Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1349,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.bo (of order \(6\), degree \(2\), 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3 x^{18} - 16 x^{16} + 87 x^{14} + 91 x^{12} - 1104 x^{10} + 819 x^{8} + 7047 x^{6} + \cdots + 59049 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1349.8 | ||
Root | \(0.368412 + 1.69242i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1349 |
Dual form | 2100.2.bo.g.1949.8 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | 1.28147 | + | 1.16526i | 0.739857 | + | 0.672765i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.93884 | − | 1.80025i | 0.732812 | − | 0.680432i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.284326 | + | 2.98650i | 0.0947754 | + | 0.995499i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.05595 | + | 2.34170i | −1.22292 | + | 0.706050i | −0.965538 | − | 0.260261i | \(-0.916192\pi\) |
−0.257377 | + | 0.966311i | \(0.582858\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.18938 | 0.607225 | 0.303612 | − | 0.952796i | \(-0.401807\pi\) | ||||
0.303612 | + | 0.952796i | \(0.401807\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.49492 | − | 3.74984i | 1.57525 | − | 0.909470i | 0.579740 | − | 0.814802i | \(-0.303154\pi\) |
0.995509 | − | 0.0946686i | \(-0.0301791\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.638109 | + | 0.368412i | 0.146392 | + | 0.0845196i | 0.571407 | − | 0.820667i | \(-0.306398\pi\) |
−0.425015 | + | 0.905186i | \(0.639731\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.58233 | − | 0.0477143i | 0.999946 | − | 0.0104121i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.03930 | + | 6.99627i | −0.842252 | + | 1.45882i | 0.0457338 | + | 0.998954i | \(0.485437\pi\) |
−0.887986 | + | 0.459870i | \(0.847896\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.11570 | + | 4.15842i | −0.599616 | + | 0.800288i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.15414i | 0.214318i | 0.994242 | + | 0.107159i | \(0.0341754\pi\) | ||||
−0.994242 | + | 0.107159i | \(0.965825\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.95201 | − | 5.16845i | 1.60783 | − | 0.928280i | 0.617974 | − | 0.786199i | \(-0.287954\pi\) |
0.989855 | − | 0.142081i | \(-0.0453794\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.92628 | − | 1.72543i | −1.37979 | − | 0.300358i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.99970 | + | 2.30923i | 0.657547 | + | 0.379635i | 0.791342 | − | 0.611374i | \(-0.209383\pi\) |
−0.133795 | + | 0.991009i | \(0.542716\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.80562 | + | 2.55120i | 0.449259 | + | 0.408519i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.43758 | 0.224513 | 0.112256 | − | 0.993679i | \(-0.464192\pi\) | ||||
0.112256 | + | 0.993679i | \(0.464192\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.24142i | 1.40930i | 0.709554 | + | 0.704651i | \(0.248897\pi\) | ||||
−0.709554 | + | 0.704651i | \(0.751103\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.52098 | − | 4.34224i | −1.09705 | − | 0.633380i | −0.161603 | − | 0.986856i | \(-0.551667\pi\) |
−0.935444 | + | 0.353475i | \(0.885000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.518179 | − | 6.98079i | 0.0740255 | − | 0.997256i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.6926 | + | 2.76298i | 1.77732 | + | 0.386894i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.06174 | + | 7.03514i | 0.557923 | + | 0.966351i | 0.997670 | + | 0.0682291i | \(0.0217349\pi\) |
−0.439747 | + | 0.898122i | \(0.644932\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.388420 | + | 1.21567i | 0.0514475 | + | 0.161020i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.48730 | + | 6.04018i | 0.454008 | + | 0.786364i | 0.998631 | − | 0.0523168i | \(-0.0166606\pi\) |
−0.544623 | + | 0.838681i | \(0.683327\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.13811 | + | 2.96649i | 0.657867 | + | 0.379820i | 0.791464 | − | 0.611216i | \(-0.209319\pi\) |
−0.133596 | + | 0.991036i | \(0.542653\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.92771 | + | 5.27847i | 0.746821 | + | 0.665025i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.19795 | + | 0.691639i | −0.146353 | + | 0.0844971i | −0.571389 | − | 0.820680i | \(-0.693595\pi\) |
0.425035 | + | 0.905177i | \(0.360262\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −13.3287 | + | 4.25866i | −1.60459 | + | 0.512683i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.26258i | 0.861909i | 0.902374 | + | 0.430955i | \(0.141823\pi\) | ||||
−0.902374 | + | 0.430955i | \(0.858177\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.122026 | + | 0.211355i | 0.0142820 | + | 0.0247372i | 0.873078 | − | 0.487580i | \(-0.162120\pi\) |
−0.858796 | + | 0.512318i | \(0.828787\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.64817 | + | 11.8419i | −0.415747 | + | 1.34951i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.79653 | − | 10.0399i | 0.652160 | − | 1.12957i | −0.330438 | − | 0.943828i | \(-0.607196\pi\) |
0.982598 | − | 0.185747i | \(-0.0594704\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.83832 | + | 1.69828i | −0.982035 | + | 0.188698i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 16.4610i | − | 1.80683i | −0.428772 | − | 0.903413i | \(-0.641054\pi\) | ||
0.428772 | − | 0.903413i | \(-0.358946\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.34488 | + | 1.47899i | −0.144186 | + | 0.158565i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.658248 | − | 1.14012i | 0.0697741 | − | 0.120852i | −0.829028 | − | 0.559208i | \(-0.811105\pi\) |
0.898802 | + | 0.438355i | \(0.144439\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.24485 | − | 3.94144i | 0.444981 | − | 0.413175i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 17.4943 | + | 3.80824i | 1.81408 | + | 0.394896i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.84232 | 0.491663 | 0.245832 | − | 0.969313i | \(-0.420939\pi\) | ||||
0.245832 | + | 0.969313i | \(0.420939\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.14670 | − | 11.4473i | −0.818775 | − | 1.15049i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.38435 | − | 2.39776i | −0.137748 | − | 0.238586i | 0.788896 | − | 0.614527i | \(-0.210653\pi\) |
−0.926644 | + | 0.375941i | \(0.877320\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.08187 | + | 7.07000i | −0.402199 | + | 0.696628i | −0.993991 | − | 0.109462i | \(-0.965087\pi\) |
0.591792 | + | 0.806090i | \(0.298421\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.107578 | + | 0.186331i | −0.0104000 | + | 0.0180133i | −0.871179 | − | 0.490966i | \(-0.836644\pi\) |
0.860779 | + | 0.508980i | \(0.169977\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.08683 | + | 1.88245i | 0.104100 | + | 0.180306i | 0.913370 | − | 0.407131i | \(-0.133471\pi\) |
