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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 149.1 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 170.149 |
Dual form | 170.2.g.f.89.1 |
$q$-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 \(\left(\mathbb{Z}/170\mathbb{Z}\right)^\times\).
\(n\) | \(71\) | \(137\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | −0.617483 | − | 0.786585i | \(-0.711847\pi\) |
0.786585 | + | 0.617483i | \(0.211847\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.707107 | − | 2.12132i | 0.316228 | − | 0.948683i | ||||
\(6\) | 0.292893 | − | 0.292893i | 0.119573 | − | 0.119573i | ||||
\(7\) | −1.00000 | − | 1.00000i | −0.377964 | − | 0.377964i | 0.492403 | − | 0.870367i | \(-0.336119\pi\) |
−0.870367 | + | 0.492403i | \(0.836119\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.82843i | 0.942809i | ||||||||
\(10\) | 0.707107 | − | 2.12132i | 0.223607 | − | 0.670820i | ||||
\(11\) | −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 | \(-0.863423\pi\) | ||
0.909353 | − | 0.416025i | \(-0.136577\pi\) | |||||||
\(14\) | −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 | \(0.687890\pi\) | |||||||
\(20\) | 0.707107 | − | 2.12132i | 0.158114 | − | 0.474342i | ||||
\(21\) | −0.585786 | −0.127829 | ||||||||
\(22\) | −1.58579 | + | 1.58579i | −0.338091 | + | 0.338091i | ||||
\(23\) | −2.82843 | − | 2.82843i | −0.589768 | − | 0.589768i | 0.347801 | − | 0.937568i | \(-0.386929\pi\) |
−0.937568 | + | 0.347801i | \(0.886929\pi\) | |||||||
\(24\) | 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 | −0.991557 | − | 0.129672i | \(-0.958608\pi\) |
0.129672 | + | 0.991557i | \(0.458608\pi\) | |||||||
\(38\) | 7.24264i | 1.17491i | ||||||||
\(39\) | −0.878680 | − | 0.878680i | −0.140701 | − | 0.140701i | ||||
\(40\) | 0.707107 | − | 2.12132i | 0.111803 | − | 0.335410i | ||||
\(41\) | 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 | \(-0.592491\pi\) | ||||
−0.286496 | + | 0.958081i | \(0.592491\pi\) | |||||||
\(44\) | −1.58579 | + | 1.58579i | −0.239066 | + | 0.239066i | ||||
\(45\) | 6.00000 | + | 2.00000i | 0.894427 | + | 0.298142i | ||||
\(46\) | −2.82843 | − | 2.82843i | −0.417029 | − | 0.417029i | ||||
\(47\) | 1.58579i | 0.231311i | 0.993289 | + | 0.115655i | \(0.0368968\pi\) | ||||
−0.993289 | + | 0.115655i | \(0.963103\pi\) | |||||||
\(48\) | 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 | \(-0.433942\pi\) | ||||
0.206041 | + | 0.978543i | \(0.433942\pi\) | |||||||
\(54\) | 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 | ||||||||
\(65\) | −6.36396 | − | 2.12132i | −0.789352 | − | 0.263117i | ||||
\(66\) | 0.928932i | 0.114344i | ||||||||
\(67\) | − | 14.4853i | − | 1.76966i | −0.465915 | − | 0.884829i | \(-0.654275\pi\) | ||
0.465915 | − | 0.884829i | \(-0.345725\pi\) | |||||||
\(68\) | 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 | −0.0208549 | − | 0.999783i | \(-0.506639\pi\) |
0.999783 | + | 0.0208549i | \(0.00663881\pi\) | |||||||
\(74\) | −5.24264 | + | 5.24264i | −0.609445 | + | 0.609445i | ||||
\(75\) | −2.05025 | + | 0.292893i | −0.236743 | + | 0.0338204i | ||||
\(76\) | 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 | \(0.256145\pi\) | |||||||
\(80\) | 0.707107 | − | 2.12132i | 0.0790569 | − | 0.237171i | ||||
\(81\) | −7.48528 | −0.831698 | ||||||||
\(82\) | 4.41421 | − | 4.41421i | 0.487468 | − | 0.487468i | ||||
\(83\) | −4.24264 | −0.465690 | −0.232845 | − | 0.972514i | \(-0.574804\pi\) | ||||
−0.232845 | + | 0.972514i | \(0.574804\pi\) | |||||||
\(84\) | −0.585786 | −0.0639145 | ||||||||
\(85\) | 9.00000 | − | 2.00000i | 0.976187 | − | 0.216930i | ||||
\(86\) | −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 | \(0.291684\pi\) | |||||||
\(90\) | 6.00000 | + | 2.00000i | 0.632456 | + | 0.210819i | ||||
\(91\) | −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 | ||||||||
\(95\) | 15.3640 | + | 5.12132i | 1.57631 | + | 0.525436i | ||||
\(96\) | 0.292893 | − | 0.292893i | 0.0298933 | − | 0.0298933i | ||||
\(97\) | −0.121320 | + | 0.121320i | −0.0123182 | + | 0.0123182i | −0.713239 | − | 0.700921i | \(-0.752773\pi\) |
