Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,2,Mod(109,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.g (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.01834519640\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 163.1 | ||
Root | \(-1.32288 + 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.163 |
Dual form | 378.2.g.h.109.1 |
$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.82288 | + | 3.15731i | −0.815215 | + | 1.41199i | 0.0939588 | + | 0.995576i | \(0.470048\pi\) |
−0.909174 | + | 0.416417i | \(0.863286\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.64575 | −1.00000 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.82288 | + | 3.15731i | 0.576444 | + | 0.998430i | ||||
\(11\) | 1.82288 | + | 3.15731i | 0.549618 | + | 0.951966i | 0.998301 | + | 0.0582747i | \(0.0185599\pi\) |
−0.448683 | + | 0.893691i | \(0.648107\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.64575 | −1.28850 | −0.644250 | − | 0.764815i | \(-0.722830\pi\) | ||||
−0.644250 | + | 0.764815i | \(0.722830\pi\) | |||||||
\(14\) | −1.32288 | + | 2.29129i | −0.353553 | + | 0.612372i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.82288 | + | 3.15731i | 0.442112 | + | 0.765761i | 0.997846 | − | 0.0655994i | \(-0.0208959\pi\) |
−0.555734 | + | 0.831360i | \(0.687563\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | + | 1.73205i | −0.229416 | + | 0.397360i | −0.957635 | − | 0.287984i | \(-0.907015\pi\) |
0.728219 | + | 0.685344i | \(0.240348\pi\) | |||||||
\(20\) | 3.64575 | 0.815215 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.64575 | 0.777277 | ||||||||
\(23\) | −0.645751 | + | 1.11847i | −0.134648 | + | 0.233218i | −0.925463 | − | 0.378838i | \(-0.876324\pi\) |
0.790815 | + | 0.612056i | \(0.209657\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.14575 | − | 7.18065i | −0.829150 | − | 1.43613i | ||||
\(26\) | −2.32288 | + | 4.02334i | −0.455553 | + | 0.789042i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.32288 | + | 2.29129i | 0.250000 | + | 0.433013i | ||||
\(29\) | −2.35425 | −0.437173 | −0.218587 | − | 0.975818i | \(-0.570145\pi\) | ||||
−0.218587 | + | 0.975818i | \(0.570145\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.32288 | + | 4.02334i | 0.417201 | + | 0.722613i | 0.995657 | − | 0.0931007i | \(-0.0296779\pi\) |
−0.578456 | + | 0.815714i | \(0.696345\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.64575 | 0.625241 | ||||||||
\(35\) | 4.82288 | − | 8.35347i | 0.815215 | − | 1.41199i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.96863 | − | 10.3380i | 0.981236 | − | 1.69955i | 0.323640 | − | 0.946180i | \(-0.395093\pi\) |
0.657596 | − | 0.753371i | \(-0.271573\pi\) | |||||||
\(38\) | 1.00000 | + | 1.73205i | 0.162221 | + | 0.280976i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.82288 | − | 3.15731i | 0.288222 | − | 0.499215i | ||||
\(41\) | −10.9373 | −1.70811 | −0.854056 | − | 0.520181i | \(-0.825864\pi\) | ||||
−0.854056 | + | 0.520181i | \(0.825864\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.00000 | 0.762493 | 0.381246 | − | 0.924473i | \(-0.375495\pi\) | ||||
0.381246 | + | 0.924473i | \(0.375495\pi\) | |||||||
\(44\) | 1.82288 | − | 3.15731i | 0.274809 | − | 0.475983i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.645751 | + | 1.11847i | 0.0952108 | + | 0.164910i | ||||
\(47\) | 2.46863 | − | 4.27579i | 0.360086 | − | 0.623688i | −0.627888 | − | 0.778303i | \(-0.716081\pi\) |
0.987975 | + | 0.154616i | \(0.0494139\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | −8.29150 | −1.17260 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.32288 | + | 4.02334i | 0.322125 | + | 0.557937i | ||||
\(53\) | 3.00000 | + | 5.19615i | 0.412082 | + | 0.713746i | 0.995117 | − | 0.0987002i | \(-0.0314685\pi\) |
−0.583036 | + | 0.812447i | \(0.698135\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.2915 | −1.79223 | ||||||||
\(56\) | 2.64575 | 0.353553 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.17712 | + | 2.03884i | −0.154564 | + | 0.267713i | ||||
\(59\) | 4.17712 | + | 7.23499i | 0.543815 | + | 0.941916i | 0.998680 | + | 0.0513554i | \(0.0163541\pi\) |
−0.454865 | + | 0.890560i | \(0.650313\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.67712 | + | 6.36897i | −0.470808 | + | 0.815463i | −0.999443 | − | 0.0333867i | \(-0.989371\pi\) |
0.528635 | + | 0.848849i | \(0.322704\pi\) | |||||||
\(62\) | 4.64575 | 0.590011 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 8.46863 | − | 14.6681i | 1.05040 | − | 1.81935i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.14575 | + | 1.98450i | 0.139976 | + | 0.242445i | 0.927487 | − | 0.373855i | \(-0.121964\pi\) |
−0.787511 | + | 0.616300i | \(0.788631\pi\) | |||||||
\(68\) | 1.82288 | − | 3.15731i | 0.221056 | − | 0.382880i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.82288 | − | 8.35347i | −0.576444 | − | 0.998430i | ||||
\(71\) | −15.6458 | −1.85681 | −0.928405 | − | 0.371571i | \(-0.878819\pi\) | ||||
−0.928405 | + | 0.371571i | \(0.878819\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.29150 | − | 9.16515i | −0.619324 | − | 1.07270i | −0.989609 | − | 0.143782i | \(-0.954074\pi\) |
0.370286 | − | 0.928918i | \(-0.379260\pi\) | |||||||
\(74\) | −5.96863 | − | 10.3380i | −0.693839 | − | 1.20176i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | −4.82288 | − | 8.35347i | −0.549618 | − | 0.951966i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.61438 | + | 9.72439i | −0.631667 | + | 1.09408i | 0.355544 | + | 0.934660i | \(0.384296\pi\) |
−0.987211 | + | 0.159420i | \(0.949038\pi\) | |||||||
\(80\) | −1.82288 | − | 3.15731i | −0.203804 | − | 0.352998i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.46863 | + | 9.47194i | −0.603909 | + | 1.04600i | ||||
\(83\) | 13.2915 | 1.45893 | 0.729466 | − | 0.684017i | \(-0.239769\pi\) | ||||
0.729466 | + | 0.684017i | \(0.239769\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.2915 | −1.44167 | ||||||||
\(86\) | 2.50000 | − | 4.33013i | 0.269582 | − | 0.466930i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.82288 | − | 3.15731i | −0.194319 | − | 0.336571i | ||||
\(89\) | 2.46863 | − | 4.27579i | 0.261674 | − | 0.453233i | −0.705013 | − | 0.709194i | \(-0.749059\pi\) |
0.966687 | + | 0.255962i | \(0.0823922\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.2915 | 1.28850 | ||||||||
\(92\) | 1.29150 | 0.134648 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.46863 | − | 4.27579i | −0.254619 | − | 0.441014i | ||||
\(95\) | −3.64575 | − | 6.31463i | −0.374046 | − | 0.647867i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.5830 | 1.37915 | 0.689573 | − | 0.724217i | \(-0.257798\pi\) | ||||
0.689573 | + | 0.724217i | \(0.257798\pi\) | |||||||
\(98\) | 3.50000 | − | 6.06218i | 0.353553 | − | 0.612372i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.14575 | + | 7.18065i | −0.414575 | + | 0.718065i | ||||
\(101\) | 4.17712 | + | 7.23499i | 0.415639 | + | 0.719909i | 0.995495 | − | 0.0948105i | \(-0.0302245\pi\) |
−0.579856 | + | 0.814719i | \(0.696891\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.96863 | + | 3.40976i | −0.193975 | + | 0.335974i | −0.946564 | − | 0.322516i | \(-0.895471\pi\) |
0.752589 | + | 0.658490i | \(0.228805\pi\) | |||||||
\(104\) | 4.64575 | 0.455553 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | −3.00000 | + | 5.19615i | −0.290021 | + | 0.502331i | −0.973814 | − | 0.227345i | \(-0.926996\pi\) |
0.683793 | + | 0.729676i | \(0.260329\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.67712 | + | 2.90486i | 0.160639 | + | 0.278236i | 0.935098 | − | 0.354389i | \(-0.115311\pi\) |
−0.774459 | + | 0.632624i | \(0.781978\pi\) | |||||||
\(110\) | −6.64575 | + | 11.5108i | −0.633648 | + | 1.09751i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.32288 | − | 2.29129i | 0.125000 | − | 0.216506i | ||||
\(113\) | −2.35425 | −0.221469 | −0.110735 | − | 0.993850i | \(-0.535320\pi\) | ||||
−0.110735 | + | 0.993850i | \(0.535320\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.35425 | − | 4.07768i | −0.219535 | − | 0.380245i | ||||
\(116\) | 1.17712 | + | 2.03884i | 0.109293 | + | 0.189301i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.35425 | 0.769071 | ||||||||
\(119\) | −4.82288 | − | 8.35347i | −0.442112 | − | 0.765761i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.14575 | + | 1.98450i | −0.104159 | + | 0.180409i | ||||