−0.809270 | + | 0.587436i | \(0.800137\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.43464 | + | 7.61990i | 0.231085 | + | 0.723249i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.2195 | −1.05544 | −0.527719 | − | 0.849419i | \(-0.676952\pi\) | ||||
−0.527719 | + | 0.849419i | \(0.676952\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.622499 | + | 6.53858i | 0.0575500 | + | 0.604492i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.84192 | − | 18.9628i | 0.535528 | − | 1.73832i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.46716 | − | 9.46940i | 0.497015 | − | 0.860854i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.84222 | + | 1.67516i | 0.166107 | + | 0.151044i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.2228i | 1.52828i | 0.645051 | + | 0.764140i | \(0.276836\pi\) | ||||
−0.645051 | + | 0.764140i | \(0.723164\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.7687 | + | 11.8426i | −0.948129 | + | 1.04268i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.65810 | − | 14.9963i | 0.756462 | − | 1.31023i | −0.188183 | − | 0.982134i | \(-0.560260\pi\) |
0.944644 | − | 0.328096i | \(-0.106407\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.90042 | − | 0.434466i | 0.164788 | − | 0.0376730i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.59375 | − | 9.68866i | −0.477907 | − | 0.827758i | 0.521773 | − | 0.853085i | \(-0.325271\pi\) |
−0.999679 | + | 0.0253261i | \(0.991938\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.16017i | 0.183223i | 0.995795 | + | 0.0916116i | \(0.0292018\pi\) | ||||
−0.995795 | + | 0.0916116i | \(0.970798\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.57805 | − | 14.3284i | −0.385542 | − | 1.20667i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.88002 | + | 5.12688i | −0.742585 | + | 0.428731i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.79849 | − | 8.34186i | 0.725687 | − | 0.688025i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.37427 | + | 0.793438i | 0.112585 | + | 0.0650010i | 0.555235 | − | 0.831693i | \(-0.312628\pi\) |
−0.442650 | + | 0.896694i | \(0.645962\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.12229 | − | 8.87206i | −0.416846 | − | 0.721998i | 0.578774 | − | 0.815488i | \(-0.303531\pi\) |
−0.995620 | + | 0.0934894i | \(0.970198\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.0456 | + | 18.3309i | 1.05467 | + | 1.48196i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.24572 | − | 5.62174i | −0.259036 | − | 0.448664i | 0.706948 | − | 0.707266i | \(-0.250072\pi\) |
−0.965984 | + | 0.258602i | \(0.916738\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.99279 | + | 13.7483i | −0.237344 | + | 1.09031i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.76352 | + | 20.8364i | 0.375418 | + | 1.64214i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.64797 | + | 2.68350i | 0.364057 | + | 0.210188i | 0.670859 | − | 0.741585i | \(-0.265926\pi\) |
−0.306802 | + | 0.951773i | \(0.599259\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.84082i | 0.529359i | 0.964336 | + | 0.264679i | \(0.0852661\pi\) | ||||
−0.964336 | + | 0.264679i | \(0.914734\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.20661 | −0.631278 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.918831 | + | 2.01046i | −0.0702648 | + | 0.153744i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.0739 | + | 5.81618i | 0.765906 | + | 0.442196i | 0.831412 | − | 0.555656i | \(-0.187533\pi\) |
−0.0655063 | + | 0.997852i | \(0.520866\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.56953 | + | 11.8039i | −0.193138 | + | 0.887237i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.95741 | + | 4.01686i | −0.520021 | + | 0.300234i | −0.736943 | − | 0.675955i | \(-0.763732\pi\) |
0.216922 | + | 0.976189i | \(0.430398\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.81789i | 0.729758i | 0.931055 | + | 0.364879i | \(0.118890\pi\) | ||||
−0.931055 | + | 0.364879i | \(0.881110\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.12759 | + | 9.78871i | 0.231198 | + | 0.723602i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.5620 | + | 30.4184i | −1.28426 | + | 2.22441i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.44537 | + | 13.6715i | 0.105136 | + | 0.994458i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.9054 | − | 8.02830i | −1.00616 | − | 0.580907i | −0.0960953 | − | 0.995372i | \(-0.530635\pi\) |
−0.910065 | + | 0.414465i | \(0.863969\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.52771 | + | 3.19143i | −0.397894 | + | 0.229724i | −0.685575 | − | 0.728002i | \(-0.740449\pi\) |
0.287681 | + | 0.957726i | \(0.407116\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.54995 | 0.181677 | 0.0908384 | − | 0.995866i | \(-0.471045\pi\) | ||||
0.0908384 | + | 0.995866i | \(0.471045\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.27973 | − | 3.62561i | 0.445159 | − | 0.257012i | −0.260625 | − | 0.965440i | \(-0.583929\pi\) |
0.705783 | + | 0.708428i | \(0.250595\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.34108 | − | 0.509617i | −0.165127 | − | 0.0359456i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.07774 | + | 2.23769i | 0.145829 | + | 0.157055i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −22.0428 | − | 10.0741i | −1.53208 | − | 0.700200i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.45085 | −0.238700 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.2654 | −0.913230 | −0.456615 | − | 0.889664i | \(-0.650938\pi\) | ||||
−0.456615 | + | 0.889664i | \(0.650938\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.46281 | + | 9.30677i | −0.579862 | + | 0.637689i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.05198 | − | 26.1367i | 0.546604 | − | 1.77427i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.0899116 | + | 0.413037i | −0.00607567 | + | 0.0279104i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.2198 | − | 8.20983i | 0.956530 | − | 0.552253i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28.1032 | −1.88193 | −0.940964 | − | 0.338506i | \(-0.890078\pi\) | ||||
−0.940964 | + | 0.338506i | \(0.890078\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.6308 | − | 6.71504i | 0.771963 | − | 0.445693i | −0.0616117 | − | 0.998100i | \(-0.519624\pi\) |
0.833574 | + | 0.552407i | \(0.186291\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.24605 | + | 4.18351i | 0.478833 | + | 0.276454i | 0.719930 | − | 0.694047i | \(-0.244174\pi\) |
−0.241097 | + | 0.970501i | \(0.577507\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.4740 | + | 10.9240i | −1.21550 | + | 0.718745i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.08689 | − | 7.07871i | 0.267741 | − | 0.463742i | −0.700537 | − | 0.713616i | \(-0.747056\pi\) |
0.968278 | + | 0.249875i | \(0.0803894\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 19.1272 | − | 6.11132i | 1.24244 | − | 0.396973i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.5553i | 0.812134i | 0.913843 | + | 0.406067i | \(0.133100\pi\) | ||||
