Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,2,Mod(295,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.295");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.f (of order \(3\), degree \(2\), 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: | \(7.04280545828\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 589.1 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.589 |
Dual form | 882.2.f.q.295.1 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −1.67303 | − | 0.448288i | −0.965926 | − | 0.258819i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.517638 | − | 0.896575i | 0.231495 | − | 0.400961i | −0.726753 | − | 0.686898i | \(-0.758972\pi\) |
0.958248 | + | 0.285938i | \(0.0923050\pi\) | |||||||
\(6\) | 0.448288 | + | 1.67303i | 0.183013 | + | 0.683013i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.59808 | + | 1.50000i | 0.866025 | + | 0.500000i | ||||
\(10\) | −1.03528 | −0.327383 | ||||||||
\(11\) | 0.133975 | + | 0.232051i | 0.0403949 | + | 0.0699660i | 0.885516 | − | 0.464609i | \(-0.153805\pi\) |
−0.845121 | + | 0.534575i | \(0.820472\pi\) | |||||||
\(12\) | 1.22474 | − | 1.22474i | 0.353553 | − | 0.353553i | ||||
\(13\) | −0.896575 | + | 1.55291i | −0.248665 | + | 0.430701i | −0.963156 | − | 0.268944i | \(-0.913325\pi\) |
0.714490 | + | 0.699645i | \(0.246659\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.26795 | + | 1.26795i | −0.327383 | + | 0.327383i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −6.83083 | −1.65672 | −0.828360 | − | 0.560196i | \(-0.810726\pi\) | ||||
−0.828360 | + | 0.560196i | \(0.810726\pi\) | |||||||
\(18\) | − | 3.00000i | − | 0.707107i | ||||||
\(19\) | 4.38134 | 1.00515 | 0.502574 | − | 0.864534i | \(-0.332386\pi\) | ||||
0.502574 | + | 0.864534i | \(0.332386\pi\) | |||||||
\(20\) | 0.517638 | + | 0.896575i | 0.115747 | + | 0.200480i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.133975 | − | 0.232051i | 0.0285635 | − | 0.0494734i | ||||
\(23\) | −2.73205 | + | 4.73205i | −0.569672 | + | 0.986701i | 0.426926 | + | 0.904286i | \(0.359596\pi\) |
−0.996598 | + | 0.0824143i | \(0.973737\pi\) | |||||||
\(24\) | −1.67303 | − | 0.448288i | −0.341506 | − | 0.0915064i | ||||
\(25\) | 1.96410 | + | 3.40192i | 0.392820 | + | 0.680385i | ||||
\(26\) | 1.79315 | 0.351666 | ||||||||
\(27\) | −3.67423 | − | 3.67423i | −0.707107 | − | 0.707107i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | + | 3.46410i | 0.371391 | + | 0.643268i | 0.989780 | − | 0.142605i | \(-0.0455477\pi\) |
−0.618389 | + | 0.785872i | \(0.712214\pi\) | |||||||
\(30\) | 1.73205 | + | 0.464102i | 0.316228 | + | 0.0847330i | ||||
\(31\) | −3.34607 | + | 5.79555i | −0.600971 | + | 1.04091i | 0.391703 | + | 0.920092i | \(0.371886\pi\) |
−0.992674 | + | 0.120821i | \(0.961447\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −0.120118 | − | 0.448288i | −0.0209099 | − | 0.0780369i | ||||
\(34\) | 3.41542 | + | 5.91567i | 0.585739 | + | 1.01453i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.59808 | + | 1.50000i | −0.433013 | + | 0.250000i | ||||
\(37\) | 7.46410 | 1.22709 | 0.613545 | − | 0.789659i | \(-0.289743\pi\) | ||||
0.613545 | + | 0.789659i | \(0.289743\pi\) | |||||||
\(38\) | −2.19067 | − | 3.79435i | −0.355374 | − | 0.615525i | ||||
\(39\) | 2.19615 | − | 2.19615i | 0.351666 | − | 0.351666i | ||||
\(40\) | 0.517638 | − | 0.896575i | 0.0818458 | − | 0.141761i | ||||
\(41\) | 4.31199 | − | 7.46859i | 0.673420 | − | 1.16640i | −0.303508 | − | 0.952829i | \(-0.598158\pi\) |
0.976928 | − | 0.213569i | \(-0.0685087\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.133975 | − | 0.232051i | −0.0204309 | − | 0.0353874i | 0.855629 | − | 0.517589i | \(-0.173170\pi\) |
−0.876060 | + | 0.482202i | \(0.839837\pi\) | |||||||
\(44\) | −0.267949 | −0.0403949 | ||||||||
\(45\) | 2.68973 | − | 1.55291i | 0.400961 | − | 0.231495i | ||||
\(46\) | 5.46410 | 0.805638 | ||||||||
\(47\) | −0.378937 | − | 0.656339i | −0.0552737 | − | 0.0957369i | 0.837065 | − | 0.547104i | \(-0.184270\pi\) |
−0.892338 | + | 0.451367i | \(0.850936\pi\) | |||||||
\(48\) | 0.448288 | + | 1.67303i | 0.0647048 | + | 0.241481i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.96410 | − | 3.40192i | 0.277766 | − | 0.481105i | ||||
\(51\) | 11.4282 | + | 3.06218i | 1.60027 | + | 0.428791i | ||||
\(52\) | −0.896575 | − | 1.55291i | −0.124333 | − | 0.215350i | ||||
\(53\) | 10.9282 | 1.50110 | 0.750552 | − | 0.660811i | \(-0.229788\pi\) | ||||
0.750552 | + | 0.660811i | \(0.229788\pi\) | |||||||
\(54\) | −1.34486 | + | 5.01910i | −0.183013 | + | 0.683013i | ||||
\(55\) | 0.277401 | 0.0374048 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.33013 | − | 1.96410i | −0.970899 | − | 0.260152i | ||||
\(58\) | 2.00000 | − | 3.46410i | 0.262613 | − | 0.454859i | ||||
\(59\) | 0.637756 | − | 1.10463i | 0.0830288 | − | 0.143810i | −0.821521 | − | 0.570179i | \(-0.806874\pi\) |
0.904550 | + | 0.426369i | \(0.140207\pi\) | |||||||
\(60\) | −0.464102 | − | 1.73205i | −0.0599153 | − | 0.223607i | ||||
\(61\) | 6.31319 | + | 10.9348i | 0.808322 | + | 1.40005i | 0.914026 | + | 0.405656i | \(0.132957\pi\) |
−0.105704 | + | 0.994398i | \(0.533710\pi\) | |||||||
\(62\) | 6.69213 | 0.849901 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.928203 | + | 1.60770i | 0.115129 | + | 0.199410i | ||||
\(66\) | −0.328169 | + | 0.328169i | −0.0403949 | + | 0.0403949i | ||||
\(67\) | −6.23205 | + | 10.7942i | −0.761366 | + | 1.31872i | 0.180780 | + | 0.983524i | \(0.442138\pi\) |
−0.942146 | + | 0.335201i | \(0.891196\pi\) | |||||||
\(68\) | 3.41542 | − | 5.91567i | 0.414180 | − | 0.717381i | ||||
\(69\) | 6.69213 | − | 6.69213i | 0.805638 | − | 0.805638i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.46410 | 1.12318 | 0.561591 | − | 0.827415i | \(-0.310189\pi\) | ||||
0.561591 | + | 0.827415i | \(0.310189\pi\) | |||||||
\(72\) | 2.59808 | + | 1.50000i | 0.306186 | + | 0.176777i | ||||
\(73\) | 5.41662 | 0.633967 | 0.316984 | − | 0.948431i | \(-0.397330\pi\) | ||||
0.316984 | + | 0.948431i | \(0.397330\pi\) | |||||||
\(74\) | −3.73205 | − | 6.46410i | −0.433842 | − | 0.751437i | ||||
\(75\) | −1.76097 | − | 6.57201i | −0.203339 | − | 0.758871i | ||||
\(76\) | −2.19067 | + | 3.79435i | −0.251287 | + | 0.435242i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.00000 | − | 0.803848i | −0.339683 | − | 0.0910178i | ||||
\(79\) | −4.46410 | − | 7.73205i | −0.502251 | − | 0.869924i | −0.999997 | − | 0.00260080i | \(-0.999172\pi\) |
0.497746 | − | 0.867323i | \(-0.334161\pi\) | |||||||
\(80\) | −1.03528 | −0.115747 | ||||||||
\(81\) | 4.50000 | + | 7.79423i | 0.500000 | + | 0.866025i | ||||
\(82\) | −8.62398 | −0.952360 | ||||||||
\(83\) | −3.29530 | − | 5.70762i | −0.361706 | − | 0.626493i | 0.626536 | − | 0.779393i | \(-0.284472\pi\) |
−0.988242 | + | 0.152900i | \(0.951139\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.53590 | + | 6.12436i | −0.383522 | + | 0.664280i | ||||
\(86\) | −0.133975 | + | 0.232051i | −0.0144469 | + | 0.0250227i | ||||
\(87\) | −1.79315 | − | 6.69213i | −0.192246 | − | 0.717472i | ||||
\(88\) | 0.133975 | + | 0.232051i | 0.0142817 | + | 0.0247367i | ||||
\(89\) | 7.07107 | 0.749532 | 0.374766 | − | 0.927119i | \(-0.377723\pi\) | ||||
0.374766 | + | 0.927119i | \(0.377723\pi\) | |||||||
\(90\) | −2.68973 | − | 1.55291i | −0.283522 | − | 0.163692i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.73205 | − | 4.73205i | −0.284836 | − | 0.493350i | ||||
\(93\) | 8.19615 | − | 8.19615i | 0.849901 | − | 0.849901i | ||||
\(94\) | −0.378937 | + | 0.656339i | −0.0390844 | + | 0.0676962i | ||||
\(95\) | 2.26795 | − | 3.92820i | 0.232687 | − | 0.403025i | ||||
\(96\) | 1.22474 | − | 1.22474i | 0.125000 | − | 0.125000i | ||||
\(97\) | 9.07227 | + | 15.7136i | 0.921149 | + | 1.59548i | 0.797640 | + | 0.603134i | \(0.206082\pi\) |
0.123510 | + | 0.992343i | \(0.460585\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.803848i | 0.0807897i | ||||||||
\(100\) | −3.92820 | −0.392820 | ||||||||
\(101\) | 2.44949 | + | 4.24264i | 0.243733 | + | 0.422159i | 0.961775 | − | 0.273842i | \(-0.0882945\pi\) |
−0.718041 | + | 0.696000i | \(0.754961\pi\) | |||||||
\(102\) | −3.06218 | − | 11.4282i | −0.303201 | − | 1.13156i | ||||
\(103\) | −6.17449 | + | 10.6945i | −0.608391 | + | 1.05376i | 0.383115 | + | 0.923701i | \(0.374851\pi\) |
−0.991506 | + | 0.130063i | \(0.958482\pi\) | |||||||
\(104\) | −0.896575 | + | 1.55291i | −0.0879165 | + | 0.152276i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.46410 | − | 9.46410i | −0.530720 | − | 0.919235i | ||||
\(107\) | −17.3923 | −1.68138 | −0.840689 | − | 0.541519i | \(-0.817850\pi\) | ||||
−0.840689 | + | 0.541519i | \(0.817850\pi\) | |||||||
\(108\) | 5.01910 | − | 1.34486i | 0.482963 | − | 0.129410i | ||||
\(109\) | 4.92820 | 0.472036 | 0.236018 | − | 0.971749i | \(-0.424158\pi\) | ||||
0.236018 | + | 0.971749i | \(0.424158\pi\) | |||||||
\(110\) | −0.138701 | − | 0.240237i | −0.0132246 | − | 0.0229057i | ||||
\(111\) | −12.4877 | − | 3.34607i | −1.18528 | − | 0.317594i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.46410 | − | 6.00000i | 0.325875 | − | 0.564433i | −0.655814 | − | 0.754923i | \(-0.727674\pi\) |
0.981689 | + | 0.190490i | \(0.0610077\pi\) | |||||||
\(114\) | 1.96410 | + | 7.33013i | 0.183955 | + | 0.686529i | ||||
\(115\) | 2.82843 | + | 4.89898i | 0.263752 | + | 0.456832i | ||||
\(116\) | −4.00000 | −0.371391 | ||||||||
\(117\) | −4.65874 | + | 2.68973i | −0.430701 | + | 0.248665i | ||||
