Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [77,2,Mod(6,77)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(77, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("77.6");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 77 = 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 77.l (of order \(10\), degree \(4\), 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: | \(0.614848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 8.0.37515625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - x^{6} + 3x^{5} - x^{4} + 6x^{3} - 4x^{2} - 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{10}]$ |
Embedding invariants
Embedding label | 13.1 | ||
Root | \(1.10362 + 0.884319i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 77.13 |
Dual form | 77.2.l.a.6.1 |
$q$-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 \(\left(\mathbb{Z}/77\mathbb{Z}\right)^\times\).
\(n\) | \(45\) | \(57\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.59471 | − | 0.843073i | −1.83474 | − | 0.596143i | −0.998886 | − | 0.0471903i | \(-0.984973\pi\) |
−0.835853 | − | 0.548953i | \(-0.815027\pi\) | |||||||
\(3\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(4\) | 4.40373 | + | 3.19950i | 2.20187 | + | 1.59975i | ||||
\(5\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.55513 | − | 2.14046i | 0.587785 | − | 0.809017i | ||||
\(8\) | −5.52176 | − | 7.60006i | −1.95224 | − | 2.68703i | ||||
\(9\) | 0.927051 | − | 2.85317i | 0.309017 | − | 0.951057i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.13429 | + | 1.08453i | 0.945025 | + | 0.326998i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(14\) | −5.83969 | + | 4.24278i | −1.56072 | + | 1.13393i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.55584 | + | 14.0214i | 1.13896 | + | 3.50536i | ||||
\(17\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(18\) | −4.81086 | + | 6.62158i | −1.13393 | + | 1.56072i | ||||
\(19\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.21825 | − | 5.45649i | −1.53894 | − | 1.16333i | ||||
\(23\) | 3.36187 | 0.700998 | 0.350499 | − | 0.936563i | \(-0.386012\pi\) | ||||
0.350499 | + | 0.936563i | \(0.386012\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.04508 | + | 2.93893i | −0.809017 | + | 0.587785i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 13.6968 | − | 4.45035i | 2.58845 | − | 0.841038i | ||||
\(29\) | −3.04028 | + | 4.18459i | −0.564567 | + | 0.777059i | −0.991898 | − | 0.127036i | \(-0.959454\pi\) |
0.427331 | + | 0.904095i | \(0.359454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(32\) | − | 21.4341i | − | 3.78905i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 13.2112 | − | 9.59849i | 2.20187 | − | 1.59975i | ||||
\(37\) | −8.95957 | − | 6.50951i | −1.47294 | − | 1.07016i | −0.979747 | − | 0.200239i | \(-0.935828\pi\) |
−0.493197 | − | 0.869918i | \(-0.664172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13.0478i | 1.98978i | 0.100978 | + | 0.994889i | \(0.467803\pi\) | ||||
−0.100978 | + | 0.994889i | \(0.532197\pi\) | |||||||
\(44\) | 10.3326 | + | 14.8041i | 1.55770 | + | 2.23181i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.72309 | − | 2.83430i | −1.28615 | − | 0.417895i | ||||
\(47\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.16312 | − | 6.65740i | −0.309017 | − | 0.951057i | ||||
\(50\) | 12.9736 | − | 4.21537i | 1.83474 | − | 0.596143i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.15535 | + | 6.63349i | −0.296060 | + | 0.911180i | 0.686803 | + | 0.726844i | \(0.259014\pi\) |
−0.982863 | + | 0.184336i | \(0.940986\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −24.8547 | −3.32135 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 11.4166 | − | 8.29464i | 1.49907 | − | 1.08914i | ||||
\(59\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.66540 | − | 6.42137i | −0.587785 | − | 0.809017i | ||||
\(64\) | −8.95886 | + | 27.5725i | −1.11986 | + | 3.44657i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.8615 | 1.69345 | 0.846725 | − | 0.532031i | \(-0.178571\pi\) | ||||
0.846725 | + | 0.532031i | \(0.178571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.0272696 | + | 0.0839271i | 0.00323630 | + | 0.00996031i | 0.952662 | − | 0.304033i | \(-0.0983332\pi\) |
−0.949425 | + | 0.313993i | \(0.898333\pi\) | |||||||
\(72\) | −26.8032 | + | 8.70889i | −3.15879 | + | 1.02635i | ||||
