Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [170,2,Mod(89,170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(170, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("170.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 170 = 2 \cdot 5 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 170.g (of order \(4\), 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: | \(1.35745683436\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 149.2 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 170.149 |
Dual form | 170.2.g.e.89.2 |
$q$-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 \(\left(\mathbb{Z}/170\mathbb{Z}\right)^\times\).
\(n\) | \(71\) | \(137\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.292893 | + | 0.292893i | −0.169102 | + | 0.169102i | −0.786585 | − | 0.617483i | \(-0.788153\pi\) |
0.617483 | + | 0.786585i | \(0.288153\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.12132 | + | 0.707107i | −0.948683 | + | 0.316228i | ||||
\(6\) | 0.292893 | − | 0.292893i | 0.119573 | − | 0.119573i | ||||
\(7\) | 1.00000 | + | 1.00000i | 0.377964 | + | 0.377964i | 0.870367 | − | 0.492403i | \(-0.163881\pi\) |
−0.492403 | + | 0.870367i | \(0.663881\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.82843i | 0.942809i | ||||||||
\(10\) | 2.12132 | − | 0.707107i | 0.670820 | − | 0.223607i | ||||
\(11\) | −1.58579 | + | 1.58579i | −0.478133 | + | 0.478133i | −0.904534 | − | 0.426401i | \(-0.859781\pi\) |
0.426401 | + | 0.904534i | \(0.359781\pi\) | |||||||
\(12\) | −0.292893 | + | 0.292893i | −0.0845510 | + | 0.0845510i | ||||
\(13\) | 3.00000i | 0.832050i | 0.909353 | + | 0.416025i | \(0.136577\pi\) | ||||
−0.909353 | + | 0.416025i | \(0.863423\pi\) | |||||||
\(14\) | −1.00000 | − | 1.00000i | −0.267261 | − | 0.267261i | ||||
\(15\) | 0.414214 | − | 0.828427i | 0.106949 | − | 0.213899i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.12132 | − | 3.53553i | −0.514496 | − | 0.857493i | ||||
\(18\) | − | 2.82843i | − | 0.666667i | ||||||
\(19\) | 7.24264i | 1.66158i | 0.556589 | + | 0.830788i | \(0.312110\pi\) | ||||
−0.556589 | + | 0.830788i | \(0.687890\pi\) | |||||||
\(20\) | −2.12132 | + | 0.707107i | −0.474342 | + | 0.158114i | ||||
\(21\) | −0.585786 | −0.127829 | ||||||||
\(22\) | 1.58579 | − | 1.58579i | 0.338091 | − | 0.338091i | ||||
\(23\) | 2.82843 | + | 2.82843i | 0.589768 | + | 0.589768i | 0.937568 | − | 0.347801i | \(-0.113071\pi\) |
−0.347801 | + | 0.937568i | \(0.613071\pi\) | |||||||
\(24\) | 0.292893 | − | 0.292893i | 0.0597866 | − | 0.0597866i | ||||
\(25\) | 4.00000 | − | 3.00000i | 0.800000 | − | 0.600000i | ||||
\(26\) | − | 3.00000i | − | 0.588348i | ||||||
\(27\) | −1.70711 | − | 1.70711i | −0.328533 | − | 0.328533i | ||||
\(28\) | 1.00000 | + | 1.00000i | 0.188982 | + | 0.188982i | ||||
\(29\) | 0.707107 | + | 0.707107i | 0.131306 | + | 0.131306i | 0.769706 | − | 0.638399i | \(-0.220403\pi\) |
−0.638399 | + | 0.769706i | \(0.720403\pi\) | |||||||
\(30\) | −0.414214 | + | 0.828427i | −0.0756247 | + | 0.151249i | ||||
\(31\) | −5.36396 | − | 5.36396i | −0.963396 | − | 0.963396i | 0.0359575 | − | 0.999353i | \(-0.488552\pi\) |
−0.999353 | + | 0.0359575i | \(0.988552\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | − | 0.928932i | − | 0.161706i | ||||||
\(34\) | 2.12132 | + | 3.53553i | 0.363803 | + | 0.606339i | ||||
\(35\) | −2.82843 | − | 1.41421i | −0.478091 | − | 0.239046i | ||||
\(36\) | 2.82843i | 0.471405i | ||||||||
\(37\) | 5.24264 | − | 5.24264i | 0.861885 | − | 0.861885i | −0.129672 | − | 0.991557i | \(-0.541392\pi\) |
0.991557 | + | 0.129672i | \(0.0413925\pi\) | |||||||
\(38\) | − | 7.24264i | − | 1.17491i | ||||||
\(39\) | −0.878680 | − | 0.878680i | −0.140701 | − | 0.140701i | ||||
\(40\) | 2.12132 | − | 0.707107i | 0.335410 | − | 0.111803i | ||||
\(41\) | 4.41421 | − | 4.41421i | 0.689384 | − | 0.689384i | −0.272712 | − | 0.962096i | \(-0.587920\pi\) |
0.962096 | + | 0.272712i | \(0.0879205\pi\) | |||||||
\(42\) | 0.585786 | 0.0903888 | ||||||||
\(43\) | 3.75736 | 0.572992 | 0.286496 | − | 0.958081i | \(-0.407509\pi\) | ||||
0.286496 | + | 0.958081i | \(0.407509\pi\) | |||||||
\(44\) | −1.58579 | + | 1.58579i | −0.239066 | + | 0.239066i | ||||
\(45\) | −2.00000 | − | 6.00000i | −0.298142 | − | 0.894427i | ||||
\(46\) | −2.82843 | − | 2.82843i | −0.417029 | − | 0.417029i | ||||
\(47\) | − | 1.58579i | − | 0.231311i | −0.993289 | − | 0.115655i | \(-0.963103\pi\) | ||
0.993289 | − | 0.115655i | \(-0.0368968\pi\) | |||||||
\(48\) | −0.292893 | + | 0.292893i | −0.0422755 | + | 0.0422755i | ||||
\(49\) | − | 5.00000i | − | 0.714286i | ||||||
\(50\) | −4.00000 | + | 3.00000i | −0.565685 | + | 0.424264i | ||||
\(51\) | 1.65685 | + | 0.414214i | 0.232006 | + | 0.0580015i | ||||
\(52\) | 3.00000i | 0.416025i | ||||||||
\(53\) | −3.00000 | −0.412082 | −0.206041 | − | 0.978543i | \(-0.566058\pi\) | ||||
−0.206041 | + | 0.978543i | \(0.566058\pi\) | |||||||
\(54\) | 1.70711 | + | 1.70711i | 0.232308 | + | 0.232308i | ||||
\(55\) | 2.24264 | − | 4.48528i | 0.302398 | − | 0.604795i | ||||
\(56\) | −1.00000 | − | 1.00000i | −0.133631 | − | 0.133631i | ||||
\(57\) | −2.12132 | − | 2.12132i | −0.280976 | − | 0.280976i | ||||
\(58\) | −0.707107 | − | 0.707107i | −0.0928477 | − | 0.0928477i | ||||
\(59\) | 12.8995i | 1.67937i | 0.543073 | + | 0.839686i | \(0.317261\pi\) | ||||
−0.543073 | + | 0.839686i | \(0.682739\pi\) | |||||||
\(60\) | 0.414214 | − | 0.828427i | 0.0534747 | − | 0.106949i | ||||
\(61\) | 6.12132 | − | 6.12132i | 0.783755 | − | 0.783755i | −0.196707 | − | 0.980462i | \(-0.563025\pi\) |
0.980462 | + | 0.196707i | \(0.0630249\pi\) | |||||||
\(62\) | 5.36396 | + | 5.36396i | 0.681224 | + | 0.681224i | ||||
\(63\) | −2.82843 | + | 2.82843i | −0.356348 | + | 0.356348i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.12132 | − | 6.36396i | −0.263117 | − | 0.789352i | ||||
\(66\) | 0.928932i | 0.114344i | ||||||||
\(67\) | 14.4853i | 1.76966i | 0.465915 | + | 0.884829i | \(0.345725\pi\) | ||||
−0.465915 | + | 0.884829i | \(0.654275\pi\) | |||||||
\(68\) | −2.12132 | − | 3.53553i | −0.257248 | − | 0.428746i | ||||
\(69\) | −1.65685 | −0.199462 | ||||||||
\(70\) | 2.82843 | + | 1.41421i | 0.338062 | + | 0.169031i | ||||
\(71\) | 3.70711 | + | 3.70711i | 0.439953 | + | 0.439953i | 0.891996 | − | 0.452043i | \(-0.149305\pi\) |
−0.452043 | + | 0.891996i | \(0.649305\pi\) | |||||||
\(72\) | − | 2.82843i | − | 0.333333i | ||||||
\(73\) | −8.36396 | + | 8.36396i | −0.978928 | + | 0.978928i | −0.999783 | − | 0.0208549i | \(-0.993361\pi\) |
0.0208549 | + | 0.999783i | \(0.493361\pi\) | |||||||
\(74\) | −5.24264 | + | 5.24264i | −0.609445 | + | 0.609445i | ||||
\(75\) | −0.292893 | + | 2.05025i | −0.0338204 | + | 0.236743i | ||||
\(76\) | 7.24264i | 0.830788i | ||||||||
\(77\) | −3.17157 | −0.361434 | ||||||||
\(78\) | 0.878680 | + | 0.878680i | 0.0994909 | + | 0.0994909i | ||||
\(79\) | −0.242641 | + | 0.242641i | −0.0272992 | + | 0.0272992i | −0.720625 | − | 0.693325i | \(-0.756145\pi\) |
0.693325 | + | 0.720625i | \(0.256145\pi\) | |||||||
\(80\) | −2.12132 | + | 0.707107i | −0.237171 | + | 0.0790569i | ||||
\(81\) | −7.48528 | −0.831698 | ||||||||
\(82\) | −4.41421 | + | 4.41421i | −0.487468 | + | 0.487468i | ||||
\(83\) | 4.24264 | 0.465690 | 0.232845 | − | 0.972514i | \(-0.425196\pi\) | ||||
0.232845 | + | 0.972514i | \(0.425196\pi\) | |||||||
\(84\) | −0.585786 | −0.0639145 | ||||||||
\(85\) | 7.00000 | + | 6.00000i | 0.759257 | + | 0.650791i | ||||
\(86\) | −3.75736 | −0.405166 | ||||||||
\(87\) | −0.414214 | −0.0444084 | ||||||||
\(88\) | 1.58579 | − | 1.58579i | 0.169045 | − | 0.169045i | ||||
\(89\) | 11.4853 | 1.21744 | 0.608719 | − | 0.793386i | \(-0.291684\pi\) | ||||
0.608719 | + | 0.793386i | \(0.291684\pi\) | |||||||
\(90\) | 2.00000 | + | 6.00000i | 0.210819 | + | 0.632456i | ||||
\(91\) | −3.00000 | + | 3.00000i | −0.314485 | + | 0.314485i | ||||
\(92\) | 2.82843 | + | 2.82843i | 0.294884 | + | 0.294884i | ||||
\(93\) | 3.14214 | 0.325824 | ||||||||
\(94\) | 1.58579i | 0.163561i | ||||||||
\(95\) | −5.12132 | − | 15.3640i | −0.525436 | − | 1.57631i | ||||
\(96\) | 0.292893 | − | 0.292893i | 0.0298933 | − | 0.0298933i | ||||
\(97\) | 0.121320 | − | 0.121320i | 0.0123182 | − | 0.0123182i | −0.700921 | − | 0.713239i | \(-0.747227\pi\) |
0.713239 | + | 0.700921i | \(0.247227\pi\) | |||||||
\(98\) | 5.00000i | 0.505076i | ||||||||
\(99\) | −4.48528 | − | 4.48528i | −0.450788 | − | 0.450788i | ||||
\(100\) | 4.00000 | − | 3.00000i | 0.400000 | − | 0.300000i | ||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | −1.65685 | − | 0.414214i | −0.164053 | − | 0.0410133i | ||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | − | 3.00000i | − | 0.294174i | ||||||
\(105\) | 1.24264 | − | 0.414214i | 0.121269 | − | 0.0404231i | ||||
\(106\) | 3.00000 | 0.291386 | ||||||||
\(107\) | −2.82843 | + | 2.82843i | −0.273434 | + | 0.273434i | −0.830481 | − | 0.557047i | \(-0.811934\pi\) |
0.557047 | + | 0.830481i | \(0.311934\pi\) | |||||||
\(108\) | −1.70711 | − | 1.70711i | −0.164266 | − | 0.164266i | ||||
\(109\) | 8.60660 | − | 8.60660i | 0.824363 | − | 0.824363i | −0.162367 | − | 0.986730i | \(-0.551913\pi\) |
0.986730 | + | 0.162367i | \(0.0519130\pi\) | |||||||
\(110\) | −2.24264 | + | 4.48528i | −0.213827 | + | 0.427655i | ||||
\(111\) | 3.07107i | 0.291493i | ||||||||
\(112\) | 1.00000 | + | 1.00000i | 0.0944911 | + | 0.0944911i | ||||
\(113\) | 2.46447 | + | 2.46447i | 0.231837 | + | 0.231837i | 0.813459 | − | 0.581622i | \(-0.197582\pi\) |