\(118\) | −1.27551 | −0.117420 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.26795 | + | 1.26795i | −0.115747 | + | 0.115747i | ||||
\(121\) | 5.46410 | − | 9.46410i | 0.496737 | − | 0.860373i | ||||
\(122\) | 6.31319 | − | 10.9348i | 0.571570 | − | 0.989988i | ||||
\(123\) | −10.5622 | + | 10.5622i | −0.952360 | + | 0.952360i | ||||
\(124\) | −3.34607 | − | 5.79555i | −0.300486 | − | 0.520456i | ||||
\(125\) | 9.24316 | 0.826733 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.4641 | 1.19475 | 0.597373 | − | 0.801964i | \(-0.296211\pi\) | ||||
0.597373 | + | 0.801964i | \(0.296211\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0.120118 | + | 0.448288i | 0.0105758 | + | 0.0394695i | ||||
\(130\) | 0.928203 | − | 1.60770i | 0.0814088 | − | 0.141004i | ||||
\(131\) | −5.46739 | + | 9.46979i | −0.477688 | + | 0.827379i | −0.999673 | − | 0.0255752i | \(-0.991858\pi\) |
0.521985 | + | 0.852955i | \(0.325192\pi\) | |||||||
\(132\) | 0.448288 | + | 0.120118i | 0.0390184 | + | 0.0104550i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 12.4641 | 1.07673 | ||||||||
\(135\) | −5.19615 | + | 1.39230i | −0.447214 | + | 0.119831i | ||||
\(136\) | −6.83083 | −0.585739 | ||||||||
\(137\) | −4.33013 | − | 7.50000i | −0.369948 | − | 0.640768i | 0.619609 | − | 0.784910i | \(-0.287291\pi\) |
−0.989557 | + | 0.144142i | \(0.953958\pi\) | |||||||
\(138\) | −9.14162 | − | 2.44949i | −0.778186 | − | 0.208514i | ||||
\(139\) | −0.397520 | + | 0.688524i | −0.0337172 | + | 0.0583999i | −0.882392 | − | 0.470516i | \(-0.844068\pi\) |
0.848674 | + | 0.528916i | \(0.177401\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.339746 | + | 1.26795i | 0.0286118 | + | 0.106781i | ||||
\(142\) | −4.73205 | − | 8.19615i | −0.397105 | − | 0.687806i | ||||
\(143\) | −0.480473 | −0.0401792 | ||||||||
\(144\) | − | 3.00000i | − | 0.250000i | ||||||
\(145\) | 4.14110 | 0.343900 | ||||||||
\(146\) | −2.70831 | − | 4.69093i | −0.224141 | − | 0.388224i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.73205 | + | 6.46410i | −0.306773 | + | 0.531346i | ||||
\(149\) | −11.4641 | + | 19.8564i | −0.939176 | + | 1.62670i | −0.172163 | + | 0.985068i | \(0.555076\pi\) |
−0.767013 | + | 0.641632i | \(0.778258\pi\) | |||||||
\(150\) | −4.81105 | + | 4.81105i | −0.392820 | + | 0.392820i | ||||
\(151\) | −9.19615 | − | 15.9282i | −0.748372 | − | 1.29622i | −0.948603 | − | 0.316470i | \(-0.897502\pi\) |
0.200230 | − | 0.979749i | \(-0.435831\pi\) | |||||||
\(152\) | 4.38134 | 0.355374 | ||||||||
\(153\) | −17.7470 | − | 10.2462i | −1.43476 | − | 0.828360i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.46410 | + | 6.00000i | 0.278243 | + | 0.481932i | ||||
\(156\) | 0.803848 | + | 3.00000i | 0.0643593 | + | 0.240192i | ||||
\(157\) | −4.76028 | + | 8.24504i | −0.379912 | + | 0.658026i | −0.991049 | − | 0.133498i | \(-0.957379\pi\) |
0.611137 | + | 0.791524i | \(0.290712\pi\) | |||||||
\(158\) | −4.46410 | + | 7.73205i | −0.355145 | + | 0.615129i | ||||
\(159\) | −18.2832 | − | 4.89898i | −1.44996 | − | 0.388514i | ||||
\(160\) | 0.517638 | + | 0.896575i | 0.0409229 | + | 0.0708805i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 4.50000 | − | 7.79423i | 0.353553 | − | 0.612372i | ||||
\(163\) | −13.3205 | −1.04334 | −0.521671 | − | 0.853147i | \(-0.674691\pi\) | ||||
−0.521671 | + | 0.853147i | \(0.674691\pi\) | |||||||
\(164\) | 4.31199 | + | 7.46859i | 0.336710 | + | 0.583199i | ||||
\(165\) | −0.464102 | − | 0.124356i | −0.0361303 | − | 0.00968107i | ||||
\(166\) | −3.29530 | + | 5.70762i | −0.255765 | + | 0.442997i | ||||
\(167\) | −0.757875 | + | 1.31268i | −0.0586461 | + | 0.101578i | −0.893858 | − | 0.448350i | \(-0.852012\pi\) |
0.835212 | + | 0.549928i | \(0.185345\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.89230 | + | 8.47372i | 0.376331 | + | 0.651825i | ||||
\(170\) | 7.07180 | 0.542382 | ||||||||
\(171\) | 11.3831 | + | 6.57201i | 0.870484 | + | 0.502574i | ||||
\(172\) | 0.267949 | 0.0204309 | ||||||||
\(173\) | −3.34607 | − | 5.79555i | −0.254397 | − | 0.440628i | 0.710335 | − | 0.703864i | \(-0.248544\pi\) |
−0.964731 | + | 0.263236i | \(0.915210\pi\) | |||||||
\(174\) | −4.89898 | + | 4.89898i | −0.371391 | + | 0.371391i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.133975 | − | 0.232051i | 0.0100987 | − | 0.0174915i | ||||
\(177\) | −1.56218 | + | 1.56218i | −0.117420 | + | 0.117420i | ||||
\(178\) | −3.53553 | − | 6.12372i | −0.264999 | − | 0.458993i | ||||
\(179\) | 5.07180 | 0.379084 | 0.189542 | − | 0.981873i | \(-0.439300\pi\) | ||||
0.189542 | + | 0.981873i | \(0.439300\pi\) | |||||||
\(180\) | 3.10583i | 0.231495i | ||||||||
\(181\) | −16.9706 | −1.26141 | −0.630706 | − | 0.776022i | \(-0.717235\pi\) | ||||
−0.630706 | + | 0.776022i | \(0.717235\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.66025 | − | 21.1244i | −0.418418 | − | 1.56156i | ||||
\(184\) | −2.73205 | + | 4.73205i | −0.201409 | + | 0.348851i | ||||
\(185\) | 3.86370 | − | 6.69213i | 0.284065 | − | 0.492015i | ||||
\(186\) | −11.1962 | − | 3.00000i | −0.820942 | − | 0.219971i | ||||
\(187\) | −0.915158 | − | 1.58510i | −0.0669230 | − | 0.115914i | ||||
\(188\) | 0.757875 | 0.0552737 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.53590 | −0.329069 | ||||||||
\(191\) | −7.46410 | − | 12.9282i | −0.540083 | − | 0.935452i | −0.998899 | − | 0.0469202i | \(-0.985059\pi\) |
0.458815 | − | 0.888532i | \(-0.348274\pi\) | |||||||
\(192\) | −1.67303 | − | 0.448288i | −0.120741 | − | 0.0323524i | ||||
\(193\) | −7.52628 | + | 13.0359i | −0.541753 | + | 0.938344i | 0.457050 | + | 0.889441i | \(0.348906\pi\) |
−0.998804 | + | 0.0489035i | \(0.984427\pi\) | |||||||
\(194\) | 9.07227 | − | 15.7136i | 0.651351 | − | 1.12817i | ||||
\(195\) | −0.832204 | − | 3.10583i | −0.0595954 | − | 0.222413i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.9282 | −1.20608 | −0.603042 | − | 0.797709i | \(-0.706045\pi\) | ||||
−0.603042 | + | 0.797709i | \(0.706045\pi\) | |||||||
\(198\) | 0.696152 | − | 0.401924i | 0.0494734 | − | 0.0285635i | ||||
\(199\) | 26.2880 | 1.86351 | 0.931755 | − | 0.363087i | \(-0.118277\pi\) | ||||
0.931755 | + | 0.363087i | \(0.118277\pi\) | |||||||
\(200\) | 1.96410 | + | 3.40192i | 0.138883 | + | 0.240552i | ||||
\(201\) | 15.2653 | − | 15.2653i | 1.07673 | − | 1.07673i | ||||
\(202\) | 2.44949 | − | 4.24264i | 0.172345 | − | 0.298511i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −8.36603 | + | 8.36603i | −0.585739 | + | 0.585739i | ||||
\(205\) | −4.46410 | − | 7.73205i | −0.311786 | − | 0.540030i | ||||
\(206\) | 12.3490 | 0.860395 | ||||||||
\(207\) | −14.1962 | + | 8.19615i | −0.986701 | + | 0.569672i | ||||
\(208\) | 1.79315 | 0.124333 | ||||||||
\(209\) | 0.586988 | + | 1.01669i | 0.0406028 | + | 0.0703262i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.46410 | + | 16.3923i | −0.651536 | + | 1.12849i | 0.331215 | + | 0.943555i | \(0.392542\pi\) |
−0.982750 | + | 0.184937i | \(0.940792\pi\) | |||||||
\(212\) | −5.46410 | + | 9.46410i | −0.375276 | + | 0.649997i | ||||
\(213\) | −15.8338 | − | 4.24264i | −1.08491 | − | 0.290701i | ||||
\(214\) | 8.69615 | + | 15.0622i | 0.594457 | + | 1.02963i | ||||
\(215\) | −0.277401 | −0.0189186 | ||||||||
\(216\) | −3.67423 | − | 3.67423i | −0.250000 | − | 0.250000i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.46410 | − | 4.26795i | −0.166890 | − | 0.289062i | ||||
\(219\) | −9.06218 | − | 2.42820i | −0.612365 | − | 0.164083i | ||||
\(220\) | −0.138701 | + | 0.240237i | −0.00935120 | + | 0.0161968i | ||||
\(221\) | 6.12436 | − | 10.6077i | 0.411969 | − | 0.713551i | ||||
\(222\) | 3.34607 | + | 12.4877i | 0.224573 | + | 0.838119i | ||||
\(223\) | 3.58630 | + | 6.21166i | 0.240157 | + | 0.415963i | 0.960759 | − | 0.277385i | \(-0.0894679\pi\) |
−0.720602 | + | 0.693349i | \(0.756135\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.7846i | 0.785641i | ||||||||
\(226\) | −6.92820 | −0.460857 | ||||||||
\(227\) | 13.8325 | + | 23.9587i | 0.918098 | + | 1.59019i | 0.802300 | + | 0.596920i | \(0.203609\pi\) |
0.115798 | + | 0.993273i | \(0.463057\pi\) | |||||||
\(228\) | 5.36603 | − | 5.36603i | 0.355374 | − | 0.355374i | ||||
\(229\) | −0.240237 | + | 0.416102i | −0.0158753 | + | 0.0274968i | −0.873854 | − | 0.486189i | \(-0.838387\pi\) |
0.857979 | + | 0.513685i | \(0.171720\pi\) | |||||||
\(230\) | 2.82843 | − | 4.89898i | 0.186501 | − | 0.323029i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.00000 | + | 3.46410i | 0.131306 | + | 0.227429i | ||||
\(233\) | 0.124356 | 0.00814681 | 0.00407340 | − | 0.999992i | \(-0.498703\pi\) | ||||
0.00407340 | + | 0.999992i | \(0.498703\pi\) | |||||||
\(234\) | 4.65874 | + | 2.68973i | 0.304552 | + | 0.175833i | ||||
\(235\) | −0.784610 | −0.0511823 | ||||||||
\(236\) | 0.637756 | + | 1.10463i | 0.0415144 | + | 0.0719051i | ||||
\(237\) | 4.00240 | + | 14.9372i | 0.259984 | + | 0.970274i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.464102 | + | 0.803848i | −0.0300202 | + | 0.0519966i | −0.880645 | − | 0.473776i | \(-0.842891\pi\) |
0.850625 | + | 0.525773i | \(0.176224\pi\) | |||||||
\(240\) | 1.73205 | + | 0.464102i | 0.111803 | + | 0.0299576i | ||||
\(241\) | −3.13801 | − | 5.43520i | −0.202137 | − | 0.350112i | 0.747080 | − | 0.664735i | \(-0.231455\pi\) |
−0.949217 | + | 0.314623i | \(0.898122\pi\) | |||||||
\(242\) | −10.9282 | −0.702492 | ||||||||
\(243\) | −4.03459 | − | 15.0573i | −0.258819 | − | 0.965926i | ||||