−0.913843 | + | 0.406067i | \(0.866900\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.1154 | − | 11.0363i | 1.23133 | − | 0.710910i | 0.264025 | − | 0.964516i | \(-0.414950\pi\) |
0.967308 | + | 0.253606i | \(0.0816166\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.3050 | − | 8.12267i | −0.853514 | − | 0.521069i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.39706 | + | 0.806595i | 0.0888930 | + | 0.0513224i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 19.1813 | − | 21.0942i | 1.21557 | − | 1.33679i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.66808 | −0.105288 | −0.0526441 | − | 0.998613i | \(-0.516765\pi\) | ||||
−0.0526441 | + | 0.998613i | \(0.516765\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 37.8354i | − | 2.37869i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.04298 | − | 0.602166i | −0.0650594 | − | 0.0375621i | 0.467117 | − | 0.884195i | \(-0.345293\pi\) |
−0.532177 | + | 0.846633i | \(0.678626\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.9120 | − | 2.72326i | 0.740173 | − | 0.169215i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.44683 | + | 0.328152i | −0.213354 | + | 0.0203121i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.50729 | − | 4.34275i | −0.154606 | − | 0.267785i | 0.778310 | − | 0.627881i | \(-0.216077\pi\) |
−0.932915 | + | 0.360095i | \(0.882744\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.17206 | − | 0.693995i | 0.132928 | − | 0.0424718i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.94487 | − | 13.7609i | −0.484407 | − | 0.839018i | 0.515432 | − | 0.856930i | \(-0.327631\pi\) |
−0.999840 | + | 0.0179121i | \(0.994298\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.4197 | − | 10.0573i | −1.05817 | − | 0.610937i | −0.133248 | − | 0.991083i | \(-0.542541\pi\) |
−0.924927 | + | 0.380146i | \(0.875874\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.0325 | − | 0.104465i | 0.607192 | − | 0.00632250i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.81938 | − | 2.20512i | 0.229484 | − | 0.132493i | −0.380850 | − | 0.924637i | \(-0.624369\pi\) |
0.610334 | + | 0.792144i | \(0.291035\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.9808 | + | 25.2656i | 1.07648 | + | 1.51261i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 17.9173i | − | 1.06886i | −0.845213 | − | 0.534429i | \(-0.820527\pi\) | ||
0.845213 | − | 0.534429i | \(-0.179473\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.77663 | − | 10.0054i | −0.343385 | − | 0.594760i | 0.641674 | − | 0.766978i | \(-0.278240\pi\) |
−0.985059 | + | 0.172217i | \(0.944907\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.78724 | − | 2.58802i | 0.164526 | − | 0.152766i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.6226 | − | 33.9874i | 1.15427 | − | 1.99926i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.20529 | + | 5.64258i | 0.363760 | + | 0.330774i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 7.17953i | − | 0.419433i | −0.977762 | − | 0.209716i | \(-0.932746\pi\) | ||
0.977762 | − | 0.209716i | \(-0.0672540\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.89933 | − | 24.1624i | 0.168236 | − | 1.40204i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.84357 | + | 15.3175i | −0.511437 | + | 0.885834i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.6369 | + | 17.9176i | 0.958934 | + | 1.03275i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.02002 | − | 4.68578i | 0.0585987 | − | 0.269191i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.44348 | 0.139457 | 0.0697284 | − | 0.997566i | \(-0.477787\pi\) | ||||
0.0697284 | + | 0.997566i | \(0.477787\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.4692 | + | 4.30354i | −0.766236 | + | 0.244820i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.56348 | − | 4.44007i | −0.145361 | − | 0.251773i | 0.784146 | − | 0.620576i | \(-0.213101\pi\) |
−0.929508 | + | 0.368803i | \(0.879768\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.819152 | + | 1.41881i | −0.0463012 | + | 0.0801961i | −0.888247 | − | 0.459366i | \(-0.848077\pi\) |
0.841946 | + | 0.539562i | \(0.181410\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.28184 | + | 14.3446i | −0.465155 | + | 0.805672i | −0.999209 | − | 0.0397789i | \(-0.987335\pi\) |
0.534054 | + | 0.845451i | \(0.320668\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.70265 | − | 4.68113i | −0.151320 | − | 0.262093i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.354983 | + | 0.113421i | −0.0198132 | + | 0.00633052i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.52595 | 0.307472 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.800804 | + | 3.67874i | −0.0442846 | + | 0.203435i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −22.3991 | + | 5.12077i | −1.23490 | + | 0.282317i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.9722 | − | 20.7364i | 0.658049 | − | 1.13977i | −0.323071 | − | 0.946375i | \(-0.604715\pi\) |
0.981120 | − | 0.193400i | \(-0.0619513\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.75928 | + | 12.6017i | −0.315607 | + | 0.690567i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 9.25410i | − | 0.504103i | −0.967714 | − | 0.252051i | \(-0.918895\pi\) | ||
0.967714 | − | 0.252051i | \(-0.0811052\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.3774 | − | 13.0736i | −0.780872 | − | 0.710061i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.2059 | + | 41.9259i | −1.31083 | + | 2.27042i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.5625 | − | 14.4675i | −0.624318 | − | 0.781170i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.2812 | + | 23.0038i | 0.712973 | + | 1.23491i | 0.963736 | + | 0.266857i | \(0.0859853\pi\) |
−0.250763 | + | 0.968049i | \(0.580681\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 14.8893i | − | 0.797004i | −0.917167 | − | 0.398502i | \(-0.869530\pi\) | ||
0.917167 | − | 0.398502i | \(-0.130470\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.82145 | + | 9.10436i | −0.364102 | + | 0.485955i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.5749 | − | 8.41481i | 0.775743 | − | 0.447875i | −0.0591766 | − | 0.998248i | \(-0.518848\pi\) |
0.834919 | + | 0.550372i | \(0.185514\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 29.5829 | − | 17.4929i | 1.56569 | − | 0.925823i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.3673 | + | 14.0685i | 1.28606 | + | 0.742506i | 0.977949 | − | 0.208846i | \(-0.0669706\pi\) |
0.308109 | + | 0.951351i | \(0.400304\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.22854 | − | 15.9843i | −0.485713 | − | 0.841279i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.0403 | − | 5.76407i | 0.946872 | − | 0.302535i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.38797 | − | 12.7963i | −0.385649 | − | 0.667963i | 0.606210 | − | 0.795304i | \(-0.292689\pi\) |