\(122\) | 3.67712 | + | 6.36897i | 0.332911 | + | 0.576619i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.32288 | − | 4.02334i | 0.208600 | − | 0.361306i | ||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.35425 | 0.120170 | 0.0600851 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600851 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.46863 | − | 14.6681i | −0.742748 | − | 1.28648i | ||||
\(131\) | −7.29150 | + | 12.6293i | −0.637062 | + | 1.10342i | 0.349013 | + | 0.937118i | \(0.386517\pi\) |
−0.986074 | + | 0.166305i | \(0.946816\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.64575 | − | 4.58258i | 0.229416 | − | 0.397360i | ||||
\(134\) | 2.29150 | 0.197956 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.82288 | − | 3.15731i | −0.156310 | − | 0.270737i | ||||
\(137\) | 0.645751 | + | 1.11847i | 0.0551703 | + | 0.0955577i | 0.892292 | − | 0.451460i | \(-0.149097\pi\) |
−0.837121 | + | 0.547017i | \(0.815763\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.58301 | 0.134269 | 0.0671344 | − | 0.997744i | \(-0.478614\pi\) | ||||
0.0671344 | + | 0.997744i | \(0.478614\pi\) | |||||||
\(140\) | −9.64575 | −0.815215 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.82288 | + | 13.5496i | −0.656481 | + | 1.13706i | ||||
\(143\) | −8.46863 | − | 14.6681i | −0.708182 | − | 1.22661i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.29150 | − | 7.43310i | 0.356390 | − | 0.617285i | ||||
\(146\) | −10.5830 | −0.875856 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −11.9373 | −0.981236 | ||||||||
\(149\) | 11.4686 | − | 19.8642i | 0.939547 | − | 1.62734i | 0.173228 | − | 0.984882i | \(-0.444580\pi\) |
0.766319 | − | 0.642461i | \(-0.222086\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.61438 | + | 16.6526i | 0.782407 | + | 1.35517i | 0.930536 | + | 0.366201i | \(0.119342\pi\) |
−0.148129 | + | 0.988968i | \(0.547325\pi\) | |||||||
\(152\) | 1.00000 | − | 1.73205i | 0.0811107 | − | 0.140488i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −9.64575 | −0.777277 | ||||||||
\(155\) | −16.9373 | −1.36043 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000 | + | 3.46410i | 0.159617 | + | 0.276465i | 0.934731 | − | 0.355357i | \(-0.115641\pi\) |
−0.775113 | + | 0.631822i | \(0.782307\pi\) | |||||||
\(158\) | 5.61438 | + | 9.72439i | 0.446656 | + | 0.773631i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.64575 | −0.288222 | ||||||||
\(161\) | 1.70850 | − | 2.95920i | 0.134648 | − | 0.233218i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.500000 | − | 0.866025i | 0.0391630 | − | 0.0678323i | −0.845780 | − | 0.533533i | \(-0.820864\pi\) |
0.884943 | + | 0.465700i | \(0.154198\pi\) | |||||||
\(164\) | 5.46863 | + | 9.47194i | 0.427028 | + | 0.739634i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.64575 | − | 11.5108i | 0.515810 | − | 0.893410i | ||||
\(167\) | 8.58301 | 0.664173 | 0.332086 | − | 0.943249i | \(-0.392247\pi\) | ||||
0.332086 | + | 0.943249i | \(0.392247\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.58301 | 0.660231 | ||||||||
\(170\) | −6.64575 | + | 11.5108i | −0.509706 | + | 0.882836i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.50000 | − | 4.33013i | −0.190623 | − | 0.330169i | ||||
\(173\) | −7.29150 | + | 12.6293i | −0.554363 | + | 0.960184i | 0.443590 | + | 0.896230i | \(0.353705\pi\) |
−0.997953 | + | 0.0639546i | \(0.979629\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.9686 | + | 18.9982i | 0.829150 | + | 1.43613i | ||||
\(176\) | −3.64575 | −0.274809 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.46863 | − | 4.27579i | −0.185031 | − | 0.320484i | ||||
\(179\) | 8.46863 | + | 14.6681i | 0.632975 | + | 1.09634i | 0.986940 | + | 0.161086i | \(0.0514997\pi\) |
−0.353965 | + | 0.935259i | \(0.615167\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.70850 | −0.201321 | −0.100661 | − | 0.994921i | \(-0.532096\pi\) | ||||
−0.100661 | + | 0.994921i | \(0.532096\pi\) | |||||||
\(182\) | 6.14575 | − | 10.6448i | 0.455553 | − | 0.789042i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.645751 | − | 1.11847i | 0.0476054 | − | 0.0824550i | ||||
\(185\) | 21.7601 | + | 37.6897i | 1.59984 | + | 2.77100i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.64575 | + | 11.5108i | −0.485985 | + | 0.841752i | ||||
\(188\) | −4.93725 | −0.360086 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.29150 | −0.528981 | ||||||||
\(191\) | −10.4059 | + | 18.0235i | −0.752943 | + | 1.30414i | 0.193447 | + | 0.981111i | \(0.438033\pi\) |
−0.946390 | + | 0.323025i | \(0.895300\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.50000 | + | 6.06218i | 0.251936 | + | 0.436365i | 0.964059 | − | 0.265689i | \(-0.0855996\pi\) |
−0.712123 | + | 0.702055i | \(0.752266\pi\) | |||||||
\(194\) | 6.79150 | − | 11.7632i | 0.487601 | − | 0.844551i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.50000 | − | 6.06218i | −0.250000 | − | 0.433013i | ||||
\(197\) | −4.70850 | −0.335467 | −0.167733 | − | 0.985832i | \(-0.553645\pi\) | ||||
−0.167733 | + | 0.985832i | \(0.553645\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.03137 | − | 5.25049i | −0.214888 | − | 0.372198i | 0.738350 | − | 0.674418i | \(-0.235605\pi\) |
−0.953238 | + | 0.302221i | \(0.902272\pi\) | |||||||
\(200\) | 4.14575 | + | 7.18065i | 0.293149 | + | 0.507749i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.35425 | 0.587803 | ||||||||
\(203\) | 6.22876 | 0.437173 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.9373 | − | 34.5323i | 1.39248 | − | 2.41184i | ||||
\(206\) | 1.96863 | + | 3.40976i | 0.137161 | + | 0.237569i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.32288 | − | 4.02334i | 0.161062 | − | 0.278968i | ||||
\(209\) | −7.29150 | −0.504364 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.8745 | 1.02400 | 0.512002 | − | 0.858984i | \(-0.328904\pi\) | ||||
0.512002 | + | 0.858984i | \(0.328904\pi\) | |||||||
\(212\) | 3.00000 | − | 5.19615i | 0.206041 | − | 0.356873i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.00000 | + | 5.19615i | 0.205076 | + | 0.355202i | ||||
\(215\) | −9.11438 | + | 15.7866i | −0.621595 | + | 1.07663i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.14575 | − | 10.6448i | −0.417201 | − | 0.722613i | ||||
\(218\) | 3.35425 | 0.227178 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.64575 | + | 11.5108i | 0.448056 | + | 0.776057i | ||||
\(221\) | −8.46863 | − | 14.6681i | −0.569661 | − | 0.986683i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.8745 | −0.929106 | −0.464553 | − | 0.885545i | \(-0.653785\pi\) | ||||
−0.464553 | + | 0.885545i | \(0.653785\pi\) | |||||||
\(224\) | −1.32288 | − | 2.29129i | −0.0883883 | − | 0.153093i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.17712 | + | 2.03884i | −0.0783011 | + | 0.135622i | ||||
\(227\) | 3.00000 | + | 5.19615i | 0.199117 | + | 0.344881i | 0.948242 | − | 0.317547i | \(-0.102859\pi\) |
−0.749125 | + | 0.662428i | \(0.769526\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.67712 | − | 8.10102i | 0.309073 | − | 0.535330i | −0.669087 | − | 0.743184i | \(-0.733315\pi\) |
0.978160 | + | 0.207854i | \(0.0666479\pi\) | |||||||
\(230\) | −4.70850 | −0.310469 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.35425 | 0.154564 | ||||||||
\(233\) | −9.64575 | + | 16.7069i | −0.631914 | + | 1.09451i | 0.355246 | + | 0.934773i | \(0.384397\pi\) |
−0.987160 | + | 0.159735i | \(0.948936\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.00000 | + | 15.5885i | 0.587095 | + | 1.01688i | ||||
\(236\) | 4.17712 | − | 7.23499i | 0.271908 | − | 0.470958i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.64575 | −0.625241 | ||||||||
\(239\) | 10.9373 | 0.707472 | 0.353736 | − | 0.935345i | \(-0.384911\pi\) | ||||
0.353736 | + | 0.935345i | \(0.384911\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.50000 | − | 4.33013i | −0.161039 | − | 0.278928i | 0.774202 | − | 0.632938i | \(-0.218151\pi\) |
−0.935242 | + | 0.354010i | \(0.884818\pi\) | |||||||
\(242\) | 1.14575 | + | 1.98450i | 0.0736517 | + | 0.127568i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.35425 | 0.470808 | ||||||||