\(244\) | −12.6264 | −0.808322 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 14.4282 | + | 3.86603i | 0.919909 | + | 0.246489i | ||||
\(247\) | −3.92820 | + | 6.80385i | −0.249946 | + | 0.432918i | ||||
\(248\) | −3.34607 | + | 5.79555i | −0.212475 | + | 0.368018i | ||||
\(249\) | 2.95448 | + | 11.0263i | 0.187233 | + | 0.698762i | ||||
\(250\) | −4.62158 | − | 8.00481i | −0.292294 | − | 0.506269i | ||||
\(251\) | 0.795040 | 0.0501824 | 0.0250912 | − | 0.999685i | \(-0.492012\pi\) | ||||
0.0250912 | + | 0.999685i | \(0.492012\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.46410 | −0.0920473 | ||||||||
\(254\) | −6.73205 | − | 11.6603i | −0.422406 | − | 0.731629i | ||||
\(255\) | 8.66115 | − | 8.66115i | 0.542382 | − | 0.542382i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −5.01910 | + | 8.69333i | −0.313083 | + | 0.542275i | −0.979028 | − | 0.203725i | \(-0.934695\pi\) |
0.665945 | + | 0.746001i | \(0.268028\pi\) | |||||||
\(258\) | 0.328169 | − | 0.328169i | 0.0204309 | − | 0.0204309i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.85641 | −0.115129 | ||||||||
\(261\) | 12.0000i | 0.742781i | ||||||||
\(262\) | 10.9348 | 0.675552 | ||||||||
\(263\) | 4.26795 | + | 7.39230i | 0.263173 | + | 0.455829i | 0.967083 | − | 0.254460i | \(-0.0818977\pi\) |
−0.703910 | + | 0.710289i | \(0.748564\pi\) | |||||||
\(264\) | −0.120118 | − | 0.448288i | −0.00739277 | − | 0.0275902i | ||||
\(265\) | 5.65685 | − | 9.79796i | 0.347498 | − | 0.601884i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.8301 | − | 3.16987i | −0.723992 | − | 0.193993i | ||||
\(268\) | −6.23205 | − | 10.7942i | −0.380683 | − | 0.659362i | ||||
\(269\) | −5.65685 | −0.344904 | −0.172452 | − | 0.985018i | \(-0.555169\pi\) | ||||
−0.172452 | + | 0.985018i | \(0.555169\pi\) | |||||||
\(270\) | 3.80385 | + | 3.80385i | 0.231495 | + | 0.231495i | ||||
\(271\) | 13.1069 | 0.796185 | 0.398093 | − | 0.917345i | \(-0.369672\pi\) | ||||
0.398093 | + | 0.917345i | \(0.369672\pi\) | |||||||
\(272\) | 3.41542 | + | 5.91567i | 0.207090 | + | 0.358690i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.33013 | + | 7.50000i | −0.261593 | + | 0.453092i | ||||
\(275\) | −0.526279 | + | 0.911543i | −0.0317358 | + | 0.0549681i | ||||
\(276\) | 2.44949 | + | 9.14162i | 0.147442 | + | 0.550261i | ||||
\(277\) | −15.7321 | − | 27.2487i | −0.945247 | − | 1.63722i | −0.755255 | − | 0.655431i | \(-0.772487\pi\) |
−0.189992 | − | 0.981786i | \(-0.560846\pi\) | |||||||
\(278\) | 0.795040 | 0.0476833 | ||||||||
\(279\) | −17.3867 | + | 10.0382i | −1.04091 | + | 0.600971i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.92820 | − | 15.4641i | −0.532612 | − | 0.922511i | −0.999275 | − | 0.0380757i | \(-0.987877\pi\) |
0.466663 | − | 0.884435i | \(-0.345456\pi\) | |||||||
\(282\) | 0.928203 | − | 0.928203i | 0.0552737 | − | 0.0552737i | ||||
\(283\) | 7.53794 | − | 13.0561i | 0.448084 | − | 0.776104i | −0.550177 | − | 0.835048i | \(-0.685440\pi\) |
0.998261 | + | 0.0589437i | \(0.0187732\pi\) | |||||||
\(284\) | −4.73205 | + | 8.19615i | −0.280796 | + | 0.486352i | ||||
\(285\) | −5.55532 | + | 5.55532i | −0.329069 | + | 0.329069i | ||||
\(286\) | 0.240237 | + | 0.416102i | 0.0142055 | + | 0.0246046i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.59808 | + | 1.50000i | −0.153093 | + | 0.0883883i | ||||
\(289\) | 29.6603 | 1.74472 | ||||||||
\(290\) | −2.07055 | − | 3.58630i | −0.121587 | − | 0.210595i | ||||
\(291\) | −8.13397 | − | 30.3564i | −0.476822 | − | 1.77952i | ||||
\(292\) | −2.70831 | + | 4.69093i | −0.158492 | + | 0.274516i | ||||
\(293\) | 4.62158 | − | 8.00481i | 0.269995 | − | 0.467646i | −0.698865 | − | 0.715254i | \(-0.746311\pi\) |
0.968860 | + | 0.247608i | \(0.0796445\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.660254 | − | 1.14359i | −0.0384415 | − | 0.0665826i | ||||
\(296\) | 7.46410 | 0.433842 | ||||||||
\(297\) | 0.360355 | − | 1.34486i | 0.0209099 | − | 0.0780369i | ||||
\(298\) | 22.9282 | 1.32820 | ||||||||
\(299\) | −4.89898 | − | 8.48528i | −0.283315 | − | 0.490716i | ||||
\(300\) | 6.57201 | + | 1.76097i | 0.379435 | + | 0.101669i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9.19615 | + | 15.9282i | −0.529179 | + | 0.916565i | ||||
\(303\) | −2.19615 | − | 8.19615i | −0.126166 | − | 0.470857i | ||||
\(304\) | −2.19067 | − | 3.79435i | −0.125644 | − | 0.217621i | ||||
\(305\) | 13.0718 | 0.748489 | ||||||||
\(306\) | 20.4925i | 1.17148i | ||||||||
\(307\) | 1.17398 | 0.0670024 | 0.0335012 | − | 0.999439i | \(-0.489334\pi\) | ||||
0.0335012 | + | 0.999439i | \(0.489334\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.1244 | − | 15.1244i | 0.860395 | − | 0.860395i | ||||
\(310\) | 3.46410 | − | 6.00000i | 0.196748 | − | 0.340777i | ||||
\(311\) | 3.72500 | − | 6.45189i | 0.211226 | − | 0.365853i | −0.740873 | − | 0.671645i | \(-0.765588\pi\) |
0.952098 | + | 0.305792i | \(0.0989212\pi\) | |||||||
\(312\) | 2.19615 | − | 2.19615i | 0.124333 | − | 0.124333i | ||||
\(313\) | −3.13801 | − | 5.43520i | −0.177371 | − | 0.307216i | 0.763608 | − | 0.645680i | \(-0.223426\pi\) |
−0.940979 | + | 0.338464i | \(0.890093\pi\) | |||||||
\(314\) | 9.52056 | 0.537276 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.92820 | 0.502251 | ||||||||
\(317\) | 13.0000 | + | 22.5167i | 0.730153 | + | 1.26466i | 0.956818 | + | 0.290689i | \(0.0938844\pi\) |
−0.226665 | + | 0.973973i | \(0.572782\pi\) | |||||||
\(318\) | 4.89898 | + | 18.2832i | 0.274721 | + | 1.02527i | ||||
\(319\) | −0.535898 | + | 0.928203i | −0.0300045 | + | 0.0519694i | ||||
\(320\) | 0.517638 | − | 0.896575i | 0.0289368 | − | 0.0501201i | ||||
\(321\) | 29.0979 | + | 7.79676i | 1.62409 | + | 0.435173i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −29.9282 | −1.66525 | ||||||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | −7.04386 | −0.390723 | ||||||||
\(326\) | 6.66025 | + | 11.5359i | 0.368877 | + | 0.638914i | ||||
\(327\) | −8.24504 | − | 2.20925i | −0.455952 | − | 0.122172i | ||||
\(328\) | 4.31199 | − | 7.46859i | 0.238090 | − | 0.412384i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.124356 | + | 0.464102i | 0.00684555 | + | 0.0255480i | ||||
\(331\) | 5.73205 | + | 9.92820i | 0.315062 | + | 0.545703i | 0.979451 | − | 0.201684i | \(-0.0646413\pi\) |
−0.664389 | + | 0.747387i | \(0.731308\pi\) | |||||||
\(332\) | 6.59059 | 0.361706 | ||||||||
\(333\) | 19.3923 | + | 11.1962i | 1.06269 | + | 0.613545i | ||||
\(334\) | 1.51575 | 0.0829381 | ||||||||
\(335\) | 6.45189 | + | 11.1750i | 0.352505 | + | 0.610556i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.50000 | − | 6.06218i | 0.190657 | − | 0.330228i | −0.754811 | − | 0.655942i | \(-0.772271\pi\) |
0.945468 | + | 0.325714i | \(0.105605\pi\) | |||||||
\(338\) | 4.89230 | − | 8.47372i | 0.266106 | − | 0.460910i | ||||
\(339\) | −8.48528 | + | 8.48528i | −0.460857 | + | 0.460857i | ||||
\(340\) | −3.53590 | − | 6.12436i | −0.191761 | − | 0.332140i | ||||
\(341\) | −1.79315 | −0.0971046 | ||||||||
\(342\) | − | 13.1440i | − | 0.710747i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.133975 | − | 0.232051i | −0.00722343 | − | 0.0125113i | ||||
\(345\) | −2.53590 | − | 9.46410i | −0.136528 | − | 0.509530i | ||||
\(346\) | −3.34607 | + | 5.79555i | −0.179886 | + | 0.311571i | ||||
\(347\) | 4.79423 | − | 8.30385i | 0.257368 | − | 0.445774i | −0.708168 | − | 0.706044i | \(-0.750478\pi\) |
0.965536 | + | 0.260270i | \(0.0838115\pi\) | |||||||
\(348\) | 6.69213 | + | 1.79315i | 0.358736 | + | 0.0961230i | ||||
\(349\) | 4.00240 | + | 6.93237i | 0.214244 | + | 0.371081i | 0.953038 | − | 0.302850i | \(-0.0979380\pi\) |
−0.738795 | + | 0.673931i | \(0.764605\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.00000 | − | 2.41154i | 0.480384 | − | 0.128719i | ||||
\(352\) | −0.267949 | −0.0142817 | ||||||||
\(353\) | −12.5063 | − | 21.6615i | −0.665641 | − | 1.15292i | −0.979111 | − | 0.203327i | \(-0.934825\pi\) |
0.313470 | − | 0.949598i | \(-0.398509\pi\) | |||||||
\(354\) | 2.13397 | + | 0.571797i | 0.113419 | + | 0.0303907i | ||||
\(355\) | 4.89898 | − | 8.48528i | 0.260011 | − | 0.450352i | ||||
\(356\) | −3.53553 | + | 6.12372i | −0.187383 | + | 0.324557i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.53590 | − | 4.39230i | −0.134026 | − | 0.232141i | ||||
\(359\) | 7.46410 | 0.393940 | 0.196970 | − | 0.980409i | \(-0.436890\pi\) | ||||
0.196970 | + | 0.980409i | \(0.436890\pi\) | |||||||
\(360\) | 2.68973 | − | 1.55291i | 0.141761 | − | 0.0818458i | ||||
\(361\) | 0.196152 | 0.0103238 | ||||||||
\(362\) | 8.48528 | + | 14.6969i | 0.445976 | + | 0.772454i | ||||
\(363\) | −13.3843 | + | 13.3843i | −0.702492 | + | 0.702492i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.80385 | − | 4.85641i | 0.146760 | − | 0.254196i | ||||
\(366\) | −15.4641 | + | 15.4641i | −0.808322 | + | 0.808322i | ||||
\(367\) | −9.28032 | − | 16.0740i | −0.484429 | − | 0.839055i | 0.515411 | − | 0.856943i | \(-0.327639\pi\) |
−0.999840 | + | 0.0178877i | \(0.994306\pi\) | |||||||
\(368\) | 5.46410 | 0.284836 | ||||||||
\(369\) | 22.4058 | − | 12.9360i | 1.16640 | − | 0.673420i | ||||
\(370\) | −7.72741 | −0.401729 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.00000 | + | 11.1962i | 0.155543 | + | 0.580493i | ||||
\(373\) | 5.39230 | − | 9.33975i | 0.279203 | − | 0.483594i | −0.691984 | − | 0.721913i | \(-0.743263\pi\) |
0.971187 | + | 0.238319i | \(0.0765964\pi\) | |||||||
\(374\) | −0.915158 | + | 1.58510i | −0.0473217 | + | 0.0819636i | ||||