−0.991859 | + | 0.127341i | \(0.959356\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.408743 | + | 4.29334i | 0.0212783 | + | 0.223502i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.5401 | + | 6.32783i | 1.06639 | + | 0.328525i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.9723 | − | 10.9537i | −0.982348 | − | 0.567159i | −0.0793696 | − | 0.996845i | \(-0.525291\pi\) |
−0.902978 | + | 0.429687i | \(0.858624\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.52685i | 0.130139i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.15057 | 0.418667 | 0.209333 | − | 0.977844i | \(-0.432871\pi\) | ||||
0.209333 | + | 0.977844i | \(0.432871\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −20.0691 | + | 22.0705i | −1.02817 | + | 1.13071i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.285399 | + | 0.164775i | 0.0145832 | + | 0.00841962i | 0.507274 | − | 0.861785i | \(-0.330653\pi\) |
−0.492691 | + | 0.870205i | \(0.663987\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −27.5995 | + | 2.62758i | −1.40296 | + | 0.133567i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.5387 | − | 6.66185i | 0.585033 | − | 0.337769i | −0.178098 | − | 0.984013i | \(-0.556994\pi\) |
0.763131 | + | 0.646244i | \(0.223661\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 60.5869i | 3.06401i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 28.5697 | − | 9.12830i | 1.44115 | − | 0.460462i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.3006 | − | 24.7694i | 0.717728 | − | 1.24314i | −0.244169 | − | 0.969733i | \(-0.578515\pi\) |
0.961898 | − | 0.273409i | \(-0.0881513\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.94160 | + | 1.65774i | 0.147264 | + | 0.0829908i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.2076 | + | 13.9763i | 1.20887 | + | 0.697941i | 0.962512 | − | 0.271238i | \(-0.0874330\pi\) |
0.246357 | + | 0.969179i | \(0.420766\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.5994 | − | 11.3157i | 0.976314 | − | 0.563675i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.6301 | −1.07217 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.852979 | + | 0.492468i | −0.0421771 | + | 0.0243510i | −0.520940 | − | 0.853593i | \(-0.674419\pi\) |
0.478763 | + | 0.877944i | \(0.341085\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.12162 | − | 18.9339i | 0.203304 | − | 0.933941i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.6352 | + | 5.43290i | 0.867769 | + | 0.267336i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.51716 | + | 2.76819i | −0.123266 | + | 0.135559i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.2166 | −1.52503 | −0.762515 | − | 0.646970i | \(-0.776036\pi\) | ||||
−0.762515 | + | 0.646970i | \(0.776036\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.7393 | −1.69309 | −0.846544 | − | 0.532319i | \(-0.821321\pi\) | ||||
−0.846544 | + | 0.532319i | \(0.821321\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.8297 | − | 23.6960i | 0.526556 | − | 1.15214i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.3024 | − | 3.49836i | 0.740534 | − | 0.169297i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −17.3536 | − | 3.77761i | −0.837841 | − | 0.182385i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.9115 | − | 9.18649i | 0.766429 | − | 0.442498i | −0.0651704 | − | 0.997874i | \(-0.520759\pi\) |
0.831599 | + | 0.555376i | \(0.187426\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.6833 | −1.18621 | −0.593103 | − | 0.805127i | \(-0.702097\pi\) | ||||
−0.593103 | + | 0.805127i | \(0.702097\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.15503 | + | 2.97626i | −0.246598 | + | 0.142374i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.1758 | + | 7.60702i | 0.628844 | + | 0.363063i | 0.780304 | − | 0.625400i | \(-0.215064\pi\) |
−0.151460 | + | 0.988463i | \(0.548398\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.9954 | − | 0.437285i | 0.999783 | − | 0.0208231i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.0876 | + | 26.1325i | −0.716834 | + | 1.24159i | 0.245414 | + | 0.969418i | \(0.421076\pi\) |
−0.962248 | + | 0.272174i | \(0.912257\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.836527 | + | 2.61816i | 0.0395664 | + | 0.123835i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 27.7596i | − | 1.31006i | −0.755603 | − | 0.655029i | \(-0.772656\pi\) | ||
0.755603 | − | 0.655029i | \(-0.227344\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.83077 | + | 3.36640i | −0.274560 | + | 0.158518i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.77423 | − | 17.3381i | 0.177329 | − | 0.814614i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.3189 | − | 16.9273i | −1.37148 | − | 0.791825i | −0.380366 | − | 0.924836i | \(-0.624202\pi\) |
−0.991115 | + | 0.133011i | \(0.957535\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.64278 | + | 38.6919i | −0.216707 | + | 1.80599i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.7084 | −1.10421 | −0.552104 | − | 0.833775i | \(-0.686175\pi\) | ||||
−0.552104 | + | 0.833775i | \(0.686175\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.60640i | − | 0.0746559i | −0.999303 | − | 0.0373280i | \(-0.988115\pi\) | ||
0.999303 | − | 0.0373280i | \(-0.0118846\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.51812 | − | 3.18589i | −0.255348 | − | 0.147425i | 0.366863 | − | 0.930275i | \(-0.380432\pi\) |
−0.622211 | + | 0.782850i | \(0.713765\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.07751 | + | 3.49759i | −0.0497549 | + | 0.161504i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.39152 | − | 10.9862i | 0.110196 | − | 0.506217i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.6407 | − | 37.4827i | −0.995039 | − | 1.72346i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.8556 | + | 14.1306i | −0.909124 | + | 0.646998i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.66105 | − | 2.87702i | −0.0758953 | − | 0.131455i | 0.825580 | − | 0.564285i | \(-0.190848\pi\) |
−0.901475 | + | 0.432831i | \(0.857515\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.75687 | + | 5.05578i | 0.399279 | + | 0.230524i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −18.1756 | + | 32.2519i | −0.827017 | + | 1.46751i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.8943 | + | 10.3313i | −0.810868 | + | 0.468155i | −0.847257 | − | 0.531183i | \(-0.821748\pi\) |
0.0363892 | + | 0.999338i | \(0.488414\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.82924 | + | 8.85493i | 0.127943 | + | 0.400434i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 15.1679i | − | 0.684518i | −0.939606 | − | 0.342259i | \(-0.888808\pi\) | ||
0.939606 | − | 0.342259i | \(-0.111192\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.32784 | + | 7.49604i | 0.194916 | + | 0.337605i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.0745 | + | 14.0810i | 0.586470 | + | 0.631617i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.10558 | − | 5.37903i | 0.139025 | − | 0.240798i | −0.788103 | − | 0.615544i | \(-0.788936\pi\) |