−0.581622 | + | 0.813459i | \(0.697582\pi\) | |||||||
\(114\) | 2.12132 | + | 2.12132i | 0.198680 | + | 0.198680i | ||||
\(115\) | −8.00000 | − | 4.00000i | −0.746004 | − | 0.373002i | ||||
\(116\) | 0.707107 | + | 0.707107i | 0.0656532 | + | 0.0656532i | ||||
\(117\) | −8.48528 | −0.784465 | ||||||||
\(118\) | − | 12.8995i | − | 1.18749i | ||||||
\(119\) | 1.41421 | − | 5.65685i | 0.129641 | − | 0.518563i | ||||
\(120\) | −0.414214 | + | 0.828427i | −0.0378124 | + | 0.0756247i | ||||
\(121\) | 5.97056i | 0.542778i | ||||||||
\(122\) | −6.12132 | + | 6.12132i | −0.554198 | + | 0.554198i | ||||
\(123\) | 2.58579i | 0.233153i | ||||||||
\(124\) | −5.36396 | − | 5.36396i | −0.481698 | − | 0.481698i | ||||
\(125\) | −6.36396 | + | 9.19239i | −0.569210 | + | 0.822192i | ||||
\(126\) | 2.82843 | − | 2.82843i | 0.251976 | − | 0.251976i | ||||
\(127\) | 17.7279 | 1.57310 | 0.786549 | − | 0.617527i | \(-0.211866\pi\) | ||||
0.786549 | + | 0.617527i | \(0.211866\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.10051 | + | 1.10051i | −0.0968941 | + | 0.0968941i | ||||
\(130\) | 2.12132 | + | 6.36396i | 0.186052 | + | 0.558156i | ||||
\(131\) | 7.58579 | + | 7.58579i | 0.662773 | + | 0.662773i | 0.956033 | − | 0.293260i | \(-0.0947400\pi\) |
−0.293260 | + | 0.956033i | \(0.594740\pi\) | |||||||
\(132\) | − | 0.928932i | − | 0.0808532i | ||||||
\(133\) | −7.24264 | + | 7.24264i | −0.628017 | + | 0.628017i | ||||
\(134\) | − | 14.4853i | − | 1.25134i | ||||||
\(135\) | 4.82843 | + | 2.41421i | 0.415565 | + | 0.207782i | ||||
\(136\) | 2.12132 | + | 3.53553i | 0.181902 | + | 0.303170i | ||||
\(137\) | − | 4.58579i | − | 0.391790i | −0.980625 | − | 0.195895i | \(-0.937239\pi\) | ||
0.980625 | − | 0.195895i | \(-0.0627612\pi\) | |||||||
\(138\) | 1.65685 | 0.141041 | ||||||||
\(139\) | −11.0000 | − | 11.0000i | −0.933008 | − | 0.933008i | 0.0648849 | − | 0.997893i | \(-0.479332\pi\) |
−0.997893 | + | 0.0648849i | \(0.979332\pi\) | |||||||
\(140\) | −2.82843 | − | 1.41421i | −0.239046 | − | 0.119523i | ||||
\(141\) | 0.464466 | + | 0.464466i | 0.0391151 | + | 0.0391151i | ||||
\(142\) | −3.70711 | − | 3.70711i | −0.311093 | − | 0.311093i | ||||
\(143\) | −4.75736 | − | 4.75736i | −0.397830 | − | 0.397830i | ||||
\(144\) | 2.82843i | 0.235702i | ||||||||
\(145\) | −2.00000 | − | 1.00000i | −0.166091 | − | 0.0830455i | ||||
\(146\) | 8.36396 | − | 8.36396i | 0.692206 | − | 0.692206i | ||||
\(147\) | 1.46447 | + | 1.46447i | 0.120787 | + | 0.120787i | ||||
\(148\) | 5.24264 | − | 5.24264i | 0.430942 | − | 0.430942i | ||||
\(149\) | −12.7279 | −1.04271 | −0.521356 | − | 0.853339i | \(-0.674574\pi\) | ||||
−0.521356 | + | 0.853339i | \(0.674574\pi\) | |||||||
\(150\) | 0.292893 | − | 2.05025i | 0.0239146 | − | 0.167402i | ||||
\(151\) | − | 12.0000i | − | 0.976546i | −0.872691 | − | 0.488273i | \(-0.837627\pi\) | ||
0.872691 | − | 0.488273i | \(-0.162373\pi\) | |||||||
\(152\) | − | 7.24264i | − | 0.587456i | ||||||
\(153\) | 10.0000 | − | 6.00000i | 0.808452 | − | 0.485071i | ||||
\(154\) | 3.17157 | 0.255573 | ||||||||
\(155\) | 15.1716 | + | 7.58579i | 1.21861 | + | 0.609305i | ||||
\(156\) | −0.878680 | − | 0.878680i | −0.0703507 | − | 0.0703507i | ||||
\(157\) | − | 12.0000i | − | 0.957704i | −0.877896 | − | 0.478852i | \(-0.841053\pi\) | ||
0.877896 | − | 0.478852i | \(-0.158947\pi\) | |||||||
\(158\) | 0.242641 | − | 0.242641i | 0.0193035 | − | 0.0193035i | ||||
\(159\) | 0.878680 | − | 0.878680i | 0.0696838 | − | 0.0696838i | ||||
\(160\) | 2.12132 | − | 0.707107i | 0.167705 | − | 0.0559017i | ||||
\(161\) | 5.65685i | 0.445823i | ||||||||
\(162\) | 7.48528 | 0.588099 | ||||||||
\(163\) | −4.48528 | − | 4.48528i | −0.351314 | − | 0.351314i | 0.509284 | − | 0.860598i | \(-0.329910\pi\) |
−0.860598 | + | 0.509284i | \(0.829910\pi\) | |||||||
\(164\) | 4.41421 | − | 4.41421i | 0.344692 | − | 0.344692i | ||||
\(165\) | 0.656854 | + | 1.97056i | 0.0511360 | + | 0.153408i | ||||
\(166\) | −4.24264 | −0.329293 | ||||||||
\(167\) | −1.07107 | + | 1.07107i | −0.0828817 | + | 0.0828817i | −0.747332 | − | 0.664451i | \(-0.768666\pi\) |
0.664451 | + | 0.747332i | \(0.268666\pi\) | |||||||
\(168\) | 0.585786 | 0.0451944 | ||||||||
\(169\) | 4.00000 | 0.307692 | ||||||||
\(170\) | −7.00000 | − | 6.00000i | −0.536875 | − | 0.460179i | ||||
\(171\) | −20.4853 | −1.56655 | ||||||||
\(172\) | 3.75736 | 0.286496 | ||||||||
\(173\) | 17.6569 | − | 17.6569i | 1.34243 | − | 1.34243i | 0.448787 | − | 0.893639i | \(-0.351856\pi\) |
0.893639 | − | 0.448787i | \(-0.148144\pi\) | |||||||
\(174\) | 0.414214 | 0.0314014 | ||||||||
\(175\) | 7.00000 | + | 1.00000i | 0.529150 | + | 0.0755929i | ||||
\(176\) | −1.58579 | + | 1.58579i | −0.119533 | + | 0.119533i | ||||
\(177\) | −3.77817 | − | 3.77817i | −0.283985 | − | 0.283985i | ||||
\(178\) | −11.4853 | −0.860858 | ||||||||
\(179\) | 0.686292i | 0.0512958i | 0.999671 | + | 0.0256479i | \(0.00816488\pi\) | ||||
−0.999671 | + | 0.0256479i | \(0.991835\pi\) | |||||||
\(180\) | −2.00000 | − | 6.00000i | −0.149071 | − | 0.447214i | ||||
\(181\) | −14.0000 | + | 14.0000i | −1.04061 | + | 1.04061i | −0.0414721 | + | 0.999140i | \(0.513205\pi\) |
−0.999140 | + | 0.0414721i | \(0.986795\pi\) | |||||||
\(182\) | 3.00000 | − | 3.00000i | 0.222375 | − | 0.222375i | ||||
\(183\) | 3.58579i | 0.265069i | ||||||||
\(184\) | −2.82843 | − | 2.82843i | −0.208514 | − | 0.208514i | ||||
\(185\) | −7.41421 | + | 14.8284i | −0.545104 | + | 1.09021i | ||||
\(186\) | −3.14214 | −0.230393 | ||||||||
\(187\) | 8.97056 | + | 2.24264i | 0.655993 | + | 0.163998i | ||||
\(188\) | − | 1.58579i | − | 0.115655i | ||||||
\(189\) | − | 3.41421i | − | 0.248347i | ||||||
\(190\) | 5.12132 | + | 15.3640i | 0.371540 | + | 1.11462i | ||||
\(191\) | 21.2132 | 1.53493 | 0.767467 | − | 0.641089i | \(-0.221517\pi\) | ||||
0.767467 | + | 0.641089i | \(0.221517\pi\) | |||||||
\(192\) | −0.292893 | + | 0.292893i | −0.0211377 | + | 0.0211377i | ||||
\(193\) | 18.4853 | + | 18.4853i | 1.33060 | + | 1.33060i | 0.904833 | + | 0.425767i | \(0.139996\pi\) |
0.425767 | + | 0.904833i | \(0.360004\pi\) | |||||||
\(194\) | −0.121320 | + | 0.121320i | −0.00871029 | + | 0.00871029i | ||||
\(195\) | 2.48528 | + | 1.24264i | 0.177975 | + | 0.0889873i | ||||
\(196\) | − | 5.00000i | − | 0.357143i | ||||||
\(197\) | 3.34315 | + | 3.34315i | 0.238189 | + | 0.238189i | 0.816100 | − | 0.577911i | \(-0.196132\pi\) |
−0.577911 | + | 0.816100i | \(0.696132\pi\) | |||||||
\(198\) | 4.48528 | + | 4.48528i | 0.318755 | + | 0.318755i | ||||
\(199\) | −7.12132 | − | 7.12132i | −0.504817 | − | 0.504817i | 0.408114 | − | 0.912931i | \(-0.366187\pi\) |
−0.912931 | + | 0.408114i | \(0.866187\pi\) | |||||||
\(200\) | −4.00000 | + | 3.00000i | −0.282843 | + | 0.212132i | ||||
\(201\) | −4.24264 | − | 4.24264i | −0.299253 | − | 0.299253i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.41421i | 0.0992583i | ||||||||
\(204\) | 1.65685 | + | 0.414214i | 0.116003 | + | 0.0290008i | ||||
\(205\) | −6.24264 | + | 12.4853i | −0.436005 | + | 0.872010i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.00000 | + | 8.00000i | −0.556038 | + | 0.556038i | ||||
\(208\) | 3.00000i | 0.208013i | ||||||||
\(209\) | −11.4853 | − | 11.4853i | −0.794454 | − | 0.794454i | ||||
\(210\) | −1.24264 | + | 0.414214i | −0.0857504 | + | 0.0285835i | ||||
\(211\) | −8.00000 | + | 8.00000i | −0.550743 | + | 0.550743i | −0.926655 | − | 0.375912i | \(-0.877329\pi\) |
0.375912 | + | 0.926655i | \(0.377329\pi\) | |||||||
\(212\) | −3.00000 | −0.206041 | ||||||||
\(213\) | −2.17157 | −0.148794 | ||||||||
\(214\) | 2.82843 | − | 2.82843i | 0.193347 | − | 0.193347i | ||||
\(215\) | −7.97056 | + | 2.65685i | −0.543588 | + | 0.181196i | ||||
\(216\) | 1.70711 | + | 1.70711i | 0.116154 | + | 0.116154i | ||||
\(217\) | − | 10.7279i | − | 0.728259i | ||||||
\(218\) | −8.60660 | + | 8.60660i | −0.582913 | + | 0.582913i | ||||
\(219\) | − | 4.89949i | − | 0.331077i | ||||||
\(220\) | 2.24264 | − | 4.48528i | 0.151199 | − | 0.302398i | ||||
\(221\) | 10.6066 | − | 6.36396i | 0.713477 | − | 0.428086i | ||||
\(222\) | − | 3.07107i | − | 0.206117i | ||||||
\(223\) | −23.2426 | −1.55644 | −0.778221 | − | 0.627990i | \(-0.783878\pi\) | ||||
−0.778221 | + | 0.627990i | \(0.783878\pi\) | |||||||
\(224\) | −1.00000 | − | 1.00000i | −0.0668153 | − | 0.0668153i | ||||
\(225\) | 8.48528 | + | 11.3137i | 0.565685 | + | 0.754247i | ||||
\(226\) | −2.46447 | − | 2.46447i | −0.163934 | − | 0.163934i | ||||
\(227\) | −4.05025 | − | 4.05025i | −0.268825 | − | 0.268825i | 0.559802 | − | 0.828627i | \(-0.310877\pi\) |
−0.828627 | + | 0.559802i | \(0.810877\pi\) | |||||||
\(228\) | −2.12132 | − | 2.12132i | −0.140488 | − | 0.140488i | ||||
\(229\) | 7.75736i | 0.512621i | 0.966595 | + | 0.256310i | \(0.0825069\pi\) | ||||
−0.966595 | + | 0.256310i | \(0.917493\pi\) | |||||||
\(230\) | 8.00000 | + | 4.00000i | 0.527504 | + | 0.263752i | ||||
\(231\) | 0.928932 | − | 0.928932i | 0.0611193 | − | 0.0611193i | ||||
\(232\) | −0.707107 | − | 0.707107i | −0.0464238 | − | 0.0464238i | ||||
\(233\) | −10.9497 | + | 10.9497i | −0.717342 | + | 0.717342i | −0.968060 | − | 0.250718i | \(-0.919333\pi\) |
0.250718 | + | 0.968060i | \(0.419333\pi\) | |||||||
\(234\) | 8.48528 | 0.554700 | ||||||||
\(235\) | 1.12132 | + | 3.36396i | 0.0731469 | + | 0.219441i | ||||
\(236\) | 12.8995i | 0.839686i | ||||||||
\(237\) | − | 0.142136i | − | 0.00923270i | ||||||
\(238\) | −1.41421 | + | 5.65685i | −0.0916698 | + | 0.366679i | ||||