\(375\) | −15.4641 | − | 4.14359i | −0.798563 | − | 0.213974i | ||||
\(376\) | −0.378937 | − | 0.656339i | −0.0195422 | − | 0.0338481i | ||||
\(377\) | −7.17260 | −0.369408 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.5885 | 0.697992 | 0.348996 | − | 0.937124i | \(-0.386523\pi\) | ||||
0.348996 | + | 0.937124i | \(0.386523\pi\) | |||||||
\(380\) | 2.26795 | + | 3.92820i | 0.116343 | + | 0.201513i | ||||
\(381\) | −22.5259 | − | 6.03579i | −1.15404 | − | 0.309223i | ||||
\(382\) | −7.46410 | + | 12.9282i | −0.381897 | + | 0.661464i | ||||
\(383\) | −13.6617 | + | 23.6627i | −0.698078 | + | 1.20911i | 0.271054 | + | 0.962564i | \(0.412628\pi\) |
−0.969132 | + | 0.246543i | \(0.920705\pi\) | |||||||
\(384\) | 0.448288 | + | 1.67303i | 0.0228766 | + | 0.0853766i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 15.0526 | 0.766155 | ||||||||
\(387\) | − | 0.803848i | − | 0.0408619i | ||||||
\(388\) | −18.1445 | −0.921149 | ||||||||
\(389\) | −4.00000 | − | 6.92820i | −0.202808 | − | 0.351274i | 0.746624 | − | 0.665246i | \(-0.231673\pi\) |
−0.949432 | + | 0.313972i | \(0.898340\pi\) | |||||||
\(390\) | −2.27362 | + | 2.27362i | −0.115129 | + | 0.115129i | ||||
\(391\) | 18.6622 | − | 32.3238i | 0.943787 | − | 1.63469i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.3923 | − | 13.3923i | 0.675552 | − | 0.675552i | ||||
\(394\) | 8.46410 | + | 14.6603i | 0.426415 | + | 0.738573i | ||||
\(395\) | −9.24316 | −0.465074 | ||||||||
\(396\) | −0.696152 | − | 0.401924i | −0.0349830 | − | 0.0201974i | ||||
\(397\) | 13.1069 | 0.657814 | 0.328907 | − | 0.944362i | \(-0.393320\pi\) | ||||
0.328907 | + | 0.944362i | \(0.393320\pi\) | |||||||
\(398\) | −13.1440 | − | 22.7661i | −0.658850 | − | 1.14116i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.96410 | − | 3.40192i | 0.0982051 | − | 0.170096i | ||||
\(401\) | 11.8923 | − | 20.5981i | 0.593873 | − | 1.02862i | −0.399831 | − | 0.916589i | \(-0.630931\pi\) |
0.993705 | − | 0.112030i | \(-0.0357353\pi\) | |||||||
\(402\) | −20.8528 | − | 5.58750i | −1.04005 | − | 0.278679i | ||||
\(403\) | −6.00000 | − | 10.3923i | −0.298881 | − | 0.517678i | ||||
\(404\) | −4.89898 | −0.243733 | ||||||||
\(405\) | 9.31749 | 0.462990 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.00000 | + | 1.73205i | 0.0495682 | + | 0.0858546i | ||||
\(408\) | 11.4282 | + | 3.06218i | 0.565780 | + | 0.151600i | ||||
\(409\) | −2.24144 | + | 3.88229i | −0.110832 | + | 0.191967i | −0.916106 | − | 0.400936i | \(-0.868685\pi\) |
0.805274 | + | 0.592903i | \(0.202018\pi\) | |||||||
\(410\) | −4.46410 | + | 7.73205i | −0.220466 | + | 0.381859i | ||||
\(411\) | 3.88229 | + | 14.4889i | 0.191499 | + | 0.714684i | ||||
\(412\) | −6.17449 | − | 10.6945i | −0.304195 | − | 0.526882i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 14.1962 | + | 8.19615i | 0.697703 | + | 0.402819i | ||||
\(415\) | −6.82309 | −0.334932 | ||||||||
\(416\) | −0.896575 | − | 1.55291i | −0.0439582 | − | 0.0761379i | ||||
\(417\) | 0.973721 | − | 0.973721i | 0.0476833 | − | 0.0476833i | ||||
\(418\) | 0.586988 | − | 1.01669i | 0.0287105 | − | 0.0497281i | ||||
\(419\) | −18.0938 | + | 31.3393i | −0.883939 | + | 1.53103i | −0.0370132 | + | 0.999315i | \(0.511784\pi\) |
−0.846925 | + | 0.531712i | \(0.821549\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.80385 | − | 6.58846i | −0.185388 | − | 0.321102i | 0.758319 | − | 0.651884i | \(-0.226021\pi\) |
−0.943707 | + | 0.330782i | \(0.892688\pi\) | |||||||
\(422\) | 18.9282 | 0.921411 | ||||||||
\(423\) | − | 2.27362i | − | 0.110547i | ||||||
\(424\) | 10.9282 | 0.530720 | ||||||||
\(425\) | −13.4164 | − | 23.2380i | −0.650793 | − | 1.12721i | ||||
\(426\) | 4.24264 | + | 15.8338i | 0.205557 | + | 0.767148i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 8.69615 | − | 15.0622i | 0.420344 | − | 0.728058i | ||||
\(429\) | 0.803848 | + | 0.215390i | 0.0388101 | + | 0.0103991i | ||||
\(430\) | 0.138701 | + | 0.240237i | 0.00668874 | + | 0.0115852i | ||||
\(431\) | −10.1436 | −0.488600 | −0.244300 | − | 0.969700i | \(-0.578558\pi\) | ||||
−0.244300 | + | 0.969700i | \(0.578558\pi\) | |||||||
\(432\) | −1.34486 | + | 5.01910i | −0.0647048 | + | 0.241481i | ||||
\(433\) | −19.8362 | −0.953265 | −0.476632 | − | 0.879103i | \(-0.658143\pi\) | ||||
−0.476632 | + | 0.879103i | \(0.658143\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.92820 | − | 1.85641i | −0.332182 | − | 0.0890079i | ||||
\(436\) | −2.46410 | + | 4.26795i | −0.118009 | + | 0.204398i | ||||
\(437\) | −11.9700 | + | 20.7327i | −0.572605 | + | 0.991781i | ||||
\(438\) | 2.42820 | + | 9.06218i | 0.116024 | + | 0.433008i | ||||
\(439\) | −9.79796 | − | 16.9706i | −0.467631 | − | 0.809961i | 0.531685 | − | 0.846942i | \(-0.321559\pi\) |
−0.999316 | + | 0.0369815i | \(0.988226\pi\) | |||||||
\(440\) | 0.277401 | 0.0132246 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.2487 | −0.582612 | ||||||||
\(443\) | −8.16025 | − | 14.1340i | −0.387705 | − | 0.671525i | 0.604435 | − | 0.796654i | \(-0.293399\pi\) |
−0.992140 | + | 0.125129i | \(0.960066\pi\) | |||||||
\(444\) | 9.14162 | − | 9.14162i | 0.433842 | − | 0.433842i | ||||
\(445\) | 3.66025 | − | 6.33975i | 0.173513 | − | 0.300533i | ||||
\(446\) | 3.58630 | − | 6.21166i | 0.169816 | − | 0.294130i | ||||
\(447\) | 28.0812 | − | 28.0812i | 1.32820 | − | 1.32820i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.7846 | 1.12247 | 0.561233 | − | 0.827658i | \(-0.310327\pi\) | ||||
0.561233 | + | 0.827658i | \(0.310327\pi\) | |||||||
\(450\) | 10.2058 | − | 5.89230i | 0.481105 | − | 0.277766i | ||||
\(451\) | 2.31079 | 0.108811 | ||||||||
\(452\) | 3.46410 | + | 6.00000i | 0.162938 | + | 0.282216i | ||||
\(453\) | 8.24504 | + | 30.7709i | 0.387386 | + | 1.44574i | ||||
\(454\) | 13.8325 | − | 23.9587i | 0.649194 | − | 1.12444i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.33013 | − | 1.96410i | −0.343265 | − | 0.0919775i | ||||
\(457\) | 15.5263 | + | 26.8923i | 0.726289 | + | 1.25797i | 0.958441 | + | 0.285290i | \(0.0920898\pi\) |
−0.232153 | + | 0.972679i | \(0.574577\pi\) | |||||||
\(458\) | 0.480473 | 0.0224510 | ||||||||
\(459\) | 25.0981 | + | 25.0981i | 1.17148 | + | 1.17148i | ||||
\(460\) | −5.65685 | −0.263752 | ||||||||
\(461\) | 5.51815 | + | 9.55772i | 0.257006 | + | 0.445148i | 0.965438 | − | 0.260631i | \(-0.0839306\pi\) |
−0.708432 | + | 0.705779i | \(0.750597\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.3205 | − | 26.5359i | 0.712004 | − | 1.23323i | −0.252099 | − | 0.967701i | \(-0.581121\pi\) |
0.964104 | − | 0.265526i | \(-0.0855457\pi\) | |||||||
\(464\) | 2.00000 | − | 3.46410i | 0.0928477 | − | 0.160817i | ||||
\(465\) | −3.10583 | − | 11.5911i | −0.144029 | − | 0.537525i | ||||
\(466\) | −0.0621778 | − | 0.107695i | −0.00288033 | − | 0.00498888i | ||||
\(467\) | 9.17878 | 0.424744 | 0.212372 | − | 0.977189i | \(-0.431881\pi\) | ||||
0.212372 | + | 0.977189i | \(0.431881\pi\) | |||||||
\(468\) | − | 5.37945i | − | 0.248665i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.392305 | + | 0.679492i | 0.0180957 | + | 0.0313426i | ||||
\(471\) | 11.6603 | − | 11.6603i | 0.537276 | − | 0.537276i | ||||
\(472\) | 0.637756 | − | 1.10463i | 0.0293551 | − | 0.0508446i | ||||
\(473\) | 0.0358984 | − | 0.0621778i | 0.00165061 | − | 0.00285894i | ||||
\(474\) | 10.9348 | − | 10.9348i | 0.502251 | − | 0.502251i | ||||
\(475\) | 8.60540 | + | 14.9050i | 0.394843 | + | 0.683888i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 28.3923 | + | 16.3923i | 1.29999 | + | 0.750552i | ||||
\(478\) | 0.928203 | 0.0424550 | ||||||||
\(479\) | 2.07055 | + | 3.58630i | 0.0946060 | + | 0.163862i | 0.909444 | − | 0.415826i | \(-0.136508\pi\) |
−0.814838 | + | 0.579689i | \(0.803174\pi\) | |||||||
\(480\) | −0.464102 | − | 1.73205i | −0.0211832 | − | 0.0790569i | ||||
\(481\) | −6.69213 | + | 11.5911i | −0.305135 | + | 0.528509i | ||||
\(482\) | −3.13801 | + | 5.43520i | −0.142933 | + | 0.247567i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.46410 | + | 9.46410i | 0.248368 | + | 0.430186i | ||||
\(485\) | 18.7846 | 0.852965 | ||||||||
\(486\) | −11.0227 | + | 11.0227i | −0.500000 | + | 0.500000i | ||||
\(487\) | −2.78461 | −0.126183 | −0.0630914 | − | 0.998008i | \(-0.520096\pi\) | ||||
−0.0630914 | + | 0.998008i | \(0.520096\pi\) | |||||||
\(488\) | 6.31319 | + | 10.9348i | 0.285785 | + | 0.494994i | ||||
\(489\) | 22.2856 | + | 5.97142i | 1.00779 | + | 0.270037i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.69615 | + | 16.7942i | −0.437581 | + | 0.757913i | −0.997502 | − | 0.0706330i | \(-0.977498\pi\) |
0.559921 | + | 0.828546i | \(0.310831\pi\) | |||||||
\(492\) | −3.86603 | − | 14.4282i | −0.174294 | − | 0.650474i | ||||
\(493\) | −13.6617 | − | 23.6627i | −0.615290 | − | 1.06571i | ||||
\(494\) | 7.85641 | 0.353476 | ||||||||
\(495\) | 0.720710 | + | 0.416102i | 0.0323935 | + | 0.0187024i | ||||
\(496\) | 6.69213 | 0.300486 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 8.07180 | − | 8.07180i | 0.361706 | − | 0.361706i | ||||
\(499\) | −16.6962 | + | 28.9186i | −0.747422 | + | 1.29457i | 0.201632 | + | 0.979461i | \(0.435376\pi\) |
−0.949054 | + | 0.315112i | \(0.897958\pi\) | |||||||
\(500\) | −4.62158 | + | 8.00481i | −0.206683 | + | 0.357986i | ||||
\(501\) | 1.85641 | − | 1.85641i | 0.0829381 | − | 0.0829381i | ||||
\(502\) | −0.397520 | − | 0.688524i | −0.0177422 | − | 0.0307303i | ||||
\(503\) | −12.3490 | −0.550614 | −0.275307 | − | 0.961356i | \(-0.588780\pi\) | ||||