\(73\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(74\) | 17.7595 | + | 24.4439i | 2.06450 | + | 2.84154i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.19564 | − | 5.02223i | 0.820019 | − | 0.572336i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.57067 | − | 0.835260i | −0.289223 | − | 0.0939741i | 0.160813 | − | 0.986985i | \(-0.448589\pi\) |
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.28115 | − | 5.29007i | −0.809017 | − | 0.587785i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 11.0003 | − | 33.8554i | 1.18619 | − | 3.65072i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.06433 | − | 29.8093i | −0.966261 | − | 3.17769i | ||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 14.8048 | + | 10.7563i | 1.54350 | + | 1.12142i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(98\) | 19.0977i | 1.92916i | ||||||||
\(99\) | 6.00000 | − | 7.93725i | 0.603023 | − | 0.797724i | ||||
\(100\) | −27.2166 | −2.72166 | ||||||||
\(101\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.1850 | − | 15.3949i | 1.08639 | − | 1.49528i | ||||
\(107\) | 4.39357 | + | 6.04723i | 0.424743 | + | 0.584608i | 0.966736 | − | 0.255774i | \(-0.0823304\pi\) |
−0.541994 | + | 0.840382i | \(0.682330\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.01830i | 0.193318i | 0.995318 | + | 0.0966592i | \(0.0308157\pi\) | ||||
−0.995318 | + | 0.0966592i | \(0.969184\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 37.0972 | + | 12.0536i | 3.50536 | + | 1.13896i | ||||
\(113\) | −16.7856 | + | 12.1954i | −1.57905 | + | 1.14725i | −0.661285 | + | 0.750135i | \(0.729988\pi\) |
−0.917769 | + | 0.397114i | \(0.870012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −26.7772 | + | 8.70044i | −2.48620 | + | 0.807815i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.64759 | + | 6.79848i | 0.786144 | + | 0.618043i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.69169 | + | 20.5949i | 0.596143 | + | 1.83474i | ||||
\(127\) | −3.26991 | + | 1.06246i | −0.290157 | + | 0.0942778i | −0.450479 | − | 0.892787i | \(-0.648747\pi\) |
0.160322 | + | 0.987065i | \(0.448747\pi\) | |||||||
\(128\) | 21.2940 | − | 29.3087i | 1.88215 | − | 2.59055i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −35.9666 | − | 11.6863i | −3.10704 | − | 1.00954i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.34450 | − | 4.13795i | −0.114869 | − | 0.353529i | 0.877051 | − | 0.480397i | \(-0.159507\pi\) |
−0.991920 | + | 0.126868i | \(0.959507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 0.240757i | − | 0.0202039i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 44.2290 | 3.68575 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −18.6284 | − | 57.3322i | −1.53124 | − | 4.71268i | ||||
\(149\) | 10.0650 | − | 3.27033i | 0.824560 | − | 0.267916i | 0.133808 | − | 0.991007i | \(-0.457280\pi\) |
0.690752 | + | 0.723092i | \(0.257280\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.8081 | − | 14.8760i | −0.879547 | − | 1.21059i | −0.976546 | − | 0.215308i | \(-0.930924\pi\) |
0.0969991 | − | 0.995284i | \(-0.469076\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −22.9047 | + | 6.96480i | −1.84572 | + | 0.561240i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(158\) | 5.96596 | + | 4.33452i | 0.474626 | + | 0.344836i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.22816 | − | 7.19594i | 0.412036 | − | 0.567119i | ||||
\(162\) | 14.4326 | + | 19.8648i | 1.13393 | + | 1.56072i | ||||
\(163\) | −7.88338 | + | 24.2625i | −0.617474 | + | 1.90039i | −0.268249 | + | 0.963350i | \(0.586445\pi\) |
−0.349225 | + | 0.937039i | \(0.613555\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.5172 | + | 7.64121i | 0.809017 | + | 0.587785i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −41.7465 | + | 57.4592i | −3.18314 | + | 4.38122i | ||||
\(173\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.2288i | 1.00000i | ||||||||
\(176\) | −0.927341 | + | 48.8882i | −0.0699009 | + | 3.68509i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.1993 | − | 11.0430i | 1.13605 | − | 0.825390i | 0.149487 | − | 0.988764i | \(-0.452238\pi\) |
0.986564 | + | 0.163374i | \(0.0522378\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −18.5634 | − | 25.5504i | −1.36852 | − | 1.88360i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.3570 | − | 16.2433i | −1.61769 | − | 1.17532i | −0.820912 | − | 0.571055i | \(-0.806534\pi\) |
−0.796781 | − | 0.604268i | \(-0.793466\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0606 | − | 3.26889i | 0.724179 | − | 0.235300i | 0.0763450 | − | 0.997081i | \(-0.475675\pi\) |
0.647834 | + | 0.761781i | \(0.275675\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.7745 | − | 36.2383i | 0.841038 | − | 2.58845i | ||||