0.927128 | + | 0.374745i | \(0.122270\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.97136 | + | 8.76631i | −0.356134 | + | 0.391650i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 5.52940i | − | 0.246544i | −0.992373 | − | 0.123272i | \(-0.960661\pi\) | ||
0.992373 | − | 0.123272i | \(-0.0393387\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.5165 | − | 9.56286i | −0.467055 | − | 0.424701i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.8857 | − | 25.7827i | 0.659796 | − | 1.14280i | −0.320872 | − | 0.947122i | \(-0.603976\pi\) |
0.980668 | − | 0.195678i | \(-0.0626906\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.617080 | + | 0.190105i | 0.0272980 | + | 0.00840977i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.52017 | + | 1.50566i | −0.155419 | + | 0.0664766i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 40.6729 | 1.78879 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.13204 | + | 19.1920i | 0.269167 | + | 0.842436i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.2112 | − | 19.4183i | −0.491170 | − | 0.850732i | 0.508778 | − | 0.860898i | \(-0.330097\pi\) |
−0.999948 | + | 0.0101659i | \(0.996764\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.7511 | − | 20.3535i | 0.513839 | − | 0.889996i | −0.486032 | − | 0.873941i | \(-0.661556\pi\) |
0.999871 | − | 0.0160547i | \(-0.00511059\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 38.7617 | − | 67.1372i | 1.68849 | − | 2.92454i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.1319 | − | 36.6015i | −0.918778 | − | 1.59137i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17.0474 | + | 12.1322i | −0.739796 | + | 0.526492i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.14742 | 0.136330 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.5964 | − | 2.95972i | −0.586728 | − | 0.127721i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14.2453 | + | 29.5272i | 0.613586 | + | 1.27183i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.0653647 | + | 0.113215i | −0.00281025 | + | 0.00486749i | −0.867427 | − | 0.497564i | \(-0.834228\pi\) |
0.864617 | + | 0.502432i | \(0.167561\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.4404 | + | 12.5813i | −0.490956 | + | 0.539916i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 41.2183i | 1.76237i | 0.472774 | + | 0.881184i | \(0.343253\pi\) | ||||
−0.472774 | + | 0.881184i | \(0.656747\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.39851 | + | 16.1884i | −0.315761 | + | 0.690904i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.425199 | + | 0.736467i | −0.0181141 | + | 0.0313745i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.83580 | − | 29.9009i | −0.290688 | − | 1.27152i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.90624 | − | 5.03375i | −0.123141 | − | 0.213287i | 0.797864 | − | 0.602838i | \(-0.205963\pi\) |
−0.921005 | + | 0.389551i | \(0.872630\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.2330i | 0.855764i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −57.9506 | + | 18.5158i | −2.44668 | + | 0.781737i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.2190 | − | 10.5187i | 0.767838 | − | 0.443312i | −0.0642647 | − | 0.997933i | \(-0.520470\pi\) |
0.832103 | + | 0.554621i | \(0.187137\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −14.0787 | + | 19.2039i | −0.591251 | + | 0.806488i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.2091 | + | 17.4412i | 1.26643 | + | 0.731173i | 0.974311 | − | 0.225209i | \(-0.0723064\pi\) |
0.292119 | + | 0.956382i | \(0.405640\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.9889 | − | 32.8897i | −0.794661 | − | 1.37639i | −0.923054 | − | 0.384670i | \(-0.874315\pi\) |
0.128394 | − | 0.991723i | \(-0.459018\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.46429 | − | 26.4915i | −0.353601 | − | 1.10670i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.71271 | − | 4.69855i | −0.112932 | − | 0.195603i | 0.804019 | − | 0.594603i | \(-0.202691\pi\) |
−0.916951 | + | 0.399000i | \(0.869357\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.8024 | − | 2.35152i | −0.448934 | − | 0.0977260i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −29.6339 | − | 31.9151i | −1.22942 | − | 1.32406i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −32.9484 | − | 19.0228i | −1.36459 | − | 0.787844i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 8.71317i | − | 0.359631i | −0.983700 | − | 0.179816i | \(-0.942450\pi\) | ||
0.983700 | − | 0.179816i | \(-0.0575501\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.61648 | 0.313832 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.26769 | + | 2.97137i | 0.134415 | + | 0.122226i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.9627 | + | 9.79341i | 0.696574 | + | 0.402167i | 0.806070 | − | 0.591820i | \(-0.201590\pi\) |
−0.109496 | + | 0.993987i | \(0.534924\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.2721 | + | 2.67144i | 0.502262 | + | 0.109335i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.2397 | + | 8.22129i | −0.581818 | + | 0.335913i | −0.761855 | − | 0.647747i | \(-0.775711\pi\) |
0.180038 | + | 0.983660i | \(0.442378\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.0177i | 0.449420i | 0.974426 | + | 0.224710i | \(0.0721435\pi\) | ||||
−0.974426 | + | 0.224710i | \(0.927857\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.40619 | − | 3.38103i | −0.0979875 | − | 0.137686i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.07323 | + | 10.5191i | −0.246505 | + | 0.426959i | −0.962554 | − | 0.271091i | \(-0.912615\pi\) |
0.716049 | + | 0.698050i | \(0.245949\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.0550690 | + | 5.28865i | 0.00223151 | + | 0.214307i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.4663 | − | 9.50681i | −0.666154 | − | 0.384604i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.3206 | − | 8.26802i | 0.578405 | − | 0.333942i | −0.182094 | − | 0.983281i | \(-0.558288\pi\) |
0.760499 | + | 0.649339i | \(0.224954\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.8433 | 1.40274 | 0.701368 | − | 0.712799i | \(-0.252573\pi\) | ||||
0.701368 | + | 0.712799i | \(0.252573\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.3120 | − | 12.3045i | 0.856603 | − | 0.494560i | −0.00627057 | − | 0.999980i | \(-0.501996\pi\) |
0.862873 | + | 0.505421i | \(0.168663\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.5082 | − | 38.5954i | −0.662451 | − | 1.54878i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.776267 | − | 3.39552i | −0.0311005 | − | 0.136039i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.42216 | − | 4.02115i | −0.176604 | − | 0.160589i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 34.6370 | 1.38107 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.4776 | −1.49196 | −0.745979 | − | 0.665969i | \(-0.768018\pi\) | ||||