−0.275307 | + | 0.961356i | \(0.588780\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.07180 | 0.225692 | ||||||||
\(506\) | 0.732051 | + | 1.26795i | 0.0325436 | + | 0.0563672i | ||||
\(507\) | −4.38632 | − | 16.3700i | −0.194803 | − | 0.727016i | ||||
\(508\) | −6.73205 | + | 11.6603i | −0.298686 | + | 0.517340i | ||||
\(509\) | −10.7961 | + | 18.6993i | −0.478527 | + | 0.828834i | −0.999697 | − | 0.0246194i | \(-0.992163\pi\) |
0.521169 | + | 0.853453i | \(0.325496\pi\) | |||||||
\(510\) | −11.8313 | − | 3.17020i | −0.523901 | − | 0.140379i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −16.0981 | − | 16.0981i | −0.710747 | − | 0.710747i | ||||
\(514\) | 10.0382 | 0.442766 | ||||||||
\(515\) | 6.39230 | + | 11.0718i | 0.281679 | + | 0.487882i | ||||
\(516\) | −0.448288 | − | 0.120118i | −0.0197348 | − | 0.00528791i | ||||
\(517\) | 0.101536 | − | 0.175865i | 0.00446555 | − | 0.00773455i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.00000 | + | 11.1962i | 0.131685 | + | 0.491457i | ||||
\(520\) | 0.928203 | + | 1.60770i | 0.0407044 | + | 0.0705021i | ||||
\(521\) | −33.7752 | −1.47972 | −0.739860 | − | 0.672761i | \(-0.765108\pi\) | ||||
−0.739860 | + | 0.672761i | \(0.765108\pi\) | |||||||
\(522\) | 10.3923 | − | 6.00000i | 0.454859 | − | 0.262613i | ||||
\(523\) | 20.7327 | 0.906579 | 0.453289 | − | 0.891363i | \(-0.350250\pi\) | ||||
0.453289 | + | 0.891363i | \(0.350250\pi\) | |||||||
\(524\) | −5.46739 | − | 9.46979i | −0.238844 | − | 0.413690i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.26795 | − | 7.39230i | 0.186091 | − | 0.322320i | ||||
\(527\) | 22.8564 | − | 39.5885i | 0.995641 | − | 1.72450i | ||||
\(528\) | −0.328169 | + | 0.328169i | −0.0142817 | + | 0.0142817i | ||||
\(529\) | −3.42820 | − | 5.93782i | −0.149052 | − | 0.258166i | ||||
\(530\) | −11.3137 | −0.491436 | ||||||||
\(531\) | 3.31388 | − | 1.91327i | 0.143810 | − | 0.0830288i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.73205 | + | 13.3923i | 0.334912 | + | 0.580085i | ||||
\(534\) | 3.16987 | + | 11.8301i | 0.137174 | + | 0.511940i | ||||
\(535\) | −9.00292 | + | 15.5935i | −0.389230 | + | 0.674166i | ||||
\(536\) | −6.23205 | + | 10.7942i | −0.269184 | + | 0.466240i | ||||
\(537\) | −8.48528 | − | 2.27362i | −0.366167 | − | 0.0981141i | ||||
\(538\) | 2.82843 | + | 4.89898i | 0.121942 | + | 0.211210i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.39230 | − | 5.19615i | 0.0599153 | − | 0.223607i | ||||
\(541\) | 15.3205 | 0.658680 | 0.329340 | − | 0.944211i | \(-0.393174\pi\) | ||||
0.329340 | + | 0.944211i | \(0.393174\pi\) | |||||||
\(542\) | −6.55343 | − | 11.3509i | −0.281494 | − | 0.487562i | ||||
\(543\) | 28.3923 | + | 7.60770i | 1.21843 | + | 0.326477i | ||||
\(544\) | 3.41542 | − | 5.91567i | 0.146435 | − | 0.253632i | ||||
\(545\) | 2.55103 | − | 4.41851i | 0.109274 | − | 0.189268i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.1865 | − | 29.7679i | −0.734843 | − | 1.27279i | −0.954792 | − | 0.297274i | \(-0.903922\pi\) |
0.219949 | − | 0.975511i | \(-0.429411\pi\) | |||||||
\(548\) | 8.66025 | 0.369948 | ||||||||
\(549\) | 37.8792i | 1.61664i | ||||||||
\(550\) | 1.05256 | 0.0448813 | ||||||||
\(551\) | 8.76268 | + | 15.1774i | 0.373303 | + | 0.646579i | ||||
\(552\) | 6.69213 | − | 6.69213i | 0.284836 | − | 0.284836i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −15.7321 | + | 27.2487i | −0.668391 | + | 1.15769i | ||||
\(555\) | −9.46410 | + | 9.46410i | −0.401729 | + | 0.401729i | ||||
\(556\) | −0.397520 | − | 0.688524i | −0.0168586 | − | 0.0291999i | ||||
\(557\) | −6.92820 | −0.293557 | −0.146779 | − | 0.989169i | \(-0.546891\pi\) | ||||
−0.146779 | + | 0.989169i | \(0.546891\pi\) | |||||||
\(558\) | 17.3867 | + | 10.0382i | 0.736036 | + | 0.424951i | ||||
\(559\) | 0.480473 | 0.0203219 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.820508 | + | 3.06218i | 0.0346419 | + | 0.129285i | ||||
\(562\) | −8.92820 | + | 15.4641i | −0.376614 | + | 0.652314i | ||||
\(563\) | 9.12304 | − | 15.8016i | 0.384490 | − | 0.665957i | −0.607208 | − | 0.794543i | \(-0.707711\pi\) |
0.991698 | + | 0.128586i | \(0.0410439\pi\) | |||||||
\(564\) | −1.26795 | − | 0.339746i | −0.0533903 | − | 0.0143059i | ||||
\(565\) | −3.58630 | − | 6.21166i | −0.150877 | − | 0.261326i | ||||
\(566\) | −15.0759 | −0.633686 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.46410 | 0.397105 | ||||||||
\(569\) | 12.8923 | + | 22.3301i | 0.540474 | + | 0.936128i | 0.998877 | + | 0.0473833i | \(0.0150882\pi\) |
−0.458403 | + | 0.888744i | \(0.651578\pi\) | |||||||
\(570\) | 7.58871 | + | 2.03339i | 0.317856 | + | 0.0851692i | ||||
\(571\) | 16.5263 | − | 28.6244i | 0.691603 | − | 1.19789i | −0.279709 | − | 0.960085i | \(-0.590238\pi\) |
0.971312 | − | 0.237807i | \(-0.0764286\pi\) | |||||||
\(572\) | 0.240237 | − | 0.416102i | 0.0100448 | − | 0.0173981i | ||||
\(573\) | 6.69213 | + | 24.9754i | 0.279568 | + | 1.04336i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.4641 | −0.895115 | ||||||||
\(576\) | 2.59808 | + | 1.50000i | 0.108253 | + | 0.0625000i | ||||
\(577\) | −27.4892 | −1.14439 | −0.572196 | − | 0.820117i | \(-0.693908\pi\) | ||||
−0.572196 | + | 0.820117i | \(0.693908\pi\) | |||||||
\(578\) | −14.8301 | − | 25.6865i | −0.616852 | − | 1.06842i | ||||
\(579\) | 18.4355 | − | 18.4355i | 0.766155 | − | 0.766155i | ||||
\(580\) | −2.07055 | + | 3.58630i | −0.0859750 | + | 0.148913i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −22.2224 | + | 22.2224i | −0.921149 | + | 0.921149i | ||||
\(583\) | 1.46410 | + | 2.53590i | 0.0606369 | + | 0.105026i | ||||
\(584\) | 5.41662 | 0.224141 | ||||||||
\(585\) | 5.56922i | 0.230259i | ||||||||
\(586\) | −9.24316 | −0.381831 | ||||||||
\(587\) | 20.9408 | + | 36.2705i | 0.864319 | + | 1.49704i | 0.867722 | + | 0.497049i | \(0.165583\pi\) |
−0.00340370 | + | 0.999994i | \(0.501083\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.6603 | + | 25.3923i | −0.604065 | + | 1.04627i | ||||
\(590\) | −0.660254 | + | 1.14359i | −0.0271822 | + | 0.0470810i | ||||
\(591\) | 28.3214 | + | 7.58871i | 1.16499 | + | 0.312158i | ||||
\(592\) | −3.73205 | − | 6.46410i | −0.153386 | − | 0.265673i | ||||
\(593\) | 16.8690 | 0.692728 | 0.346364 | − | 0.938100i | \(-0.387416\pi\) | ||||
0.346364 | + | 0.938100i | \(0.387416\pi\) | |||||||
\(594\) | −1.34486 | + | 0.360355i | −0.0551804 | + | 0.0147855i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.4641 | − | 19.8564i | −0.469588 | − | 0.813350i | ||||
\(597\) | −43.9808 | − | 11.7846i | −1.80001 | − | 0.482312i | ||||
\(598\) | −4.89898 | + | 8.48528i | −0.200334 | + | 0.346989i | ||||
\(599\) | −2.39230 | + | 4.14359i | −0.0977469 | + | 0.169303i | −0.910752 | − | 0.412954i | \(-0.864497\pi\) |
0.813005 | + | 0.582257i | \(0.197830\pi\) | |||||||
\(600\) | −1.76097 | − | 6.57201i | −0.0718911 | − | 0.268301i | ||||
\(601\) | 1.67303 | + | 2.89778i | 0.0682444 | + | 0.118203i | 0.898129 | − | 0.439733i | \(-0.144927\pi\) |
−0.829884 | + | 0.557936i | \(0.811594\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −32.3827 | + | 18.6962i | −1.31872 | + | 0.761366i | ||||
\(604\) | 18.3923 | 0.748372 | ||||||||
\(605\) | −5.65685 | − | 9.79796i | −0.229984 | − | 0.398344i | ||||
\(606\) | −6.00000 | + | 6.00000i | −0.243733 | + | 0.243733i | ||||
\(607\) | 1.13681 | − | 1.96902i | 0.0461418 | − | 0.0799199i | −0.842032 | − | 0.539427i | \(-0.818641\pi\) |
0.888174 | + | 0.459507i | \(0.151974\pi\) | |||||||
\(608\) | −2.19067 | + | 3.79435i | −0.0888434 | + | 0.153881i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.53590 | − | 11.3205i | −0.264631 | − | 0.458354i | ||||
\(611\) | 1.35898 | 0.0549786 | ||||||||
\(612\) | 17.7470 | − | 10.2462i | 0.717381 | − | 0.414180i | ||||
\(613\) | 24.9282 | 1.00684 | 0.503420 | − | 0.864042i | \(-0.332075\pi\) | ||||
0.503420 | + | 0.864042i | \(0.332075\pi\) | |||||||
\(614\) | −0.586988 | − | 1.01669i | −0.0236889 | − | 0.0410304i | ||||
\(615\) | 4.00240 | + | 14.9372i | 0.161393 | + | 0.602325i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.57180 | − | 2.72243i | 0.0632782 | − | 0.109601i | −0.832651 | − | 0.553798i | \(-0.813178\pi\) |
0.895929 | + | 0.444197i | \(0.146511\pi\) | |||||||
\(618\) | −20.6603 | − | 5.53590i | −0.831077 | − | 0.222686i | ||||
\(619\) | 15.8523 | + | 27.4570i | 0.637159 | + | 1.10359i | 0.986053 | + | 0.166430i | \(0.0532239\pi\) |
−0.348894 | + | 0.937162i | \(0.613443\pi\) | |||||||
\(620\) | −6.92820 | −0.278243 | ||||||||
\(621\) | 27.4249 | − | 7.34847i | 1.10052 | − | 0.294884i | ||||
\(622\) | −7.45001 | −0.298718 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.00000 | − | 0.803848i | −0.120096 | − | 0.0321797i | ||||
\(625\) | −5.03590 | + | 8.72243i | −0.201436 | + | 0.348897i | ||||
\(626\) | −3.13801 | + | 5.43520i | −0.125420 | + | 0.217234i | ||||
\(627\) | −0.526279 | − | 1.96410i | −0.0210176 | − | 0.0784387i | ||||
\(628\) | −4.76028 | − | 8.24504i | −0.189956 | − | 0.329013i | ||||
\(629\) | −50.9860 | −2.03295 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.7128 | −0.784755 | −0.392377 | − | 0.919804i | \(-0.628347\pi\) | ||||
−0.392377 | + | 0.919804i | \(0.628347\pi\) | |||||||
\(632\) | −4.46410 | − | 7.73205i | −0.177572 | − | 0.307564i | ||||
\(633\) | 23.1822 | − | 23.1822i | 0.921411 | − | 0.921411i | ||||
\(634\) | 13.0000 | − | 22.5167i | 0.516296 | − | 0.894251i | ||||
\(635\) | 6.96953 | − | 12.0716i | 0.276577 | − | 0.479046i | ||||