\(239\) | 22.2426 | 1.43876 | 0.719378 | − | 0.694618i | \(-0.244427\pi\) | ||||
0.719378 | + | 0.694618i | \(0.244427\pi\) | |||||||
\(240\) | 0.414214 | − | 0.828427i | 0.0267374 | − | 0.0534747i | ||||
\(241\) | 2.75736 | + | 2.75736i | 0.177617 | + | 0.177617i | 0.790316 | − | 0.612699i | \(-0.209916\pi\) |
−0.612699 | + | 0.790316i | \(0.709916\pi\) | |||||||
\(242\) | − | 5.97056i | − | 0.383802i | ||||||
\(243\) | 7.31371 | − | 7.31371i | 0.469175 | − | 0.469175i | ||||
\(244\) | 6.12132 | − | 6.12132i | 0.391877 | − | 0.391877i | ||||
\(245\) | 3.53553 | + | 10.6066i | 0.225877 | + | 0.677631i | ||||
\(246\) | − | 2.58579i | − | 0.164864i | ||||||
\(247\) | −21.7279 | −1.38251 | ||||||||
\(248\) | 5.36396 | + | 5.36396i | 0.340612 | + | 0.340612i | ||||
\(249\) | −1.24264 | + | 1.24264i | −0.0787492 | + | 0.0787492i | ||||
\(250\) | 6.36396 | − | 9.19239i | 0.402492 | − | 0.581378i | ||||
\(251\) | 20.4853 | 1.29302 | 0.646510 | − | 0.762906i | \(-0.276228\pi\) | ||||
0.646510 | + | 0.762906i | \(0.276228\pi\) | |||||||
\(252\) | −2.82843 | + | 2.82843i | −0.178174 | + | 0.178174i | ||||
\(253\) | −8.97056 | −0.563974 | ||||||||
\(254\) | −17.7279 | −1.11235 | ||||||||
\(255\) | −3.80761 | + | 0.292893i | −0.238442 | + | 0.0183417i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.72792 | 0.419676 | 0.209838 | − | 0.977736i | \(-0.432706\pi\) | ||||
0.209838 | + | 0.977736i | \(0.432706\pi\) | |||||||
\(258\) | 1.10051 | − | 1.10051i | 0.0685145 | − | 0.0685145i | ||||
\(259\) | 10.4853 | 0.651524 | ||||||||
\(260\) | −2.12132 | − | 6.36396i | −0.131559 | − | 0.394676i | ||||
\(261\) | −2.00000 | + | 2.00000i | −0.123797 | + | 0.123797i | ||||
\(262\) | −7.58579 | − | 7.58579i | −0.468651 | − | 0.468651i | ||||
\(263\) | 4.75736 | 0.293351 | 0.146676 | − | 0.989185i | \(-0.453143\pi\) | ||||
0.146676 | + | 0.989185i | \(0.453143\pi\) | |||||||
\(264\) | 0.928932i | 0.0571718i | ||||||||
\(265\) | 6.36396 | − | 2.12132i | 0.390935 | − | 0.130312i | ||||
\(266\) | 7.24264 | − | 7.24264i | 0.444075 | − | 0.444075i | ||||
\(267\) | −3.36396 | + | 3.36396i | −0.205871 | + | 0.205871i | ||||
\(268\) | 14.4853i | 0.884829i | ||||||||
\(269\) | −11.2929 | − | 11.2929i | −0.688540 | − | 0.688540i | 0.273369 | − | 0.961909i | \(-0.411862\pi\) |
−0.961909 | + | 0.273369i | \(0.911862\pi\) | |||||||
\(270\) | −4.82843 | − | 2.41421i | −0.293849 | − | 0.146924i | ||||
\(271\) | −6.48528 | −0.393953 | −0.196976 | − | 0.980408i | \(-0.563112\pi\) | ||||
−0.196976 | + | 0.980408i | \(0.563112\pi\) | |||||||
\(272\) | −2.12132 | − | 3.53553i | −0.128624 | − | 0.214373i | ||||
\(273\) | − | 1.75736i | − | 0.106360i | ||||||
\(274\) | 4.58579i | 0.277037i | ||||||||
\(275\) | −1.58579 | + | 11.1005i | −0.0956265 | + | 0.669386i | ||||
\(276\) | −1.65685 | −0.0997309 | ||||||||
\(277\) | 8.24264 | − | 8.24264i | 0.495252 | − | 0.495252i | −0.414704 | − | 0.909956i | \(-0.636115\pi\) |
0.909956 | + | 0.414704i | \(0.136115\pi\) | |||||||
\(278\) | 11.0000 | + | 11.0000i | 0.659736 | + | 0.659736i | ||||
\(279\) | 15.1716 | − | 15.1716i | 0.908298 | − | 0.908298i | ||||
\(280\) | 2.82843 | + | 1.41421i | 0.169031 | + | 0.0845154i | ||||
\(281\) | − | 3.34315i | − | 0.199435i | −0.995016 | − | 0.0997177i | \(-0.968206\pi\) | ||
0.995016 | − | 0.0997177i | \(-0.0317940\pi\) | |||||||
\(282\) | −0.464466 | − | 0.464466i | −0.0276586 | − | 0.0276586i | ||||
\(283\) | −19.1213 | − | 19.1213i | −1.13664 | − | 1.13664i | −0.989048 | − | 0.147597i | \(-0.952846\pi\) |
−0.147597 | − | 0.989048i | \(-0.547154\pi\) | |||||||
\(284\) | 3.70711 | + | 3.70711i | 0.219976 | + | 0.219976i | ||||
\(285\) | 6.00000 | + | 3.00000i | 0.355409 | + | 0.177705i | ||||
\(286\) | 4.75736 | + | 4.75736i | 0.281309 | + | 0.281309i | ||||
\(287\) | 8.82843 | 0.521126 | ||||||||
\(288\) | − | 2.82843i | − | 0.166667i | ||||||
\(289\) | −8.00000 | + | 15.0000i | −0.470588 | + | 0.882353i | ||||
\(290\) | 2.00000 | + | 1.00000i | 0.117444 | + | 0.0587220i | ||||
\(291\) | 0.0710678i | 0.00416607i | ||||||||
\(292\) | −8.36396 | + | 8.36396i | −0.489464 | + | 0.489464i | ||||
\(293\) | 20.6569i | 1.20679i | 0.797444 | + | 0.603393i | \(0.206185\pi\) | ||||
−0.797444 | + | 0.603393i | \(0.793815\pi\) | |||||||
\(294\) | −1.46447 | − | 1.46447i | −0.0854094 | − | 0.0854094i | ||||
\(295\) | −9.12132 | − | 27.3640i | −0.531064 | − | 1.59319i | ||||
\(296\) | −5.24264 | + | 5.24264i | −0.304722 | + | 0.304722i | ||||
\(297\) | 5.41421 | 0.314165 | ||||||||
\(298\) | 12.7279 | 0.737309 | ||||||||
\(299\) | −8.48528 | + | 8.48528i | −0.490716 | + | 0.490716i | ||||
\(300\) | −0.292893 | + | 2.05025i | −0.0169102 | + | 0.118371i | ||||
\(301\) | 3.75736 | + | 3.75736i | 0.216571 | + | 0.216571i | ||||
\(302\) | 12.0000i | 0.690522i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.24264i | 0.415394i | ||||||||
\(305\) | −8.65685 | + | 17.3137i | −0.495690 | + | 0.991380i | ||||
\(306\) | −10.0000 | + | 6.00000i | −0.571662 | + | 0.342997i | ||||
\(307\) | 33.2132i | 1.89558i | 0.318899 | + | 0.947789i | \(0.396687\pi\) | ||||
−0.318899 | + | 0.947789i | \(0.603313\pi\) | |||||||
\(308\) | −3.17157 | −0.180717 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.1716 | − | 7.58579i | −0.861687 | − | 0.430844i | ||||
\(311\) | −1.41421 | − | 1.41421i | −0.0801927 | − | 0.0801927i | 0.665873 | − | 0.746065i | \(-0.268059\pi\) |
−0.746065 | + | 0.665873i | \(0.768059\pi\) | |||||||
\(312\) | 0.878680 | + | 0.878680i | 0.0497454 | + | 0.0497454i | ||||
\(313\) | −22.4853 | − | 22.4853i | −1.27094 | − | 1.27094i | −0.945594 | − | 0.325349i | \(-0.894518\pi\) |
−0.325349 | − | 0.945594i | \(-0.605482\pi\) | |||||||
\(314\) | 12.0000i | 0.677199i | ||||||||
\(315\) | 4.00000 | − | 8.00000i | 0.225374 | − | 0.450749i | ||||
\(316\) | −0.242641 | + | 0.242641i | −0.0136496 | + | 0.0136496i | ||||
\(317\) | −14.1421 | − | 14.1421i | −0.794301 | − | 0.794301i | 0.187889 | − | 0.982190i | \(-0.439836\pi\) |
−0.982190 | + | 0.187889i | \(0.939836\pi\) | |||||||
\(318\) | −0.878680 | + | 0.878680i | −0.0492739 | + | 0.0492739i | ||||
\(319\) | −2.24264 | −0.125564 | ||||||||
\(320\) | −2.12132 | + | 0.707107i | −0.118585 | + | 0.0395285i | ||||
\(321\) | − | 1.65685i | − | 0.0924766i | ||||||
\(322\) | − | 5.65685i | − | 0.315244i | ||||||
\(323\) | 25.6066 | − | 15.3640i | 1.42479 | − | 0.854874i | ||||
\(324\) | −7.48528 | −0.415849 | ||||||||
\(325\) | 9.00000 | + | 12.0000i | 0.499230 | + | 0.665640i | ||||
\(326\) | 4.48528 | + | 4.48528i | 0.248417 | + | 0.248417i | ||||
\(327\) | 5.04163i | 0.278803i | ||||||||
\(328\) | −4.41421 | + | 4.41421i | −0.243734 | + | 0.243734i | ||||
\(329\) | 1.58579 | − | 1.58579i | 0.0874272 | − | 0.0874272i | ||||
\(330\) | −0.656854 | − | 1.97056i | −0.0361586 | − | 0.108476i | ||||
\(331\) | − | 15.7279i | − | 0.864485i | −0.901757 | − | 0.432242i | \(-0.857722\pi\) | ||
0.901757 | − | 0.432242i | \(-0.142278\pi\) | |||||||
\(332\) | 4.24264 | 0.232845 | ||||||||
\(333\) | 14.8284 | + | 14.8284i | 0.812593 | + | 0.812593i | ||||
\(334\) | 1.07107 | − | 1.07107i | 0.0586062 | − | 0.0586062i | ||||
\(335\) | −10.2426 | − | 30.7279i | −0.559615 | − | 1.67885i | ||||
\(336\) | −0.585786 | −0.0319573 | ||||||||
\(337\) | 12.8492 | − | 12.8492i | 0.699943 | − | 0.699943i | −0.264455 | − | 0.964398i | \(-0.585192\pi\) |
0.964398 | + | 0.264455i | \(0.0851921\pi\) | |||||||
\(338\) | −4.00000 | −0.217571 | ||||||||
\(339\) | −1.44365 | −0.0784083 | ||||||||
\(340\) | 7.00000 | + | 6.00000i | 0.379628 | + | 0.325396i | ||||
\(341\) | 17.0122 | 0.921262 | ||||||||
\(342\) | 20.4853 | 1.10772 | ||||||||
\(343\) | 12.0000 | − | 12.0000i | 0.647939 | − | 0.647939i | ||||
\(344\) | −3.75736 | −0.202583 | ||||||||
\(345\) | 3.51472 | − | 1.17157i | 0.189226 | − | 0.0630754i | ||||
\(346\) | −17.6569 | + | 17.6569i | −0.949238 | + | 0.949238i | ||||
\(347\) | 15.7071 | + | 15.7071i | 0.843202 | + | 0.843202i | 0.989274 | − | 0.146072i | \(-0.0466632\pi\) |
−0.146072 | + | 0.989274i | \(0.546663\pi\) | |||||||
\(348\) | −0.414214 | −0.0222042 | ||||||||
\(349\) | 10.9706i | 0.587241i | 0.955922 | + | 0.293620i | \(0.0948602\pi\) | ||||
−0.955922 | + | 0.293620i | \(0.905140\pi\) | |||||||
\(350\) | −7.00000 | − | 1.00000i | −0.374166 | − | 0.0534522i | ||||
\(351\) | 5.12132 | − | 5.12132i | 0.273356 | − | 0.273356i | ||||
\(352\) | 1.58579 | − | 1.58579i | 0.0845227 | − | 0.0845227i | ||||
\(353\) | − | 11.3137i | − | 0.602168i | −0.953598 | − | 0.301084i | \(-0.902652\pi\) | ||
0.953598 | − | 0.301084i | \(-0.0973484\pi\) | |||||||
\(354\) | 3.77817 | + | 3.77817i | 0.200808 | + | 0.200808i | ||||
\(355\) | −10.4853 | − | 5.24264i | −0.556501 | − | 0.278250i | ||||
\(356\) | 11.4853 | 0.608719 | ||||||||
\(357\) | 1.24264 | + | 2.07107i | 0.0657675 | + | 0.109613i | ||||
\(358\) | − | 0.686292i | − | 0.0362716i | ||||||
\(359\) | − | 7.07107i | − | 0.373197i | −0.982436 | − | 0.186598i | \(-0.940254\pi\) | ||
0.982436 | − | 0.186598i | \(-0.0597463\pi\) | |||||||
\(360\) | 2.00000 | + | 6.00000i | 0.105409 | + | 0.316228i | ||||
\(361\) | −33.4558 | −1.76083 | ||||||||
\(362\) | 14.0000 | − | 14.0000i | 0.735824 | − | 0.735824i | ||||
\(363\) | −1.74874 | − | 1.74874i | −0.0917849 | − | 0.0917849i | ||||
\(364\) | −3.00000 | + | 3.00000i | −0.157243 | + | 0.157243i | ||||
\(365\) | 11.8284 | − | 23.6569i | 0.619128 | − | 1.23826i | ||||
\(366\) | − | 3.58579i | − | 0.187432i | ||||||