−0.745979 | + | 0.665969i | \(0.768018\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.9992 | − | 15.4577i | −0.675659 | − | 0.614389i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.13449 | − | 15.2836i | 0.0449501 | − | 0.605559i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −21.6897 | + | 2.06494i | −0.858029 | + | 0.0816878i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.6348 | − | 7.87204i | 0.538541 | − | 0.310927i | −0.205946 | − | 0.978563i | \(-0.566027\pi\) |
0.744488 | + | 0.667636i | \(0.232694\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.7173 | −0.462086 | −0.231043 | − | 0.972943i | \(-0.574214\pi\) | ||||
−0.231043 | + | 0.972943i | \(0.574214\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.9086 | + | 13.2263i | −0.900632 | + | 0.519980i | −0.877405 | − | 0.479750i | \(-0.840727\pi\) |
−0.0232268 | + | 0.999730i | \(0.507394\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28.2886 | − | 16.3324i | −1.11043 | − | 0.641105i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 40.7744 | − | 24.1106i | 1.59808 | − | 0.944971i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.81151 | − | 3.13762i | 0.0708898 | − | 0.122785i | −0.828402 | − | 0.560134i | \(-0.810749\pi\) |
0.899292 | + | 0.437350i | \(0.144083\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.596515 | + | 0.424523i | −0.0232723 | + | 0.0165622i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 24.1855i | − | 0.942132i | −0.882098 | − | 0.471066i | \(-0.843869\pi\) | ||
0.882098 | − | 0.471066i | \(-0.156131\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.7414 | − | 7.93363i | 0.534480 | − | 0.308582i | −0.208359 | − | 0.978053i | \(-0.566812\pi\) |
0.742839 | + | 0.669470i | \(0.233479\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 27.7889 | + | 6.04921i | 1.07923 | + | 0.234932i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.07468 | − | 4.66192i | −0.312653 | − | 0.180510i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −36.0134 | − | 32.7476i | −1.39236 | − | 1.26609i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −27.7866 | −1.07269 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.48623i | 0.134384i | 0.997740 | + | 0.0671922i | \(0.0214041\pi\) | ||||
−0.997740 | + | 0.0671922i | \(0.978596\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.6859 | − | 19.4486i | −1.29465 | − | 0.747469i | −0.315179 | − | 0.949032i | \(-0.602064\pi\) |
−0.979475 | + | 0.201564i | \(0.935398\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.38847 | − | 8.71741i | 0.360297 | − | 0.334543i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.7293 | + | 4.94781i | 0.870988 | + | 0.189600i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.05116 | + | 10.4809i | 0.231541 | + | 0.401041i | 0.958262 | − | 0.285892i | \(-0.0922898\pi\) |
−0.726721 | + | 0.686933i | \(0.758956\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.41070 | + | 13.8046i | 0.168279 | + | 0.526678i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.89270 | + | 15.4026i | 0.338785 | + | 0.586792i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.7139 | − | 10.8044i | −0.711908 | − | 0.411021i | 0.0998588 | − | 0.995002i | \(-0.468161\pi\) |
−0.811767 | + | 0.583981i | \(0.801494\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −36.4031 | − | 7.52827i | −1.38284 | − | 0.285975i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.33699 | − | 5.39071i | 0.353664 | − | 0.204188i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.4858 | − | 4.30884i | 0.510079 | − | 0.162975i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 25.2893i | − | 0.955163i | −0.878587 | − | 0.477582i | \(-0.841513\pi\) | ||
0.878587 | − | 0.477582i | \(-0.158487\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.70150 | + | 2.94708i | 0.0641732 | + | 0.111151i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.00059 | − | 2.15669i | −0.263284 | − | 0.0811106i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.13129 | + | 8.88765i | −0.192710 | + | 0.333783i | −0.946147 | − | 0.323737i | \(-0.895061\pi\) |
0.753438 | + | 0.657519i | \(0.228394\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 31.6322 | + | 14.4567i | 1.18630 | + | 0.542169i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 83.5076i | 3.12738i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.6302 | + | 16.0892i | −0.546375 | + | 0.600862i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.3969 | − | 42.2566i | 0.909850 | − | 1.57591i | 0.0955793 | − | 0.995422i | \(-0.469530\pi\) |
0.814271 | − | 0.580485i | \(-0.197137\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.81372 | + | 21.0560i | 0.179272 | + | 0.784166i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 37.3560 | + | 8.13181i | 1.38928 | + | 0.302425i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.98665 | −0.370384 | −0.185192 | − | 0.982702i | \(-0.559291\pi\) | ||||
−0.185192 | + | 0.982702i | \(0.559291\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.58487 | − | 25.9127i | −0.280921 | − | 0.959731i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 34.6538 | + | 60.0222i | 1.28172 | + | 2.22000i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.4538 | + | 31.9630i | −0.681608 | + | 1.18058i | 0.292881 | + | 0.956149i | \(0.405386\pi\) |
−0.974490 | + | 0.224432i | \(0.927947\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.23923 | − | 5.61051i | 0.119318 | − | 0.206666i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.7107 | + | 34.1399i | 0.725070 | + | 1.25586i | 0.958945 | + | 0.283591i | \(0.0915259\pi\) |
−0.233875 | + | 0.972267i | \(0.575141\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.850399 | + | 2.66157i | 0.0312402 | + | 0.0977753i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.7786 | −0.468800 | −0.234400 | − | 0.972140i | \(-0.575312\pi\) | ||||
−0.234400 | + | 0.972140i | \(0.575312\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 49.1606 | − | 4.68028i | 1.79869 | − | 0.171243i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.126866 | + | 0.554934i | 0.00463559 | + | 0.0202768i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.32518 | + | 7.49143i | −0.157828 | + | 0.273366i | −0.934085 | − | 0.357050i | \(-0.883782\pi\) |
0.776257 | + | 0.630416i | \(0.217116\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.13759 | − | 1.94375i | −0.0778982 | − | 0.0708342i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.6532i | 0.968727i | 0.874867 | + | 0.484364i | \(0.160949\pi\) | ||||
−0.874867 | + | 0.484364i | \(0.839051\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 44.0882 | − | 48.4849i | 1.60030 | − | 1.75989i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.2462 | − | 31.6034i | 0.661425 | − | 1.14562i | −0.318816 | − | 0.947817i | \(-0.603285\pi\) |
0.980241 | − | 0.197805i | \(-0.0633814\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.49607 | + | 1.69319i | 0.198971 | + | 0.0612975i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.63502 | + | 13.2242i | 0.275685 | + | 0.477500i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.0781i | 0.940400i | 0.882560 | + | 0.470200i | \(0.155818\pi\) | ||||