0.700921 | + | 0.713239i | \(0.252773\pi\) | |||||||
\(98\) | − | 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 | ||||||
\(105\) | −0.414214 | + | 1.24264i | −0.0404231 | + | 0.121269i | ||||
\(106\) | 3.00000 | 0.291386 | ||||||||
\(107\) | 2.82843 | − | 2.82843i | 0.273434 | − | 0.273434i | −0.557047 | − | 0.830481i | \(-0.688066\pi\) |
0.830481 | + | 0.557047i | \(0.188066\pi\) | |||||||
\(108\) | 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 | 0.581622 | − | 0.813459i | \(-0.302418\pi\) |
−0.813459 | + | 0.581622i | \(0.802418\pi\) | |||||||
\(114\) | 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 | ||||
\(125\) | −9.19239 | + | 6.36396i | −0.822192 | + | 0.569210i | ||||
\(126\) | 2.82843 | − | 2.82843i | 0.251976 | − | 0.251976i | ||||
\(127\) | −17.7279 | −1.57310 | −0.786549 | − | 0.617527i | \(-0.788134\pi\) | ||||
−0.786549 | + | 0.617527i | \(0.788134\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −1.10051 | + | 1.10051i | −0.0968941 | + | 0.0968941i | ||||
\(130\) | −6.36396 | − | 2.12132i | −0.558156 | − | 0.186052i | ||||
\(131\) | 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 | \(0.0627612\pi\) | ||||
−0.980625 | + | 0.195895i | \(0.937239\pi\) | |||||||
\(138\) | −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 | \(0.674574\pi\) | |||||||
\(150\) | −2.05025 | + | 0.292893i | −0.167402 | + | 0.0239146i | ||||
\(151\) | − | 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 | \(0.158947\pi\) | ||||
−0.877896 | + | 0.478852i | \(0.841053\pi\) | |||||||
\(158\) | −0.242641 | + | 0.242641i | −0.0193035 | + | 0.0193035i | ||||
\(159\) | 0.878680 | − | 0.878680i | 0.0696838 | − | 0.0696838i | ||||
\(160\) | 0.707107 | − | 2.12132i | 0.0559017 | − | 0.167705i | ||||
\(161\) | 5.65685i | 0.445823i | ||||||||
\(162\) | −7.48528 | −0.588099 | ||||||||
\(163\) | 4.48528 | + | 4.48528i | 0.351314 | + | 0.351314i | 0.860598 | − | 0.509284i | \(-0.170090\pi\) |
−0.509284 | + | 0.860598i | \(0.670090\pi\) | |||||||
\(164\) | 4.41421 | − | 4.41421i | 0.344692 | − | 0.344692i | ||||
\(165\) | 1.97056 | + | 0.656854i | 0.153408 | + | 0.0511360i | ||||
\(166\) | −4.24264 | −0.329293 | ||||||||
\(167\) | 1.07107 | − | 1.07107i | 0.0828817 | − | 0.0828817i | −0.664451 | − | 0.747332i | \(-0.731334\pi\) |
0.747332 | + | 0.664451i | \(0.231334\pi\) | |||||||
\(168\) | −0.585786 | −0.0451944 | ||||||||
\(169\) | 4.00000 | 0.307692 | ||||||||
\(170\) | 9.00000 | − | 2.00000i | 0.690268 | − | 0.153393i | ||||
\(171\) | −20.4853 | −1.56655 | ||||||||
\(172\) | −3.75736 | −0.286496 | ||||||||
\(173\) | −17.6569 | + | 17.6569i | −1.34243 | + | 1.34243i | −0.448787 | + | 0.893639i | \(0.648144\pi\) |
−0.893639 | + | 0.448787i | \(0.851856\pi\) | |||||||
\(174\) | 0.414214 | 0.0314014 | ||||||||
\(175\) | 1.00000 | + | 7.00000i | 0.0755929 | + | 0.529150i | ||||
\(176\) | −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 | \(0.991835\pi\) | |||||||
\(180\) | 6.00000 | + | 2.00000i | 0.447214 | + | 0.149071i | ||||
\(181\) | −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 | ||||||
\(190\) | 15.3640 | + | 5.12132i | 1.11462 | + | 0.371540i | ||||
\(191\) | 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 | \(-0.860004\pi\) |
−0.425767 | − | 0.904833i | \(-0.639996\pi\) | |||||||
\(194\) | −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 | 0.577911 | − | 0.816100i | \(-0.303868\pi\) |
−0.816100 | + | 0.577911i | \(0.803868\pi\) | |||||||
\(198\) | −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 | ||||
\(210\) | −0.414214 | + | 1.24264i | −0.0285835 | + | 0.0857504i | ||||
\(211\) | −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 | ||||
\(215\) | −2.65685 | + | 7.97056i | −0.181196 | + | 0.543588i | ||||
\(216\) | 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 | \(-0.216122\pi\) | ||||
0.778221 | + | 0.627990i | \(0.216122\pi\) | |||||||
\(224\) | −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 | 0.828627 | − | 0.559802i | \(-0.189123\pi\) |
−0.559802 | + | 0.828627i | \(0.689123\pi\) | |||||||