\(367\) | −18.2426 | − | 18.2426i | −0.952258 | − | 0.952258i | 0.0466531 | − | 0.998911i | \(-0.485144\pi\) |
−0.998911 | + | 0.0466531i | \(0.985144\pi\) | |||||||
\(368\) | 2.82843 | + | 2.82843i | 0.147442 | + | 0.147442i | ||||
\(369\) | 12.4853 | + | 12.4853i | 0.649958 | + | 0.649958i | ||||
\(370\) | 7.41421 | − | 14.8284i | 0.385447 | − | 0.770893i | ||||
\(371\) | −3.00000 | − | 3.00000i | −0.155752 | − | 0.155752i | ||||
\(372\) | 3.14214 | 0.162912 | ||||||||
\(373\) | − | 32.4853i | − | 1.68202i | −0.541016 | − | 0.841012i | \(-0.681960\pi\) | ||
0.541016 | − | 0.841012i | \(-0.318040\pi\) | |||||||
\(374\) | −8.97056 | − | 2.24264i | −0.463857 | − | 0.115964i | ||||
\(375\) | −0.828427 | − | 4.55635i | −0.0427798 | − | 0.235289i | ||||
\(376\) | 1.58579i | 0.0817807i | ||||||||
\(377\) | −2.12132 | + | 2.12132i | −0.109254 | + | 0.109254i | ||||
\(378\) | 3.41421i | 0.175608i | ||||||||
\(379\) | 0.485281 | + | 0.485281i | 0.0249272 | + | 0.0249272i | 0.719461 | − | 0.694533i | \(-0.244389\pi\) |
−0.694533 | + | 0.719461i | \(0.744389\pi\) | |||||||
\(380\) | −5.12132 | − | 15.3640i | −0.262718 | − | 0.788155i | ||||
\(381\) | −5.19239 | + | 5.19239i | −0.266014 | + | 0.266014i | ||||
\(382\) | −21.2132 | −1.08536 | ||||||||
\(383\) | −13.2426 | −0.676667 | −0.338334 | − | 0.941026i | \(-0.609863\pi\) | ||||
−0.338334 | + | 0.941026i | \(0.609863\pi\) | |||||||
\(384\) | 0.292893 | − | 0.292893i | 0.0149466 | − | 0.0149466i | ||||
\(385\) | 6.72792 | − | 2.24264i | 0.342887 | − | 0.114296i | ||||
\(386\) | −18.4853 | − | 18.4853i | −0.940876 | − | 0.940876i | ||||
\(387\) | 10.6274i | 0.540222i | ||||||||
\(388\) | 0.121320 | − | 0.121320i | 0.00615911 | − | 0.00615911i | ||||
\(389\) | 16.6274i | 0.843044i | 0.906818 | + | 0.421522i | \(0.138504\pi\) | ||||
−0.906818 | + | 0.421522i | \(0.861496\pi\) | |||||||
\(390\) | −2.48528 | − | 1.24264i | −0.125847 | − | 0.0629236i | ||||
\(391\) | 4.00000 | − | 16.0000i | 0.202289 | − | 0.809155i | ||||
\(392\) | 5.00000i | 0.252538i | ||||||||
\(393\) | −4.44365 | −0.224153 | ||||||||
\(394\) | −3.34315 | − | 3.34315i | −0.168425 | − | 0.168425i | ||||
\(395\) | 0.343146 | − | 0.686292i | 0.0172655 | − | 0.0345311i | ||||
\(396\) | −4.48528 | − | 4.48528i | −0.225394 | − | 0.225394i | ||||
\(397\) | 4.72792 | + | 4.72792i | 0.237288 | + | 0.237288i | 0.815726 | − | 0.578438i | \(-0.196338\pi\) |
−0.578438 | + | 0.815726i | \(0.696338\pi\) | |||||||
\(398\) | 7.12132 | + | 7.12132i | 0.356960 | + | 0.356960i | ||||
\(399\) | − | 4.24264i | − | 0.212398i | ||||||
\(400\) | 4.00000 | − | 3.00000i | 0.200000 | − | 0.150000i | ||||
\(401\) | −2.10051 | + | 2.10051i | −0.104894 | + | 0.104894i | −0.757606 | − | 0.652712i | \(-0.773631\pi\) |
0.652712 | + | 0.757606i | \(0.273631\pi\) | |||||||
\(402\) | 4.24264 | + | 4.24264i | 0.211604 | + | 0.211604i | ||||
\(403\) | 16.0919 | − | 16.0919i | 0.801594 | − | 0.801594i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.8787 | − | 5.29289i | 0.789018 | − | 0.263006i | ||||
\(406\) | − | 1.41421i | − | 0.0701862i | ||||||
\(407\) | 16.6274i | 0.824190i | ||||||||
\(408\) | −1.65685 | − | 0.414214i | −0.0820265 | − | 0.0205066i | ||||
\(409\) | 25.4853 | 1.26017 | 0.630083 | − | 0.776528i | \(-0.283021\pi\) | ||||
0.630083 | + | 0.776528i | \(0.283021\pi\) | |||||||
\(410\) | 6.24264 | − | 12.4853i | 0.308302 | − | 0.616604i | ||||
\(411\) | 1.34315 | + | 1.34315i | 0.0662525 | + | 0.0662525i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.8995 | + | 12.8995i | −0.634743 | + | 0.634743i | ||||
\(414\) | 8.00000 | − | 8.00000i | 0.393179 | − | 0.393179i | ||||
\(415\) | −9.00000 | + | 3.00000i | −0.441793 | + | 0.147264i | ||||
\(416\) | − | 3.00000i | − | 0.147087i | ||||||
\(417\) | 6.44365 | 0.315547 | ||||||||
\(418\) | 11.4853 | + | 11.4853i | 0.561763 | + | 0.561763i | ||||
\(419\) | −11.3137 | + | 11.3137i | −0.552711 | + | 0.552711i | −0.927222 | − | 0.374511i | \(-0.877810\pi\) |
0.374511 | + | 0.927222i | \(0.377810\pi\) | |||||||
\(420\) | 1.24264 | − | 0.414214i | 0.0606347 | − | 0.0202116i | ||||
\(421\) | −19.2132 | −0.936394 | −0.468197 | − | 0.883624i | \(-0.655096\pi\) | ||||
−0.468197 | + | 0.883624i | \(0.655096\pi\) | |||||||
\(422\) | 8.00000 | − | 8.00000i | 0.389434 | − | 0.389434i | ||||
\(423\) | 4.48528 | 0.218082 | ||||||||
\(424\) | 3.00000 | 0.145693 | ||||||||
\(425\) | −19.0919 | − | 7.77817i | −0.926092 | − | 0.377297i | ||||
\(426\) | 2.17157 | 0.105213 | ||||||||
\(427\) | 12.2426 | 0.592463 | ||||||||
\(428\) | −2.82843 | + | 2.82843i | −0.136717 | + | 0.136717i | ||||
\(429\) | 2.78680 | 0.134548 | ||||||||
\(430\) | 7.97056 | − | 2.65685i | 0.384375 | − | 0.128125i | ||||
\(431\) | 17.6569 | − | 17.6569i | 0.850501 | − | 0.850501i | −0.139694 | − | 0.990195i | \(-0.544612\pi\) |
0.990195 | + | 0.139694i | \(0.0446119\pi\) | |||||||
\(432\) | −1.70711 | − | 1.70711i | −0.0821332 | − | 0.0821332i | ||||
\(433\) | −5.75736 | −0.276681 | −0.138341 | − | 0.990385i | \(-0.544177\pi\) | ||||
−0.138341 | + | 0.990385i | \(0.544177\pi\) | |||||||
\(434\) | 10.7279i | 0.514957i | ||||||||
\(435\) | 0.878680 | − | 0.292893i | 0.0421295 | − | 0.0140432i | ||||
\(436\) | 8.60660 | − | 8.60660i | 0.412181 | − | 0.412181i | ||||
\(437\) | −20.4853 | + | 20.4853i | −0.979944 | + | 0.979944i | ||||
\(438\) | 4.89949i | 0.234107i | ||||||||
\(439\) | 20.9706 | + | 20.9706i | 1.00087 | + | 1.00087i | 1.00000 | 0.000870732i | \(0.000277162\pi\) | |
0.000870732 | 1.00000i | \(0.499723\pi\) | ||||||||
\(440\) | −2.24264 | + | 4.48528i | −0.106914 | + | 0.213827i | ||||
\(441\) | 14.1421 | 0.673435 | ||||||||
\(442\) | −10.6066 | + | 6.36396i | −0.504505 | + | 0.302703i | ||||
\(443\) | − | 37.7990i | − | 1.79588i | −0.440114 | − | 0.897942i | \(-0.645062\pi\) | ||
0.440114 | − | 0.897942i | \(-0.354938\pi\) | |||||||
\(444\) | 3.07107i | 0.145746i | ||||||||
\(445\) | −24.3640 | + | 8.12132i | −1.15496 | + | 0.384988i | ||||
\(446\) | 23.2426 | 1.10057 | ||||||||
\(447\) | 3.72792 | − | 3.72792i | 0.176325 | − | 0.176325i | ||||
\(448\) | 1.00000 | + | 1.00000i | 0.0472456 | + | 0.0472456i | ||||
\(449\) | −28.7990 | + | 28.7990i | −1.35911 | + | 1.35911i | −0.484090 | + | 0.875018i | \(0.660849\pi\) |
−0.875018 | + | 0.484090i | \(0.839151\pi\) | |||||||
\(450\) | −8.48528 | − | 11.3137i | −0.400000 | − | 0.533333i | ||||
\(451\) | 14.0000i | 0.659234i | ||||||||
\(452\) | 2.46447 | + | 2.46447i | 0.115919 | + | 0.115919i | ||||
\(453\) | 3.51472 | + | 3.51472i | 0.165136 | + | 0.165136i | ||||
\(454\) | 4.05025 | + | 4.05025i | 0.190088 | + | 0.190088i | ||||
\(455\) | 4.24264 | − | 8.48528i | 0.198898 | − | 0.397796i | ||||
\(456\) | 2.12132 | + | 2.12132i | 0.0993399 | + | 0.0993399i | ||||
\(457\) | −2.24264 | −0.104906 | −0.0524532 | − | 0.998623i | \(-0.516704\pi\) | ||||
−0.0524532 | + | 0.998623i | \(0.516704\pi\) | |||||||
\(458\) | − | 7.75736i | − | 0.362478i | ||||||
\(459\) | −2.41421 | + | 9.65685i | −0.112686 | + | 0.450743i | ||||
\(460\) | −8.00000 | − | 4.00000i | −0.373002 | − | 0.186501i | ||||
\(461\) | − | 40.2843i | − | 1.87623i | −0.346330 | − | 0.938113i | \(-0.612572\pi\) | ||
0.346330 | − | 0.938113i | \(-0.387428\pi\) | |||||||
\(462\) | −0.928932 | + | 0.928932i | −0.0432178 | + | 0.0432178i | ||||
\(463\) | 25.2426i | 1.17312i | 0.809904 | + | 0.586562i | \(0.199519\pi\) | ||||
−0.809904 | + | 0.586562i | \(0.800481\pi\) | |||||||
\(464\) | 0.707107 | + | 0.707107i | 0.0328266 | + | 0.0328266i | ||||
\(465\) | −6.66548 | + | 2.22183i | −0.309104 | + | 0.103035i | ||||
\(466\) | 10.9497 | − | 10.9497i | 0.507237 | − | 0.507237i | ||||
\(467\) | −18.7279 | −0.866625 | −0.433312 | − | 0.901244i | \(-0.642655\pi\) | ||||
−0.433312 | + | 0.901244i | \(0.642655\pi\) | |||||||
\(468\) | −8.48528 | −0.392232 | ||||||||
\(469\) | −14.4853 | + | 14.4853i | −0.668868 | + | 0.668868i | ||||
\(470\) | −1.12132 | − | 3.36396i | −0.0517227 | − | 0.155168i | ||||
\(471\) | 3.51472 | + | 3.51472i | 0.161950 | + | 0.161950i | ||||
\(472\) | − | 12.8995i | − | 0.593747i | ||||||
\(473\) | −5.95837 | + | 5.95837i | −0.273966 | + | 0.273966i | ||||
\(474\) | 0.142136i | 0.00652851i | ||||||||
\(475\) | 21.7279 | + | 28.9706i | 0.996945 | + | 1.32926i | ||||
\(476\) | 1.41421 | − | 5.65685i | 0.0648204 | − | 0.259281i | ||||
\(477\) | − | 8.48528i | − | 0.388514i | ||||||
\(478\) | −22.2426 | −1.01735 | ||||||||
\(479\) | −10.0503 | − | 10.0503i | −0.459208 | − | 0.459208i | 0.439188 | − | 0.898395i | \(-0.355266\pi\) |
−0.898395 | + | 0.439188i | \(0.855266\pi\) | |||||||
\(480\) | −0.414214 | + | 0.828427i | −0.0189062 | + | 0.0378124i | ||||
\(481\) | 15.7279 | + | 15.7279i | 0.717132 | + | 0.717132i | ||||
\(482\) | −2.75736 | − | 2.75736i | −0.125594 | − | 0.125594i | ||||
\(483\) | −1.65685 | − | 1.65685i | −0.0753895 | − | 0.0753895i | ||||
\(484\) | 5.97056i | 0.271389i | ||||||||
\(485\) | −0.171573 | + | 0.343146i | −0.00779072 | + | 0.0155814i | ||||
\(486\) | −7.31371 | + | 7.31371i | −0.331757 | + | 0.331757i | ||||
\(487\) | 11.2426 | + | 11.2426i | 0.509453 | + | 0.509453i | 0.914358 | − | 0.404906i | \(-0.132696\pi\) |
−0.404906 | + | 0.914358i | \(0.632696\pi\) | |||||||
\(488\) | −6.12132 | + | 6.12132i | −0.277099 | + | 0.277099i | ||||
\(489\) | 2.62742 | 0.118816 | ||||||||
\(490\) | −3.53553 | − | 10.6066i | −0.159719 | − | 0.479157i | ||||
\(491\) | 6.89949i | 0.311370i | 0.987807 | + | 0.155685i | \(0.0497585\pi\) | ||||
−0.987807 | + | 0.155685i | \(0.950242\pi\) | |||||||