\(245\) | −12.7601 | + | 22.1012i | −0.815215 | + | 1.41199i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.64575 | − | 8.04668i | 0.295602 | − | 0.511998i | ||||
\(248\) | −2.32288 | − | 4.02334i | −0.147503 | − | 0.255482i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.00000 | − | 10.3923i | 0.379473 | − | 0.657267i | ||||
\(251\) | 18.0000 | 1.13615 | 0.568075 | − | 0.822977i | \(-0.307688\pi\) | ||||
0.568075 | + | 0.822977i | \(0.307688\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.70850 | −0.296021 | ||||||||
\(254\) | 0.677124 | − | 1.17281i | 0.0424866 | − | 0.0735889i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 7.93725 | − | 13.7477i | 0.495112 | − | 0.857560i | −0.504872 | − | 0.863194i | \(-0.668460\pi\) |
0.999984 | + | 0.00563467i | \(0.00179358\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.7915 | + | 27.3517i | −0.981236 | + | 1.69955i | ||||
\(260\) | −16.9373 | −1.05040 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.29150 | + | 12.6293i | 0.450471 | + | 0.780238i | ||||
\(263\) | −2.46863 | − | 4.27579i | −0.152222 | − | 0.263656i | 0.779822 | − | 0.626001i | \(-0.215310\pi\) |
−0.932044 | + | 0.362345i | \(0.881976\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −21.8745 | −1.34374 | ||||||||
\(266\) | −2.64575 | − | 4.58258i | −0.162221 | − | 0.280976i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.14575 | − | 1.98450i | 0.0699879 | − | 0.121223i | ||||
\(269\) | −8.35425 | − | 14.4700i | −0.509368 | − | 0.882250i | −0.999941 | − | 0.0108507i | \(-0.996546\pi\) |
0.490574 | − | 0.871400i | \(-0.336787\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.61438 | + | 4.52824i | −0.158812 | + | 0.275071i | −0.934441 | − | 0.356119i | \(-0.884100\pi\) |
0.775628 | + | 0.631190i | \(0.217433\pi\) | |||||||
\(272\) | −3.64575 | −0.221056 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.29150 | 0.0780225 | ||||||||
\(275\) | 15.1144 | − | 26.1789i | 0.911431 | − | 1.57865i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.03137 | + | 1.78639i | 0.0619692 | + | 0.107334i | 0.895346 | − | 0.445372i | \(-0.146929\pi\) |
−0.833376 | + | 0.552706i | \(0.813595\pi\) | |||||||
\(278\) | 0.791503 | − | 1.37092i | 0.0474712 | − | 0.0822225i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.82288 | + | 8.35347i | −0.288222 | + | 0.499215i | ||||
\(281\) | −19.5203 | −1.16448 | −0.582241 | − | 0.813017i | \(-0.697824\pi\) | ||||
−0.582241 | + | 0.813017i | \(0.697824\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.14575 | + | 1.98450i | 0.0681078 | + | 0.117966i | 0.898068 | − | 0.439856i | \(-0.144970\pi\) |
−0.829961 | + | 0.557822i | \(0.811637\pi\) | |||||||
\(284\) | 7.82288 | + | 13.5496i | 0.464202 | + | 0.804022i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −16.9373 | −1.00152 | ||||||||
\(287\) | 28.9373 | 1.70811 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.85425 | − | 3.21165i | 0.109073 | − | 0.188921i | ||||
\(290\) | −4.29150 | − | 7.43310i | −0.252006 | − | 0.436487i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.29150 | + | 9.16515i | −0.309662 | + | 0.536350i | ||||
\(293\) | −7.06275 | −0.412610 | −0.206305 | − | 0.978488i | \(-0.566144\pi\) | ||||
−0.206305 | + | 0.978488i | \(0.566144\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −30.4575 | −1.77330 | ||||||||
\(296\) | −5.96863 | + | 10.3380i | −0.346919 | + | 0.600882i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −11.4686 | − | 19.8642i | −0.664360 | − | 1.15070i | ||||
\(299\) | 3.00000 | − | 5.19615i | 0.173494 | − | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.2288 | −0.762493 | ||||||||
\(302\) | 19.2288 | 1.10649 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | − | 1.73205i | −0.0573539 | − | 0.0993399i | ||||
\(305\) | −13.4059 | − | 23.2197i | −0.767619 | − | 1.32955i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.58301 | 0.432785 | 0.216392 | − | 0.976306i | \(-0.430571\pi\) | ||||
0.216392 | + | 0.976306i | \(0.430571\pi\) | |||||||
\(308\) | −4.82288 | + | 8.35347i | −0.274809 | + | 0.475983i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.46863 | + | 14.6681i | −0.480986 | + | 0.833092i | ||||
\(311\) | −6.76013 | − | 11.7089i | −0.383332 | − | 0.663950i | 0.608204 | − | 0.793780i | \(-0.291890\pi\) |
−0.991536 | + | 0.129830i | \(0.958557\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.35425 | + | 11.0059i | −0.359163 | + | 0.622089i | −0.987821 | − | 0.155593i | \(-0.950271\pi\) |
0.628658 | + | 0.777682i | \(0.283605\pi\) | |||||||
\(314\) | 4.00000 | 0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.2288 | 0.631667 | ||||||||
\(317\) | 13.4059 | − | 23.2197i | 0.752949 | − | 1.30415i | −0.193438 | − | 0.981112i | \(-0.561964\pi\) |
0.946387 | − | 0.323034i | \(-0.104703\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.29150 | − | 7.43310i | −0.240278 | − | 0.416174i | ||||
\(320\) | −1.82288 | + | 3.15731i | −0.101902 | + | 0.176499i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.70850 | − | 2.95920i | −0.0952108 | − | 0.164910i | ||||
\(323\) | −7.29150 | −0.405710 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.2601 | + | 33.3595i | 1.06836 | + | 1.85045i | ||||
\(326\) | −0.500000 | − | 0.866025i | −0.0276924 | − | 0.0479647i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10.9373 | 0.603909 | ||||||||
\(329\) | −6.53137 | + | 11.3127i | −0.360086 | + | 0.623688i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.9373 | − | 27.6041i | 0.875991 | − | 1.51726i | 0.0202871 | − | 0.999794i | \(-0.493542\pi\) |
0.855704 | − | 0.517466i | \(-0.173125\pi\) | |||||||
\(332\) | −6.64575 | − | 11.5108i | −0.364733 | − | 0.631736i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.29150 | − | 7.43310i | 0.234821 | − | 0.406721i | ||||
\(335\) | −8.35425 | −0.456441 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.5830 | −1.66596 | −0.832981 | − | 0.553301i | \(-0.813368\pi\) | ||||
−0.832981 | + | 0.553301i | \(0.813368\pi\) | |||||||
\(338\) | 4.29150 | − | 7.43310i | 0.233427 | − | 0.404307i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.64575 | + | 11.5108i | 0.360416 | + | 0.624260i | ||||
\(341\) | −8.46863 | + | 14.6681i | −0.458602 | + | 0.794322i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5203 | −1.00000 | ||||||||
\(344\) | −5.00000 | −0.269582 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.29150 | + | 12.6293i | 0.391994 | + | 0.678953i | ||||
\(347\) | −6.00000 | − | 10.3923i | −0.322097 | − | 0.557888i | 0.658824 | − | 0.752297i | \(-0.271054\pi\) |
−0.980921 | + | 0.194409i | \(0.937721\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.22876 | −0.0657738 | −0.0328869 | − | 0.999459i | \(-0.510470\pi\) | ||||
−0.0328869 | + | 0.999459i | \(0.510470\pi\) | |||||||
\(350\) | 21.9373 | 1.17260 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.82288 | + | 3.15731i | −0.0971596 | + | 0.168285i | ||||
\(353\) | −6.00000 | − | 10.3923i | −0.319348 | − | 0.553127i | 0.661004 | − | 0.750382i | \(-0.270130\pi\) |
−0.980352 | + | 0.197256i | \(0.936797\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 28.5203 | − | 49.3985i | 1.51370 | − | 2.62180i | ||||
\(356\) | −4.93725 | −0.261674 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16.9373 | 0.895162 | ||||||||
\(359\) | 5.58301 | − | 9.67005i | 0.294660 | − | 0.510366i | −0.680246 | − | 0.732984i | \(-0.738127\pi\) |
0.974906 | + | 0.222618i | \(0.0714604\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | + | 12.9904i | 0.394737 | + | 0.683704i | ||||
\(362\) | −1.35425 | + | 2.34563i | −0.0711777 | + | 0.123283i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.14575 | − | 10.6448i | −0.322125 | − | 0.557937i | ||||
\(365\) | 38.5830 | 2.01953 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.9373 | − | 25.8721i | −0.779718 | − | 1.35051i | −0.932104 | − | 0.362191i | \(-0.882029\pi\) |
0.152386 | − | 0.988321i | \(-0.451304\pi\) | |||||||
\(368\) | −0.645751 | − | 1.11847i | −0.0336621 | − | 0.0583045i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 43.5203 | 2.26251 | ||||||||
\(371\) | −7.93725 | − | 13.7477i | −0.412082 | − | 0.713746i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.29150 | + | 3.96900i | −0.118650 | + | 0.205507i | −0.919233 | − | 0.393715i | \(-0.871190\pi\) |
0.800583 | + | 0.599222i | \(0.204523\pi\) | |||||||