\(228\) | 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 | −0.250718 | − | 0.968060i | \(-0.580667\pi\) |
0.968060 | + | 0.250718i | \(0.0806668\pi\) | |||||||
\(234\) | 8.48528 | 0.554700 | ||||||||
\(235\) | 3.36396 | + | 1.12132i | 0.219441 | + | 0.0731469i | ||||
\(236\) | 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 | ||||
\(245\) | −10.6066 | − | 3.53553i | −0.677631 | − | 0.225877i | ||||
\(246\) | − | 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 | ||||
\(250\) | −9.19239 | + | 6.36396i | −0.581378 | + | 0.402492i | ||||
\(251\) | 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 | ||||||||
\(255\) | 2.05025 | − | 3.22183i | 0.128392 | − | 0.201759i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.72792 | −0.419676 | −0.209838 | − | 0.977736i | \(-0.567294\pi\) | ||||
−0.209838 | + | 0.977736i | \(0.567294\pi\) | |||||||
\(258\) | −1.10051 | + | 1.10051i | −0.0685145 | + | 0.0685145i | ||||
\(259\) | 10.4853 | 0.651524 | ||||||||
\(260\) | −6.36396 | − | 2.12132i | −0.394676 | − | 0.131559i | ||||
\(261\) | −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 | \(-0.546857\pi\) | ||||
−0.146676 | + | 0.989185i | \(0.546857\pi\) | |||||||
\(264\) | 0.928932i | 0.0571718i | ||||||||
\(265\) | 2.12132 | − | 6.36396i | 0.130312 | − | 0.390935i | ||||
\(266\) | 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 | ||||||||
\(275\) | 11.1005 | − | 1.58579i | 0.669386 | − | 0.0956265i | ||||
\(276\) | −1.65685 | −0.0997309 | ||||||||
\(277\) | −8.24264 | + | 8.24264i | −0.495252 | + | 0.495252i | −0.909956 | − | 0.414704i | \(-0.863885\pi\) |
0.414704 | + | 0.909956i | \(0.363885\pi\) | |||||||
\(278\) | −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 | \(0.0471538\pi\) |
0.147597 | + | 0.989048i | \(0.452846\pi\) | |||||||
\(284\) | 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 | \(-0.793815\pi\) | ||
0.797444 | − | 0.603393i | \(-0.206185\pi\) | |||||||
\(294\) | −1.46447 | − | 1.46447i | −0.0854094 | − | 0.0854094i | ||||
\(295\) | 27.3640 | + | 9.12132i | 1.59319 | + | 0.531064i | ||||
\(296\) | −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 | ||||
\(300\) | −2.05025 | + | 0.292893i | −0.118371 | + | 0.0169102i | ||||
\(301\) | 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 | \(-0.603313\pi\) | ||
0.318899 | − | 0.947789i | \(-0.396687\pi\) | |||||||
\(308\) | 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 | \(0.105482\pi\) |
0.325349 | + | 0.945594i | \(0.394518\pi\) | |||||||
\(314\) | 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 | 0.982190 | − | 0.187889i | \(-0.0601645\pi\) |
−0.187889 | + | 0.982190i | \(0.560164\pi\) | |||||||
\(318\) | 0.878680 | − | 0.878680i | 0.0492739 | − | 0.0492739i | ||||
\(319\) | −2.24264 | −0.125564 | ||||||||
\(320\) | 0.707107 | − | 2.12132i | 0.0395285 | − | 0.118585i | ||||
\(321\) | − | 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 | ||||
\(330\) | 1.97056 | + | 0.656854i | 0.108476 | + | 0.0361586i | ||||
\(331\) | − | 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 | ||||
\(335\) | −30.7279 | − | 10.2426i | −1.67885 | − | 0.559615i | ||||
\(336\) | −0.585786 | −0.0319573 | ||||||||
\(337\) | −12.8492 | + | 12.8492i | −0.699943 | + | 0.699943i | −0.964398 | − | 0.264455i | \(-0.914808\pi\) |
0.264455 | + | 0.964398i | \(0.414808\pi\) | |||||||
\(338\) | 4.00000 | 0.217571 | ||||||||
\(339\) | −1.44365 | −0.0784083 | ||||||||
\(340\) | 9.00000 | − | 2.00000i | 0.488094 | − | 0.108465i | ||||
\(341\) | 17.0122 | 0.921262 | ||||||||
\(342\) | −20.4853 | −1.10772 | ||||||||
\(343\) | −12.0000 | + | 12.0000i | −0.647939 | + | 0.647939i | ||||
\(344\) | −3.75736 | −0.202583 | ||||||||
\(345\) | −1.17157 | + | 3.51472i | −0.0630754 | + | 0.189226i | ||||
\(346\) | −17.6569 | + | 17.6569i | −0.949238 | + | 0.949238i | ||||
\(347\) | −15.7071 | − | 15.7071i | −0.843202 | − | 0.843202i | 0.146072 | − | 0.989274i | \(-0.453337\pi\) |
−0.989274 | + | 0.146072i | \(0.953337\pi\) | |||||||
\(348\) | 0.414214 | 0.0222042 | ||||||||
\(349\) | 10.9706i | 0.587241i | 0.955922 | + | 0.293620i | \(0.0948602\pi\) | ||||