\(197\) | − | 23.8442i | − | 1.69883i | −0.527724 | − | 0.849416i | \(-0.676954\pi\) | ||
0.527724 | − | 0.849416i | \(-0.323046\pi\) | |||||||
\(198\) | −22.2600 | + | 15.5365i | −1.58195 | + | 1.10413i | ||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 44.6720 | + | 14.5148i | 3.15879 | + | 1.02635i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.22890 | + | 13.0152i | 0.296810 | + | 0.913488i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.11662 | − | 9.59198i | 0.216620 | − | 0.666689i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.6488 | + | 4.43475i | 0.939619 | + | 0.305301i | 0.738490 | − | 0.674264i | \(-0.235539\pi\) |
0.201129 | + | 0.979565i | \(0.435539\pi\) | |||||||
\(212\) | −30.7154 | + | 22.3161i | −2.10954 | + | 1.53267i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.30180 | − | 19.3949i | −0.430782 | − | 1.32581i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.70158 | − | 5.23692i | 0.115245 | − | 0.354689i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(224\) | −45.8788 | − | 33.3329i | −3.06541 | − | 2.22715i | ||||
\(225\) | 4.63525 | + | 14.2658i | 0.309017 | + | 0.951057i | ||||
\(226\) | 53.8354 | − | 17.4922i | 3.58108 | − | 1.16356i | ||||
\(227\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 48.5909 | 3.19015 | ||||||||
\(233\) | 20.1301 | + | 6.54066i | 1.31876 | + | 0.428493i | 0.882071 | − | 0.471117i | \(-0.156149\pi\) |
0.436694 | + | 0.899610i | \(0.356149\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.7499 | − | 18.9251i | −0.889407 | − | 1.22416i | −0.973726 | − | 0.227725i | \(-0.926871\pi\) |
0.0843185 | − | 0.996439i | \(-0.473129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | −16.7064 | − | 24.9306i | −1.07393 | − | 1.60260i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(252\) | − | 43.2049i | − | 2.72166i | ||||||
\(253\) | 10.5371 | + | 3.64605i | 0.662461 | + | 0.229225i | ||||
\(254\) | 9.38020 | 0.588566 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −33.0521 | + | 24.0138i | −2.06576 | + | 1.50086i | ||||
\(257\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27.8667 | + | 9.05442i | −1.73155 | + | 0.562615i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.12085 | + | 12.5538i | 0.564567 | + | 0.777059i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 28.7986i | − | 1.77580i | −0.460036 | − | 0.887900i | \(-0.652164\pi\) | ||
0.460036 | − | 0.887900i | \(-0.347836\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 61.0422 | + | 44.3498i | 3.72875 | + | 2.70909i | ||||
\(269\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.8703i | 0.717112i | ||||||||
\(275\) | −15.8658 | + | 4.82444i | −0.956746 | + | 0.290924i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.8382 | − | 6.12090i | −1.13188 | − | 0.367769i | −0.317588 | − | 0.948229i | \(-0.602873\pi\) |
−0.814289 | + | 0.580460i | \(0.802873\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.7378 | + | 9.66238i | −1.77401 | + | 0.576409i | −0.998491 | − | 0.0549198i | \(-0.982510\pi\) |
−0.775515 | + | 0.631329i | \(0.782510\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(284\) | −0.148437 | + | 0.456841i | −0.00880809 | + | 0.0271085i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −61.1552 | − | 19.8705i | −3.60360 | − | 1.17088i | ||||
\(289\) | 13.7533 | − | 9.99235i | 0.809017 | − | 0.587785i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 104.037i | 6.04704i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −28.8730 | −1.67257 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 27.9284 | + | 20.2911i | 1.60976 | + | 1.16956i | ||||
\(302\) | 15.5022 | + | 47.7110i | 0.892053 | + | 2.74546i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | 47.7563 | + | 0.905869i | 2.72117 | + | 0.0516167i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.64811 | − | 11.9031i | −0.486494 | − | 0.669602i | ||||
\(317\) | −6.35698 | + | 19.5648i | −0.357043 | + | 1.09887i | 0.597772 | + | 0.801666i | \(0.296053\pi\) |
−0.954815 | + | 0.297200i | \(0.903947\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.0675 | + | 9.81846i | −0.787627 | + | 0.549728i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −19.6323 | + | 14.2637i | −1.09406 | + | 0.794884i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −15.1387 | − | 46.5921i | −0.841038 | − | 2.58845i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 40.9102 | − | 56.3081i | 2.26581 | − | 3.11862i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.2349 | −1.77179 | −0.885895 | − | 0.463887i | \(-0.846455\pi\) | ||||