\(374\) | 6.64575 | + | 11.5108i | 0.343644 | + | 0.595208i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.46863 | + | 4.27579i | −0.127310 | + | 0.220507i | ||||
\(377\) | 10.9373 | 0.563297 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.5830 | 1.31411 | 0.657055 | − | 0.753842i | \(-0.271802\pi\) | ||||
0.657055 | + | 0.753842i | \(0.271802\pi\) | |||||||
\(380\) | −3.64575 | + | 6.31463i | −0.187023 | + | 0.323934i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.4059 | + | 18.0235i | 0.532411 | + | 0.922163i | ||||
\(383\) | 10.2915 | − | 17.8254i | 0.525871 | − | 0.910836i | −0.473675 | − | 0.880700i | \(-0.657073\pi\) |
0.999546 | − | 0.0301357i | \(-0.00959395\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 35.1660 | 1.79223 | ||||||||
\(386\) | 7.00000 | 0.356291 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.79150 | − | 11.7632i | −0.344786 | − | 0.597187i | ||||
\(389\) | 9.64575 | + | 16.7069i | 0.489059 | + | 0.847075i | 0.999921 | − | 0.0125878i | \(-0.00400694\pi\) |
−0.510862 | + | 0.859663i | \(0.670674\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.70850 | −0.238119 | ||||||||
\(392\) | −7.00000 | −0.353553 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.35425 | + | 4.07768i | −0.118605 | + | 0.205430i | ||||
\(395\) | −20.4686 | − | 35.4527i | −1.02989 | − | 1.78382i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.32288 | − | 14.4156i | 0.417713 | − | 0.723500i | −0.577996 | − | 0.816040i | \(-0.696165\pi\) |
0.995709 | + | 0.0925393i | \(0.0294984\pi\) | |||||||
\(398\) | −6.06275 | −0.303898 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.29150 | 0.414575 | ||||||||
\(401\) | −10.4059 | + | 18.0235i | −0.519645 | + | 0.900051i | 0.480094 | + | 0.877217i | \(0.340602\pi\) |
−0.999739 | + | 0.0228345i | \(0.992731\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.7915 | − | 18.6914i | −0.537563 | − | 0.931086i | ||||
\(404\) | 4.17712 | − | 7.23499i | 0.207820 | − | 0.359954i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.11438 | − | 5.39426i | 0.154564 | − | 0.267713i | ||||
\(407\) | 43.5203 | 2.15722 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.43725 | − | 12.8817i | −0.367749 | − | 0.636959i | 0.621465 | − | 0.783442i | \(-0.286538\pi\) |
−0.989213 | + | 0.146483i | \(0.953205\pi\) | |||||||
\(410\) | −19.9373 | − | 34.5323i | −0.984631 | − | 1.70543i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.93725 | 0.193975 | ||||||||
\(413\) | −11.0516 | − | 19.1420i | −0.543815 | − | 0.941916i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.2288 | + | 41.9654i | −1.18934 | + | 2.06000i | ||||
\(416\) | −2.32288 | − | 4.02334i | −0.113888 | − | 0.197260i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.64575 | + | 6.31463i | −0.178320 | + | 0.308858i | ||||
\(419\) | −28.9373 | −1.41368 | −0.706839 | − | 0.707375i | \(-0.749879\pi\) | ||||
−0.706839 | + | 0.707375i | \(0.749879\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.7085 | −0.716848 | −0.358424 | − | 0.933559i | \(-0.616686\pi\) | ||||
−0.358424 | + | 0.933559i | \(0.616686\pi\) | |||||||
\(422\) | 7.43725 | − | 12.8817i | 0.362040 | − | 0.627071i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.00000 | − | 5.19615i | −0.145693 | − | 0.252347i | ||||
\(425\) | 15.1144 | − | 26.1789i | 0.733155 | − | 1.26986i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.72876 | − | 16.8507i | 0.470808 | − | 0.815463i | ||||
\(428\) | 6.00000 | 0.290021 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9.11438 | + | 15.7866i | 0.439534 | + | 0.761296i | ||||
\(431\) | 19.4059 | + | 33.6120i | 0.934748 | + | 1.61903i | 0.775082 | + | 0.631861i | \(0.217709\pi\) |
0.159666 | + | 0.987171i | \(0.448958\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.0000 | −0.913082 | −0.456541 | − | 0.889702i | \(-0.650912\pi\) | ||||
−0.456541 | + | 0.889702i | \(0.650912\pi\) | |||||||
\(434\) | −12.2915 | −0.590011 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.67712 | − | 2.90486i | 0.0803197 | − | 0.139118i | ||||
\(437\) | −1.29150 | − | 2.23695i | −0.0617809 | − | 0.107008i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.5830 | + | 21.7944i | −0.600554 | + | 1.04019i | 0.392183 | + | 0.919887i | \(0.371720\pi\) |
−0.992737 | + | 0.120303i | \(0.961613\pi\) | |||||||
\(440\) | 13.2915 | 0.633648 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −16.9373 | −0.805623 | ||||||||
\(443\) | −9.64575 | + | 16.7069i | −0.458283 | + | 0.793770i | −0.998870 | − | 0.0475179i | \(-0.984869\pi\) |
0.540587 | + | 0.841288i | \(0.318202\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.00000 | + | 15.5885i | 0.426641 | + | 0.738964i | ||||
\(446\) | −6.93725 | + | 12.0157i | −0.328488 | + | 0.568959i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.64575 | −0.125000 | ||||||||
\(449\) | −2.35425 | −0.111104 | −0.0555519 | − | 0.998456i | \(-0.517692\pi\) | ||||
−0.0555519 | + | 0.998456i | \(0.517692\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.9373 | − | 34.5323i | −0.938809 | − | 1.62606i | ||||
\(452\) | 1.17712 | + | 2.03884i | 0.0553673 | + | 0.0958989i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.00000 | 0.281594 | ||||||||
\(455\) | −22.4059 | + | 38.8081i | −1.05040 | + | 1.81935i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.14575 | − | 7.18065i | 0.193930 | − | 0.335897i | −0.752619 | − | 0.658456i | \(-0.771210\pi\) |
0.946549 | + | 0.322559i | \(0.104543\pi\) | |||||||
\(458\) | −4.67712 | − | 8.10102i | −0.218548 | − | 0.378536i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.35425 | + | 4.07768i | −0.109767 | + | 0.190123i | ||||
\(461\) | −24.2288 | −1.12845 | −0.564223 | − | 0.825623i | \(-0.690824\pi\) | ||||
−0.564223 | + | 0.825623i | \(0.690824\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.7085 | 0.869458 | 0.434729 | − | 0.900561i | \(-0.356844\pi\) | ||||
0.434729 | + | 0.900561i | \(0.356844\pi\) | |||||||
\(464\) | 1.17712 | − | 2.03884i | 0.0546466 | − | 0.0946507i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.64575 | + | 16.7069i | 0.446831 | + | 0.773934i | ||||
\(467\) | 0.114378 | − | 0.198109i | 0.00529280 | − | 0.00916739i | −0.863367 | − | 0.504577i | \(-0.831649\pi\) |
0.868660 | + | 0.495409i | \(0.164982\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.03137 | − | 5.25049i | −0.139976 | − | 0.242445i | ||||
\(470\) | 18.0000 | 0.830278 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.17712 | − | 7.23499i | −0.192268 | − | 0.333017i | ||||
\(473\) | 9.11438 | + | 15.7866i | 0.419080 | + | 0.725867i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.5830 | 0.760880 | ||||||||
\(476\) | −4.82288 | + | 8.35347i | −0.221056 | + | 0.382880i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.46863 | − | 9.47194i | 0.250129 | − | 0.433236i | ||||
\(479\) | 1.82288 | + | 3.15731i | 0.0832893 | + | 0.144261i | 0.904661 | − | 0.426132i | \(-0.140124\pi\) |
−0.821372 | + | 0.570393i | \(0.806791\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.7288 | + | 48.0276i | −1.26432 | + | 2.18987i | ||||
\(482\) | −5.00000 | −0.227744 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.29150 | 0.104159 | ||||||||
\(485\) | −24.7601 | + | 42.8858i | −1.12430 | + | 1.94734i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.9373 | − | 20.6759i | −0.540929 | − | 0.936916i | −0.998851 | − | 0.0479237i | \(-0.984740\pi\) |
0.457922 | − | 0.888992i | \(-0.348594\pi\) | |||||||
\(488\) | 3.67712 | − | 6.36897i | 0.166456 | − | 0.288310i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 12.7601 | + | 22.1012i | 0.576444 | + | 0.998430i | ||||
\(491\) | −25.7490 | −1.16204 | −0.581018 | − | 0.813890i | \(-0.697346\pi\) | ||||
−0.581018 | + | 0.813890i | \(0.697346\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.29150 | − | 7.43310i | −0.193280 | − | 0.334770i | ||||
\(494\) | −4.64575 | − | 8.04668i | −0.209022 | − | 0.362037i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.64575 | −0.208600 | ||||||||
\(497\) | 41.3948 | 1.85681 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.08301 | − | 5.33992i | 0.138014 | − | 0.239048i | −0.788731 | − | 0.614739i | \(-0.789261\pi\) |
0.926745 | + | 0.375691i | \(0.122595\pi\) | |||||||
\(500\) | −6.00000 | − | 10.3923i | −0.268328 | − | 0.464758i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.00000 | − | 15.5885i | 0.401690 | − | 0.695747i | ||||