−0.955922 | + | 0.293620i | \(0.905140\pi\) | |||||||
\(350\) | 1.00000 | + | 7.00000i | 0.0534522 | + | 0.374166i | ||||
\(351\) | 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 | \(0.0973484\pi\) | ||||
−0.953598 | + | 0.301084i | \(0.902652\pi\) | |||||||
\(354\) | 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 | \(-0.0597463\pi\) | |||||||
\(360\) | 6.00000 | + | 2.00000i | 0.316228 | + | 0.105409i | ||||
\(361\) | −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 | 0.998911 | − | 0.0466531i | \(-0.0148555\pi\) |
−0.0466531 | + | 0.998911i | \(0.514856\pi\) | |||||||
\(368\) | −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 | \(0.318040\pi\) | ||||
−0.541016 | + | 0.841012i | \(0.681960\pi\) | |||||||
\(374\) | −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 | \(0.744389\pi\) | |||||||
\(380\) | 15.3640 | + | 5.12132i | 0.788155 | + | 0.262718i | ||||
\(381\) | −5.19239 | + | 5.19239i | −0.266014 | + | 0.266014i | ||||
\(382\) | 21.2132 | 1.08536 | ||||||||
\(383\) | 13.2426 | 0.676667 | 0.338334 | − | 0.941026i | \(-0.390137\pi\) | ||||
0.338334 | + | 0.941026i | \(0.390137\pi\) | |||||||
\(384\) | 0.292893 | − | 0.292893i | 0.0149466 | − | 0.0149466i | ||||
\(385\) | 2.24264 | − | 6.72792i | 0.114296 | − | 0.342887i | ||||
\(386\) | −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 | 0.578438 | − | 0.815726i | \(-0.303662\pi\) |
−0.815726 | + | 0.578438i | \(0.803662\pi\) | |||||||
\(398\) | −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 | ||||||||
\(405\) | −5.29289 | + | 15.8787i | −0.263006 | + | 0.789018i | ||||
\(406\) | − | 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 | ||||
\(415\) | −3.00000 | + | 9.00000i | −0.147264 | + | 0.441793i | ||||
\(416\) | − | 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 | \(0.377810\pi\) | |||||||
\(420\) | −0.414214 | + | 1.24264i | −0.0202116 | + | 0.0606347i | ||||
\(421\) | −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 | ||||||||
\(425\) | 2.12132 | − | 20.5061i | 0.102899 | − | 0.994692i | ||||
\(426\) | 2.17157 | 0.105213 | ||||||||
\(427\) | −12.2426 | −0.592463 | ||||||||
\(428\) | 2.82843 | − | 2.82843i | 0.136717 | − | 0.136717i | ||||
\(429\) | 2.78680 | 0.134548 | ||||||||
\(430\) | −2.65685 | + | 7.97056i | −0.128125 | + | 0.384375i | ||||
\(431\) | 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 | \(-0.455823\pi\) | ||||
0.138341 | + | 0.990385i | \(0.455823\pi\) | |||||||
\(434\) | 10.7279i | 0.514957i | ||||||||
\(435\) | 0.292893 | − | 0.878680i | 0.0140432 | − | 0.0421295i | ||||
\(436\) | 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 | \(0.354938\pi\) | ||||
−0.440114 | + | 0.897942i | \(0.645062\pi\) | |||||||
\(444\) | 3.07107i | 0.145746i | ||||||||
\(445\) | 8.12132 | − | 24.3640i | 0.384988 | − | 1.15496i | ||||
\(446\) | 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 | \(-0.483296\pi\) | ||||
0.0524532 | + | 0.998623i | \(0.483296\pi\) | |||||||
\(458\) | 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 | \(-0.800481\pi\) | ||
0.809904 | − | 0.586562i | \(-0.199519\pi\) | |||||||
\(464\) | 0.707107 | + | 0.707107i | 0.0328266 | + | 0.0328266i | ||||
\(465\) | −2.22183 | + | 6.66548i | −0.103035 | + | 0.309104i | ||||
\(466\) | 10.9497 | − | 10.9497i | 0.507237 | − | 0.507237i | ||||
\(467\) | 18.7279 | 0.866625 | 0.433312 | − | 0.901244i | \(-0.357345\pi\) | ||||
0.433312 | + | 0.901244i | \(0.357345\pi\) | |||||||
\(468\) | 8.48528 | 0.392232 | ||||||||
\(469\) | −14.4853 | + | 14.4853i | −0.668868 | + | 0.668868i | ||||
\(470\) | 3.36396 | + | 1.12132i | 0.155168 | + | 0.0517227i | ||||
\(471\) | 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 | 0.404906 | − | 0.914358i | \(-0.367304\pi\) |
−0.914358 | + | 0.404906i | \(0.867304\pi\) | |||||||
\(488\) | 6.12132 | − | 6.12132i | 0.277099 | − | 0.277099i | ||||
\(489\) | 2.62742 | 0.118816 | ||||||||
\(490\) | −10.6066 | − | 3.53553i | −0.479157 | − | 0.159719i | ||||
\(491\) | 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 | \(0.336868\pi\) | |||||||
\(500\) | −9.19239 | + | 6.36396i | −0.411096 | + | 0.284605i | ||||