\(492\) | 2.58579i | 0.116576i | ||||||||
\(493\) | 1.00000 | − | 4.00000i | 0.0450377 | − | 0.180151i | ||||
\(494\) | 21.7279 | 0.977585 | ||||||||
\(495\) | 12.6863 | + | 6.34315i | 0.570206 | + | 0.285103i | ||||
\(496\) | −5.36396 | − | 5.36396i | −0.240849 | − | 0.240849i | ||||
\(497\) | 7.41421i | 0.332573i | ||||||||
\(498\) | 1.24264 | − | 1.24264i | 0.0556841 | − | 0.0556841i | ||||
\(499\) | −8.51472 | + | 8.51472i | −0.381171 | + | 0.381171i | −0.871524 | − | 0.490353i | \(-0.836868\pi\) |
0.490353 | + | 0.871524i | \(0.336868\pi\) | |||||||
\(500\) | −6.36396 | + | 9.19239i | −0.284605 | + | 0.411096i | ||||
\(501\) | − | 0.627417i | − | 0.0280309i | ||||||
\(502\) | −20.4853 | −0.914303 | ||||||||
\(503\) | 13.0711 | + | 13.0711i | 0.582810 | + | 0.582810i | 0.935674 | − | 0.352864i | \(-0.114792\pi\) |
−0.352864 | + | 0.935674i | \(0.614792\pi\) | |||||||
\(504\) | 2.82843 | − | 2.82843i | 0.125988 | − | 0.125988i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 8.97056 | 0.398790 | ||||||||
\(507\) | −1.17157 | + | 1.17157i | −0.0520314 | + | 0.0520314i | ||||
\(508\) | 17.7279 | 0.786549 | ||||||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 3.80761 | − | 0.292893i | 0.168604 | − | 0.0129695i | ||||
\(511\) | −16.7279 | −0.740000 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 12.3640 | − | 12.3640i | 0.545882 | − | 0.545882i | ||||
\(514\) | −6.72792 | −0.296756 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.10051 | + | 1.10051i | −0.0484470 | + | 0.0484470i | ||||
\(517\) | 2.51472 | + | 2.51472i | 0.110597 | + | 0.110597i | ||||
\(518\) | −10.4853 | −0.460697 | ||||||||
\(519\) | 10.3431i | 0.454014i | ||||||||
\(520\) | 2.12132 | + | 6.36396i | 0.0930261 | + | 0.279078i | ||||
\(521\) | −11.3137 | + | 11.3137i | −0.495663 | + | 0.495663i | −0.910085 | − | 0.414422i | \(-0.863984\pi\) |
0.414422 | + | 0.910085i | \(0.363984\pi\) | |||||||
\(522\) | 2.00000 | − | 2.00000i | 0.0875376 | − | 0.0875376i | ||||
\(523\) | 26.4853i | 1.15812i | 0.815285 | + | 0.579060i | \(0.196580\pi\) | ||||
−0.815285 | + | 0.579060i | \(0.803420\pi\) | |||||||
\(524\) | 7.58579 | + | 7.58579i | 0.331387 | + | 0.331387i | ||||
\(525\) | −2.34315 | + | 1.75736i | −0.102263 | + | 0.0766974i | ||||
\(526\) | −4.75736 | −0.207431 | ||||||||
\(527\) | −7.58579 | + | 30.3431i | −0.330442 | + | 1.32177i | ||||
\(528\) | − | 0.928932i | − | 0.0404266i | ||||||
\(529\) | − | 7.00000i | − | 0.304348i | ||||||
\(530\) | −6.36396 | + | 2.12132i | −0.276433 | + | 0.0921443i | ||||
\(531\) | −36.4853 | −1.58333 | ||||||||
\(532\) | −7.24264 | + | 7.24264i | −0.314008 | + | 0.314008i | ||||
\(533\) | 13.2426 | + | 13.2426i | 0.573602 | + | 0.573602i | ||||
\(534\) | 3.36396 | − | 3.36396i | 0.145573 | − | 0.145573i | ||||
\(535\) | 4.00000 | − | 8.00000i | 0.172935 | − | 0.345870i | ||||
\(536\) | − | 14.4853i | − | 0.625669i | ||||||
\(537\) | −0.201010 | − | 0.201010i | −0.00867423 | − | 0.00867423i | ||||
\(538\) | 11.2929 | + | 11.2929i | 0.486871 | + | 0.486871i | ||||
\(539\) | 7.92893 | + | 7.92893i | 0.341523 | + | 0.341523i | ||||
\(540\) | 4.82843 | + | 2.41421i | 0.207782 | + | 0.103891i | ||||
\(541\) | 20.9706 | + | 20.9706i | 0.901595 | + | 0.901595i | 0.995574 | − | 0.0939792i | \(-0.0299587\pi\) |
−0.0939792 | + | 0.995574i | \(0.529959\pi\) | |||||||
\(542\) | 6.48528 | 0.278567 | ||||||||
\(543\) | − | 8.20101i | − | 0.351939i | ||||||
\(544\) | 2.12132 | + | 3.53553i | 0.0909509 | + | 0.151585i | ||||
\(545\) | −12.1716 | + | 24.3431i | −0.521373 | + | 1.04275i | ||||
\(546\) | 1.75736i | 0.0752080i | ||||||||
\(547\) | 2.39340 | − | 2.39340i | 0.102334 | − | 0.102334i | −0.654086 | − | 0.756420i | \(-0.726947\pi\) |
0.756420 | + | 0.654086i | \(0.226947\pi\) | |||||||
\(548\) | − | 4.58579i | − | 0.195895i | ||||||
\(549\) | 17.3137 | + | 17.3137i | 0.738931 | + | 0.738931i | ||||
\(550\) | 1.58579 | − | 11.1005i | 0.0676182 | − | 0.473327i | ||||
\(551\) | −5.12132 | + | 5.12132i | −0.218176 | + | 0.218176i | ||||
\(552\) | 1.65685 | 0.0705204 | ||||||||
\(553\) | −0.485281 | −0.0206363 | ||||||||
\(554\) | −8.24264 | + | 8.24264i | −0.350196 | + | 0.350196i | ||||
\(555\) | −2.17157 | − | 6.51472i | −0.0921781 | − | 0.276534i | ||||
\(556\) | −11.0000 | − | 11.0000i | −0.466504 | − | 0.466504i | ||||
\(557\) | − | 34.7990i | − | 1.47448i | −0.675631 | − | 0.737240i | \(-0.736129\pi\) | ||
0.675631 | − | 0.737240i | \(-0.263871\pi\) | |||||||
\(558\) | −15.1716 | + | 15.1716i | −0.642264 | + | 0.642264i | ||||
\(559\) | 11.2721i | 0.476758i | ||||||||
\(560\) | −2.82843 | − | 1.41421i | −0.119523 | − | 0.0597614i | ||||
\(561\) | −3.28427 | + | 1.97056i | −0.138662 | + | 0.0831972i | ||||
\(562\) | 3.34315i | 0.141022i | ||||||||
\(563\) | −45.9411 | −1.93619 | −0.968094 | − | 0.250588i | \(-0.919376\pi\) | ||||
−0.968094 | + | 0.250588i | \(0.919376\pi\) | |||||||
\(564\) | 0.464466 | + | 0.464466i | 0.0195576 | + | 0.0195576i | ||||
\(565\) | −6.97056 | − | 3.48528i | −0.293254 | − | 0.146627i | ||||
\(566\) | 19.1213 | + | 19.1213i | 0.803729 | + | 0.803729i | ||||
\(567\) | −7.48528 | − | 7.48528i | −0.314352 | − | 0.314352i | ||||
\(568\) | −3.70711 | − | 3.70711i | −0.155547 | − | 0.155547i | ||||
\(569\) | − | 20.3137i | − | 0.851595i | −0.904818 | − | 0.425797i | \(-0.859994\pi\) | ||
0.904818 | − | 0.425797i | \(-0.140006\pi\) | |||||||
\(570\) | −6.00000 | − | 3.00000i | −0.251312 | − | 0.125656i | ||||
\(571\) | −20.2132 | + | 20.2132i | −0.845896 | + | 0.845896i | −0.989618 | − | 0.143722i | \(-0.954093\pi\) |
0.143722 | + | 0.989618i | \(0.454093\pi\) | |||||||
\(572\) | −4.75736 | − | 4.75736i | −0.198915 | − | 0.198915i | ||||
\(573\) | −6.21320 | + | 6.21320i | −0.259560 | + | 0.259560i | ||||
\(574\) | −8.82843 | −0.368491 | ||||||||
\(575\) | 19.7990 | + | 2.82843i | 0.825675 | + | 0.117954i | ||||
\(576\) | 2.82843i | 0.117851i | ||||||||
\(577\) | − | 4.97056i | − | 0.206927i | −0.994633 | − | 0.103464i | \(-0.967007\pi\) | ||
0.994633 | − | 0.103464i | \(-0.0329925\pi\) | |||||||
\(578\) | 8.00000 | − | 15.0000i | 0.332756 | − | 0.623918i | ||||
\(579\) | −10.8284 | −0.450014 | ||||||||
\(580\) | −2.00000 | − | 1.00000i | −0.0830455 | − | 0.0415227i | ||||
\(581\) | 4.24264 | + | 4.24264i | 0.176014 | + | 0.176014i | ||||
\(582\) | − | 0.0710678i | − | 0.00294586i | ||||||
\(583\) | 4.75736 | − | 4.75736i | 0.197030 | − | 0.197030i | ||||
\(584\) | 8.36396 | − | 8.36396i | 0.346103 | − | 0.346103i | ||||
\(585\) | 18.0000 | − | 6.00000i | 0.744208 | − | 0.248069i | ||||
\(586\) | − | 20.6569i | − | 0.853327i | ||||||
\(587\) | 24.0000 | 0.990586 | 0.495293 | − | 0.868726i | \(-0.335061\pi\) | ||||
0.495293 | + | 0.868726i | \(0.335061\pi\) | |||||||
\(588\) | 1.46447 | + | 1.46447i | 0.0603936 | + | 0.0603936i | ||||
\(589\) | 38.8492 | − | 38.8492i | 1.60076 | − | 1.60076i | ||||
\(590\) | 9.12132 | + | 27.3640i | 0.375519 | + | 1.12656i | ||||
\(591\) | −1.95837 | −0.0805566 | ||||||||
\(592\) | 5.24264 | − | 5.24264i | 0.215471 | − | 0.215471i | ||||
\(593\) | 18.0000 | 0.739171 | 0.369586 | − | 0.929197i | \(-0.379500\pi\) | ||||
0.369586 | + | 0.929197i | \(0.379500\pi\) | |||||||
\(594\) | −5.41421 | −0.222148 | ||||||||
\(595\) | 1.00000 | + | 13.0000i | 0.0409960 | + | 0.532948i | ||||
\(596\) | −12.7279 | −0.521356 | ||||||||
\(597\) | 4.17157 | 0.170731 | ||||||||
\(598\) | 8.48528 | − | 8.48528i | 0.346989 | − | 0.346989i | ||||
\(599\) | −12.0000 | −0.490307 | −0.245153 | − | 0.969484i | \(-0.578838\pi\) | ||||
−0.245153 | + | 0.969484i | \(0.578838\pi\) | |||||||
\(600\) | 0.292893 | − | 2.05025i | 0.0119573 | − | 0.0837012i | ||||
\(601\) | 28.7279 | − | 28.7279i | 1.17184 | − | 1.17184i | 0.190065 | − | 0.981772i | \(-0.439130\pi\) |
0.981772 | − | 0.190065i | \(-0.0608698\pi\) | |||||||
\(602\) | −3.75736 | − | 3.75736i | −0.153139 | − | 0.153139i | ||||
\(603\) | −40.9706 | −1.66845 | ||||||||
\(604\) | − | 12.0000i | − | 0.488273i | ||||||
\(605\) | −4.22183 | − | 12.6655i | −0.171642 | − | 0.514925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.4558 | − | 26.4558i | 1.07381 | − | 1.07381i | 0.0767600 | − | 0.997050i | \(-0.475542\pi\) |
0.997050 | − | 0.0767600i | \(-0.0244575\pi\) | |||||||
\(608\) | − | 7.24264i | − | 0.293728i | ||||||
\(609\) | −0.414214 | − | 0.414214i | −0.0167848 | − | 0.0167848i | ||||
\(610\) | 8.65685 | − | 17.3137i | 0.350506 | − | 0.701012i | ||||
\(611\) | 4.75736 | 0.192462 | ||||||||
\(612\) | 10.0000 | − | 6.00000i | 0.404226 | − | 0.242536i | ||||
\(613\) | − | 4.02944i | − | 0.162747i | −0.996684 | − | 0.0813737i | \(-0.974069\pi\) | ||
0.996684 | − | 0.0813737i | \(-0.0259307\pi\) | |||||||
\(614\) | − | 33.2132i | − | 1.34038i | ||||||
\(615\) | −1.82843 | − | 5.48528i | −0.0737293 | − | 0.221188i | ||||
\(616\) | 3.17157 | 0.127786 | ||||||||
\(617\) | −19.4350 | + | 19.4350i | −0.782425 | + | 0.782425i | −0.980239 | − | 0.197815i | \(-0.936616\pi\) |
0.197815 | + | 0.980239i | \(0.436616\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.75736 | − | 5.75736i | 0.231408 | − | 0.231408i | −0.581872 | − | 0.813280i | \(-0.697680\pi\) |
0.813280 | + | 0.581872i | \(0.197680\pi\) | |||||||
\(620\) | 15.1716 | + | 7.58579i | 0.609305 | + | 0.304653i | ||||
\(621\) | − | 9.65685i | − | 0.387516i | ||||||
\(622\) | 1.41421 | + | 1.41421i | 0.0567048 | + | 0.0567048i | ||||
\(623\) | 11.4853 | + | 11.4853i | 0.460148 | + | 0.460148i | ||||
\(624\) | −0.878680 | − | 0.878680i | −0.0351753 | − | 0.0351753i | ||||