−0.885895 | + | 0.463887i | \(0.846455\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −26.8787 | + | 19.5285i | −1.47294 | + | 1.07016i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.4298 | − | 28.1192i | 1.11288 | − | 1.53175i | 0.295779 | − | 0.955256i | \(-0.404421\pi\) |
0.817102 | − | 0.576493i | \(-0.195579\pi\) | |||||||
\(338\) | −20.8471 | − | 28.6935i | −1.13393 | − | 1.56072i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.6138 | − | 5.72307i | −0.951057 | − | 0.309017i | ||||
\(344\) | 99.1643 | − | 72.0471i | 5.34658 | − | 3.88452i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.26790 | − | 2.36148i | 0.390161 | − | 0.126771i | −0.107366 | − | 0.994220i | \(-0.534242\pi\) |
0.497527 | + | 0.867448i | \(0.334242\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(350\) | 11.1528 | − | 34.3248i | 0.596143 | − | 1.83474i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 23.2460 | − | 67.1808i | 1.23901 | − | 3.58075i | ||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −48.7479 | + | 15.8392i | −2.57641 | + | 0.837126i | ||||
\(359\) | −14.8499 | + | 20.4391i | −0.783747 | + | 1.07873i | 0.211112 | + | 0.977462i | \(0.432292\pi\) |
−0.994859 | + | 0.101273i | \(0.967708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.87132 | + | 18.0701i | −0.309017 | + | 0.951057i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(368\) | 15.3161 | + | 47.1382i | 0.798409 | + | 2.45725i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.8468 | + | 14.9294i | 0.563140 | + | 0.775096i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 31.7490i | − | 1.64390i | −0.569558 | − | 0.821951i | \(-0.692886\pi\) | ||
0.569558 | − | 0.821951i | \(-0.307114\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.72788 | + | 11.4732i | 0.191488 | + | 0.589340i | 1.00000 | 0.000859657i | \(0.000273637\pi\) | |
−0.808511 | + | 0.588481i | \(0.799726\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 44.3156 | + | 60.9952i | 2.26738 | + | 3.12079i | ||||
\(383\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −28.8603 | −1.46895 | ||||||||
\(387\) | 37.2277 | + | 12.0960i | 1.89239 | + | 0.614875i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.8388 | + | 14.4137i | 1.00587 | + | 0.730805i | 0.963338 | − | 0.268290i | \(-0.0864585\pi\) |
0.0425291 | + | 0.999095i | \(0.486458\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −38.6524 | + | 53.2004i | −1.95224 | + | 2.68703i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −20.1025 | + | 61.8690i | −1.01275 | + | 3.11691i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 51.8176 | − | 15.7565i | 2.60393 | − | 0.791796i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −59.6367 | − | 43.3286i | −2.98184 | − | 2.16643i | ||||
\(401\) | −12.3445 | − | 37.9925i | −0.616455 | − | 1.89725i | −0.376168 | − | 0.926552i | \(-0.622758\pi\) |
−0.240287 | − | 0.970702i | \(-0.577242\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 37.3360i | − | 1.85295i | ||||||
\(407\) | −21.0222 | − | 30.1196i | −1.04203 | − | 1.49297i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −16.1735 | + | 22.2609i | −0.794884 | + | 1.09406i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.91967 | − | 1.39472i | 0.0935588 | − | 0.0679745i | −0.540022 | − | 0.841651i | \(-0.681584\pi\) |
0.633581 | + | 0.773676i | \(0.281584\pi\) | |||||||
\(422\) | −31.6758 | − | 23.0138i | −1.54195 | − | 1.12029i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 62.3163 | − | 20.2478i | 3.02635 | − | 0.983319i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 40.6876i | 1.96671i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38.2455 | + | 12.4267i | 1.84222 | + | 0.598574i | 0.998044 | + | 0.0625092i | \(0.0199103\pi\) |
0.844177 | + | 0.536065i | \(0.180090\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.45756 | + | 8.88806i | −0.309261 | + | 0.425661i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −21.0000 | −1.00000 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 33.4997 | − | 24.3390i | 1.59162 | − | 1.15638i | 0.690039 | − | 0.723772i | \(-0.257593\pi\) |
0.901582 | − | 0.432608i | \(-0.142407\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 45.0856 | + | 62.0551i | 2.13010 | + | 2.93183i | ||||
\(449\) | 8.18900 | − | 25.2032i | 0.386463 | − | 1.18941i | −0.548950 | − | 0.835855i | \(-0.684972\pi\) |
0.935413 | − | 0.353556i | \(-0.115028\pi\) | |||||||
