Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [31,2,Mod(5,31)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(31, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("31.5");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 31.c (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: | \(0.247536246266\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 5.1 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 31.5 |
Dual form | 31.2.c.a.25.1 |
$q$-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 \(\left(\mathbb{Z}/31\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41421 | −1.70711 | −0.853553 | − | 0.521005i | \(-0.825557\pi\) | ||||
−0.853553 | + | 0.521005i | \(0.825557\pi\) | |||||||
\(3\) | 1.20711 | − | 2.09077i | 0.696923 | − | 1.20711i | −0.272605 | − | 0.962126i | \(-0.587885\pi\) |
0.969528 | − | 0.244981i | \(-0.0787816\pi\) | |||||||
\(4\) | 3.82843 | 1.91421 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | 0.732294 | − | 0.680989i | \(-0.238450\pi\) |
−0.955901 | + | 0.293691i | \(0.905116\pi\) | |||||||
\(6\) | −2.91421 | + | 5.04757i | −1.18972 | + | 2.06066i | ||||
\(7\) | −1.20711 | + | 2.09077i | −0.456243 | + | 0.790237i | −0.998759 | − | 0.0498090i | \(-0.984139\pi\) |
0.542515 | + | 0.840046i | \(0.317472\pi\) | |||||||
\(8\) | −4.41421 | −1.56066 | ||||||||
\(9\) | −1.41421 | − | 2.44949i | −0.471405 | − | 0.816497i | ||||
\(10\) | 1.20711 | + | 2.09077i | 0.381721 | + | 0.661160i | ||||
\(11\) | 2.62132 | + | 4.54026i | 0.790358 | + | 1.36894i | 0.925745 | + | 0.378147i | \(0.123439\pi\) |
−0.135388 | + | 0.990793i | \(0.543228\pi\) | |||||||
\(12\) | 4.62132 | − | 8.00436i | 1.33406 | − | 2.31066i | ||||
\(13\) | −0.914214 | − | 1.58346i | −0.253557 | − | 0.439174i | 0.710945 | − | 0.703247i | \(-0.248267\pi\) |
−0.964503 | + | 0.264073i | \(0.914934\pi\) | |||||||
\(14\) | 2.91421 | − | 5.04757i | 0.778856 | − | 1.34902i | ||||
\(15\) | −2.41421 | −0.623347 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 0.0857864 | − | 0.148586i | 0.0208063 | − | 0.0360375i | −0.855435 | − | 0.517911i | \(-0.826710\pi\) |
0.876241 | + | 0.481873i | \(0.160043\pi\) | |||||||
\(18\) | 3.41421 | + | 5.91359i | 0.804738 | + | 1.39385i | ||||
\(19\) | −0.792893 | + | 1.37333i | −0.181902 | + | 0.315064i | −0.942528 | − | 0.334126i | \(-0.891559\pi\) |
0.760626 | + | 0.649190i | \(0.224892\pi\) | |||||||
\(20\) | −1.91421 | − | 3.31552i | −0.428031 | − | 0.741372i | ||||
\(21\) | 2.91421 | + | 5.04757i | 0.635934 | + | 1.10147i | ||||
\(22\) | −6.32843 | − | 10.9612i | −1.34923 | − | 2.33693i | ||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | −5.32843 | + | 9.22911i | −1.08766 | + | 1.88388i | ||||
