711693\pi\) | ||||
−0.975109 | + | 0.221727i | \(0.928831\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 5.07048i | − | 0.162887i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39.0911i | 1.25449i | 0.778821 | + | 0.627246i | \(0.215818\pi\) | ||||
−0.778821 | + | 0.627246i | \(0.784182\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.117671 | − | 0.375059i | 0.00377236 | − | 0.0120238i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.673485i | 0.0215688i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.1910 | −0.581982 | −0.290991 | − | 0.956726i | \(-0.593985\pi\) | ||||
−0.290991 | + | 0.956726i | \(0.593985\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.89968i | 0.284435i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 29.7835i | − | 0.950913i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −44.1968 | −1.40966 | −0.704830 | − | 0.709376i | \(-0.748977\pi\) | ||||
−0.704830 | + | 0.709376i | \(0.748977\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 6.30785i | − | 0.200985i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.65847 | − | 5.28614i | 0.0527898 | − | 0.168260i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 12.1031i | − | 0.384857i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.9016i | 0.505132i | 0.967580 | + | 0.252566i | \(0.0812745\pi\) | ||||
−0.967580 | + | 0.252566i | \(0.918726\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 10.3310i | − | 0.327845i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.9770 | −0.379698 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.5139 | −0.427988 | −0.213994 | − | 0.976835i | \(-0.568647\pi\) | ||||
−0.213994 | + | 0.976835i | \(0.568647\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14.4431 | −0.456959 |
(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 | 1120.2.h.b.111.10 | 16 | ||
4.3 | odd | 2 | 280.2.h.b.251.13 | yes | 16 | ||
7.6 | odd | 2 | 1120.2.h.a.111.7 | 16 | |||
8.3 | odd | 2 | 1120.2.h.a.111.10 | 16 | |||
8.5 | even | 2 | 280.2.h.a.251.14 | yes | 16 | ||
28.27 | even | 2 | 280.2.h.a.251.13 | ✓ | 16 | ||
56.13 | odd | 2 | 280.2.h.b.251.14 | yes | 16 | ||
56.27 | even | 2 | inner | 1120.2.h.b.111.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.h.a.251.13 | ✓ | 16 | 28.27 | even | 2 | ||
280.2.h.a.251.14 | yes | 16 | 8.5 | even | 2 | ||
280.2.h.b.251.13 | yes | 16 | 4.3 | odd | 2 | ||
280.2.h.b.251.14 | yes | 16 | 56.13 | odd | 2 | ||
1120.2.h.a.111.7 | 16 | 7.6 | odd | 2 | |||
1120.2.h.a.111.10 | 16 | 8.3 | odd | 2 | |||
1120.2.h.b.111.7 | 16 | 56.27 | even | 2 | inner | ||
1120.2.h.b.111.10 | 16 | 1.1 | even | 1 | trivial |