\(450\) | − | 40.9236i | − | 1.92916i | ||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −112.938 | −5.31217 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.2170 | − | 9.49319i | 1.36672 | − | 0.444073i | 0.468436 | − | 0.883497i | \(-0.344818\pi\) |
0.898279 | + | 0.439425i | \(0.144818\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.4582 | 1.27609 | 0.638046 | − | 0.769998i | \(-0.279743\pi\) | ||||
0.638046 | + | 0.769998i | \(0.279743\pi\) | |||||||
\(464\) | −72.5250 | − | 23.5648i | −3.36689 | − | 1.09397i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −46.7175 | − | 33.9423i | −2.16415 | − | 1.57234i | ||||
\(467\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.5565 | − | 29.6699i | 0.995385 | − | 1.37003i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.1508 | + | 40.8958i | −0.650654 | + | 1.88039i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.9284 | + | 12.2992i | 0.775096 | + | 0.563140i | ||||
\(478\) | 19.7218 | + | 60.6974i | 0.902053 | + | 2.77624i | ||||
\(479\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.3299 | + | 57.6066i | 0.742270 | + | 2.61848i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.4997 | − | 16.3470i | 1.01956 | − | 0.740754i | 0.0533681 | − | 0.998575i | \(-0.483004\pi\) |
0.966193 | + | 0.257821i | \(0.0830043\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.11027 | − | 4.28092i | 0.140364 | − | 0.193195i | −0.733047 | − | 0.680178i | \(-0.761903\pi\) |
0.873412 | + | 0.486983i | \(0.161903\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.222050 | + | 0.0721485i | 0.00996031 | + | 0.00323630i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.3570 | − | 8.25132i | −0.508407 | − | 0.369380i | 0.303812 | − | 0.952732i | \(-0.401741\pi\) |
−0.812219 | + | 0.583352i | \(0.801741\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(504\) | −23.0416 | + | 70.9146i | −1.02635 | + | 3.15879i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −24.2668 | − | 18.3440i | −1.07879 | − | 0.815490i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −17.7991 | − | 5.78328i | −0.789708 | − | 0.256592i | ||||
\(509\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 37.0972 | − | 12.0536i | 1.63948 | − | 0.532700i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 79.9395 | 3.51234 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(522\) | −13.0822 | − | 40.2630i | −0.572594 | − | 1.76226i | ||||
\(523\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.2794 | + | 74.7242i | −1.05863 | + | 3.25813i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.6978 | −0.508602 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −76.5399 | − | 105.348i | −3.30602 | − | 4.55034i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.440303 | − | 23.2122i | 0.0189652 | − | 0.999820i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.4349 | − | 14.1129i | −1.86741 | − | 0.606759i | −0.992463 | − | 0.122548i | \(-0.960893\pi\) |
−0.874951 | − | 0.484211i | \(-0.839107\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.33080 | − | 12.8427i | −0.398956 | − | 0.549116i | 0.561525 | − | 0.827460i | \(-0.310215\pi\) |
−0.960482 | + | 0.278343i | \(0.910215\pi\) | |||||||
\(548\) | 7.31854 | − | 22.5241i | 0.312633 | − | 0.962184i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 45.2347 | + | 0.858038i | 1.92881 | + | 0.0365869i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.78557 | + | 4.20346i | −0.246027 | + | 0.178749i | ||||
\(554\) | 43.7193 | + | 31.7639i | 1.85746 | + | 1.34952i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.6370 | + | 38.0391i | −1.17102 | + | 1.61177i | −0.514384 | + | 0.857560i | \(0.671980\pi\) |
−0.656634 | + | 0.754209i | \(0.728020\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 85.3070 | 3.59846 | ||||||||
\(563\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22.6463 | + | 7.35824i | −0.951057 | + | 0.309017i | ||||
\(568\) | 0.487274 | − | 0.670676i | 0.0204456 | − | 0.0281409i | ||||
\(569\) | 24.8821 | + | 34.2473i | 1.04311 | + | 1.43572i | 0.894630 | + | 0.446808i | \(0.147439\pi\) |
0.148483 | + | 0.988915i | \(0.452561\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.1771i | 1.51396i | 0.653435 | + | 0.756982i | \(0.273327\pi\) | ||||
−0.653435 | + | 0.756982i | \(0.726673\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.5990 | + | 9.88028i | −0.567119 | + | 0.412036i | ||||
\(576\) | 70.3638 | + | 51.1223i | 2.93183 | + | 2.13010i | ||||