\(501\) | − | 0.627417i | − | 0.0280309i | ||||||
\(502\) | 20.4853 | 0.914303 | ||||||||
\(503\) | −13.0711 | − | 13.0711i | −0.582810 | − | 0.582810i | 0.352864 | − | 0.935674i | \(-0.385208\pi\) |
−0.935674 | + | 0.352864i | \(0.885208\pi\) | |||||||
\(504\) | 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 | \(0.5\pi\) | |||||||||
\(510\) | 2.05025 | − | 3.22183i | 0.0907867 | − | 0.142665i | ||||
\(511\) | −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 | ||||||||
\(520\) | −6.36396 | − | 2.12132i | −0.279078 | − | 0.0930261i | ||||
\(521\) | −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 | \(-0.803420\pi\) | ||
0.815285 | − | 0.579060i | \(-0.196580\pi\) | |||||||
\(524\) | 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 | ||||||
\(530\) | 2.12132 | − | 6.36396i | 0.0921443 | − | 0.276433i | ||||
\(531\) | −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 | −0.756420 | − | 0.654086i | \(-0.773053\pi\) |
0.654086 | + | 0.756420i | \(0.273053\pi\) | |||||||
\(548\) | 4.58579i | 0.195895i | ||||||||
\(549\) | 17.3137 | + | 17.3137i | 0.738931 | + | 0.738931i | ||||
\(550\) | 11.1005 | − | 1.58579i | 0.473327 | − | 0.0676182i | ||||
\(551\) | −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 | ||||
\(555\) | 6.51472 | + | 2.17157i | 0.276534 | + | 0.0921781i | ||||
\(556\) | −11.0000 | − | 11.0000i | −0.466504 | − | 0.466504i | ||||
\(557\) | 34.7990i | 1.47448i | 0.675631 | + | 0.737240i | \(0.263871\pi\) | ||||
−0.675631 | + | 0.737240i | \(0.736129\pi\) | |||||||
\(558\) | 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 | \(-0.0806240\pi\) | ||||
0.968094 | + | 0.250588i | \(0.0806240\pi\) | |||||||
\(564\) | 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 | ||||||||
\(575\) | 2.82843 | + | 19.7990i | 0.117954 | + | 0.825675i | ||||
\(576\) | 2.82843i | 0.117851i | ||||||||
\(577\) | 4.97056i | 0.206927i | 0.994633 | + | 0.103464i | \(0.0329925\pi\) | ||||
−0.994633 | + | 0.103464i | \(0.967007\pi\) | |||||||
\(578\) | −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 | ||||
\(585\) | 6.00000 | − | 18.0000i | 0.248069 | − | 0.744208i | ||||
\(586\) | − | 20.6569i | − | 0.853327i | ||||||
\(587\) | −24.0000 | −0.990586 | −0.495293 | − | 0.868726i | \(-0.664939\pi\) | ||||
−0.495293 | + | 0.868726i | \(0.664939\pi\) | |||||||
\(588\) | −1.46447 | − | 1.46447i | −0.0603936 | − | 0.0603936i | ||||
\(589\) | 38.8492 | − | 38.8492i | 1.60076 | − | 1.60076i | ||||
\(590\) | 27.3640 | + | 9.12132i | 1.12656 | + | 0.375519i | ||||
\(591\) | −1.95837 | −0.0805566 | ||||||||
\(592\) | −5.24264 | + | 5.24264i | −0.215471 | + | 0.215471i | ||||
\(593\) | −18.0000 | −0.739171 | −0.369586 | − | 0.929197i | \(-0.620500\pi\) | ||||
−0.369586 | + | 0.929197i | \(0.620500\pi\) | |||||||
\(594\) | −5.41421 | −0.222148 | ||||||||
\(595\) | −11.0000 | − | 7.00000i | −0.450956 | − | 0.286972i | ||||
\(596\) | −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 | \(0.578838\pi\) | |||||||
\(600\) | −2.05025 | + | 0.292893i | −0.0837012 | + | 0.0119573i | ||||
\(601\) | 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 | ||||||
\(605\) | 12.6655 | + | 4.22183i | 0.514925 | + | 0.171642i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.4558 | + | 26.4558i | −1.07381 | + | 1.07381i | −0.0767600 | + | 0.997050i | \(0.524458\pi\) |
−0.997050 | + | 0.0767600i | \(0.975542\pi\) | |||||||
\(608\) | 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 | \(0.0259307\pi\) | ||||
−0.996684 | + | 0.0813737i | \(0.974069\pi\) | |||||||
\(614\) | − | 33.2132i | − | 1.34038i | ||||||
\(615\) | −5.48528 | − | 1.82843i | −0.221188 | − | 0.0737293i | ||||
\(616\) | 3.17157 | 0.127786 | ||||||||
\(617\) | 19.4350 | − | 19.4350i | 0.782425 | − | 0.782425i | −0.197815 | − | 0.980239i | \(-0.563384\pi\) |
0.980239 | + | 0.197815i | \(0.0633844\pi\) | |||||||
\(618\) | 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 | ||||
\(635\) | −12.5355 | + | 37.6066i | −0.497457 | + | 1.49237i | ||||
\(636\) | 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 | ||||