\(503\) | −3.87451 | −0.172756 | −0.0863779 | − | 0.996262i | \(-0.527529\pi\) | ||||
−0.0863779 | + | 0.996262i | \(0.527529\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −30.4575 | −1.35534 | ||||||||
\(506\) | −2.35425 | + | 4.07768i | −0.104659 | + | 0.181275i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.677124 | − | 1.17281i | −0.0300425 | − | 0.0520352i | ||||
\(509\) | 4.06275 | − | 7.03688i | 0.180078 | − | 0.311904i | −0.761829 | − | 0.647778i | \(-0.775698\pi\) |
0.941907 | + | 0.335874i | \(0.109032\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.0000 | + | 24.2487i | 0.619324 | + | 1.07270i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.93725 | − | 13.7477i | −0.350097 | − | 0.606386i | ||||
\(515\) | −7.17712 | − | 12.4311i | −0.316262 | − | 0.547782i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.0000 | 0.791639 | ||||||||
\(518\) | 15.7915 | + | 27.3517i | 0.693839 | + | 1.20176i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.46863 | + | 14.6681i | −0.371374 | + | 0.643238i | ||||
\(521\) | −4.06275 | − | 7.03688i | −0.177992 | − | 0.308291i | 0.763201 | − | 0.646162i | \(-0.223627\pi\) |
−0.941193 | + | 0.337870i | \(0.890293\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.500000 | − | 0.866025i | 0.0218635 | − | 0.0378686i | −0.854887 | − | 0.518815i | \(-0.826373\pi\) |
0.876750 | + | 0.480946i | \(0.159707\pi\) | |||||||
\(524\) | 14.5830 | 0.637062 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.93725 | −0.215275 | ||||||||
\(527\) | −8.46863 | + | 14.6681i | −0.368899 | + | 0.638952i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.6660 | + | 18.4741i | 0.463740 | + | 0.803221i | ||||
\(530\) | −10.9373 | + | 18.9439i | −0.475084 | + | 0.822870i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.29150 | −0.229416 | ||||||||
\(533\) | 50.8118 | 2.20090 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.9373 | − | 18.9439i | −0.472859 | − | 0.819015i | ||||
\(536\) | −1.14575 | − | 1.98450i | −0.0494889 | − | 0.0857173i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16.7085 | −0.720354 | ||||||||
\(539\) | 12.7601 | + | 22.1012i | 0.549618 | + | 0.951966i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.583005 | + | 1.00979i | −0.0250654 | + | 0.0434145i | −0.878286 | − | 0.478136i | \(-0.841313\pi\) |
0.853221 | + | 0.521550i | \(0.174646\pi\) | |||||||
\(542\) | 2.61438 | + | 4.52824i | 0.112297 | + | 0.194504i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.82288 | + | 3.15731i | −0.0781551 | + | 0.135369i | ||||
\(545\) | −12.2288 | −0.523822 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.2915 | 0.782088 | 0.391044 | − | 0.920372i | \(-0.372114\pi\) | ||||
0.391044 | + | 0.920372i | \(0.372114\pi\) | |||||||
\(548\) | 0.645751 | − | 1.11847i | 0.0275851 | − | 0.0477788i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −15.1144 | − | 26.1789i | −0.644479 | − | 1.11627i | ||||
\(551\) | 2.35425 | − | 4.07768i | 0.100294 | − | 0.173715i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.8542 | − | 25.7283i | 0.631667 | − | 1.09408i | ||||
\(554\) | 2.06275 | 0.0876377 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.791503 | − | 1.37092i | −0.0335672 | − | 0.0581401i | ||||
\(557\) | −2.88562 | − | 4.99804i | −0.122268 | − | 0.211774i | 0.798394 | − | 0.602136i | \(-0.205683\pi\) |
−0.920662 | + | 0.390362i | \(0.872350\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.2288 | −0.982472 | ||||||||
\(560\) | 4.82288 | + | 8.35347i | 0.203804 | + | 0.352998i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.76013 | + | 16.9050i | −0.411706 | + | 0.713096i | ||||
\(563\) | 9.22876 | + | 15.9847i | 0.388946 | + | 0.673674i | 0.992308 | − | 0.123793i | \(-0.0395060\pi\) |
−0.603362 | + | 0.797467i | \(0.706173\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.29150 | − | 7.43310i | 0.180545 | − | 0.312713i | ||||
\(566\) | 2.29150 | 0.0963190 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.6458 | 0.656481 | ||||||||
\(569\) | −8.46863 | + | 14.6681i | −0.355023 | + | 0.614918i | −0.987122 | − | 0.159970i | \(-0.948860\pi\) |
0.632099 | + | 0.774888i | \(0.282194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.64575 | − | 8.04668i | −0.194419 | − | 0.336743i | 0.752291 | − | 0.658831i | \(-0.228949\pi\) |
−0.946710 | + | 0.322088i | \(0.895615\pi\) | |||||||
\(572\) | −8.46863 | + | 14.6681i | −0.354091 | + | 0.613304i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 14.4686 | − | 25.0604i | 0.603909 | − | 1.04600i | ||||
\(575\) | 10.7085 | 0.446575 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.1458 | + | 27.9653i | 0.672156 | + | 1.16421i | 0.977291 | + | 0.211900i | \(0.0679651\pi\) |
−0.305135 | + | 0.952309i | \(0.598702\pi\) | |||||||
\(578\) | −1.85425 | − | 3.21165i | −0.0771266 | − | 0.133587i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.58301 | −0.356390 | ||||||||
\(581\) | −35.1660 | −1.45893 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.9373 | + | 18.9439i | −0.452975 | + | 0.784575i | ||||
\(584\) | 5.29150 | + | 9.16515i | 0.218964 | + | 0.379257i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.53137 | + | 6.11652i | −0.145880 | + | 0.252671i | ||||
\(587\) | −11.7712 | −0.485851 | −0.242926 | − | 0.970045i | \(-0.578107\pi\) | ||||
−0.242926 | + | 0.970045i | \(0.578107\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.29150 | −0.382850 | ||||||||
\(590\) | −15.2288 | + | 26.3770i | −0.626958 | + | 1.08592i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.96863 | + | 10.3380i | 0.245309 | + | 0.424888i | ||||
\(593\) | 20.4686 | − | 35.4527i | 0.840546 | − | 1.45587i | −0.0488882 | − | 0.998804i | \(-0.515568\pi\) |
0.889434 | − | 0.457064i | \(-0.151099\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 35.1660 | 1.44167 | ||||||||
\(596\) | −22.9373 | −0.939547 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.00000 | − | 5.19615i | −0.122679 | − | 0.212486i | ||||
\(599\) | 4.93725 | + | 8.55157i | 0.201731 | + | 0.349408i | 0.949086 | − | 0.315017i | \(-0.102010\pi\) |
−0.747355 | + | 0.664424i | \(0.768677\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.8745 | 1.09623 | 0.548117 | − | 0.836402i | \(-0.315345\pi\) | ||||
0.548117 | + | 0.836402i | \(0.315345\pi\) | |||||||
\(602\) | −6.61438 | + | 11.4564i | −0.269582 | + | 0.466930i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.61438 | − | 16.6526i | 0.391204 | − | 0.677584i | ||||
\(605\) | −4.17712 | − | 7.23499i | −0.169824 | − | 0.294144i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.70850 | + | 4.69126i | −0.109935 | + | 0.190412i | −0.915744 | − | 0.401763i | \(-0.868397\pi\) |
0.805809 | + | 0.592176i | \(0.201731\pi\) | |||||||
\(608\) | −2.00000 | −0.0811107 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −26.8118 | −1.08558 | ||||||||
\(611\) | −11.4686 | + | 19.8642i | −0.463971 | + | 0.803621i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.1974 | + | 36.7149i | 0.856154 | + | 1.48290i | 0.875570 | + | 0.483091i | \(0.160486\pi\) |
−0.0194158 | + | 0.999811i | \(0.506181\pi\) | |||||||
\(614\) | 3.79150 | − | 6.56708i | 0.153013 | − | 0.265026i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.82288 | + | 8.35347i | 0.194319 | + | 0.336571i | ||||
\(617\) | −1.52026 | −0.0612033 | −0.0306017 | − | 0.999532i | \(-0.509742\pi\) | ||||
−0.0306017 | + | 0.999532i | \(0.509742\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.14575 | + | 7.18065i | 0.166632 | + | 0.288615i | 0.937234 | − | 0.348702i | \(-0.113378\pi\) |
−0.770602 | + | 0.637317i | \(0.780044\pi\) | |||||||
\(620\) | 8.46863 | + | 14.6681i | 0.340108 | + | 0.589085i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −13.5203 | −0.542113 | ||||||||
\(623\) | −6.53137 | + | 11.3127i | −0.261674 | + | 0.453233i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.14575 | + | 1.98450i | −0.0458301 | + | 0.0793800i | ||||
\(626\) | 6.35425 | + | 11.0059i | 0.253967 | + | 0.439883i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.00000 | − | 3.46410i | 0.0798087 | − | 0.138233i | ||||
\(629\) | 43.5203 | 1.73527 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.06275 | 0.241354 | 0.120677 | − | 0.992692i | \(-0.461493\pi\) | ||||