\(577\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(578\) | −44.1101 | + | 14.3322i | −1.83474 | + | 0.596143i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.9497 | + | 18.4538i | −0.577739 | + | 0.764277i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 50.4543 | − | 155.282i | 2.07366 | − | 6.38206i | ||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 54.7871 | + | 17.8014i | 2.24417 | + | 0.729174i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.7279 | + | 45.3277i | 0.601765 | + | 1.85204i | 0.517663 | + | 0.855584i | \(0.326802\pi\) |
0.0841014 | + | 0.996457i | \(0.473198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(602\) | −55.3592 | − | 76.1953i | −2.25627 | − | 3.10549i | ||||
\(603\) | 12.8503 | − | 39.5492i | 0.523305 | − | 1.61057i | ||||
\(604\) | − | 100.090i | − | 4.07262i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.4759 | − | 21.3007i | −0.625065 | − | 0.860329i | 0.372644 | − | 0.927974i | \(-0.378451\pi\) |
−0.997709 | + | 0.0676456i | \(0.978451\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −77.9019 | − | 26.9557i | −3.13876 | − | 1.08607i | ||||
\(617\) | −48.2946 | −1.94427 | −0.972133 | − | 0.234428i | \(-0.924678\pi\) | ||||
−0.972133 | + | 0.234428i | \(0.924678\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.72542 | − | 23.7764i | 0.309017 | − | 0.951057i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.1185 | + | 24.0620i | 1.31843 | + | 0.957892i | 0.999950 | + | 0.00996082i | \(0.00317068\pi\) |
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(632\) | 7.84659 | + | 24.1493i | 0.312121 | + | 0.960609i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 32.9891 | − | 45.4056i | 1.31016 | − | 1.80329i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 44.7787 | − | 13.6162i | 1.77281 | − | 0.539070i | ||||
\(639\) | 0.264738 | 0.0104729 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.7856 | + | 20.1874i | −1.09746 | + | 0.797354i | −0.980644 | − | 0.195799i | \(-0.937270\pi\) |
−0.116820 | + | 0.993153i | \(0.537270\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(644\) | 46.0468 | − | 14.9615i | 1.81450 | − | 0.589566i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(648\) | 84.5477i | 3.32135i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −112.344 | + | 81.6228i | −4.39974 | + | 3.19660i | ||||
\(653\) | −37.7579 | − | 27.4328i | −1.47758 | − | 1.07353i | −0.978326 | − | 0.207072i | \(-0.933606\pi\) |
−0.499257 | − | 0.866454i | \(-0.666394\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.4575i | 1.03064i | 0.856998 | + | 0.515319i | \(0.172327\pi\) | ||||
−0.856998 | + | 0.515319i | \(0.827673\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 83.6403 | + | 27.1764i | 3.25077 | + | 1.05624i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 86.2065 | − | 28.0102i | 3.34043 | − | 1.08537i | ||||
\(667\) | −10.2210 | + | 14.0681i | −0.395760 | + | 0.544717i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.5763 | − | 12.8591i | −1.52556 | − | 0.495683i | −0.578208 | − | 0.815890i | \(-0.696248\pi\) |
−0.947348 | + | 0.320207i | \(0.896248\pi\) | |||||||
\(674\) | −76.7160 | + | 55.7374i | −2.95499 | + | 2.14692i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 21.8670 | + | 67.2996i | 0.841038 | + | 2.58845i | ||||
\(677\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.9586 | 1.49071 | 0.745355 | − | 0.666668i | \(-0.232280\pi\) | ||||
0.745355 | + | 0.666668i | \(0.232280\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 40.8778 | + | 29.6995i | 1.56072 | + | 1.13393i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −182.949 | + | 59.4439i | −6.97488 | + | 2.26628i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.65856 | − | 25.1862i | −0.290924 | − | 0.956746i | ||||
\(694\) | −20.8490 | −0.791418 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −42.3254 | + | 58.2559i | −1.59975 | + | 2.20187i | ||||
\(701\) | 24.4716 | + | 33.6823i | 0.924280 | + | 1.27216i | 0.962049 | + | 0.272876i | \(0.0879747\pi\) |
−0.0377695 | + | 0.999286i | \(0.512025\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −57.9830 | + | 76.7043i | −2.18532 | + | 2.89090i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.9784 | − | 46.0987i | −0.562525 | − | 1.73127i | −0.675192 | − | 0.737642i | \(-0.735939\pi\) |
0.112667 | − | 0.993633i | \(-0.464061\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.76628 | + | 6.56022i | −0.178749 | + | 0.246027i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 102.266 | 3.82185 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 55.7629 | − | 40.5141i | 2.08105 | − | 1.51197i | ||||