\(640\) | 0.707107 | − | 2.12132i | 0.0279508 | − | 0.0838525i | ||||
\(641\) | 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 | −0.629127 | − | 0.777303i | \(-0.716587\pi\) |
0.777303 | + | 0.629127i | \(0.216587\pi\) | |||||||
\(644\) | 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 | \(0.383919\pi\) | ||||
−0.356651 | + | 0.934238i | \(0.616081\pi\) | |||||||
\(648\) | −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 | 0.606945 | − | 0.794744i | \(-0.292395\pi\) |
−0.794744 | + | 0.606945i | \(0.792395\pi\) | |||||||
\(654\) | − | 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 | \(0.299731\pi\) | |||||||
\(660\) | 1.97056 | + | 0.656854i | 0.0767041 | + | 0.0255680i | ||||
\(661\) | − | 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 | ||||
\(670\) | −30.7279 | − | 10.2426i | −1.18712 | − | 0.395708i | ||||
\(671\) | 19.4142i | 0.749477i | ||||||||
\(672\) | −0.585786 | −0.0225972 | ||||||||
\(673\) | −25.8787 | − | 25.8787i | −0.997550 | − | 0.997550i | 0.00244721 | − | 0.999997i | \(-0.499221\pi\) |
−0.999997 | + | 0.00244721i | \(0.999221\pi\) | |||||||
\(674\) | −12.8492 | + | 12.8492i | −0.494934 | + | 0.494934i | ||||
\(675\) | −1.70711 | − | 11.9497i | −0.0657066 | − | 0.459946i | ||||
\(676\) | 4.00000 | 0.153846 | ||||||||
\(677\) | −22.4142 | + | 22.4142i | −0.861448 | + | 0.861448i | −0.991506 | − | 0.130058i | \(-0.958484\pi\) |
0.130058 | + | 0.991506i | \(0.458484\pi\) | |||||||
\(678\) | −1.44365 | −0.0554431 | ||||||||
\(679\) | 0.242641 | 0.00931169 | ||||||||
\(680\) | 9.00000 | − | 2.00000i | 0.345134 | − | 0.0766965i | ||||
\(681\) | 2.37258 | 0.0909176 | ||||||||
\(682\) | 17.0122 | 0.651431 | ||||||||
\(683\) | −24.5355 | + | 24.5355i | −0.938826 | + | 0.938826i | −0.998234 | − | 0.0594077i | \(-0.981079\pi\) |
0.0594077 | + | 0.998234i | \(0.481079\pi\) | |||||||
\(684\) | −20.4853 | −0.783274 | ||||||||
\(685\) | 9.72792 | + | 3.24264i | 0.371685 | + | 0.123895i | ||||
\(686\) | −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 | ||||||
\(690\) | −1.17157 | + | 3.51472i | −0.0446010 | + | 0.133803i | ||||
\(691\) | 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 | ||||||
\(700\) | 1.00000 | + | 7.00000i | 0.0377964 | + | 0.264575i | ||||
\(701\) | −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 | \(-0.511297\pi\) | |||||||
\(720\) | 6.00000 | + | 2.00000i | 0.223607 | + | 0.0745356i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −33.4558 | −1.24510 | ||||||||
\(723\) | 1.61522 | 0.0600708 | ||||||||
\(724\) | −14.0000 | + | 14.0000i | −0.520306 | + | 0.520306i | ||||
\(725\) | −0.707107 | − | 4.94975i | −0.0262613 | − | 0.183829i | ||||
\(726\) | 1.74874 | + | 1.74874i | 0.0649017 | + | 0.0649017i | ||||
\(727\) | − | 16.7574i | − | 0.621496i | −0.950492 | − | 0.310748i | \(-0.899420\pi\) | ||
0.950492 | − | 0.310748i | \(-0.100580\pi\) | |||||||
\(728\) | −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 | \(-0.291612\pi\) | ||||
0.608898 | + | 0.793249i | \(0.291612\pi\) | |||||||
\(734\) | 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 | −0.299907 | − | 0.953968i | \(-0.596956\pi\) |
0.953968 | + | 0.299907i | \(0.0969556\pi\) | |||||||
\(744\) | −3.14214 | −0.115196 | ||||||||
\(745\) | −9.00000 | + | 27.0000i | −0.329734 | + | 0.989203i | ||||
\(746\) | 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 | ||||
\(755\) | −25.4558 | − | 8.48528i | −0.926433 | − | 0.308811i | ||||
\(756\) | − | 3.41421i | − | 0.124174i | ||||||
\(757\) | −32.9411 | −1.19727 | −0.598633 | − | 0.801024i | \(-0.704289\pi\) | ||||
−0.598633 | + | 0.801024i | \(0.704289\pi\) | |||||||
\(758\) | 0.485281 | + | 0.485281i | 0.0176262 | + | 0.0176262i | ||||
\(759\) | 2.62742 | − | 2.62742i | 0.0953692 | − | 0.0953692i | ||||
\(760\) | 15.3640 | + | 5.12132i | 0.557309 | + | 0.185770i | ||||
\(761\) | 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 | ||||||||
\(765\) | 5.65685 | + | 25.4558i | 0.204524 | + | 0.920358i | ||||
\(766\) | 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 | \(0.583935\pi\) | |||||||
\(770\) | 2.24264 | − | 6.72792i | 0.0808192 | − | 0.242457i | ||||