0.120677 | + | 0.992692i | \(0.461493\pi\) | |||||||
\(632\) | 5.61438 | − | 9.72439i | 0.223328 | − | 0.386815i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.4059 | − | 23.2197i | −0.532416 | − | 0.922171i | ||||
\(635\) | −2.46863 | + | 4.27579i | −0.0979645 | + | 0.169679i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −32.5203 | −1.28850 | ||||||||
\(638\) | −8.58301 | −0.339804 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.82288 | + | 3.15731i | 0.0720555 | + | 0.124804i | ||||
\(641\) | −9.11438 | − | 15.7866i | −0.359996 | − | 0.623532i | 0.627963 | − | 0.778243i | \(-0.283889\pi\) |
−0.987960 | + | 0.154711i | \(0.950555\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.12549 | −0.123257 | −0.0616287 | − | 0.998099i | \(-0.519629\pi\) | ||||
−0.0616287 | + | 0.998099i | \(0.519629\pi\) | |||||||
\(644\) | −3.41699 | −0.134648 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.64575 | + | 6.31463i | −0.143440 | + | 0.248446i | ||||
\(647\) | 4.93725 | + | 8.55157i | 0.194103 | + | 0.336197i | 0.946606 | − | 0.322392i | \(-0.104487\pi\) |
−0.752503 | + | 0.658589i | \(0.771154\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.2288 | + | 26.3770i | −0.597781 | + | 1.03539i | ||||
\(650\) | 38.5203 | 1.51089 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.00000 | −0.0391630 | ||||||||
\(653\) | −3.00000 | + | 5.19615i | −0.117399 | + | 0.203341i | −0.918736 | − | 0.394872i | \(-0.870789\pi\) |
0.801337 | + | 0.598213i | \(0.204122\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.5830 | − | 46.0431i | −1.03868 | − | 1.79905i | ||||
\(656\) | 5.46863 | − | 9.47194i | 0.213514 | − | 0.369817i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.53137 | + | 11.3127i | 0.254619 | + | 0.441014i | ||||
\(659\) | 24.2288 | 0.943818 | 0.471909 | − | 0.881647i | \(-0.343565\pi\) | ||||
0.471909 | + | 0.881647i | \(0.343565\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.58301 | + | 2.74185i | 0.0615718 | + | 0.106645i | 0.895168 | − | 0.445729i | \(-0.147055\pi\) |
−0.833596 | + | 0.552374i | \(0.813722\pi\) | |||||||
\(662\) | −15.9373 | − | 27.6041i | −0.619419 | − | 1.07287i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.2915 | −0.515810 | ||||||||
\(665\) | 9.64575 | + | 16.7069i | 0.374046 | + | 0.647867i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.52026 | − | 2.63317i | 0.0588647 | − | 0.101957i | ||||
\(668\) | −4.29150 | − | 7.43310i | −0.166043 | − | 0.287595i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.17712 | + | 7.23499i | −0.161376 | + | 0.279512i | ||||
\(671\) | −26.8118 | −1.03506 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.7490 | 0.607080 | 0.303540 | − | 0.952819i | \(-0.401831\pi\) | ||||
0.303540 | + | 0.952819i | \(0.401831\pi\) | |||||||
\(674\) | −15.2915 | + | 26.4857i | −0.589007 | + | 1.02019i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.29150 | − | 7.43310i | −0.165058 | − | 0.285888i | ||||
\(677\) | −22.9373 | + | 39.7285i | −0.881550 | + | 1.52689i | −0.0319331 | + | 0.999490i | \(0.510166\pi\) |
−0.849617 | + | 0.527400i | \(0.823167\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −35.9373 | −1.37915 | ||||||||
\(680\) | 13.2915 | 0.509706 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.46863 | + | 14.6681i | 0.324280 | + | 0.561670i | ||||
\(683\) | −13.4059 | − | 23.2197i | −0.512962 | − | 0.888476i | −0.999887 | − | 0.0150322i | \(-0.995215\pi\) |
0.486925 | − | 0.873444i | \(-0.338118\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.70850 | −0.179902 | ||||||||
\(686\) | −9.26013 | + | 16.0390i | −0.353553 | + | 0.612372i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.50000 | + | 4.33013i | −0.0953116 | + | 0.165085i | ||||
\(689\) | −13.9373 | − | 24.1400i | −0.530967 | − | 0.919662i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.3745 | − | 33.5576i | 0.737041 | − | 1.27659i | −0.216781 | − | 0.976220i | \(-0.569556\pi\) |
0.953822 | − | 0.300372i | \(-0.0971109\pi\) | |||||||
\(692\) | 14.5830 | 0.554363 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | −2.88562 | + | 4.99804i | −0.109458 | + | 0.189587i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.9373 | − | 34.5323i | −0.755177 | − | 1.30801i | ||||
\(698\) | −0.614378 | + | 1.06413i | −0.0232546 | + | 0.0402781i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 10.9686 | − | 18.9982i | 0.414575 | − | 0.718065i | ||||
\(701\) | 26.5830 | 1.00403 | 0.502013 | − | 0.864860i | \(-0.332593\pi\) | ||||
0.502013 | + | 0.864860i | \(0.332593\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.9373 | + | 20.6759i | 0.450222 | + | 0.779807i | ||||
\(704\) | 1.82288 | + | 3.15731i | 0.0687022 | + | 0.118996i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.0000 | −0.451626 | ||||||||
\(707\) | −11.0516 | − | 19.1420i | −0.415639 | − | 0.719909i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.9059 | + | 32.7459i | −0.710025 | + | 1.22980i | 0.254822 | + | 0.966988i | \(0.417983\pi\) |
−0.964847 | + | 0.262812i | \(0.915350\pi\) | |||||||
\(710\) | −28.5203 | − | 49.3985i | −1.07035 | − | 1.85389i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.46863 | + | 4.27579i | −0.0925157 | + | 0.160242i | ||||
\(713\) | −6.00000 | −0.224702 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 61.7490 | 2.30928 | ||||||||
\(716\) | 8.46863 | − | 14.6681i | 0.316487 | − | 0.548172i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.58301 | − | 9.67005i | −0.208356 | − | 0.360883i | ||||
\(719\) | 11.4686 | − | 19.8642i | 0.427708 | − | 0.740811i | −0.568961 | − | 0.822364i | \(-0.692655\pi\) |
0.996669 | + | 0.0815529i | \(0.0259880\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.20850 | − | 9.02138i | 0.193975 | − | 0.335974i | ||||
\(722\) | 15.0000 | 0.558242 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.35425 | + | 2.34563i | 0.0503303 | + | 0.0871746i | ||||
\(725\) | 9.76013 | + | 16.9050i | 0.362482 | + | 0.627837i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.22876 | −0.0455721 | −0.0227860 | − | 0.999740i | \(-0.507254\pi\) | ||||
−0.0227860 | + | 0.999740i | \(0.507254\pi\) | |||||||
\(728\) | −12.2915 | −0.455553 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 19.2915 | − | 33.4139i | 0.714011 | − | 1.23670i | ||||
\(731\) | 9.11438 | + | 15.7866i | 0.337107 | + | 0.583887i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.6144 | + | 30.5090i | −0.650602 | + | 1.12688i | 0.332375 | + | 0.943147i | \(0.392150\pi\) |
−0.982977 | + | 0.183728i | \(0.941183\pi\) | |||||||
\(734\) | −29.8745 | −1.10269 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.29150 | −0.0476054 | ||||||||
\(737\) | −4.17712 | + | 7.23499i | −0.153866 | + | 0.266504i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.7288 | + | 27.2430i | 0.578592 | + | 1.00215i | 0.995641 | + | 0.0932664i | \(0.0297308\pi\) |
−0.417050 | + | 0.908884i | \(0.636936\pi\) | |||||||
\(740\) | 21.7601 | − | 37.6897i | 0.799918 | − | 1.38550i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15.8745 | −0.582772 | ||||||||
\(743\) | 28.9373 | 1.06160 | 0.530802 | − | 0.847496i | \(-0.321891\pi\) | ||||
0.530802 | + | 0.847496i | \(0.321891\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 41.8118 | + | 72.4201i | 1.53186 | + | 2.65327i | ||||
\(746\) | 2.29150 | + | 3.96900i | 0.0838979 | + | 0.145315i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 13.2915 | 0.485985 | ||||||||
\(749\) | 7.93725 | − | 13.7477i | 0.290021 | − | 0.502331i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.2288 | − | 45.4295i | 0.957101 | − | 1.65775i | 0.227615 | − | 0.973751i | \(-0.426907\pi\) |
0.729485 | − | 0.683996i | \(-0.239760\pi\) | |||||||
\(752\) | 2.46863 | + | 4.27579i | 0.0900216 | + | 0.155922i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.46863 | − | 9.47194i | 0.199156 | − | 0.344948i | ||||
\(755\) | −70.1033 | −2.55132 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.9778 | 1.78013 | 0.890064 | − | 0.455836i | \(-0.150660\pi\) | ||||
0.890064 | + | 0.455836i | \(0.150660\pi\) | |||||||
\(758\) | 12.7915 | − | 22.1555i | 0.464608 | − | 0.804725i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.64575 | + | 6.31463i | 0.132245 | + | 0.229056i | ||||