\(25\) | 2.00000 | − | 3.46410i | 0.400000 | − | 0.692820i | ||||
\(26\) | 2.20711 | + | 3.82282i | 0.432849 | + | 0.749717i | ||||
\(27\) | 0.414214 | 0.0797154 | ||||||||
\(28\) | −4.62132 | + | 8.00436i | −0.873347 | + | 1.51268i | ||||
\(29\) | −1.17157 | −0.217556 | −0.108778 | − | 0.994066i | \(-0.534694\pi\) | ||||
−0.108778 | + | 0.994066i | \(0.534694\pi\) | |||||||
\(30\) | 5.82843 | 1.06412 | ||||||||
\(31\) | −5.00000 | − | 2.44949i | −0.898027 | − | 0.439941i | ||||
\(32\) | 1.58579 | 0.280330 | ||||||||
\(33\) | 12.6569 | 2.20328 | ||||||||
\(34\) | −0.207107 | + | 0.358719i | −0.0355185 | + | 0.0615199i | ||||
\(35\) | 2.41421 | 0.408077 | ||||||||
\(36\) | −5.41421 | − | 9.37769i | −0.902369 | − | 1.56295i | ||||
\(37\) | −0.500000 | + | 0.866025i | −0.0821995 | + | 0.142374i | −0.904194 | − | 0.427121i | \(-0.859528\pi\) |
0.821995 | + | 0.569495i | \(0.192861\pi\) | |||||||
\(38\) | 1.91421 | − | 3.31552i | 0.310526 | − | 0.537848i | ||||
\(39\) | −4.41421 | −0.706840 | ||||||||
\(40\) | 2.20711 | + | 3.82282i | 0.348974 | + | 0.604441i | ||||
\(41\) | −4.74264 | − | 8.21449i | −0.740676 | − | 1.28289i | −0.952188 | − | 0.305513i | \(-0.901172\pi\) |
0.211512 | − | 0.977375i | \(-0.432161\pi\) | |||||||
\(42\) | −7.03553 | − | 12.1859i | −1.08561 | − | 1.88033i | ||||
\(43\) | −4.44975 | + | 7.70719i | −0.678580 | + | 1.17534i | 0.296828 | + | 0.954931i | \(0.404071\pi\) |
−0.975409 | + | 0.220404i | \(0.929262\pi\) | |||||||
\(44\) | 10.0355 | + | 17.3821i | 1.51291 | + | 2.62044i | ||||
\(45\) | −1.41421 | + | 2.44949i | −0.210819 | + | 0.365148i | ||||
\(46\) | 9.65685 | 1.42383 | ||||||||
\(47\) | −1.65685 | −0.241677 | −0.120839 | − | 0.992672i | \(-0.538558\pi\) | ||||
−0.120839 | + | 0.992672i | \(0.538558\pi\) | |||||||
\(48\) | 3.62132 | − | 6.27231i | 0.522693 | − | 0.905330i | ||||
\(49\) | 0.585786 | + | 1.01461i | 0.0836838 | + | 0.144945i | ||||
\(50\) | −4.82843 | + | 8.36308i | −0.682843 | + | 1.18272i | ||||
\(51\) | −0.207107 | − | 0.358719i | −0.0290008 | − | 0.0502308i | ||||
\(52\) | −3.50000 | − | 6.06218i | −0.485363 | − | 0.840673i | ||||
\(53\) | −0.0857864 | − | 0.148586i | −0.0117837 | − | 0.0204099i | 0.860073 | − | 0.510170i | \(-0.170418\pi\) |
−0.871857 | + | 0.489760i | \(0.837084\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 2.62132 | − | 4.54026i | 0.353459 | − | 0.612209i | ||||
\(56\) | 5.32843 | − | 9.22911i | 0.712041 | − | 1.23329i | ||||
\(57\) | 1.91421 | + | 3.31552i | 0.253544 | + | 0.439151i | ||||
\(58\) | 2.82843 | 0.371391 | ||||||||
\(59\) | 5.03553 | − | 8.72180i | 0.655571 | − | 1.13548i | −0.326180 | − | 0.945308i | \(-0.605761\pi\) |