\(625\) | 7.00000 | − | 24.0000i | 0.280000 | − | 0.960000i | ||||
\(626\) | 22.4853 | + | 22.4853i | 0.898693 | + | 0.898693i | ||||
\(627\) | 6.72792 | 0.268687 | ||||||||
\(628\) | − | 12.0000i | − | 0.478852i | ||||||
\(629\) | −29.6569 | − | 7.41421i | −1.18250 | − | 0.295624i | ||||
\(630\) | −4.00000 | + | 8.00000i | −0.159364 | + | 0.318728i | ||||
\(631\) | − | 2.48528i | − | 0.0989375i | −0.998776 | − | 0.0494687i | \(-0.984247\pi\) | ||
0.998776 | − | 0.0494687i | \(-0.0157528\pi\) | |||||||
\(632\) | 0.242641 | − | 0.242641i | 0.00965173 | − | 0.00965173i | ||||
\(633\) | − | 4.68629i | − | 0.186263i | ||||||
\(634\) | 14.1421 | + | 14.1421i | 0.561656 | + | 0.561656i | ||||
\(635\) | −37.6066 | + | 12.5355i | −1.49237 | + | 0.497457i | ||||
\(636\) | 0.878680 | − | 0.878680i | 0.0348419 | − | 0.0348419i | ||||
\(637\) | 15.0000 | 0.594322 | ||||||||
\(638\) | 2.24264 | 0.0887870 | ||||||||
\(639\) | −10.4853 | + | 10.4853i | −0.414791 | + | 0.414791i | ||||
\(640\) | 2.12132 | − | 0.707107i | 0.0838525 | − | 0.0279508i | ||||
\(641\) | 3.55635 | + | 3.55635i | 0.140467 | + | 0.140467i | 0.773844 | − | 0.633376i | \(-0.218332\pi\) |
−0.633376 | + | 0.773844i | \(0.718332\pi\) | |||||||
\(642\) | 1.65685i | 0.0653908i | ||||||||
\(643\) | −3.75736 | + | 3.75736i | −0.148176 | + | 0.148176i | −0.777303 | − | 0.629127i | \(-0.783413\pi\) |
0.629127 | + | 0.777303i | \(0.283413\pi\) | |||||||
\(644\) | 5.65685i | 0.222911i | ||||||||
\(645\) | 1.55635 | − | 3.11270i | 0.0612812 | − | 0.122562i | ||||
\(646\) | −25.6066 | + | 15.3640i | −1.00748 | + | 0.604487i | ||||
\(647\) | − | 47.5269i | − | 1.86848i | −0.356651 | − | 0.934238i | \(-0.616081\pi\) | ||
0.356651 | − | 0.934238i | \(-0.383919\pi\) | |||||||
\(648\) | 7.48528 | 0.294050 | ||||||||
\(649\) | −20.4558 | − | 20.4558i | −0.802962 | − | 0.802962i | ||||
\(650\) | −9.00000 | − | 12.0000i | −0.353009 | − | 0.470679i | ||||
\(651\) | 3.14214 | + | 3.14214i | 0.123150 | + | 0.123150i | ||||
\(652\) | −4.48528 | − | 4.48528i | −0.175657 | − | 0.175657i | ||||
\(653\) | 4.79899 | + | 4.79899i | 0.187799 | + | 0.187799i | 0.794744 | − | 0.606945i | \(-0.207605\pi\) |
−0.606945 | + | 0.794744i | \(0.707605\pi\) | |||||||
\(654\) | − | 5.04163i | − | 0.197143i | ||||||
\(655\) | −21.4558 | − | 10.7279i | −0.838349 | − | 0.419175i | ||||
\(656\) | 4.41421 | − | 4.41421i | 0.172346 | − | 0.172346i | ||||
\(657\) | −23.6569 | − | 23.6569i | −0.922942 | − | 0.922942i | ||||
\(658\) | −1.58579 | + | 1.58579i | −0.0618204 | + | 0.0618204i | ||||
\(659\) | 30.2132 | 1.17694 | 0.588470 | − | 0.808519i | \(-0.299731\pi\) | ||||
0.588470 | + | 0.808519i | \(0.299731\pi\) | |||||||
\(660\) | 0.656854 | + | 1.97056i | 0.0255680 | + | 0.0767041i | ||||
\(661\) | − | 12.0000i | − | 0.466746i | −0.972387 | − | 0.233373i | \(-0.925024\pi\) | ||
0.972387 | − | 0.233373i | \(-0.0749763\pi\) | |||||||
\(662\) | 15.7279i | 0.611283i | ||||||||
\(663\) | −1.24264 | + | 4.97056i | −0.0482602 | + | 0.193041i | ||||
\(664\) | −4.24264 | −0.164646 | ||||||||
\(665\) | 10.2426 | − | 20.4853i | 0.397193 | − | 0.794385i | ||||
\(666\) | −14.8284 | − | 14.8284i | −0.574590 | − | 0.574590i | ||||
\(667\) | 4.00000i | 0.154881i | ||||||||
\(668\) | −1.07107 | + | 1.07107i | −0.0414409 | + | 0.0414409i | ||||
\(669\) | 6.80761 | − | 6.80761i | 0.263197 | − | 0.263197i | ||||
\(670\) | 10.2426 | + | 30.7279i | 0.395708 | + | 1.18712i | ||||
\(671\) | 19.4142i | 0.749477i | ||||||||
\(672\) | 0.585786 | 0.0225972 | ||||||||
\(673\) | 25.8787 | + | 25.8787i | 0.997550 | + | 0.997550i | 0.999997 | − | 0.00244721i | \(-0.000778973\pi\) |
−0.00244721 | + | 0.999997i | \(0.500779\pi\) | |||||||
\(674\) | −12.8492 | + | 12.8492i | −0.494934 | + | 0.494934i | ||||
\(675\) | −11.9497 | − | 1.70711i | −0.459946 | − | 0.0657066i | ||||
\(676\) | 4.00000 | 0.153846 | ||||||||
\(677\) | 22.4142 | − | 22.4142i | 0.861448 | − | 0.861448i | −0.130058 | − | 0.991506i | \(-0.541516\pi\) |
0.991506 | + | 0.130058i | \(0.0415164\pi\) | |||||||
\(678\) | 1.44365 | 0.0554431 | ||||||||
\(679\) | 0.242641 | 0.00931169 | ||||||||
\(680\) | −7.00000 | − | 6.00000i | −0.268438 | − | 0.230089i | ||||
\(681\) | 2.37258 | 0.0909176 | ||||||||
\(682\) | −17.0122 | −0.651431 | ||||||||
\(683\) | 24.5355 | − | 24.5355i | 0.938826 | − | 0.938826i | −0.0594077 | − | 0.998234i | \(-0.518921\pi\) |
0.998234 | + | 0.0594077i | \(0.0189212\pi\) | |||||||
\(684\) | −20.4853 | −0.783274 | ||||||||
\(685\) | 3.24264 | + | 9.72792i | 0.123895 | + | 0.371685i | ||||
\(686\) | −12.0000 | + | 12.0000i | −0.458162 | + | 0.458162i | ||||
\(687\) | −2.27208 | − | 2.27208i | −0.0866852 | − | 0.0866852i | ||||
\(688\) | 3.75736 | 0.143248 | ||||||||
\(689\) | − | 9.00000i | − | 0.342873i | ||||||
\(690\) | −3.51472 | + | 1.17157i | −0.133803 | + | 0.0446010i | ||||
\(691\) | 9.48528 | − | 9.48528i | 0.360837 | − | 0.360837i | −0.503284 | − | 0.864121i | \(-0.667875\pi\) |
0.864121 | + | 0.503284i | \(0.167875\pi\) | |||||||
\(692\) | 17.6569 | − | 17.6569i | 0.671213 | − | 0.671213i | ||||
\(693\) | − | 8.97056i | − | 0.340764i | ||||||
\(694\) | −15.7071 | − | 15.7071i | −0.596234 | − | 0.596234i | ||||
\(695\) | 31.1127 | + | 15.5563i | 1.18017 | + | 0.590086i | ||||
\(696\) | 0.414214 | 0.0157007 | ||||||||
\(697\) | −24.9706 | − | 6.24264i | −0.945828 | − | 0.236457i | ||||
\(698\) | − | 10.9706i | − | 0.415242i | ||||||
\(699\) | − | 6.41421i | − | 0.242608i | ||||||
\(700\) | 7.00000 | + | 1.00000i | 0.264575 | + | 0.0377964i | ||||
\(701\) | −12.0000 | −0.453234 | −0.226617 | − | 0.973984i | \(-0.572767\pi\) | ||||
−0.226617 | + | 0.973984i | \(0.572767\pi\) | |||||||
\(702\) | −5.12132 | + | 5.12132i | −0.193292 | + | 0.193292i | ||||
\(703\) | 37.9706 | + | 37.9706i | 1.43209 | + | 1.43209i | ||||
\(704\) | −1.58579 | + | 1.58579i | −0.0597666 | + | 0.0597666i | ||||
\(705\) | −1.31371 | − | 0.656854i | −0.0494771 | − | 0.0247386i | ||||
\(706\) | 11.3137i | 0.425797i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.77817 | − | 3.77817i | −0.141992 | − | 0.141992i | ||||
\(709\) | 2.60660 | + | 2.60660i | 0.0978930 | + | 0.0978930i | 0.754357 | − | 0.656464i | \(-0.227949\pi\) |
−0.656464 | + | 0.754357i | \(0.727949\pi\) | |||||||
\(710\) | 10.4853 | + | 5.24264i | 0.393506 | + | 0.196753i | ||||
\(711\) | −0.686292 | − | 0.686292i | −0.0257379 | − | 0.0257379i | ||||
\(712\) | −11.4853 | −0.430429 | ||||||||
\(713\) | − | 30.3431i | − | 1.13636i | ||||||
\(714\) | −1.24264 | − | 2.07107i | −0.0465047 | − | 0.0775078i | ||||
\(715\) | 13.4558 | + | 6.72792i | 0.503220 | + | 0.251610i | ||||
\(716\) | 0.686292i | 0.0256479i | ||||||||
\(717\) | −6.51472 | + | 6.51472i | −0.243297 | + | 0.243297i | ||||
\(718\) | 7.07107i | 0.263890i | ||||||||
\(719\) | −27.7487 | − | 27.7487i | −1.03485 | − | 1.03485i | −0.999370 | − | 0.0354830i | \(-0.988703\pi\) |
−0.0354830 | − | 0.999370i | \(-0.511297\pi\) | |||||||
\(720\) | −2.00000 | − | 6.00000i | −0.0745356 | − | 0.223607i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 33.4558 | 1.24510 | ||||||||
\(723\) | −1.61522 | −0.0600708 | ||||||||
\(724\) | −14.0000 | + | 14.0000i | −0.520306 | + | 0.520306i | ||||
\(725\) | 4.94975 | + | 0.707107i | 0.183829 | + | 0.0262613i | ||||
\(726\) | 1.74874 | + | 1.74874i | 0.0649017 | + | 0.0649017i | ||||
\(727\) | 16.7574i | 0.621496i | 0.950492 | + | 0.310748i | \(0.100580\pi\) | ||||
−0.950492 | + | 0.310748i | \(0.899420\pi\) | |||||||
\(728\) | 3.00000 | − | 3.00000i | 0.111187 | − | 0.111187i | ||||
\(729\) | − | 18.1716i | − | 0.673021i | ||||||
\(730\) | −11.8284 | + | 23.6569i | −0.437790 | + | 0.875579i | ||||
\(731\) | −7.97056 | − | 13.2843i | −0.294802 | − | 0.491337i | ||||
\(732\) | 3.58579i | 0.132534i | ||||||||
\(733\) | −32.9706 | −1.21780 | −0.608898 | − | 0.793249i | \(-0.708388\pi\) | ||||
−0.608898 | + | 0.793249i | \(0.708388\pi\) | |||||||
\(734\) | 18.2426 | + | 18.2426i | 0.673348 | + | 0.673348i | ||||
\(735\) | −4.14214 | − | 2.07107i | −0.152785 | − | 0.0763925i | ||||
\(736\) | −2.82843 | − | 2.82843i | −0.104257 | − | 0.104257i | ||||
\(737\) | −22.9706 | − | 22.9706i | −0.846132 | − | 0.846132i | ||||
\(738\) | −12.4853 | − | 12.4853i | −0.459590 | − | 0.459590i | ||||
\(739\) | − | 35.1838i | − | 1.29426i | −0.762381 | − | 0.647128i | \(-0.775970\pi\) | ||
0.762381 | − | 0.647128i | \(-0.224030\pi\) | |||||||
\(740\) | −7.41421 | + | 14.8284i | −0.272552 | + | 0.545104i | ||||
\(741\) | 6.36396 | − | 6.36396i | 0.233786 | − | 0.233786i | ||||
\(742\) | 3.00000 | + | 3.00000i | 0.110133 | + | 0.110133i | ||||
\(743\) | −17.8284 | + | 17.8284i | −0.654062 | + | 0.654062i | −0.953968 | − | 0.299907i | \(-0.903044\pi\) |
0.299907 | + | 0.953968i | \(0.403044\pi\) | |||||||
\(744\) | −3.14214 | −0.115196 | ||||||||
\(745\) | 27.0000 | − | 9.00000i | 0.989203 | − | 0.329734i | ||||
\(746\) | 32.4853i | 1.18937i | ||||||||
\(747\) | 12.0000i | 0.439057i | ||||||||
\(748\) | 8.97056 | + | 2.24264i | 0.327996 | + | 0.0819991i | ||||
\(749\) | −5.65685 | −0.206697 | ||||||||
\(750\) | 0.828427 | + | 4.55635i | 0.0302499 | + | 0.166374i | ||||
\(751\) | 19.3640 | + | 19.3640i | 0.706601 | + | 0.706601i | 0.965819 | − | 0.259218i | \(-0.0834648\pi\) |
−0.259218 | + | 0.965819i | \(0.583465\pi\) | |||||||
\(752\) | − | 1.58579i | − | 0.0578277i | ||||||
\(753\) | −6.00000 | + | 6.00000i | −0.218652 | + | 0.218652i | ||||
\(754\) | 2.12132 | − | 2.12132i | 0.0772539 | − | 0.0772539i | ||||