\(761\) | 1.29150 | − | 2.23695i | 0.0468169 | − | 0.0810893i | −0.841667 | − | 0.539996i | \(-0.818426\pi\) |
0.888484 | + | 0.458907i | \(0.151759\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.43725 | − | 7.68555i | −0.160639 | − | 0.278236i | ||||
\(764\) | 20.8118 | 0.752943 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.2915 | − | 17.8254i | −0.371847 | − | 0.644058i | ||||
\(767\) | −19.4059 | − | 33.6120i | −0.700706 | − | 1.21366i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.5830 | 1.46346 | 0.731730 | − | 0.681594i | \(-0.238713\pi\) | ||||
0.731730 | + | 0.681594i | \(0.238713\pi\) | |||||||
\(770\) | 17.5830 | − | 30.4547i | 0.633648 | − | 1.09751i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.50000 | − | 6.06218i | 0.125968 | − | 0.218183i | ||||
\(773\) | −23.1660 | − | 40.1247i | −0.833223 | − | 1.44319i | −0.895469 | − | 0.445125i | \(-0.853159\pi\) |
0.0622452 | − | 0.998061i | \(-0.480174\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19.2601 | − | 33.3595i | 0.691844 | − | 1.19831i | ||||
\(776\) | −13.5830 | −0.487601 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 19.2915 | 0.691634 | ||||||||
\(779\) | 10.9373 | − | 18.9439i | 0.391868 | − | 0.678735i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.5203 | − | 49.3985i | −1.02054 | − | 1.76762i | ||||
\(782\) | −2.35425 | + | 4.07768i | −0.0841878 | + | 0.145817i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.50000 | + | 6.06218i | −0.125000 | + | 0.216506i | ||||
\(785\) | −14.5830 | −0.520490 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.85425 | + | 10.1399i | 0.208681 | + | 0.361447i | 0.951299 | − | 0.308268i | \(-0.0997495\pi\) |
−0.742618 | + | 0.669715i | \(0.766416\pi\) | |||||||
\(788\) | 2.35425 | + | 4.07768i | 0.0838666 | + | 0.145261i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −40.9373 | −1.45648 | ||||||||
\(791\) | 6.22876 | 0.221469 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.0830 | − | 29.5886i | 0.606635 | − | 1.05072i | ||||
\(794\) | −8.32288 | − | 14.4156i | −0.295368 | − | 0.511592i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.03137 | + | 5.25049i | −0.107444 | + | 0.186099i | ||||
\(797\) | 14.8118 | 0.524660 | 0.262330 | − | 0.964978i | \(-0.415509\pi\) | ||||
0.262330 | + | 0.964978i | \(0.415509\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.0000 | 0.636794 | ||||||||
\(800\) | 4.14575 | − | 7.18065i | 0.146574 | − | 0.253874i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10.4059 | + | 18.0235i | 0.367444 | + | 0.636432i | ||||
\(803\) | 19.2915 | − | 33.4139i | 0.680782 | − | 1.17915i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.22876 | + | 10.7885i | 0.219535 | + | 0.380245i | ||||
\(806\) | −21.5830 | −0.760229 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.17712 | − | 7.23499i | −0.146951 | − | 0.254526i | ||||
\(809\) | 7.70850 | + | 13.3515i | 0.271016 | + | 0.469414i | 0.969122 | − | 0.246580i | \(-0.0793069\pi\) |
−0.698106 | + | 0.715994i | \(0.745974\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.2915 | −1.02856 | −0.514282 | − | 0.857621i | \(-0.671941\pi\) | ||||
−0.514282 | + | 0.857621i | \(0.671941\pi\) | |||||||
\(812\) | −3.11438 | − | 5.39426i | −0.109293 | − | 0.189301i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 21.7601 | − | 37.6897i | 0.762692 | − | 1.32102i | ||||
\(815\) | 1.82288 | + | 3.15731i | 0.0638525 | + | 0.110596i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.00000 | + | 8.66025i | −0.174928 | + | 0.302984i | ||||
\(818\) | −14.8745 | −0.520075 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −39.8745 | −1.39248 | ||||||||
\(821\) | 10.2915 | − | 17.8254i | 0.359176 | − | 0.622111i | −0.628647 | − | 0.777690i | \(-0.716391\pi\) |
0.987823 | + | 0.155579i | \(0.0497245\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.5516 | + | 30.4003i | 0.611811 | + | 1.05969i | 0.990935 | + | 0.134342i | \(0.0428922\pi\) |
−0.379124 | + | 0.925346i | \(0.623774\pi\) | |||||||
\(824\) | 1.96863 | − | 3.40976i | 0.0685804 | − | 0.118785i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −22.1033 | −0.769071 | ||||||||
\(827\) | 43.7490 | 1.52130 | 0.760651 | − | 0.649161i | \(-0.224880\pi\) | ||||
0.760651 | + | 0.649161i | \(0.224880\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.6458 | + | 25.3672i | 0.508668 | + | 0.881039i | 0.999950 | + | 0.0100380i | \(0.00319525\pi\) |
−0.491282 | + | 0.871001i | \(0.663471\pi\) | |||||||
\(830\) | 24.2288 | + | 41.9654i | 0.840992 | + | 1.45664i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.64575 | −0.161062 | ||||||||
\(833\) | 12.7601 | + | 22.1012i | 0.442112 | + | 0.765761i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.6458 | + | 27.0992i | −0.541444 | + | 0.937808i | ||||
\(836\) | 3.64575 | + | 6.31463i | 0.126091 | + | 0.218396i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −14.4686 | + | 25.0604i | −0.499810 | + | 0.865697i | ||||
\(839\) | 49.2915 | 1.70173 | 0.850866 | − | 0.525383i | \(-0.176078\pi\) | ||||
0.850866 | + | 0.525383i | \(0.176078\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.4575 | −0.808880 | ||||||||
\(842\) | −7.35425 | + | 12.7379i | −0.253444 | + | 0.438978i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.43725 | − | 12.8817i | −0.256001 | − | 0.443406i | ||||
\(845\) | −15.6458 | + | 27.0992i | −0.538230 | + | 0.932242i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.03137 | − | 5.25049i | 0.104159 | − | 0.180409i | ||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −15.1144 | − | 26.1789i | −0.518419 | − | 0.897928i | ||||
\(851\) | 7.70850 | + | 13.3515i | 0.264244 | + | 0.457684i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.8745 | 1.63919 | 0.819596 | − | 0.572942i | \(-0.194198\pi\) | ||||
0.819596 | + | 0.572942i | \(0.194198\pi\) | |||||||
\(854\) | −9.72876 | − | 16.8507i | −0.332911 | − | 0.576619i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.00000 | − | 5.19615i | 0.102538 | − | 0.177601i | ||||
\(857\) | −13.4059 | − | 23.2197i | −0.457936 | − | 0.793169i | 0.540916 | − | 0.841077i | \(-0.318078\pi\) |
−0.998852 | + | 0.0479082i | \(0.984745\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.50000 | − | 6.06218i | 0.119418 | − | 0.206839i | −0.800119 | − | 0.599841i | \(-0.795230\pi\) |
0.919537 | + | 0.393003i | \(0.128564\pi\) | |||||||
\(860\) | 18.2288 | 0.621595 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 38.8118 | 1.32193 | ||||||||
\(863\) | 14.5830 | − | 25.2585i | 0.496411 | − | 0.859810i | −0.503580 | − | 0.863949i | \(-0.667984\pi\) |
0.999991 | + | 0.00413896i | \(0.00131748\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26.5830 | − | 46.0431i | −0.903849 | − | 1.56551i | ||||
\(866\) | −9.50000 | + | 16.4545i | −0.322823 | + | 0.559146i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.14575 | + | 10.6448i | −0.208600 | + | 0.361306i | ||||
\(869\) | −40.9373 | −1.38870 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.32288 | − | 9.21949i | −0.180359 | − | 0.312391i | ||||
\(872\) | −1.67712 | − | 2.90486i | −0.0567946 | − | 0.0983711i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.58301 | −0.0873715 | ||||||||
\(875\) | −31.7490 | −1.07331 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.3229 | + | 23.0759i | −0.449882 | + | 0.779218i | −0.998378 | − | 0.0569353i | \(-0.981867\pi\) |
0.548496 | + | 0.836153i | \(0.315200\pi\) | |||||||
\(878\) | 12.5830 | + | 21.7944i | 0.424656 | + | 0.735526i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.64575 | − | 11.5108i | 0.224028 | − | 0.388028i | ||||
\(881\) | 3.87451 | 0.130535 | 0.0652677 | − | 0.997868i | \(-0.479210\pi\) | ||||
0.0652677 | + | 0.997868i | \(0.479210\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.8745 | −0.668830 | −0.334415 | − | 0.942426i | \(-0.608539\pi\) | ||||
−0.334415 | + | 0.942426i | \(0.608539\pi\) | |||||||
\(884\) | −8.46863 | + | 14.6681i | −0.284831 | + | 0.493341i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.64575 | + | 16.7069i | 0.324055 | + | 0.561280i | ||||
\(887\) | 7.93725 | − | 13.7477i | 0.266507 | − | 0.461603i | −0.701450 | − | 0.712718i | \(-0.747464\pi\) |
0.967957 | + | 0.251115i | \(0.0807972\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.58301 | −0.120170 | ||||||||