\(636\) | 13.3843 | − | 13.3843i | 0.530720 | − | 0.530720i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.07180 | 0.0424328 | ||||||||
\(639\) | 24.5885 | + | 14.1962i | 0.972704 | + | 0.561591i | ||||
\(640\) | −1.03528 | −0.0409229 | ||||||||
\(641\) | −2.03590 | − | 3.52628i | −0.0804132 | − | 0.139280i | 0.823014 | − | 0.568021i | \(-0.192291\pi\) |
−0.903427 | + | 0.428741i | \(0.858957\pi\) | |||||||
\(642\) | −7.79676 | − | 29.0979i | −0.307713 | − | 1.14840i | ||||
\(643\) | 22.4565 | − | 38.8959i | 0.885599 | − | 1.53390i | 0.0405737 | − | 0.999177i | \(-0.487081\pi\) |
0.845025 | − | 0.534726i | \(-0.179585\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.464102 | + | 0.124356i | 0.0182740 | + | 0.00489650i | ||||
\(646\) | 14.9641 | + | 25.9186i | 0.588755 | + | 1.01975i | ||||
\(647\) | 21.8695 | 0.859780 | 0.429890 | − | 0.902881i | \(-0.358552\pi\) | ||||
0.429890 | + | 0.902881i | \(0.358552\pi\) | |||||||
\(648\) | 4.50000 | + | 7.79423i | 0.176777 | + | 0.306186i | ||||
\(649\) | 0.341773 | 0.0134157 | ||||||||
\(650\) | 3.52193 | + | 6.10016i | 0.138141 | + | 0.239268i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.66025 | − | 11.5359i | 0.260836 | − | 0.451781i | ||||
\(653\) | −3.00000 | + | 5.19615i | −0.117399 | + | 0.203341i | −0.918736 | − | 0.394872i | \(-0.870789\pi\) |
0.801337 | + | 0.598213i | \(0.204122\pi\) | |||||||
\(654\) | 2.20925 | + | 8.24504i | 0.0863886 | + | 0.322407i | ||||
\(655\) | 5.66025 | + | 9.80385i | 0.221164 | + | 0.383068i | ||||
\(656\) | −8.62398 | −0.336710 | ||||||||
\(657\) | 14.0728 | + | 8.12493i | 0.549032 | + | 0.316984i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.1244 | + | 41.7846i | 0.939751 | + | 1.62770i | 0.765934 | + | 0.642919i | \(0.222277\pi\) |
0.173818 | + | 0.984778i | \(0.444390\pi\) | |||||||
\(660\) | 0.339746 | − | 0.339746i | 0.0132246 | − | 0.0132246i | ||||
\(661\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(662\) | 5.73205 | − | 9.92820i | 0.222782 | − | 0.385871i | ||||
\(663\) | −15.0015 | + | 15.0015i | −0.582612 | + | 0.582612i | ||||
\(664\) | −3.29530 | − | 5.70762i | −0.127882 | − | 0.221499i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 22.3923i | − | 0.867684i | ||||||
\(667\) | −21.8564 | −0.846283 | ||||||||
\(668\) | −0.757875 | − | 1.31268i | −0.0293231 | − | 0.0507890i | ||||
\(669\) | −3.21539 | − | 12.0000i | −0.124314 | − | 0.463947i | ||||
\(670\) | 6.45189 | − | 11.1750i | 0.249258 | − | 0.431728i | ||||
\(671\) | −1.69161 | + | 2.92996i | −0.0653041 | + | 0.113110i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.7846 | − | 36.0000i | −0.801188 | − | 1.38770i | −0.918835 | − | 0.394643i | \(-0.870868\pi\) |
0.117647 | − | 0.993055i | \(-0.462465\pi\) | |||||||
\(674\) | −7.00000 | −0.269630 | ||||||||
\(675\) | 5.28290 | − | 19.7160i | 0.203339 | − | 0.758871i | ||||
\(676\) | −9.78461 | −0.376331 | ||||||||
\(677\) | 2.68973 | + | 4.65874i | 0.103375 | + | 0.179050i | 0.913073 | − | 0.407796i | \(-0.133703\pi\) |
−0.809698 | + | 0.586846i | \(0.800369\pi\) | |||||||
\(678\) | 11.5911 | + | 3.10583i | 0.445154 | + | 0.119279i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.53590 | + | 6.12436i | −0.135596 | + | 0.234858i | ||||
\(681\) | −12.4019 | − | 46.2846i | −0.475243 | − | 1.77363i | ||||
\(682\) | 0.896575 | + | 1.55291i | 0.0343316 | + | 0.0594642i | ||||
\(683\) | −38.3205 | −1.46629 | −0.733147 | − | 0.680070i | \(-0.761949\pi\) | ||||
−0.733147 | + | 0.680070i | \(0.761949\pi\) | |||||||
\(684\) | −11.3831 | + | 6.57201i | −0.435242 | + | 0.251287i | ||||
\(685\) | −8.96575 | −0.342564 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.588457 | − | 0.588457i | 0.0224510 | − | 0.0224510i | ||||
\(688\) | −0.133975 | + | 0.232051i | −0.00510773 | + | 0.00884685i | ||||
\(689\) | −9.79796 | + | 16.9706i | −0.373273 | + | 0.646527i | ||||
\(690\) | −6.92820 | + | 6.92820i | −0.263752 | + | 0.263752i | ||||
\(691\) | −12.1595 | − | 21.0609i | −0.462570 | − | 0.801194i | 0.536518 | − | 0.843889i | \(-0.319739\pi\) |
−0.999088 | + | 0.0426942i | \(0.986406\pi\) | |||||||
\(692\) | 6.69213 | 0.254397 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.58846 | −0.363973 | ||||||||
\(695\) | 0.411543 | + | 0.712813i | 0.0156107 | + | 0.0270385i | ||||
\(696\) | −1.79315 | − | 6.69213i | −0.0679692 | − | 0.253665i | ||||
\(697\) | −29.4545 | + | 51.0167i | −1.11567 | + | 1.93239i | ||||
\(698\) | 4.00240 | − | 6.93237i | 0.151493 | − | 0.262394i | ||||
\(699\) | −0.208051 | − | 0.0557471i | −0.00786921 | − | 0.00210855i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.7846 | −0.785024 | −0.392512 | − | 0.919747i | \(-0.628394\pi\) | ||||
−0.392512 | + | 0.919747i | \(0.628394\pi\) | |||||||
\(702\) | −6.58846 | − | 6.58846i | −0.248665 | − | 0.248665i | ||||
\(703\) | 32.7028 | 1.23341 | ||||||||
\(704\) | 0.133975 | + | 0.232051i | 0.00504936 | + | 0.00874574i | ||||
\(705\) | 1.31268 | + | 0.351731i | 0.0494383 | + | 0.0132470i | ||||
\(706\) | −12.5063 | + | 21.6615i | −0.470680 | + | 0.815241i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.571797 | − | 2.13397i | −0.0214894 | − | 0.0801997i | ||||
\(709\) | 6.19615 | + | 10.7321i | 0.232701 | + | 0.403051i | 0.958602 | − | 0.284749i | \(-0.0919102\pi\) |
−0.725901 | + | 0.687799i | \(0.758577\pi\) | |||||||
\(710\) | −9.79796 | −0.367711 | ||||||||
\(711\) | − | 26.7846i | − | 1.00450i | ||||||
\(712\) | 7.07107 | 0.264999 | ||||||||
\(713\) | −18.2832 | − | 31.6675i | −0.684713 | − | 1.18596i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.248711 | + | 0.430781i | −0.00930128 | + | 0.0161103i | ||||
\(716\) | −2.53590 | + | 4.39230i | −0.0947710 | + | 0.164148i | ||||
\(717\) | 1.13681 | − | 1.13681i | 0.0424550 | − | 0.0424550i | ||||
\(718\) | −3.73205 | − | 6.46410i | −0.139279 | − | 0.241238i | ||||
\(719\) | −49.6733 | −1.85250 | −0.926251 | − | 0.376906i | \(-0.876988\pi\) | ||||
−0.926251 | + | 0.376906i | \(0.876988\pi\) | |||||||
\(720\) | −2.68973 | − | 1.55291i | −0.100240 | − | 0.0578737i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.0980762 | − | 0.169873i | −0.00365002 | − | 0.00632202i | ||||
\(723\) | 2.81347 | + | 10.5000i | 0.104634 | + | 0.390499i | ||||
\(724\) | 8.48528 | − | 14.6969i | 0.315353 | − | 0.546207i | ||||
\(725\) | −7.85641 | + | 13.6077i | −0.291780 | + | 0.505377i | ||||
\(726\) | 18.2832 | + | 4.89898i | 0.678555 | + | 0.181818i | ||||
\(727\) | −16.3514 | − | 28.3214i | −0.606439 | − | 1.05038i | −0.991822 | − | 0.127627i | \(-0.959264\pi\) |
0.385383 | − | 0.922757i | \(-0.374069\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 1.00000i | ||||||||
\(730\) | −5.60770 | −0.207550 | ||||||||
\(731\) | 0.915158 | + | 1.58510i | 0.0338483 | + | 0.0586270i | ||||
\(732\) | 21.1244 | + | 5.66025i | 0.780779 | + | 0.209209i | ||||
\(733\) | −4.00240 | + | 6.93237i | −0.147832 | + | 0.256053i | −0.930426 | − | 0.366480i | \(-0.880563\pi\) |
0.782594 | + | 0.622533i | \(0.213896\pi\) | |||||||
\(734\) | −9.28032 | + | 16.0740i | −0.342543 | + | 0.593302i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.73205 | − | 4.73205i | −0.100705 | − | 0.174426i | ||||
\(737\) | −3.33975 | −0.123021 | ||||||||
\(738\) | −22.4058 | − | 12.9360i | −0.824768 | − | 0.476180i | ||||
\(739\) | 6.12436 | 0.225288 | 0.112644 | − | 0.993635i | \(-0.464068\pi\) | ||||
0.112644 | + | 0.993635i | \(0.464068\pi\) | |||||||
\(740\) | 3.86370 | + | 6.69213i | 0.142033 | + | 0.246008i | ||||
\(741\) | 9.62209 | − | 9.62209i | 0.353476 | − | 0.353476i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.7846 | − | 27.3397i | 0.579081 | − | 1.00300i | −0.416504 | − | 0.909134i | \(-0.636745\pi\) |
0.995585 | − | 0.0938641i | \(-0.0299219\pi\) | |||||||
\(744\) | 8.19615 | − | 8.19615i | 0.300486 | − | 0.300486i | ||||
\(745\) | 11.8685 | + | 20.5569i | 0.434829 | + | 0.753145i | ||||
\(746\) | −10.7846 | −0.394853 | ||||||||
\(747\) | − | 19.7718i | − | 0.723412i | ||||||
\(748\) | 1.83032 | 0.0669230 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 4.14359 | + | 15.4641i | 0.151303 | + | 0.564669i | ||||
\(751\) | −17.3923 | + | 30.1244i | −0.634654 | + | 1.09925i | 0.351934 | + | 0.936025i | \(0.385524\pi\) |
−0.986588 | + | 0.163229i | \(0.947809\pi\) | |||||||
\(752\) | −0.378937 | + | 0.656339i | −0.0138184 | + | 0.0239342i | ||||
\(753\) | −1.33013 | − | 0.356406i | −0.0484725 | − | 0.0129882i | ||||
\(754\) | 3.58630 | + | 6.21166i | 0.130605 | + | 0.226215i | ||||
\(755\) | −19.0411 | −0.692977 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.3205 | 0.702216 | 0.351108 | − | 0.936335i | \(-0.385805\pi\) | ||||
0.351108 | + | 0.936335i | \(0.385805\pi\) | |||||||
\(758\) | −6.79423 | − | 11.7679i | −0.246777 | − | 0.427431i | ||||
\(759\) | 2.44949 | + | 0.656339i | 0.0889108 | + | 0.0238236i | ||||
\(760\) | 2.26795 | − | 3.92820i | 0.0822672 | − | 0.142491i | ||||
\(761\) | 20.1272 | − | 34.8613i | 0.729609 | − | 1.26372i | −0.227440 | − | 0.973792i | \(-0.573035\pi\) |
0.957049 | − | 0.289928i | \(-0.0936312\pi\) | |||||||
\(762\) | 6.03579 | + | 22.5259i | 0.218654 | + | 0.816027i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 14.9282 | 0.540083 | ||||||||
\(765\) | −18.3731 | + | 10.6077i | −0.664280 | + | 0.383522i | ||||
\(766\) | 27.3233 | 0.987232 | ||||||||
\(767\) | 1.14359 | + | 1.98076i | 0.0412928 | + | 0.0715212i | ||||
\(768\) | 1.22474 | − | 1.22474i | 0.0441942 | − | 0.0441942i | ||||