\(755\) | 8.48528 | + | 25.4558i | 0.308811 | + | 0.926433i | ||||
\(756\) | − | 3.41421i | − | 0.124174i | ||||||
\(757\) | 32.9411 | 1.19727 | 0.598633 | − | 0.801024i | \(-0.295711\pi\) | ||||
0.598633 | + | 0.801024i | \(0.295711\pi\) | |||||||
\(758\) | −0.485281 | − | 0.485281i | −0.0176262 | − | 0.0176262i | ||||
\(759\) | 2.62742 | − | 2.62742i | 0.0953692 | − | 0.0953692i | ||||
\(760\) | 5.12132 | + | 15.3640i | 0.185770 | + | 0.557309i | ||||
\(761\) | 20.4853 | 0.742591 | 0.371295 | − | 0.928515i | \(-0.378914\pi\) | ||||
0.371295 | + | 0.928515i | \(0.378914\pi\) | |||||||
\(762\) | 5.19239 | − | 5.19239i | 0.188100 | − | 0.188100i | ||||
\(763\) | 17.2132 | 0.623160 | ||||||||
\(764\) | 21.2132 | 0.767467 | ||||||||
\(765\) | −16.9706 | + | 19.7990i | −0.613572 | + | 0.715834i | ||||
\(766\) | 13.2426 | 0.478476 | ||||||||
\(767\) | −38.6985 | −1.39732 | ||||||||
\(768\) | −0.292893 | + | 0.292893i | −0.0105689 | + | 0.0105689i | ||||
\(769\) | −14.4558 | −0.521291 | −0.260646 | − | 0.965435i | \(-0.583935\pi\) | ||||
−0.260646 | + | 0.965435i | \(0.583935\pi\) | |||||||
\(770\) | −6.72792 | + | 2.24264i | −0.242457 | + | 0.0808192i | ||||
\(771\) | −1.97056 | + | 1.97056i | −0.0709681 | + | 0.0709681i | ||||
\(772\) | 18.4853 | + | 18.4853i | 0.665300 | + | 0.665300i | ||||
\(773\) | −32.4853 | −1.16841 | −0.584207 | − | 0.811605i | \(-0.698594\pi\) | ||||
−0.584207 | + | 0.811605i | \(0.698594\pi\) | |||||||
\(774\) | − | 10.6274i | − | 0.381995i | ||||||
\(775\) | −37.5477 | − | 5.36396i | −1.34875 | − | 0.192679i | ||||
\(776\) | −0.121320 | + | 0.121320i | −0.00435515 | + | 0.00435515i | ||||
\(777\) | −3.07107 | + | 3.07107i | −0.110174 | + | 0.110174i | ||||
\(778\) | − | 16.6274i | − | 0.596122i | ||||||
\(779\) | 31.9706 | + | 31.9706i | 1.14546 | + | 1.14546i | ||||
\(780\) | 2.48528 | + | 1.24264i | 0.0889873 | + | 0.0444937i | ||||
\(781\) | −11.7574 | −0.420711 | ||||||||
\(782\) | −4.00000 | + | 16.0000i | −0.143040 | + | 0.572159i | ||||
\(783\) | − | 2.41421i | − | 0.0862770i | ||||||
\(784\) | − | 5.00000i | − | 0.178571i | ||||||
\(785\) | 8.48528 | + | 25.4558i | 0.302853 | + | 0.908558i | ||||
\(786\) | 4.44365 | 0.158500 | ||||||||
\(787\) | 1.36396 | − | 1.36396i | 0.0486200 | − | 0.0486200i | −0.682379 | − | 0.730999i | \(-0.739055\pi\) |
0.730999 | + | 0.682379i | \(0.239055\pi\) | |||||||
\(788\) | 3.34315 | + | 3.34315i | 0.119095 | + | 0.119095i | ||||
\(789\) | −1.39340 | + | 1.39340i | −0.0496063 | + | 0.0496063i | ||||
\(790\) | −0.343146 | + | 0.686292i | −0.0122086 | + | 0.0244172i | ||||
\(791\) | 4.92893i | 0.175253i | ||||||||
\(792\) | 4.48528 | + | 4.48528i | 0.159378 | + | 0.159378i | ||||
\(793\) | 18.3640 | + | 18.3640i | 0.652123 | + | 0.652123i | ||||
\(794\) | −4.72792 | − | 4.72792i | −0.167788 | − | 0.167788i | ||||
\(795\) | −1.24264 | + | 2.48528i | −0.0440719 | + | 0.0881438i | ||||
\(796\) | −7.12132 | − | 7.12132i | −0.252409 | − | 0.252409i | ||||
\(797\) | −28.9706 | −1.02619 | −0.513095 | − | 0.858332i | \(-0.671501\pi\) | ||||
−0.513095 | + | 0.858332i | \(0.671501\pi\) | |||||||
\(798\) | 4.24264i | 0.150188i | ||||||||
\(799\) | −5.60660 | + | 3.36396i | −0.198347 | + | 0.119008i | ||||
\(800\) | −4.00000 | + | 3.00000i | −0.141421 | + | 0.106066i | ||||
\(801\) | 32.4853i | 1.14781i | ||||||||
\(802\) | 2.10051 | − | 2.10051i | 0.0741714 | − | 0.0741714i | ||||
\(803\) | − | 26.5269i | − | 0.936114i | ||||||
\(804\) | −4.24264 | − | 4.24264i | −0.149626 | − | 0.149626i | ||||
\(805\) | −4.00000 | − | 12.0000i | −0.140981 | − | 0.422944i | ||||
\(806\) | −16.0919 | + | 16.0919i | −0.566812 | + | 0.566812i | ||||
\(807\) | 6.61522 | 0.232867 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35.1421 | − | 35.1421i | 1.23553 | − | 1.23553i | 0.273723 | − | 0.961809i | \(-0.411745\pi\) |
0.961809 | − | 0.273723i | \(-0.0882552\pi\) | |||||||
\(810\) | −15.8787 | + | 5.29289i | −0.557920 | + | 0.185973i | ||||
\(811\) | 9.48528 | + | 9.48528i | 0.333073 | + | 0.333073i | 0.853752 | − | 0.520679i | \(-0.174321\pi\) |
−0.520679 | + | 0.853752i | \(0.674321\pi\) | |||||||
\(812\) | 1.41421i | 0.0496292i | ||||||||
\(813\) | 1.89949 | − | 1.89949i | 0.0666182 | − | 0.0666182i | ||||
\(814\) | − | 16.6274i | − | 0.582791i | ||||||
\(815\) | 12.6863 | + | 6.34315i | 0.444381 | + | 0.222191i | ||||
\(816\) | 1.65685 | + | 0.414214i | 0.0580015 | + | 0.0145004i | ||||
\(817\) | 27.2132i | 0.952069i | ||||||||
\(818\) | −25.4853 | −0.891072 | ||||||||
\(819\) | −8.48528 | − | 8.48528i | −0.296500 | − | 0.296500i | ||||
\(820\) | −6.24264 | + | 12.4853i | −0.218002 | + | 0.436005i | ||||
\(821\) | −18.0208 | − | 18.0208i | −0.628931 | − | 0.628931i | 0.318868 | − | 0.947799i | \(-0.396697\pi\) |
−0.947799 | + | 0.318868i | \(0.896697\pi\) | |||||||
\(822\) | −1.34315 | − | 1.34315i | −0.0468476 | − | 0.0468476i | ||||
\(823\) | 10.7279 | + | 10.7279i | 0.373952 | + | 0.373952i | 0.868914 | − | 0.494962i | \(-0.164818\pi\) |
−0.494962 | + | 0.868914i | \(0.664818\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.78680 | − | 3.71573i | −0.0970238 | − | 0.129365i | ||||
\(826\) | 12.8995 | − | 12.8995i | 0.448831 | − | 0.448831i | ||||
\(827\) | 5.31371 | + | 5.31371i | 0.184776 | + | 0.184776i | 0.793433 | − | 0.608657i | \(-0.208292\pi\) |
−0.608657 | + | 0.793433i | \(0.708292\pi\) | |||||||
\(828\) | −8.00000 | + | 8.00000i | −0.278019 | + | 0.278019i | ||||
\(829\) | 14.0000 | 0.486240 | 0.243120 | − | 0.969996i | \(-0.421829\pi\) | ||||
0.243120 | + | 0.969996i | \(0.421829\pi\) | |||||||
\(830\) | 9.00000 | − | 3.00000i | 0.312395 | − | 0.104132i | ||||
\(831\) | 4.82843i | 0.167496i | ||||||||
\(832\) | 3.00000i | 0.104006i | ||||||||
\(833\) | −17.6777 | + | 10.6066i | −0.612495 | + | 0.367497i | ||||
\(834\) | −6.44365 | −0.223125 | ||||||||
\(835\) | 1.51472 | − | 3.02944i | 0.0524190 | − | 0.104838i | ||||
\(836\) | −11.4853 | − | 11.4853i | −0.397227 | − | 0.397227i | ||||
\(837\) | 18.3137i | 0.633014i | ||||||||
\(838\) | 11.3137 | − | 11.3137i | 0.390826 | − | 0.390826i | ||||
\(839\) | −2.97918 | + | 2.97918i | −0.102853 | + | 0.102853i | −0.756661 | − | 0.653808i | \(-0.773170\pi\) |
0.653808 | + | 0.756661i | \(0.273170\pi\) | |||||||
\(840\) | −1.24264 | + | 0.414214i | −0.0428752 | + | 0.0142917i | ||||
\(841\) | − | 28.0000i | − | 0.965517i | ||||||
\(842\) | 19.2132 | 0.662131 | ||||||||
\(843\) | 0.979185 | + | 0.979185i | 0.0337249 | + | 0.0337249i | ||||
\(844\) | −8.00000 | + | 8.00000i | −0.275371 | + | 0.275371i | ||||
\(845\) | −8.48528 | + | 2.82843i | −0.291903 | + | 0.0973009i | ||||
\(846\) | −4.48528 | −0.154207 | ||||||||
\(847\) | −5.97056 | + | 5.97056i | −0.205151 | + | 0.205151i | ||||
\(848\) | −3.00000 | −0.103020 | ||||||||
\(849\) | 11.2010 | 0.384418 | ||||||||
\(850\) | 19.0919 | + | 7.77817i | 0.654846 | + | 0.266789i | ||||
\(851\) | 29.6569 | 1.01662 | ||||||||
\(852\) | −2.17157 | −0.0743969 | ||||||||
\(853\) | −8.51472 | + | 8.51472i | −0.291538 | + | 0.291538i | −0.837688 | − | 0.546149i | \(-0.816093\pi\) |
0.546149 | + | 0.837688i | \(0.316093\pi\) | |||||||
\(854\) | −12.2426 | −0.418935 | ||||||||
\(855\) | 43.4558 | − | 14.4853i | 1.48616 | − | 0.495386i | ||||
\(856\) | 2.82843 | − | 2.82843i | 0.0966736 | − | 0.0966736i | ||||
\(857\) | 25.4350 | + | 25.4350i | 0.868844 | + | 0.868844i | 0.992345 | − | 0.123500i | \(-0.0394120\pi\) |
−0.123500 | + | 0.992345i | \(0.539412\pi\) | |||||||
\(858\) | −2.78680 | −0.0951397 | ||||||||
\(859\) | − | 45.7279i | − | 1.56022i | −0.625645 | − | 0.780108i | \(-0.715164\pi\) | ||
0.625645 | − | 0.780108i | \(-0.284836\pi\) | |||||||
\(860\) | −7.97056 | + | 2.65685i | −0.271794 | + | 0.0905980i | ||||
\(861\) | −2.58579 | + | 2.58579i | −0.0881234 | + | 0.0881234i | ||||
\(862\) | −17.6569 | + | 17.6569i | −0.601395 | + | 0.601395i | ||||
\(863\) | 55.1127i | 1.87606i | 0.346557 | + | 0.938029i | \(0.387351\pi\) | ||||
−0.346557 | + | 0.938029i | \(0.612649\pi\) | |||||||
\(864\) | 1.70711 | + | 1.70711i | 0.0580770 | + | 0.0580770i | ||||
\(865\) | −24.9706 | + | 49.9411i | −0.849025 | + | 1.69805i | ||||
\(866\) | 5.75736 | 0.195643 | ||||||||
\(867\) | −2.05025 | − | 6.73654i | −0.0696302 | − | 0.228785i | ||||
\(868\) | − | 10.7279i | − | 0.364129i | ||||||
\(869\) | − | 0.769553i | − | 0.0261053i | ||||||
\(870\) | −0.878680 | + | 0.292893i | −0.0297900 | + | 0.00993001i | ||||
\(871\) | −43.4558 | −1.47245 | ||||||||
\(872\) | −8.60660 | + | 8.60660i | −0.291456 | + | 0.291456i | ||||
\(873\) | 0.343146 | + | 0.343146i | 0.0116137 | + | 0.0116137i | ||||
\(874\) | 20.4853 | − | 20.4853i | 0.692925 | − | 0.692925i | ||||
\(875\) | −15.5563 | + | 2.82843i | −0.525901 | + | 0.0956183i | ||||
\(876\) | − | 4.89949i | − | 0.165539i | ||||||
\(877\) | −8.51472 | − | 8.51472i | −0.287522 | − | 0.287522i | 0.548578 | − | 0.836099i | \(-0.315169\pi\) |
−0.836099 | + | 0.548578i | \(0.815169\pi\) | |||||||
\(878\) | −20.9706 | − | 20.9706i | −0.707722 | − | 0.707722i | ||||
\(879\) | −6.05025 | − | 6.05025i | −0.204070 | − | 0.204070i | ||||
\(880\) | 2.24264 | − | 4.48528i | 0.0755994 | − | 0.151199i | ||||
\(881\) | −8.44365 | − | 8.44365i | −0.284474 | − | 0.284474i | 0.550416 | − | 0.834890i | \(-0.314469\pi\) |
−0.834890 | + | 0.550416i | \(0.814469\pi\) | |||||||
\(882\) | −14.1421 | −0.476190 | ||||||||
\(883\) | − | 18.7279i | − | 0.630245i | −0.949051 | − | 0.315122i | \(-0.897954\pi\) | ||
0.949051 | − | 0.315122i | \(-0.102046\pi\) | |||||||