\(890\) | 18.0000 | 0.603361 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.93725 | + | 12.0157i | 0.232276 | + | 0.402315i | ||||
\(893\) | 4.93725 | + | 8.55157i | 0.165219 | + | 0.286168i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −61.7490 | −2.06404 | ||||||||
\(896\) | −1.32288 | + | 2.29129i | −0.0441942 | + | 0.0765466i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.17712 | + | 2.03884i | −0.0392811 | + | 0.0680369i | ||||
\(899\) | −5.46863 | − | 9.47194i | −0.182389 | − | 0.315907i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.9373 | + | 18.9439i | −0.364373 | + | 0.631112i | ||||
\(902\) | −39.8745 | −1.32768 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.35425 | 0.0783011 | ||||||||
\(905\) | 4.93725 | − | 8.55157i | 0.164120 | − | 0.284264i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.1458 | − | 31.4294i | −0.602520 | − | 1.04359i | −0.992438 | − | 0.122745i | \(-0.960830\pi\) |
0.389918 | − | 0.920849i | \(-0.372503\pi\) | |||||||
\(908\) | 3.00000 | − | 5.19615i | 0.0995585 | − | 0.172440i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 22.4059 | + | 38.8081i | 0.742748 | + | 1.28648i | ||||
\(911\) | −28.9373 | −0.958734 | −0.479367 | − | 0.877615i | \(-0.659134\pi\) | ||||
−0.479367 | + | 0.877615i | \(0.659134\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.2288 | + | 41.9654i | 0.801855 | + | 1.38885i | ||||
\(914\) | −4.14575 | − | 7.18065i | −0.137129 | − | 0.237515i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.35425 | −0.309073 | ||||||||
\(917\) | 19.2915 | − | 33.4139i | 0.637062 | − | 1.10342i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.3856 | + | 24.9166i | −0.474538 | + | 0.821924i | −0.999575 | − | 0.0291557i | \(-0.990718\pi\) |
0.525037 | + | 0.851079i | \(0.324051\pi\) | |||||||
\(920\) | 2.35425 | + | 4.07768i | 0.0776173 | + | 0.134437i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.1144 | + | 20.9827i | −0.398966 | + | 0.691029i | ||||
\(923\) | 72.6863 | 2.39250 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −98.9778 | −3.25437 | ||||||||
\(926\) | 9.35425 | − | 16.2020i | 0.307400 | − | 0.532432i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.17712 | − | 2.03884i | −0.0386410 | − | 0.0669282i | ||||
\(929\) | −8.46863 | + | 14.6681i | −0.277847 | + | 0.481244i | −0.970849 | − | 0.239690i | \(-0.922954\pi\) |
0.693003 | + | 0.720935i | \(0.256287\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.00000 | + | 12.1244i | −0.229416 | + | 0.397360i | ||||
\(932\) | 19.2915 | 0.631914 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.114378 | − | 0.198109i | −0.00374257 | − | 0.00648232i | ||||
\(935\) | −24.2288 | − | 41.9654i | −0.792365 | − | 1.37242i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44.7490 | −1.46189 | −0.730943 | − | 0.682438i | \(-0.760920\pi\) | ||||
−0.730943 | + | 0.682438i | \(0.760920\pi\) | |||||||
\(938\) | −6.06275 | −0.197956 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.00000 | − | 15.5885i | 0.293548 | − | 0.508439i | ||||
\(941\) | −26.6974 | − | 46.2412i | −0.870310 | − | 1.50742i | −0.861676 | − | 0.507458i | \(-0.830585\pi\) |
−0.00863340 | − | 0.999963i | \(-0.502748\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.06275 | − | 12.2330i | 0.229995 | − | 0.398362i | ||||
\(944\) | −8.35425 | −0.271908 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18.2288 | 0.592668 | ||||||||
\(947\) | 5.23987 | − | 9.07572i | 0.170273 | − | 0.294921i | −0.768242 | − | 0.640159i | \(-0.778868\pi\) |
0.938515 | + | 0.345238i | \(0.112202\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.5830 | + | 42.5790i | 0.797998 | + | 1.38217i | ||||
\(950\) | 8.29150 | − | 14.3613i | 0.269012 | − | 0.465942i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.82288 | + | 8.35347i | 0.156310 | + | 0.270737i | ||||
\(953\) | −52.3320 | −1.69520 | −0.847600 | − | 0.530635i | \(-0.821953\pi\) | ||||
−0.847600 | + | 0.530635i | \(0.821953\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −37.9373 | − | 65.7093i | −1.22762 | − | 2.12630i | ||||
\(956\) | −5.46863 | − | 9.47194i | −0.176868 | − | 0.306344i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.64575 | 0.117789 | ||||||||
\(959\) | −1.70850 | − | 2.95920i | −0.0551703 | − | 0.0955577i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.70850 | − | 8.15536i | 0.151887 | − | 0.263076i | ||||
\(962\) | 27.7288 | + | 48.0276i | 0.894011 | + | 1.54847i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.50000 | + | 4.33013i | −0.0805196 | + | 0.139464i | ||||
\(965\) | −25.5203 | −0.821526 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.0627 | 1.15970 | 0.579850 | − | 0.814723i | \(-0.303111\pi\) | ||||
0.579850 | + | 0.814723i | \(0.303111\pi\) | |||||||
\(968\) | 1.14575 | − | 1.98450i | 0.0368258 | − | 0.0637842i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 24.7601 | + | 42.8858i | 0.795000 | + | 1.37698i | ||||
\(971\) | −4.93725 | + | 8.55157i | −0.158444 | + | 0.274433i | −0.934308 | − | 0.356467i | \(-0.883981\pi\) |
0.775864 | + | 0.630901i | \(0.217314\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.18824 | −0.134269 | ||||||||
\(974\) | −23.8745 | −0.764989 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.67712 | − | 6.36897i | −0.117702 | − | 0.203866i | ||||
\(977\) | −25.9373 | − | 44.9246i | −0.829806 | − | 1.43727i | −0.898190 | − | 0.439608i | \(-0.855118\pi\) |
0.0683837 | − | 0.997659i | \(-0.478216\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.0000 | 0.575282 | ||||||||
\(980\) | 25.5203 | 0.815215 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12.8745 | + | 22.2993i | −0.410842 | + | 0.711599i | ||||
\(983\) | 10.4059 | + | 18.0235i | 0.331896 | + | 0.574861i | 0.982884 | − | 0.184228i | \(-0.0589783\pi\) |
−0.650988 | + | 0.759088i | \(0.725645\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.58301 | − | 14.8662i | 0.273477 | − | 0.473677i | ||||
\(986\) | −8.58301 | −0.273339 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.29150 | −0.295602 | ||||||||
\(989\) | −3.22876 | + | 5.59237i | −0.102668 | + | 0.177827i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.0314 | + | 22.5710i | 0.413955 | + | 0.716991i | 0.995318 | − | 0.0966529i | \(-0.0308137\pi\) |
−0.581363 | + | 0.813644i | \(0.697480\pi\) | |||||||
\(992\) | −2.32288 | + | 4.02334i | −0.0737514 | + | 0.127741i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 20.6974 | − | 35.8489i | 0.656481 | − | 1.13706i | ||||
\(995\) | 22.1033 | 0.700721 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.8431 | − | 20.5129i | −0.375076 | − | 0.649650i | 0.615263 | − | 0.788322i | \(-0.289050\pi\) |
−0.990338 | + | 0.138672i | \(0.955717\pi\) | |||||||
\(998\) | −3.08301 | − | 5.33992i | −0.0975908 | − | 0.169032i | ||||
\(999\) | 0 | 0 |
(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 | 378.2.g.h.163.1 | yes | 4 | |
3.2 | odd | 2 | 378.2.g.g.163.2 | yes | 4 | ||
7.2 | even | 3 | 2646.2.a.bi.1.2 | 2 | |||
7.4 | even | 3 | inner | 378.2.g.h.109.1 | yes | 4 | |
7.5 | odd | 6 | 2646.2.a.bf.1.1 | 2 | |||
9.2 | odd | 6 | 1134.2.e.t.919.2 | 4 | |||
9.4 | even | 3 | 1134.2.h.t.541.2 | 4 | |||
9.5 | odd | 6 | 1134.2.h.q.541.1 | 4 | |||
9.7 | even | 3 | 1134.2.e.q.919.1 | 4 | |||
21.2 | odd | 6 | 2646.2.a.bl.1.1 | 2 | |||
21.5 | even | 6 | 2646.2.a.bo.1.2 | 2 | |||
21.11 | odd | 6 | 378.2.g.g.109.2 | ✓ | 4 | ||
63.4 | even | 3 | 1134.2.e.q.865.1 | 4 | |||
63.11 | odd | 6 | 1134.2.h.q.109.1 | 4 | |||
63.25 | even | 3 | 1134.2.h.t.109.2 | 4 | |||
63.32 | odd | 6 | 1134.2.e.t.865.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.g.g.109.2 | ✓ | 4 | 21.11 | odd | 6 | ||
378.2.g.g.163.2 | yes | 4 | 3.2 | odd | 2 | ||
378.2.g.h.109.1 | yes | 4 | 7.4 | even | 3 | inner | |
378.2.g.h.163.1 | yes | 4 | 1.1 | even | 1 | trivial | |
1134.2.e.q.865.1 | 4 | 63.4 | even | 3 | |||
1134.2.e.q.919.1 | 4 | 9.7 | even | 3 | |||
1134.2.e.t.865.2 | 4 | 63.32 | odd | 6 | |||
1134.2.e.t.919.2 | 4 | 9.2 | odd | 6 | |||
1134.2.h.q.109.1 | 4 | 63.11 | odd | 6 | |||
1134.2.h.q.541.1 | 4 | 9.5 | odd | 6 | |||
1134.2.h.t.109.2 | 4 | 63.25 | even | 3 | |||
1134.2.h.t.541.2 | 4 | 9.4 | even | 3 | |||
2646.2.a.bf.1.1 | 2 | 7.5 | odd | 6 | |||
2646.2.a.bi.1.2 | 2 | 7.2 | even | 3 | |||
2646.2.a.bl.1.1 | 2 | 21.2 | odd | 6 | |||
2646.2.a.bo.1.2 | 2 | 21.5 | even | 6 |