\(769\) | −19.0919 | + | 33.0681i | −0.688471 | + | 1.19247i | 0.283862 | + | 0.958865i | \(0.408384\pi\) |
−0.972332 | + | 0.233601i | \(0.924949\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.2942 | − | 12.2942i | 0.442766 | − | 0.442766i | ||||
\(772\) | −7.52628 | − | 13.0359i | −0.270877 | − | 0.469172i | ||||
\(773\) | 39.3949 | 1.41694 | 0.708468 | − | 0.705743i | \(-0.249387\pi\) | ||||
0.708468 | + | 0.705743i | \(0.249387\pi\) | |||||||
\(774\) | −0.696152 | + | 0.401924i | −0.0250227 | + | 0.0144469i | ||||
\(775\) | −26.2880 | −0.944295 | ||||||||
\(776\) | 9.07227 | + | 15.7136i | 0.325676 | + | 0.564087i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.00000 | + | 6.92820i | −0.143407 | + | 0.248388i | ||||
\(779\) | 18.8923 | − | 32.7224i | 0.676887 | − | 1.17240i | ||||
\(780\) | 3.10583 | + | 0.832204i | 0.111207 | + | 0.0297977i | ||||
\(781\) | 1.26795 | + | 2.19615i | 0.0453708 | + | 0.0785845i | ||||
\(782\) | −37.3244 | −1.33472 | ||||||||
\(783\) | 5.37945 | − | 20.0764i | 0.192246 | − | 0.717472i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.92820 | + | 8.53590i | 0.175895 | + | 0.304659i | ||||
\(786\) | −18.2942 | − | 4.90192i | −0.652534 | − | 0.174846i | ||||
\(787\) | −3.57270 | + | 6.18810i | −0.127353 | + | 0.220582i | −0.922650 | − | 0.385638i | \(-0.873981\pi\) |
0.795297 | + | 0.606220i | \(0.207315\pi\) | |||||||
\(788\) | 8.46410 | − | 14.6603i | 0.301521 | − | 0.522250i | ||||
\(789\) | −3.82654 | − | 14.2808i | −0.136228 | − | 0.508411i | ||||
\(790\) | 4.62158 | + | 8.00481i | 0.164428 | + | 0.284798i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.803848i | 0.0285635i | ||||||||
\(793\) | −22.6410 | −0.804006 | ||||||||
\(794\) | −6.55343 | − | 11.3509i | −0.232573 | − | 0.402827i | ||||
\(795\) | −13.8564 | + | 13.8564i | −0.491436 | + | 0.491436i | ||||
\(796\) | −13.1440 | + | 22.7661i | −0.465878 | + | 0.806924i | ||||
\(797\) | 18.9396 | − | 32.8043i | 0.670874 | − | 1.16199i | −0.306782 | − | 0.951780i | \(-0.599252\pi\) |
0.977657 | − | 0.210209i | \(-0.0674143\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.58846 | + | 4.48334i | 0.0915730 | + | 0.158609i | ||||
\(800\) | −3.92820 | −0.138883 | ||||||||
\(801\) | 18.3712 | + | 10.6066i | 0.649113 | + | 0.374766i | ||||
\(802\) | −23.7846 | −0.839864 | ||||||||
\(803\) | 0.725689 | + | 1.25693i | 0.0256090 | + | 0.0443561i | ||||
\(804\) | 5.58750 | + | 20.8528i | 0.197056 | + | 0.735423i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.00000 | + | 10.3923i | −0.211341 | + | 0.366053i | ||||
\(807\) | 9.46410 | + | 2.53590i | 0.333152 | + | 0.0892679i | ||||
\(808\) | 2.44949 | + | 4.24264i | 0.0861727 | + | 0.149256i | ||||
\(809\) | −29.7321 | −1.04532 | −0.522662 | − | 0.852540i | \(-0.675061\pi\) | ||||
−0.522662 | + | 0.852540i | \(0.675061\pi\) | |||||||
\(810\) | −4.65874 | − | 8.06918i | −0.163692 | − | 0.283522i | ||||
\(811\) | −24.9110 | −0.874744 | −0.437372 | − | 0.899281i | \(-0.644091\pi\) | ||||
−0.437372 | + | 0.899281i | \(0.644091\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.9282 | − | 5.87564i | −0.769056 | − | 0.206068i | ||||
\(814\) | 1.00000 | − | 1.73205i | 0.0350500 | − | 0.0607083i | ||||
\(815\) | −6.89520 | + | 11.9428i | −0.241528 | + | 0.418339i | ||||
\(816\) | −3.06218 | − | 11.4282i | −0.107198 | − | 0.400067i | ||||
\(817\) | −0.586988 | − | 1.01669i | −0.0205361 | − | 0.0355696i | ||||
\(818\) | 4.48288 | 0.156740 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.92820 | 0.311786 | ||||||||
\(821\) | −5.19615 | − | 9.00000i | −0.181347 | − | 0.314102i | 0.760993 | − | 0.648761i | \(-0.224712\pi\) |
−0.942339 | + | 0.334659i | \(0.891379\pi\) | |||||||
\(822\) | 10.6066 | − | 10.6066i | 0.369948 | − | 0.369948i | ||||
\(823\) | 5.39230 | − | 9.33975i | 0.187964 | − | 0.325563i | −0.756607 | − | 0.653870i | \(-0.773145\pi\) |
0.944571 | + | 0.328306i | \(0.106478\pi\) | |||||||
\(824\) | −6.17449 | + | 10.6945i | −0.215099 | + | 0.372562i | ||||
\(825\) | 1.28912 | − | 1.28912i | 0.0448813 | − | 0.0448813i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | − | 16.3923i | − | 0.569672i | ||||||
\(829\) | 7.93048 | 0.275437 | 0.137718 | − | 0.990471i | \(-0.456023\pi\) | ||||
0.137718 | + | 0.990471i | \(0.456023\pi\) | |||||||
\(830\) | 3.41154 | + | 5.90897i | 0.118416 | + | 0.205103i | ||||
\(831\) | 14.1050 | + | 52.6405i | 0.489296 | + | 1.82608i | ||||
\(832\) | −0.896575 | + | 1.55291i | −0.0310832 | + | 0.0538376i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.33013 | − | 0.356406i | −0.0460585 | − | 0.0123413i | ||||
\(835\) | 0.784610 | + | 1.35898i | 0.0271525 | + | 0.0470296i | ||||
\(836\) | −1.17398 | −0.0406028 | ||||||||
\(837\) | 33.5885 | − | 9.00000i | 1.16099 | − | 0.311086i | ||||
\(838\) | 36.1875 | 1.25008 | ||||||||
\(839\) | −11.3137 | − | 19.5959i | −0.390593 | − | 0.676526i | 0.601935 | − | 0.798545i | \(-0.294397\pi\) |
−0.992528 | + | 0.122019i | \(0.961063\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.50000 | − | 11.2583i | 0.224138 | − | 0.388218i | ||||
\(842\) | −3.80385 | + | 6.58846i | −0.131089 | + | 0.227053i | ||||
\(843\) | 8.00481 | + | 29.8744i | 0.275700 | + | 1.02893i | ||||
\(844\) | −9.46410 | − | 16.3923i | −0.325768 | − | 0.564246i | ||||
\(845\) | 10.1298 | 0.348475 | ||||||||
\(846\) | −1.96902 | + | 1.13681i | −0.0676962 | + | 0.0390844i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.46410 | − | 9.46410i | −0.187638 | − | 0.324999i | ||||
\(849\) | −18.4641 | + | 18.4641i | −0.633686 | + | 0.633686i | ||||
\(850\) | −13.4164 | + | 23.2380i | −0.460180 | + | 0.797056i | ||||
\(851\) | −20.3923 | + | 35.3205i | −0.699039 | + | 1.21077i | ||||
\(852\) | 11.5911 | − | 11.5911i | 0.397105 | − | 0.397105i | ||||
\(853\) | −16.4901 | − | 28.5617i | −0.564610 | − | 0.977933i | −0.997086 | − | 0.0762876i | \(-0.975693\pi\) |
0.432476 | − | 0.901645i | \(-0.357640\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.7846 | − | 6.80385i | 0.403025 | − | 0.232687i | ||||
\(856\) | −17.3923 | −0.594457 | ||||||||
\(857\) | 5.60609 | + | 9.71003i | 0.191500 | + | 0.331688i | 0.945748 | − | 0.324902i | \(-0.105331\pi\) |
−0.754247 | + | 0.656590i | \(0.771998\pi\) | |||||||
\(858\) | −0.215390 | − | 0.803848i | −0.00735330 | − | 0.0274429i | ||||
\(859\) | 20.8021 | − | 36.0303i | 0.709758 | − | 1.22934i | −0.255189 | − | 0.966891i | \(-0.582138\pi\) |
0.964947 | − | 0.262445i | \(-0.0845290\pi\) | |||||||
\(860\) | 0.138701 | − | 0.240237i | 0.00472965 | − | 0.00819200i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.07180 | + | 8.78461i | 0.172746 | + | 0.299205i | ||||
\(863\) | −54.1051 | −1.84176 | −0.920880 | − | 0.389847i | \(-0.872528\pi\) | ||||
−0.920880 | + | 0.389847i | \(0.872528\pi\) | |||||||
\(864\) | 5.01910 | − | 1.34486i | 0.170753 | − | 0.0457532i | ||||
\(865\) | −6.92820 | −0.235566 | ||||||||
\(866\) | 9.91808 | + | 17.1786i | 0.337030 | + | 0.583753i | ||||
\(867\) | −49.6226 | − | 13.2963i | −1.68527 | − | 0.451567i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.19615 | − | 2.07180i | 0.0405767 | − | 0.0702809i | ||||
\(870\) | 1.85641 | + | 6.92820i | 0.0629381 | + | 0.234888i | ||||
\(871\) | −11.1750 | − | 19.3557i | −0.378651 | − | 0.655842i | ||||
\(872\) | 4.92820 | 0.166890 | ||||||||
\(873\) | 54.4336i | 1.84230i | ||||||||
\(874\) | 23.9401 | 0.809786 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.63397 | − | 6.63397i | 0.224141 | − | 0.224141i | ||||
\(877\) | 14.5885 | − | 25.2679i | 0.492617 | − | 0.853238i | −0.507347 | − | 0.861742i | \(-0.669374\pi\) |
0.999964 | + | 0.00850405i | \(0.00270695\pi\) | |||||||
\(878\) | −9.79796 | + | 16.9706i | −0.330665 | + | 0.572729i | ||||
\(879\) | −11.3205 | + | 11.3205i | −0.381831 | + | 0.381831i | ||||
\(880\) | −0.138701 | − | 0.240237i | −0.00467560 | − | 0.00809838i | ||||
\(881\) | −12.7279 | −0.428815 | −0.214407 | − | 0.976744i | \(-0.568782\pi\) | ||||
−0.214407 | + | 0.976744i | \(0.568782\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.4641 | 0.486756 | 0.243378 | − | 0.969932i | \(-0.421744\pi\) | ||||
0.243378 | + | 0.969932i | \(0.421744\pi\) | |||||||
\(884\) | 6.12436 | + | 10.6077i | 0.205984 | + | 0.356775i | ||||
\(885\) | 0.591968 | + | 2.20925i | 0.0198988 | + | 0.0742632i | ||||
\(886\) | −8.16025 | + | 14.1340i | −0.274149 | + | 0.474840i | ||||
\(887\) | −26.6298 | + | 46.1242i | −0.894142 | + | 1.54870i | −0.0592788 | + | 0.998241i | \(0.518880\pi\) |
−0.834863 | + | 0.550458i | \(0.814453\pi\) | |||||||
\(888\) | −12.4877 | − | 3.34607i | −0.419059 | − | 0.112287i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −7.32051 | −0.245384 | ||||||||
\(891\) | −1.20577 | + | 2.08846i | −0.0403949 | + | 0.0699660i | ||||
\(892\) | −7.17260 | −0.240157 | ||||||||
\(893\) | −1.66025 | − | 2.87564i | −0.0555583 | − | 0.0962298i | ||||
\(894\) | −38.3596 | − | 10.2784i | −1.28294 | − | 0.343762i | ||||
\(895\) | 2.62536 | − | 4.54725i | 0.0877559 | − | 0.151998i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.39230 | + | 16.3923i | 0.146655 | + | 0.547323i | ||||
\(898\) | −11.8923 | − | 20.5981i | −0.396851 | − | 0.687367i | ||||
\(899\) | −26.7685 | −0.892780 | ||||||||
\(900\) | −10.2058 | − | 5.89230i | −0.340192 | − | 0.196410i | ||||
\(901\) | −74.6487 | −2.48691 | ||||||||
\(902\) | −1.15539 | − | 2.00120i | −0.0384704 | − | 0.0666327i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.46410 | − | 6.00000i | 0.115214 | − | 0.199557i | ||||