−0.882560 | + | 0.470200i | \(0.844182\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.634868 | − | 1.98700i | −0.0228642 | − | 0.0715602i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −34.5210 | + | 19.9307i | −1.24163 | + | 0.716858i | −0.969427 | − | 0.245381i | \(-0.921087\pi\) |
−0.272208 | + | 0.962239i | \(0.587754\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 18.4381 | + | 10.3908i | 0.661464 | + | 0.372768i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.917336 | + | 0.529624i | 0.0328670 | + | 0.0189757i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.0068 | − | 29.4566i | −0.608551 | − | 1.05404i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.79939 | − | 3.59595i | −0.171516 | − | 0.128509i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.2663 | + | 21.2458i | 0.437245 | + | 0.757331i | 0.997476 | − | 0.0710057i | \(-0.0226208\pi\) |
−0.560231 | + | 0.828337i | \(0.689288\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.84743 | − | 8.48675i | 0.0657703 | − | 0.302136i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.7527 | + | 20.1978i | −0.773436 | + | 0.718153i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.2493 | + | 6.49477i | 0.399473 | + | 0.230636i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.4163i | 1.18367i | 0.806060 | + | 0.591834i | \(0.201596\pi\) | ||||
−0.806060 | + | 0.591834i | \(0.798404\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −65.1308 | −2.30416 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.59212 | + | 1.64169i | 0.126921 | + | 0.0580062i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.989861 | − | 0.571497i | −0.0349315 | − | 0.0201677i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.85398 | − | 26.8921i | 0.206070 | − | 0.946645i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.1974 | + | 24.9400i | −1.51874 | + | 0.876845i | −0.518984 | + | 0.854784i | \(0.673690\pi\) |
−0.999757 | + | 0.0220612i | \(0.992977\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.9220i | 0.594210i | 0.954845 | + | 0.297105i | \(0.0960212\pi\) | ||||
−0.954845 | + | 0.297105i | \(0.903979\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.6035 | − | 33.1867i | −0.371880 | − | 1.16391i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.40465 | + | 5.89703i | −0.119114 | + | 0.206311i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.9780 | + | 11.5566i | 0.453489 | + | 0.403820i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.856494 | + | 0.494497i | 0.0298918 | + | 0.0172581i | 0.514871 | − | 0.857267i | \(-0.327840\pi\) |
−0.484980 | + | 0.874525i | \(0.661173\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.8549 | − | 17.8141i | 1.07553 | − | 0.620960i | 0.145846 | − | 0.989307i | \(-0.453409\pi\) |
0.929688 | + | 0.368347i | \(0.120076\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −48.8191 | −1.69761 | −0.848803 | − | 0.528709i | \(-0.822676\pi\) | ||||
−0.848803 | + | 0.528709i | \(0.822676\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.5060 | + | 6.64300i | −0.399621 | + | 0.230721i | −0.686320 | − | 0.727299i | \(-0.740775\pi\) |
0.286700 | + | 0.958021i | \(0.407442\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.46395 | + | 1.62479i | 0.258922 | + | 0.0563632i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22.8113 | − | 47.2828i | −0.790366 | − | 1.63825i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.39919 | + | 53.3295i | −0.221189 | + | 1.84334i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.5549 | −1.46916 | −0.734579 | − | 0.678523i | \(-0.762620\pi\) | ||||
−0.734579 | + | 0.678523i | \(0.762620\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.6680 | 0.954068 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.8784 | − | 22.9605i | 0.719090 | − | 0.790802i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.44738 | − | 28.2019i | −0.221535 | − | 0.969028i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.25637 | − | 19.5529i | 0.146078 | − | 0.671055i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32.3120 | + | 18.6553i | −1.10764 | + | 0.639496i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.4196 | 0.938830 | 0.469415 | − | 0.882978i | \(-0.344465\pi\) | ||||
0.469415 | + | 0.882978i | \(0.344465\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.40476 | − | 4.27514i | 0.252942 | − | 0.146036i | −0.368169 | − | 0.929759i | \(-0.620015\pi\) |
0.621111 | + | 0.783723i | \(0.286682\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.23617 | + | 1.29105i | 0.0762970 | + | 0.0440501i | 0.537663 | − | 0.843160i | \(-0.319307\pi\) |
−0.461366 | + | 0.887210i | \(0.652641\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.58748 | − | 0.0685934i | 0.224501 | − | 0.00233766i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.7086 | − | 18.5478i | 0.364523 | − | 0.631373i | −0.624176 | − | 0.781284i | \(-0.714565\pi\) |
0.988700 | + | 0.149911i | \(0.0478986\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 64.7500 | − | 20.6883i | 2.19903 | − | 0.702611i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 54.2950i | 1.84183i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.62278 | + | 1.51426i | −0.0888694 | + | 0.0513088i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.37680 | + | 14.4616i | 0.0465976 | + | 0.489450i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.5112 | − | 23.9665i | −1.40173 | − | 0.809291i | −0.407163 | − | 0.913355i | \(-0.633482\pi\) |
−0.994571 | + | 0.104064i | \(0.966815\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.36604 | − | 9.20035i | 0.282179 | − | 0.310320i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.0526 | 0.540827 | 0.270413 | − | 0.962744i | \(-0.412840\pi\) | ||||
0.270413 | + | 0.962744i | \(0.412840\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 57.8898i | 1.94815i | 0.226236 | + | 0.974073i | \(0.427358\pi\) | ||||
−0.226236 | + | 0.974073i | \(0.572642\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.719272 | + | 0.415272i | 0.0241508 | + | 0.0139435i | 0.512027 | − | 0.858969i | \(-0.328895\pi\) |
−0.487876 | + | 0.872913i | \(0.662228\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.0055 | + | 33.3923i | 1.03989 | + | 1.11994i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 31.8709 | − | 27.5849i | 1.06772 | − | 0.924128i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.19947 | − | 5.54164i | −0.107066 | − | 0.185444i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −29.1817 | + | 9.32383i | −0.974348 | + | 0.311314i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.96511 | + | 10.3319i | 0.198947 | + | 0.344587i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 52.7613 | + | 30.4618i | 1.75773 | + | 1.01483i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.440948 | + | 42.3472i | 0.0146738 | + | 1.40923i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38.0267 | + | 21.9547i | −1.26266 | + | 0.728995i | −0.973588 | − | 0.228313i | \(-0.926679\pi\) |