\(719\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 30.4688 | − | 41.9367i | 1.13393 | − | 1.56072i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 25.8622i | − | 0.960498i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.8435 | + | 15.8702i | −0.809017 | + | 0.587785i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 72.0587i | − | 2.65612i | ||||||
\(737\) | 43.4460 | + | 15.0332i | 1.60035 | + | 0.553755i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.3690 | − | 13.7665i | −1.55857 | − | 0.506410i | −0.602145 | − | 0.798387i | \(-0.705687\pi\) |
−0.956425 | + | 0.291977i | \(0.905687\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15.5579 | − | 47.8822i | −0.571148 | − | 1.75781i | ||||
\(743\) | 47.0663 | − | 15.2928i | 1.72669 | − | 0.561037i | 0.733729 | − | 0.679442i | \(-0.237778\pi\) |
0.992965 | + | 0.118405i | \(0.0377783\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −26.7668 | + | 82.3796i | −0.980000 | + | 3.01613i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.7764 | 0.722615 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.9977 | − | 31.9662i | 1.60550 | − | 1.16646i | 0.729727 | − | 0.683739i | \(-0.239647\pi\) |
0.875772 | − | 0.482724i | \(-0.160353\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.04627 | − | 6.29778i | 0.0743731 | − | 0.228897i | −0.906959 | − | 0.421220i | \(-0.861602\pi\) |
0.981332 | + | 0.192323i | \(0.0616021\pi\) | |||||||
\(758\) | − | 32.9126i | − | 1.19544i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.32009 | + | 3.13873i | 0.156398 | + | 0.113630i | ||||
\(764\) | −46.4837 | − | 143.062i | −1.68172 | − | 5.17580i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 54.7631 | + | 17.7936i | 1.97097 | + | 0.640406i | ||||
\(773\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(774\) | −86.3974 | − | 62.7714i | −3.10549 | − | 2.25627i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −39.3242 | − | 54.1251i | −1.40984 | − | 1.94048i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.00555072 | + | 0.292627i | −0.000198620 | + | 0.0104710i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 83.4914 | − | 60.6600i | 2.98184 | − | 2.16643i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(788\) | 76.2896 | − | 105.004i | 2.71770 | − | 3.74060i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 54.8943i | 1.95182i | ||||||||
\(792\) | −93.4542 | − | 1.77269i | −3.32075 | − | 0.0629899i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 62.9933 | + | 86.7029i | 2.22715 | + | 3.06541i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 108.987i | 3.84846i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 53.8138 | − | 17.4852i | 1.89199 | − | 0.614745i | 0.914160 | − | 0.405353i | \(-0.132851\pi\) |
0.977832 | − | 0.209393i | \(-0.0671487\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(812\) | −23.0192 | + | 70.8458i | −0.807815 | + | 2.48620i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 29.1534 | + | 95.8750i | 1.02183 | + | 3.36042i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.1027 | + | 42.8092i | −1.08549 | + | 1.49405i | −0.232162 | + | 0.972677i | \(0.574580\pi\) |
−0.853329 | + | 0.521373i | \(0.825420\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.0519 | − | 52.4804i | 0.594393 | − | 1.82935i | 0.0366680 | − | 0.999328i | \(-0.488326\pi\) |
0.557725 | − | 0.830026i | \(-0.311674\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35.2276 | − | 11.4461i | −1.22498 | − | 0.398022i | −0.376090 | − | 0.926583i | \(-0.622732\pi\) |
−0.848895 | + | 0.528562i | \(0.822732\pi\) | |||||||
\(828\) | 44.4143 | − | 32.2689i | 1.54350 | − | 1.12142i | ||||
\(829\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.694005 | + | 2.13593i | 0.0239312 | + | 0.0736527i | ||||
\(842\) | −6.15684 | + | 2.00048i | −0.212179 | + | 0.0689410i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 45.9165 | + | 63.1986i | 1.58051 | + | 2.17539i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.0000 | − | 7.93725i | 0.962091 | − | 0.272727i | ||||
\(848\) | −102.830 | −3.53121 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.1209 | − | 21.8841i | −1.03253 | − | 0.750178i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 21.6990 | − | 66.7828i | 0.741658 | − | 2.28259i | ||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −88.7595 | − | 64.4875i | −3.02316 | − | 2.19645i | ||||
\(863\) | 2.47214 | + | 7.60845i | 0.0841525 | + | 0.258995i | 0.984275 | − | 0.176642i | \(-0.0565234\pi\) |