\(884\) | 10.6066 | − | 6.36396i | 0.356739 | − | 0.214043i | ||||
\(885\) | 10.6863 | + | 5.34315i | 0.359216 | + | 0.179608i | ||||
\(886\) | 37.7990i | 1.26988i | ||||||||
\(887\) | −19.5858 | + | 19.5858i | −0.657626 | + | 0.657626i | −0.954818 | − | 0.297192i | \(-0.903950\pi\) |
0.297192 | + | 0.954818i | \(0.403950\pi\) | |||||||
\(888\) | − | 3.07107i | − | 0.103058i | ||||||
\(889\) | 17.7279 | + | 17.7279i | 0.594575 | + | 0.594575i | ||||
\(890\) | 24.3640 | − | 8.12132i | 0.816682 | − | 0.272227i | ||||
\(891\) | 11.8701 | − | 11.8701i | 0.397662 | − | 0.397662i | ||||
\(892\) | −23.2426 | −0.778221 | ||||||||
\(893\) | 11.4853 | 0.384340 | ||||||||
\(894\) | −3.72792 | + | 3.72792i | −0.124680 | + | 0.124680i | ||||
\(895\) | −0.485281 | − | 1.45584i | −0.0162212 | − | 0.0486635i | ||||
\(896\) | −1.00000 | − | 1.00000i | −0.0334077 | − | 0.0334077i | ||||
\(897\) | − | 4.97056i | − | 0.165962i | ||||||
\(898\) | 28.7990 | − | 28.7990i | 0.961035 | − | 0.961035i | ||||
\(899\) | − | 7.58579i | − | 0.253000i | ||||||
\(900\) | 8.48528 | + | 11.3137i | 0.282843 | + | 0.377124i | ||||
\(901\) | 6.36396 | + | 10.6066i | 0.212014 | + | 0.353357i | ||||
\(902\) | − | 14.0000i | − | 0.466149i | ||||||
\(903\) | −2.20101 | −0.0732450 | ||||||||
\(904\) | −2.46447 | − | 2.46447i | −0.0819669 | − | 0.0819669i | ||||
\(905\) | 19.7990 | − | 39.5980i | 0.658141 | − | 1.31628i | ||||
\(906\) | −3.51472 | − | 3.51472i | −0.116769 | − | 0.116769i | ||||
\(907\) | −7.84924 | − | 7.84924i | −0.260630 | − | 0.260630i | 0.564680 | − | 0.825310i | \(-0.309000\pi\) |
−0.825310 | + | 0.564680i | \(0.809000\pi\) | |||||||
\(908\) | −4.05025 | − | 4.05025i | −0.134412 | − | 0.134412i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.24264 | + | 8.48528i | −0.140642 | + | 0.281284i | ||||
\(911\) | −35.3137 | + | 35.3137i | −1.17000 | + | 1.17000i | −0.187785 | + | 0.982210i | \(0.560131\pi\) |
−0.982210 | + | 0.187785i | \(0.939869\pi\) | |||||||
\(912\) | −2.12132 | − | 2.12132i | −0.0702439 | − | 0.0702439i | ||||
\(913\) | −6.72792 | + | 6.72792i | −0.222662 | + | 0.222662i | ||||
\(914\) | 2.24264 | 0.0741800 | ||||||||
\(915\) | −2.53553 | − | 7.60660i | −0.0838222 | − | 0.251466i | ||||
\(916\) | 7.75736i | 0.256310i | ||||||||
\(917\) | 15.1716i | 0.501009i | ||||||||
\(918\) | 2.41421 | − | 9.65685i | 0.0796809 | − | 0.318724i | ||||
\(919\) | −31.2132 | −1.02963 | −0.514814 | − | 0.857302i | \(-0.672139\pi\) | ||||
−0.514814 | + | 0.857302i | \(0.672139\pi\) | |||||||
\(920\) | 8.00000 | + | 4.00000i | 0.263752 | + | 0.131876i | ||||
\(921\) | −9.72792 | − | 9.72792i | −0.320546 | − | 0.320546i | ||||
\(922\) | 40.2843i | 1.32669i | ||||||||
\(923\) | −11.1213 | + | 11.1213i | −0.366063 | + | 0.366063i | ||||
\(924\) | 0.928932 | − | 0.928932i | 0.0305596 | − | 0.0305596i | ||||
\(925\) | 5.24264 | − | 36.6985i | 0.172377 | − | 1.20664i | ||||
\(926\) | − | 25.2426i | − | 0.829525i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.707107 | − | 0.707107i | −0.0232119 | − | 0.0232119i | ||||
\(929\) | −15.3431 | + | 15.3431i | −0.503392 | + | 0.503392i | −0.912490 | − | 0.409098i | \(-0.865843\pi\) |
0.409098 | + | 0.912490i | \(0.365843\pi\) | |||||||
\(930\) | 6.66548 | − | 2.22183i | 0.218570 | − | 0.0728565i | ||||
\(931\) | 36.2132 | 1.18684 | ||||||||
\(932\) | −10.9497 | + | 10.9497i | −0.358671 | + | 0.358671i | ||||
\(933\) | 0.828427 | 0.0271215 | ||||||||
\(934\) | 18.7279 | 0.612796 | ||||||||
\(935\) | −20.6152 | + | 1.58579i | −0.674190 | + | 0.0518608i | ||||
\(936\) | 8.48528 | 0.277350 | ||||||||
\(937\) | 47.2132 | 1.54239 | 0.771194 | − | 0.636600i | \(-0.219660\pi\) | ||||
0.771194 | + | 0.636600i | \(0.219660\pi\) | |||||||
\(938\) | 14.4853 | − | 14.4853i | 0.472961 | − | 0.472961i | ||||
\(939\) | 13.1716 | 0.429838 | ||||||||
\(940\) | 1.12132 | + | 3.36396i | 0.0365734 | + | 0.109720i | ||||
\(941\) | 14.8076 | − | 14.8076i | 0.482714 | − | 0.482714i | −0.423283 | − | 0.905997i | \(-0.639122\pi\) |
0.905997 | + | 0.423283i | \(0.139122\pi\) | |||||||
\(942\) | −3.51472 | − | 3.51472i | −0.114516 | − | 0.114516i | ||||
\(943\) | 24.9706 | 0.813153 | ||||||||
\(944\) | 12.8995i | 0.419843i | ||||||||
\(945\) | 2.41421 | + | 7.24264i | 0.0785344 | + | 0.235603i | ||||
\(946\) | 5.95837 | − | 5.95837i | 0.193723 | − | 0.193723i | ||||
\(947\) | 26.2929 | − | 26.2929i | 0.854404 | − | 0.854404i | −0.136268 | − | 0.990672i | \(-0.543511\pi\) |
0.990672 | + | 0.136268i | \(0.0435108\pi\) | |||||||
\(948\) | − | 0.142136i | − | 0.00461635i | ||||||
\(949\) | −25.0919 | − | 25.0919i | −0.814517 | − | 0.814517i | ||||
\(950\) | −21.7279 | − | 28.9706i | −0.704947 | − | 0.939929i | ||||
\(951\) | 8.28427 | 0.268636 | ||||||||
\(952\) | −1.41421 | + | 5.65685i | −0.0458349 | + | 0.183340i | ||||
\(953\) | − | 4.58579i | − | 0.148548i | −0.997238 | − | 0.0742741i | \(-0.976336\pi\) | ||
0.997238 | − | 0.0742741i | \(-0.0236640\pi\) | |||||||
\(954\) | 8.48528i | 0.274721i | ||||||||
\(955\) | −45.0000 | + | 15.0000i | −1.45617 | + | 0.485389i | ||||
\(956\) | 22.2426 | 0.719378 | ||||||||
\(957\) | 0.656854 | − | 0.656854i | 0.0212331 | − | 0.0212331i | ||||
\(958\) | 10.0503 | + | 10.0503i | 0.324709 | + | 0.324709i | ||||
\(959\) | 4.58579 | − | 4.58579i | 0.148083 | − | 0.148083i | ||||
\(960\) | 0.414214 | − | 0.828427i | 0.0133687 | − | 0.0267374i | ||||
\(961\) | 26.5442i | 0.856263i | ||||||||
\(962\) | −15.7279 | − | 15.7279i | −0.507089 | − | 0.507089i | ||||
\(963\) | −8.00000 | − | 8.00000i | −0.257796 | − | 0.257796i | ||||
\(964\) | 2.75736 | + | 2.75736i | 0.0888086 | + | 0.0888086i | ||||
\(965\) | −52.2843 | − | 26.1421i | −1.68309 | − | 0.841545i | ||||
\(966\) | 1.65685 | + | 1.65685i | 0.0533084 | + | 0.0533084i | ||||
\(967\) | 30.9706 | 0.995946 | 0.497973 | − | 0.867192i | \(-0.334078\pi\) | ||||
0.497973 | + | 0.867192i | \(0.334078\pi\) | |||||||
\(968\) | − | 5.97056i | − | 0.191901i | ||||||
\(969\) | −3.00000 | + | 12.0000i | −0.0963739 | + | 0.385496i | ||||
\(970\) | 0.171573 | − | 0.343146i | 0.00550887 | − | 0.0110177i | ||||
\(971\) | − | 30.5563i | − | 0.980600i | −0.871554 | − | 0.490300i | \(-0.836887\pi\) | ||
0.871554 | − | 0.490300i | \(-0.163113\pi\) | |||||||
\(972\) | 7.31371 | − | 7.31371i | 0.234587 | − | 0.234587i | ||||
\(973\) | − | 22.0000i | − | 0.705288i | ||||||
\(974\) | −11.2426 | − | 11.2426i | −0.360237 | − | 0.360237i | ||||
\(975\) | −6.15076 | − | 0.878680i | −0.196982 | − | 0.0281403i | ||||
\(976\) | 6.12132 | − | 6.12132i | 0.195939 | − | 0.195939i | ||||
\(977\) | 0.727922 | 0.0232883 | 0.0116441 | − | 0.999932i | \(-0.496293\pi\) | ||||
0.0116441 | + | 0.999932i | \(0.496293\pi\) | |||||||
\(978\) | −2.62742 | −0.0840155 | ||||||||
\(979\) | −18.2132 | + | 18.2132i | −0.582097 | + | 0.582097i | ||||
\(980\) | 3.53553 | + | 10.6066i | 0.112938 | + | 0.338815i | ||||
\(981\) | 24.3431 | + | 24.3431i | 0.777217 | + | 0.777217i | ||||
\(982\) | − | 6.89949i | − | 0.220172i | ||||||
\(983\) | −44.0122 | + | 44.0122i | −1.40377 | + | 1.40377i | −0.616114 | + | 0.787657i | \(0.711294\pi\) |
−0.787657 | + | 0.616114i | \(0.788706\pi\) | |||||||
\(984\) | − | 2.58579i | − | 0.0824319i | ||||||
\(985\) | −9.45584 | − | 4.72792i | −0.301288 | − | 0.150644i | ||||
\(986\) | −1.00000 | + | 4.00000i | −0.0318465 | + | 0.127386i | ||||
\(987\) | 0.928932i | 0.0295682i | ||||||||
\(988\) | −21.7279 | −0.691257 | ||||||||
\(989\) | 10.6274 | + | 10.6274i | 0.337932 | + | 0.337932i | ||||
\(990\) | −12.6863 | − | 6.34315i | −0.403197 | − | 0.201598i | ||||
\(991\) | 21.1213 | + | 21.1213i | 0.670941 | + | 0.670941i | 0.957933 | − | 0.286992i | \(-0.0926553\pi\) |
−0.286992 | + | 0.957933i | \(0.592655\pi\) | |||||||
\(992\) | 5.36396 | + | 5.36396i | 0.170306 | + | 0.170306i | ||||
\(993\) | 4.60660 | + | 4.60660i | 0.146186 | + | 0.146186i | ||||
\(994\) | − | 7.41421i | − | 0.235165i | ||||||
\(995\) | 20.1421 | + | 10.0711i | 0.638549 | + | 0.319274i | ||||
\(996\) | −1.24264 | + | 1.24264i | −0.0393746 | + | 0.0393746i | ||||
\(997\) | 30.6985 | + | 30.6985i | 0.972231 | + | 0.972231i | 0.999625 | − | 0.0273939i | \(-0.00872086\pi\) |
−0.0273939 | + | 0.999625i | \(0.508721\pi\) | |||||||
\(998\) | 8.51472 | − | 8.51472i | 0.269529 | − | 0.269529i | ||||
\(999\) | −17.8995 | −0.566315 |
(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 | 170.2.g.e.149.2 | yes | 4 | |
3.2 | odd | 2 | 1530.2.n.o.829.2 | 4 | |||
5.2 | odd | 4 | 850.2.h.k.251.1 | 4 | |||
5.3 | odd | 4 | 850.2.h.h.251.2 | 4 | |||
5.4 | even | 2 | 170.2.g.f.149.1 | yes | 4 | ||
15.14 | odd | 2 | 1530.2.n.j.829.1 | 4 | |||
17.4 | even | 4 | 170.2.g.f.89.1 | yes | 4 | ||
51.38 | odd | 4 | 1530.2.n.j.1279.1 | 4 | |||
85.4 | even | 4 | inner | 170.2.g.e.89.2 | ✓ | 4 | |
85.38 | odd | 4 | 850.2.h.h.701.2 | 4 | |||
85.72 | odd | 4 | 850.2.h.k.701.1 | 4 | |||
255.89 | odd | 4 | 1530.2.n.o.1279.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
170.2.g.e.89.2 | ✓ | 4 | 85.4 | even | 4 | inner | |
170.2.g.e.149.2 | yes | 4 | 1.1 | even | 1 | trivial | |
170.2.g.f.89.1 | yes | 4 | 17.4 | even | 4 | ||
170.2.g.f.149.1 | yes | 4 | 5.4 | even | 2 | ||
850.2.h.h.251.2 | 4 | 5.3 | odd | 4 | |||
850.2.h.h.701.2 | 4 | 85.38 | odd | 4 | |||
850.2.h.k.251.1 | 4 | 5.2 | odd | 4 | |||
850.2.h.k.701.1 | 4 | 85.72 | odd | 4 | |||
1530.2.n.j.829.1 | 4 | 15.14 | odd | 2 | |||
1530.2.n.j.1279.1 | 4 | 51.38 | odd | 4 | |||
1530.2.n.o.829.2 | 4 | 3.2 | odd | 2 | |||
1530.2.n.o.1279.2 | 4 | 255.89 | odd | 4 |