\(905\) | −8.78461 | + | 15.2154i | −0.292010 | + | 0.505777i | ||||
\(906\) | 22.5259 | − | 22.5259i | 0.748372 | − | 0.748372i | ||||
\(907\) | 2.62436 | + | 4.54552i | 0.0871403 | + | 0.150931i | 0.906301 | − | 0.422632i | \(-0.138894\pi\) |
−0.819161 | + | 0.573564i | \(0.805560\pi\) | |||||||
\(908\) | −27.6651 | −0.918098 | ||||||||
\(909\) | 14.6969i | 0.487467i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.5359 | + | 28.6410i | 0.547859 | + | 0.948919i | 0.998421 | + | 0.0561742i | \(0.0178902\pi\) |
−0.450562 | + | 0.892745i | \(0.648776\pi\) | |||||||
\(912\) | 1.96410 | + | 7.33013i | 0.0650379 | + | 0.242725i | ||||
\(913\) | 0.882972 | − | 1.52935i | 0.0292221 | − | 0.0506142i | ||||
\(914\) | 15.5263 | − | 26.8923i | 0.513564 | − | 0.889518i | ||||
\(915\) | −21.8695 | − | 5.85993i | −0.722985 | − | 0.193723i | ||||
\(916\) | −0.240237 | − | 0.416102i | −0.00793764 | − | 0.0137484i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 9.18653 | − | 34.2846i | 0.303201 | − | 1.13156i | ||||
\(919\) | 9.07180 | 0.299251 | 0.149625 | − | 0.988743i | \(-0.452193\pi\) | ||||
0.149625 | + | 0.988743i | \(0.452193\pi\) | |||||||
\(920\) | 2.82843 | + | 4.89898i | 0.0932505 | + | 0.161515i | ||||
\(921\) | −1.96410 | − | 0.526279i | −0.0647193 | − | 0.0173415i | ||||
\(922\) | 5.51815 | − | 9.55772i | 0.181731 | − | 0.314767i | ||||
\(923\) | −8.48528 | + | 14.6969i | −0.279296 | + | 0.483756i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.6603 | + | 25.3923i | 0.482026 | + | 0.834894i | ||||
\(926\) | −30.6410 | −1.00693 | ||||||||
\(927\) | −32.0836 | + | 18.5235i | −1.05376 | + | 0.608391i | ||||
\(928\) | −4.00000 | −0.131306 | ||||||||
\(929\) | −15.4040 | − | 26.6806i | −0.505390 | − | 0.875362i | −0.999981 | − | 0.00623544i | \(-0.998015\pi\) |
0.494590 | − | 0.869126i | \(-0.335318\pi\) | |||||||
\(930\) | −8.48528 | + | 8.48528i | −0.278243 | + | 0.278243i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.0621778 | + | 0.107695i | −0.00203670 | + | 0.00352767i | ||||
\(933\) | −9.12436 | + | 9.12436i | −0.298718 | + | 0.298718i | ||||
\(934\) | −4.58939 | − | 7.94906i | −0.150170 | − | 0.260101i | ||||
\(935\) | −1.89488 | −0.0619693 | ||||||||
\(936\) | −4.65874 | + | 2.68973i | −0.152276 | + | 0.0879165i | ||||
\(937\) | −9.89949 | −0.323402 | −0.161701 | − | 0.986840i | \(-0.551698\pi\) | ||||
−0.161701 | + | 0.986840i | \(0.551698\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.81347 | + | 10.5000i | 0.0918140 | + | 0.342655i | ||||
\(940\) | 0.392305 | − | 0.679492i | 0.0127956 | − | 0.0221626i | ||||
\(941\) | 23.9401 | − | 41.4655i | 0.780425 | − | 1.35174i | −0.151270 | − | 0.988493i | \(-0.548336\pi\) |
0.931694 | − | 0.363243i | \(-0.118330\pi\) | |||||||
\(942\) | −15.9282 | − | 4.26795i | −0.518969 | − | 0.139057i | ||||
\(943\) | 23.5612 | + | 40.8091i | 0.767257 | + | 1.32893i | ||||
\(944\) | −1.27551 | −0.0415144 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.0717968 | −0.00233431 | ||||||||
\(947\) | 9.06218 | + | 15.6962i | 0.294481 | + | 0.510056i | 0.974864 | − | 0.222800i | \(-0.0715198\pi\) |
−0.680383 | + | 0.732857i | \(0.738186\pi\) | |||||||
\(948\) | −14.9372 | − | 4.00240i | −0.485137 | − | 0.129992i | ||||
\(949\) | −4.85641 | + | 8.41154i | −0.157646 | + | 0.273050i | ||||
\(950\) | 8.60540 | − | 14.9050i | 0.279196 | − | 0.483582i | ||||
\(951\) | −11.6555 | − | 43.4988i | −0.377955 | − | 1.41055i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.0000 | 0.615470 | 0.307735 | − | 0.951472i | \(-0.400429\pi\) | ||||
0.307735 | + | 0.951472i | \(0.400429\pi\) | |||||||
\(954\) | − | 32.7846i | − | 1.06144i | ||||||
\(955\) | −15.4548 | −0.500106 | ||||||||
\(956\) | −0.464102 | − | 0.803848i | −0.0150101 | − | 0.0259983i | ||||
\(957\) | 1.31268 | − | 1.31268i | 0.0424328 | − | 0.0424328i | ||||
\(958\) | 2.07055 | − | 3.58630i | 0.0668965 | − | 0.115868i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.26795 | + | 1.26795i | −0.0409229 | + | 0.0409229i | ||||
\(961\) | −6.89230 | − | 11.9378i | −0.222332 | − | 0.385091i | ||||
\(962\) | 13.3843 | 0.431526 | ||||||||
\(963\) | −45.1865 | − | 26.0885i | −1.45612 | − | 0.840689i | ||||
\(964\) | 6.27603 | 0.202137 | ||||||||
\(965\) | 7.79178 | + | 13.4958i | 0.250826 | + | 0.434444i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.7846 | − | 41.1962i | 0.764861 | − | 1.32478i | −0.175458 | − | 0.984487i | \(-0.556141\pi\) |
0.940320 | − | 0.340292i | \(-0.110526\pi\) | |||||||
\(968\) | 5.46410 | − | 9.46410i | 0.175623 | − | 0.304188i | ||||
\(969\) | 50.0709 | + | 13.4164i | 1.60851 | + | 0.430998i | ||||
\(970\) | −9.39230 | − | 16.2679i | −0.301569 | − | 0.522332i | ||||
\(971\) | 31.2886 | 1.00410 | 0.502049 | − | 0.864839i | \(-0.332580\pi\) | ||||
0.502049 | + | 0.864839i | \(0.332580\pi\) | |||||||
\(972\) | 15.0573 | + | 4.03459i | 0.482963 | + | 0.129410i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.39230 | + | 2.41154i | 0.0446123 | + | 0.0772708i | ||||
\(975\) | 11.7846 | + | 3.15768i | 0.377410 | + | 0.101127i | ||||
\(976\) | 6.31319 | − | 10.9348i | 0.202080 | − | 0.350013i | ||||
\(977\) | −0.990381 | + | 1.71539i | −0.0316851 | + | 0.0548802i | −0.881433 | − | 0.472309i | \(-0.843421\pi\) |
0.849748 | + | 0.527189i | \(0.176754\pi\) | |||||||
\(978\) | −5.97142 | − | 22.2856i | −0.190945 | − | 0.712616i | ||||
\(979\) | 0.947343 | + | 1.64085i | 0.0302772 | + | 0.0524417i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.8038 | + | 7.39230i | 0.408795 | + | 0.236018i | ||||
\(982\) | 19.3923 | 0.618833 | ||||||||
\(983\) | −6.31319 | − | 10.9348i | −0.201360 | − | 0.348765i | 0.747607 | − | 0.664141i | \(-0.231203\pi\) |
−0.948967 | + | 0.315376i | \(0.897869\pi\) | |||||||
\(984\) | −10.5622 | + | 10.5622i | −0.336710 | + | 0.336710i | ||||
\(985\) | −8.76268 | + | 15.1774i | −0.279202 | + | 0.483593i | ||||
\(986\) | −13.6617 | + | 23.6627i | −0.435076 | + | 0.753574i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.92820 | − | 6.80385i | −0.124973 | − | 0.216459i | ||||
\(989\) | 1.46410 | 0.0465557 | ||||||||
\(990\) | − | 0.832204i | − | 0.0264492i | ||||||
\(991\) | 50.2487 | 1.59620 | 0.798101 | − | 0.602523i | \(-0.205838\pi\) | ||||
0.798101 | + | 0.602523i | \(0.205838\pi\) | |||||||
\(992\) | −3.34607 | − | 5.79555i | −0.106238 | − | 0.184009i | ||||
\(993\) | −5.13922 | − | 19.1798i | −0.163088 | − | 0.608653i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.6077 | − | 23.5692i | 0.431393 | − | 0.747194i | ||||
\(996\) | −11.0263 | − | 2.95448i | −0.349381 | − | 0.0936164i | ||||
\(997\) | 18.8009 | + | 32.5641i | 0.595430 | + | 1.03131i | 0.993486 | + | 0.113954i | \(0.0363515\pi\) |
−0.398056 | + | 0.917361i | \(0.630315\pi\) | |||||||
\(998\) | 33.3923 | 1.05701 | ||||||||
\(999\) | −27.4249 | − | 27.4249i | −0.867684 | − | 0.867684i |
(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 | 882.2.f.q.589.1 | yes | 8 | |
3.2 | odd | 2 | 2646.2.f.r.1765.2 | 8 | |||
7.2 | even | 3 | 882.2.h.q.67.3 | 8 | |||
7.3 | odd | 6 | 882.2.e.s.373.2 | 8 | |||
7.4 | even | 3 | 882.2.e.s.373.3 | 8 | |||
7.5 | odd | 6 | 882.2.h.q.67.2 | 8 | |||
7.6 | odd | 2 | inner | 882.2.f.q.589.4 | yes | 8 | |
9.2 | odd | 6 | 2646.2.f.r.883.2 | 8 | |||
9.4 | even | 3 | 7938.2.a.cp.1.2 | 4 | |||
9.5 | odd | 6 | 7938.2.a.ci.1.3 | 4 | |||
9.7 | even | 3 | inner | 882.2.f.q.295.1 | ✓ | 8 | |
21.2 | odd | 6 | 2646.2.h.t.361.3 | 8 | |||
21.5 | even | 6 | 2646.2.h.t.361.2 | 8 | |||
21.11 | odd | 6 | 2646.2.e.q.1549.2 | 8 | |||
21.17 | even | 6 | 2646.2.e.q.1549.3 | 8 | |||
21.20 | even | 2 | 2646.2.f.r.1765.3 | 8 | |||
63.2 | odd | 6 | 2646.2.e.q.2125.2 | 8 | |||
63.11 | odd | 6 | 2646.2.h.t.667.3 | 8 | |||
63.13 | odd | 6 | 7938.2.a.cp.1.3 | 4 | |||
63.16 | even | 3 | 882.2.e.s.655.3 | 8 | |||
63.20 | even | 6 | 2646.2.f.r.883.3 | 8 | |||
63.25 | even | 3 | 882.2.h.q.79.4 | 8 | |||
63.34 | odd | 6 | inner | 882.2.f.q.295.4 | yes | 8 | |
63.38 | even | 6 | 2646.2.h.t.667.2 | 8 | |||
63.41 | even | 6 | 7938.2.a.ci.1.2 | 4 | |||
63.47 | even | 6 | 2646.2.e.q.2125.3 | 8 | |||
63.52 | odd | 6 | 882.2.h.q.79.1 | 8 | |||
63.61 | odd | 6 | 882.2.e.s.655.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.2.e.s.373.2 | 8 | 7.3 | odd | 6 | |||
882.2.e.s.373.3 | 8 | 7.4 | even | 3 | |||
882.2.e.s.655.2 | 8 | 63.61 | odd | 6 | |||
882.2.e.s.655.3 | 8 | 63.16 | even | 3 | |||
882.2.f.q.295.1 | ✓ | 8 | 9.7 | even | 3 | inner | |
882.2.f.q.295.4 | yes | 8 | 63.34 | odd | 6 | inner | |
882.2.f.q.589.1 | yes | 8 | 1.1 | even | 1 | trivial | |
882.2.f.q.589.4 | yes | 8 | 7.6 | odd | 2 | inner | |
882.2.h.q.67.2 | 8 | 7.5 | odd | 6 | |||
882.2.h.q.67.3 | 8 | 7.2 | even | 3 | |||
882.2.h.q.79.1 | 8 | 63.52 | odd | 6 | |||
882.2.h.q.79.4 | 8 | 63.25 | even | 3 | |||
2646.2.e.q.1549.2 | 8 | 21.11 | odd | 6 | |||
2646.2.e.q.1549.3 | 8 | 21.17 | even | 6 | |||
2646.2.e.q.2125.2 | 8 | 63.2 | odd | 6 | |||
2646.2.e.q.2125.3 | 8 | 63.47 | even | 6 | |||
2646.2.f.r.883.2 | 8 | 9.2 | odd | 6 | |||
2646.2.f.r.883.3 | 8 | 63.20 | even | 6 | |||
2646.2.f.r.1765.2 | 8 | 3.2 | odd | 2 | |||
2646.2.f.r.1765.3 | 8 | 21.20 | even | 2 | |||
2646.2.h.t.361.2 | 8 | 21.5 | even | 6 | |||
2646.2.h.t.361.3 | 8 | 21.2 | odd | 6 | |||
2646.2.h.t.667.2 | 8 | 63.38 | even | 6 | |||
2646.2.h.t.667.3 | 8 | 63.11 | odd | 6 | |||
7938.2.a.ci.1.2 | 4 | 63.41 | even | 6 | |||
7938.2.a.ci.1.3 | 4 | 9.5 | odd | 6 | |||
7938.2.a.cp.1.2 | 4 | 9.4 | even | 3 | |||
7938.2.a.cp.1.3 | 4 | 63.13 | odd | 6 |