−0.289069 | + | 0.957308i | \(0.593346\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.76729 | − | 4.81609i | 0.224457 | − | 0.159740i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.64586i | − | 0.0545299i | −0.999628 | − | 0.0272649i | \(-0.991320\pi\) | ||
0.999628 | − | 0.0272649i | \(-0.00867978\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38.5467 | + | 66.7649i | 1.27571 | + | 2.20959i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.2104 | − | 44.6621i | −0.337178 | − | 1.47487i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.9387 | + | 39.7309i | −0.756677 | + | 1.31060i | 0.187860 | + | 0.982196i | \(0.439845\pi\) |
−0.944537 | + | 0.328406i | \(0.893488\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.13124 | + | 2.84730i | 0.103178 | + | 0.0938216i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.9005i | 0.523373i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −22.2751 | − | 10.1803i | −0.731611 | − | 0.334365i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.79774 | + | 10.0420i | −0.190218 | + | 0.329467i | −0.945322 | − | 0.326137i | \(-0.894253\pi\) |
0.755105 | + | 0.655604i | \(0.227586\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.90247 | − | 4.26360i | 0.0951245 | − | 0.139734i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.88883 | − | 8.67694i | 0.0618376 | − | 0.284070i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.7618 | 1.29896 | 0.649481 | − | 0.760378i | \(-0.274986\pi\) | ||||
0.649481 | + | 0.760378i | \(0.274986\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.70301 | + | 0.863638i | −0.0882094 | + | 0.0281838i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.7590 | + | 35.9557i | 0.676724 | + | 1.17212i | 0.975962 | + | 0.217942i | \(0.0699345\pi\) |
−0.299237 | + | 0.954179i | \(0.596732\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.80684 | + | 10.0577i | −0.189097 | + | 0.327525i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.3288 | + | 26.5502i | −0.498119 | + | 0.862767i | −0.999998 | − | 0.00217116i | \(-0.999309\pi\) |
0.501879 | + | 0.864938i | \(0.332642\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.267161 | + | 0.462736i | 0.00867241 | + | 0.0150211i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27.3281 | + | 8.73161i | −0.886175 | + | 0.283142i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.7409 | 0.736650 | 0.368325 | − | 0.929697i | \(-0.379931\pi\) | ||||
0.368325 | + | 0.929697i | \(0.379931\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.99138 | − | 9.14803i | 0.0643723 | − | 0.295714i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −28.2874 | − | 8.71457i | −0.913449 | − | 0.281408i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.9257 | − | 65.6892i | 1.22341 | − | 2.11901i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.587064 | − | 0.268303i | −0.0189179 | − | 0.00864595i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.4381i | 0.592928i | 0.955044 | + | 0.296464i | \(0.0958074\pi\) | ||||
−0.955044 | + | 0.296464i | \(0.904193\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.08134 | + | 6.43919i | 0.227485 | + | 0.206856i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.784910 | + | 1.35950i | −0.0251889 | + | 0.0436285i | −0.878345 | − | 0.478027i | \(-0.841352\pi\) |
0.853156 | + | 0.521656i | \(0.174685\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.88885 | + | 4.18822i | 0.124671 | + | 0.134268i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.6070 | + | 18.3718i | 0.339347 | + | 0.587766i | 0.984310 | − | 0.176448i | \(-0.0564607\pi\) |
−0.644963 | + | 0.764214i | \(0.723127\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.16569i | 0.197056i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.31291 | + | 3.78105i | −0.169628 | + | 0.120720i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31.6340 | − | 18.2639i | 1.00897 | − | 0.582528i | 0.0980782 | − | 0.995179i | \(-0.468730\pi\) |
0.910889 | + | 0.412651i | \(0.135397\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −34.6708 | − | 19.5387i | −1.10358 | − | 0.621924i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −64.6555 | − | 37.3289i | −2.05592 | − | 1.18699i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.43293 | + | 16.3383i | 0.299647 | + | 0.519004i | 0.976055 | − | 0.217523i | \(-0.0697978\pi\) |
−0.676408 | + | 0.736527i | \(0.736464\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 39.5053 | − | 12.6223i | 1.25366 | − | 0.400557i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.0098 | + | 24.2658i | 0.443696 | + | 0.768504i | 0.997960 | − | 0.0638366i | \(-0.0203337\pi\) |
−0.554264 | + | 0.832341i | \(0.687000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −22.0646 | + | 9.43757i | −0.698093 | + | 0.298591i |
(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 | 2100.2.bo.g.1349.8 | 20 | ||
3.2 | odd | 2 | 2100.2.bo.h.1349.7 | 20 | |||
5.2 | odd | 4 | 2100.2.bi.j.1601.4 | 10 | |||
5.3 | odd | 4 | 420.2.bh.b.341.2 | yes | 10 | ||
5.4 | even | 2 | inner | 2100.2.bo.g.1349.3 | 20 | ||
7.3 | odd | 6 | 2100.2.bo.h.1949.4 | 20 | |||
15.2 | even | 4 | 2100.2.bi.k.1601.5 | 10 | |||
15.8 | even | 4 | 420.2.bh.a.341.1 | yes | 10 | ||
15.14 | odd | 2 | 2100.2.bo.h.1349.4 | 20 | |||
21.17 | even | 6 | inner | 2100.2.bo.g.1949.3 | 20 | ||
35.3 | even | 12 | 420.2.bh.a.101.1 | ✓ | 10 | ||
35.17 | even | 12 | 2100.2.bi.k.101.5 | 10 | |||
35.23 | odd | 12 | 2940.2.d.a.881.5 | 10 | |||
35.24 | odd | 6 | 2100.2.bo.h.1949.7 | 20 | |||
35.33 | even | 12 | 2940.2.d.b.881.6 | 10 | |||
105.17 | odd | 12 | 2100.2.bi.j.101.4 | 10 | |||
105.23 | even | 12 | 2940.2.d.b.881.5 | 10 | |||
105.38 | odd | 12 | 420.2.bh.b.101.2 | yes | 10 | ||
105.59 | even | 6 | inner | 2100.2.bo.g.1949.8 | 20 | ||
105.68 | odd | 12 | 2940.2.d.a.881.6 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.bh.a.101.1 | ✓ | 10 | 35.3 | even | 12 | ||
420.2.bh.a.341.1 | yes | 10 | 15.8 | even | 4 | ||
420.2.bh.b.101.2 | yes | 10 | 105.38 | odd | 12 | ||
420.2.bh.b.341.2 | yes | 10 | 5.3 | odd | 4 | ||
2100.2.bi.j.101.4 | 10 | 105.17 | odd | 12 | |||
2100.2.bi.j.1601.4 | 10 | 5.2 | odd | 4 | |||
2100.2.bi.k.101.5 | 10 | 35.17 | even | 12 | |||
2100.2.bi.k.1601.5 | 10 | 15.2 | even | 4 | |||
2100.2.bo.g.1349.3 | 20 | 5.4 | even | 2 | inner | ||
2100.2.bo.g.1349.8 | 20 | 1.1 | even | 1 | trivial | ||
2100.2.bo.g.1949.3 | 20 | 21.17 | even | 6 | inner | ||
2100.2.bo.g.1949.8 | 20 | 105.59 | even | 6 | inner | ||
2100.2.bo.h.1349.4 | 20 | 15.14 | odd | 2 | |||
2100.2.bo.h.1349.7 | 20 | 3.2 | odd | 2 | |||
2100.2.bo.h.1949.4 | 20 | 7.3 | odd | 6 | |||
2100.2.bo.h.1949.7 | 20 | 35.24 | odd | 6 | |||
2940.2.d.a.881.5 | 10 | 35.23 | odd | 12 | |||
2940.2.d.a.881.6 | 10 | 105.68 | odd | 12 | |||
2940.2.d.b.881.5 | 10 | 105.23 | even | 12 | |||
2940.2.d.b.881.6 | 10 | 35.33 | even | 12 |