\(771\) | −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 | \(-0.301406\pi\) | ||||
0.584207 | + | 0.811605i | \(0.301406\pi\) | |||||||
\(774\) | − | 10.6274i | − | 0.381995i | ||||||
\(775\) | 5.36396 | + | 37.5477i | 0.192679 | + | 1.34875i | ||||
\(776\) | −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 | ||||||
\(785\) | 25.4558 | + | 8.48528i | 0.908558 | + | 0.302853i | ||||
\(786\) | 4.44365 | 0.158500 | ||||||||
\(787\) | −1.36396 | + | 1.36396i | −0.0486200 | + | 0.0486200i | −0.730999 | − | 0.682379i | \(-0.760945\pi\) |
0.682379 | + | 0.730999i | \(0.260945\pi\) | |||||||
\(788\) | −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 | \(-0.328499\pi\) | ||||
0.513095 | + | 0.858332i | \(0.328499\pi\) | |||||||
\(798\) | − | 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 | ||||
\(805\) | 12.0000 | + | 4.00000i | 0.422944 | + | 0.140981i | ||||
\(806\) | −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 | \(-0.0882552\pi\) | |||||||
\(810\) | −5.29289 | + | 15.8787i | −0.185973 | + | 0.557920i | ||||
\(811\) | 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 | 0.494962 | − | 0.868914i | \(-0.335182\pi\) |
−0.868914 | + | 0.494962i | \(0.835182\pi\) | |||||||
\(824\) | 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 | 0.608657 | − | 0.793433i | \(-0.291708\pi\) |
−0.793433 | + | 0.608657i | \(0.791708\pi\) | |||||||
\(828\) | 8.00000 | − | 8.00000i | 0.278019 | − | 0.278019i | ||||
\(829\) | 14.0000 | 0.486240 | 0.243120 | − | 0.969996i | \(-0.421829\pi\) | ||||
0.243120 | + | 0.969996i | \(0.421829\pi\) | |||||||
\(830\) | −3.00000 | + | 9.00000i | −0.104132 | + | 0.312395i | ||||
\(831\) | 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 | \(0.273170\pi\) | |||||||
\(840\) | −0.414214 | + | 1.24264i | −0.0142917 | + | 0.0428752i | ||||
\(841\) | − | 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 | ||||
\(845\) | 2.82843 | − | 8.48528i | 0.0973009 | − | 0.291903i | ||||
\(846\) | −4.48528 | −0.154207 | ||||||||
\(847\) | 5.97056 | − | 5.97056i | 0.205151 | − | 0.205151i | ||||
\(848\) | 3.00000 | 0.103020 | ||||||||
\(849\) | 11.2010 | 0.384418 | ||||||||
\(850\) | 2.12132 | − | 20.5061i | 0.0727607 | − | 0.703353i | ||||
\(851\) | 29.6569 | 1.01662 | ||||||||
\(852\) | 2.17157 | 0.0743969 | ||||||||
\(853\) | 8.51472 | − | 8.51472i | 0.291538 | − | 0.291538i | −0.546149 | − | 0.837688i | \(-0.683907\pi\) |
0.837688 | + | 0.546149i | \(0.183907\pi\) | |||||||
\(854\) | −12.2426 | −0.418935 | ||||||||
\(855\) | −14.4853 | + | 43.4558i | −0.495386 | + | 1.48616i | ||||
\(856\) | 2.82843 | − | 2.82843i | 0.0966736 | − | 0.0966736i | ||||
\(857\) | −25.4350 | − | 25.4350i | −0.868844 | − | 0.868844i | 0.123500 | − | 0.992345i | \(-0.460588\pi\) |
−0.992345 | + | 0.123500i | \(0.960588\pi\) | |||||||
\(858\) | 2.78680 | 0.0951397 | ||||||||
\(859\) | − | 45.7279i | − | 1.56022i | −0.625645 | − | 0.780108i | \(-0.715164\pi\) | ||
0.625645 | − | 0.780108i | \(-0.284836\pi\) | |||||||
\(860\) | −2.65685 | + | 7.97056i | −0.0905980 | + | 0.271794i | ||||
\(861\) | −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 | \(-0.612649\pi\) | ||
0.346557 | − | 0.938029i | \(-0.387351\pi\) | |||||||
\(864\) | 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 | ||||||
\(870\) | 0.292893 | − | 0.878680i | 0.00993001 | − | 0.0297900i | ||||
\(871\) | −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 | 0.836099 | − | 0.548578i | \(-0.184831\pi\) |
−0.548578 | + | 0.836099i | \(0.684831\pi\) | |||||||
\(878\) | 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 | \(0.102046\pi\) | ||||
−0.949051 | + | 0.315122i | \(0.897954\pi\) | |||||||
\(884\) | 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 | −0.297192 | − | 0.954818i | \(-0.596050\pi\) |
0.954818 | + | 0.297192i | \(0.0960500\pi\) | |||||||
\(888\) | 3.07107i | 0.103058i | ||||||||
\(889\) | 17.7279 | + | 17.7279i | 0.594575 | + | 0.594575i | ||||
\(890\) | 8.12132 | − | 24.3640i | 0.272227 | − | 0.816682i | ||||
\(891\) | 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 | ||||