−0.900123 | + | 0.435636i | \(0.856523\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.15136 | − | 5.40592i | −0.242593 | − | 0.183383i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 15.3392 | − | 11.1446i | 0.519452 | − | 0.377404i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.7176 | + | 46.4083i | 1.13856 | + | 1.56710i | 0.770677 | + | 0.637226i | \(0.219918\pi\) |
0.367885 | + | 0.929871i | \(0.380082\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 54.4890 | + | 17.7045i | 1.83474 | + | 0.596143i | ||||
\(883\) | 9.70820 | − | 7.05342i | 0.326707 | − | 0.237367i | −0.412325 | − | 0.911037i | \(-0.635283\pi\) |
0.739032 | + | 0.673670i | \(0.235283\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −107.442 | + | 34.9100i | −3.60958 | + | 1.17282i | ||||
\(887\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.81100 | + | 8.65136i | −0.0942778 | + | 0.290157i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.0840 | − | 24.4773i | −0.572336 | − | 0.820019i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −29.6190 | − | 91.1580i | −0.989502 | − | 3.04537i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −42.4962 | + | 58.4910i | −1.41812 | + | 1.95187i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −25.2311 | + | 77.6534i | −0.841038 | + | 2.58845i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 185.372 | + | 60.2310i | 6.16538 | + | 2.00325i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.17436 | − | 12.8473i | −0.138607 | − | 0.426589i | 0.857526 | − | 0.514440i | \(-0.172000\pi\) |
−0.996134 | + | 0.0878507i | \(0.972000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.94427 | + | 15.2169i | −0.163811 | + | 0.504159i | −0.998947 | − | 0.0458855i | \(-0.985389\pi\) |
0.835136 | + | 0.550044i | \(0.185389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −83.8133 | −2.77230 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.5305 | + | 10.5698i | −1.07308 | + | 0.348665i | −0.791687 | − | 0.610927i | \(-0.790797\pi\) |
−0.281394 | + | 0.959592i | \(0.590797\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 55.3732 | 1.82066 | ||||||||
\(926\) | −71.2462 | − | 23.1493i | −2.34130 | − | 0.760733i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 89.6931 | + | 65.1658i | 2.94432 | + | 2.13917i | ||||
\(929\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 67.7206 | + | 93.2094i | 2.21826 | + | 3.05318i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(938\) | −80.9468 | + | 58.8113i | −2.64301 | + | 1.92026i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 71.1954 | − | 94.1826i | 2.31476 | − | 3.06214i | ||||
\(947\) | −20.0000 | −0.649913 | −0.324956 | − | 0.945729i | \(-0.605350\pi\) | ||||
−0.324956 | + | 0.945729i | \(0.605350\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.97347 | + | 13.7273i | −0.323072 | + | 0.444671i | −0.939402 | − | 0.342817i | \(-0.888619\pi\) |
0.616330 | + | 0.787488i | \(0.288619\pi\) | |||||||
\(954\) | −33.5551 | − | 46.1847i | −1.08639 | − | 1.49528i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 127.334i | − | 4.11827i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.9480 | − | 3.55722i | −0.353529 | − | 0.114869i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.0795 | − | 18.2213i | −0.809017 | − | 0.587785i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21.3268 | − | 6.92951i | 0.687248 | − | 0.223300i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 62.0397i | 1.99506i | 0.0702371 | + | 0.997530i | \(0.477624\pi\) | ||||
−0.0702371 | + | 0.997530i | \(0.522376\pi\) | |||||||
\(968\) | 3.91887 | − | 103.262i | 0.125957 | − | 3.31896i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −72.1621 | + | 23.4469i | −2.31222 | + | 0.751287i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.1890 | − | 59.0577i | 0.613911 | − | 1.88942i | 0.197278 | − | 0.980348i | \(-0.436790\pi\) |
0.416632 | − | 0.909075i | \(-0.363210\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.75856 | + | 1.87107i | 0.183857 | + | 0.0597387i | ||||
\(982\) | −11.6794 | + | 8.48556i | −0.372704 | + | 0.270785i | ||||
\(983\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 43.8651i | 1.39483i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.0000 | 0.762385 | 0.381193 | − | 0.924496i | \(-0.375513\pi\) | ||||
0.381193 | + | 0.924496i | \(0.375513\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.515330 | − | 0.374409i | −0.0163453 | − | 0.0118755i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(998\) | 22.5116 | + | 30.9846i | 0.712592 | + | 0.980799i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))