\(895\) | 1.45584 | + | 0.485281i | 0.0486635 | + | 0.0162212i | ||||
\(896\) | −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 | 0.825310 | − | 0.564680i | \(-0.191000\pi\) |
−0.564680 | + | 0.825310i | \(0.691000\pi\) | |||||||
\(908\) | 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 | ||||||||
\(915\) | −7.60660 | − | 2.53553i | −0.251466 | − | 0.0838222i | ||||
\(916\) | 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 | ||||
\(925\) | 36.6985 | − | 5.24264i | 1.20664 | − | 0.172377i | ||||
\(926\) | − | 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 | \(0.365843\pi\) | |||||||
\(930\) | −2.22183 | + | 6.66548i | −0.0728565 | + | 0.218570i | ||||
\(931\) | 36.2132 | 1.18684 | ||||||||
\(932\) | 10.9497 | − | 10.9497i | 0.358671 | − | 0.358671i | ||||
\(933\) | −0.828427 | −0.0271215 | ||||||||
\(934\) | 18.7279 | 0.612796 | ||||||||
\(935\) | −11.1005 | + | 17.4437i | −0.363025 | + | 0.570468i | ||||
\(936\) | 8.48528 | 0.277350 | ||||||||
\(937\) | −47.2132 | −1.54239 | −0.771194 | − | 0.636600i | \(-0.780340\pi\) | ||||
−0.771194 | + | 0.636600i | \(0.780340\pi\) | |||||||
\(938\) | −14.4853 | + | 14.4853i | −0.472961 | + | 0.472961i | ||||
\(939\) | 13.1716 | 0.429838 | ||||||||
\(940\) | 3.36396 | + | 1.12132i | 0.109720 | + | 0.0365734i | ||||
\(941\) | 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 | ||||||||
\(945\) | −7.24264 | − | 2.41421i | −0.235603 | − | 0.0785344i | ||||
\(946\) | 5.95837 | − | 5.95837i | 0.193723 | − | 0.193723i | ||||
\(947\) | −26.2929 | + | 26.2929i | −0.854404 | + | 0.854404i | −0.990672 | − | 0.136268i | \(-0.956489\pi\) |
0.136268 | + | 0.990672i | \(0.456489\pi\) | |||||||
\(948\) | 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 | \(0.0236640\pi\) | ||||
−0.997238 | + | 0.0742741i | \(0.976336\pi\) | |||||||
\(954\) | 8.48528i | 0.274721i | ||||||||
\(955\) | 15.0000 | − | 45.0000i | 0.485389 | − | 1.45617i | ||||
\(956\) | 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 | \(-0.665922\pi\) | ||||
−0.497973 | + | 0.867192i | \(0.665922\pi\) | |||||||
\(968\) | 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 | ||||
\(975\) | 0.878680 | + | 6.15076i | 0.0281403 | + | 0.196982i | ||||
\(976\) | 6.12132 | − | 6.12132i | 0.195939 | − | 0.195939i | ||||
\(977\) | −0.727922 | −0.0232883 | −0.0116441 | − | 0.999932i | \(-0.503707\pi\) | ||||
−0.0116441 | + | 0.999932i | \(0.503707\pi\) | |||||||
\(978\) | 2.62742 | 0.0840155 | ||||||||
\(979\) | −18.2132 | + | 18.2132i | −0.582097 | + | 0.582097i | ||||
\(980\) | −10.6066 | − | 3.53553i | −0.338815 | − | 0.112938i | ||||
\(981\) | 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 | \(-0.288706\pi\) |
0.787657 | − | 0.616114i | \(-0.211294\pi\) | |||||||
\(984\) | − | 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 | 0.0273939 | − | 0.999625i | \(-0.491279\pi\) |
−0.999625 | + | 0.0273939i | \(0.991279\pi\) | |||||||
\(998\) | −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.f.149.1 | yes | 4 | |
3.2 | odd | 2 | 1530.2.n.j.829.1 | 4 | |||
5.2 | odd | 4 | 850.2.h.h.251.2 | 4 | |||
5.3 | odd | 4 | 850.2.h.k.251.1 | 4 | |||
5.4 | even | 2 | 170.2.g.e.149.2 | yes | 4 | ||
15.14 | odd | 2 | 1530.2.n.o.829.2 | 4 | |||
17.4 | even | 4 | 170.2.g.e.89.2 | ✓ | 4 | ||
51.38 | odd | 4 | 1530.2.n.o.1279.2 | 4 | |||
85.4 | even | 4 | inner | 170.2.g.f.89.1 | yes | 4 | |
85.38 | odd | 4 | 850.2.h.k.701.1 | 4 | |||
85.72 | odd | 4 | 850.2.h.h.701.2 | 4 | |||
255.89 | odd | 4 | 1530.2.n.j.1279.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
170.2.g.e.89.2 | ✓ | 4 | 17.4 | even | 4 | ||
170.2.g.e.149.2 | yes | 4 | 5.4 | even | 2 | ||
170.2.g.f.89.1 | yes | 4 | 85.4 | even | 4 | inner | |
170.2.g.f.149.1 | yes | 4 | 1.1 | even | 1 | trivial | |
850.2.h.h.251.2 | 4 | 5.2 | odd | 4 | |||
850.2.h.h.701.2 | 4 | 85.72 | odd | 4 | |||
850.2.h.k.251.1 | 4 | 5.3 | odd | 4 | |||
850.2.h.k.701.1 | 4 | 85.38 | odd | 4 | |||
1530.2.n.j.829.1 | 4 | 3.2 | odd | 2 | |||
1530.2.n.j.1279.1 | 4 | 255.89 | odd | 4 | |||
1530.2.n.o.829.2 | 4 | 15.14 | odd | 2 | |||
1530.2.n.o.1279.2 | 4 | 51.38 | odd | 4 |