0.981750 | − | 0.190174i | \(-0.0609052\pi\) | |||||||
\(60\) | −9.24264 | −1.19322 | ||||||||
\(61\) | 2.82843 | 0.362143 | 0.181071 | − | 0.983470i | \(-0.442043\pi\) | ||||
0.181071 | + | 0.983470i | \(0.442043\pi\) | |||||||
\(62\) | 12.0711 | + | 5.91359i | 1.53303 | + | 0.751027i | ||||
\(63\) | 6.82843 | 0.860301 | ||||||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | −0.914214 | + | 1.58346i | −0.113394 | + | 0.196405i | ||||
\(66\) | −30.5563 | −3.76123 | ||||||||
\(67\) | 2.62132 | + | 4.54026i | 0.320245 | + | 0.554681i | 0.980539 | − | 0.196327i | \(-0.0629013\pi\) |
−0.660293 | + | 0.751008i | \(0.729568\pi\) | |||||||
\(68\) | 0.328427 | − | 0.568852i | 0.0398276 | − | 0.0689835i | ||||
\(69\) | −4.82843 | + | 8.36308i | −0.581274 | + | 1.00680i | ||||
\(70\) | −5.82843 | −0.696630 | ||||||||
\(71\) | 7.03553 | + | 12.1859i | 0.834964 | + | 1.44620i | 0.894060 | + | 0.447948i | \(0.147845\pi\) |
−0.0590953 | + | 0.998252i | \(0.518822\pi\) | |||||||
\(72\) | 6.24264 | + | 10.8126i | 0.735702 | + | 1.27427i | ||||
\(73\) | −1.91421 | − | 3.31552i | −0.224042 | − | 0.388052i | 0.731990 | − | 0.681316i | \(-0.238592\pi\) |
−0.956032 | + | 0.293264i | \(0.905259\pi\) | |||||||
\(74\) | 1.20711 | − | 2.09077i | 0.140323 | − | 0.243047i | ||||
\(75\) | −4.82843 | − | 8.36308i | −0.557539 | − | 0.965685i | ||||
\(76\) | −3.03553 | + | 5.25770i | −0.348200 | + | 0.603099i | ||||
\(77\) | −12.6569 | −1.44238 | ||||||||
\(78\) | 10.6569 | 1.20665 | ||||||||
\(79\) | 7.62132 | − | 13.2005i | 0.857466 | − | 1.48517i | −0.0168732 | − | 0.999858i | \(-0.505371\pi\) |
0.874339 | − | 0.485316i | \(-0.161296\pi\) | |||||||
\(80\) | −1.50000 | − | 2.59808i | −0.167705 | − | 0.290474i | ||||
\(81\) | 4.74264 | − | 8.21449i | 0.526960 | − | 0.912722i | ||||
\(82\) | 11.4497 | + | 19.8315i | 1.26441 | + | 2.19003i | ||||
\(83\) | −2.03553 | − | 3.52565i | −0.223429 | − | 0.386990i | 0.732418 | − | 0.680855i | \(-0.238392\pi\) |
−0.955847 | + | 0.293865i | \(0.905058\pi\) | |||||||
\(84\) | 11.1569 | + | 19.3242i | 1.21731 | + | 2.10845i | ||||
\(85\) | −0.171573 | −0.0186097 | ||||||||
\(86\) | 10.7426 | − | 18.6068i | 1.15841 | − | 2.00642i | ||||
\(87\) | −1.41421 | + | 2.44949i | −0.151620 | + | 0.262613i | ||||
\(88\) | −11.5711 | − | 20.0417i | −1.23348 | − | 2.13645i | ||||
\(89\) | −12.4853 | −1.32344 | −0.661719 | − | 0.749752i | \(-0.730173\pi\) | ||||
−0.661719 | + | 0.749752i | \(0.730173\pi\) | |||||||
\(90\) | 3.41421 | − | 5.91359i | 0.359890 | − | 0.623347i | ||||
\(91\) | 4.41421 | 0.462735 | ||||||||
\(92\) | −15.3137 | −1.59656 | ||||||||
\(93\) | −11.1569 | + | 7.49706i | −1.15691 | + | 0.777408i | ||||
\(94\) | 4.00000 | 0.412568 | ||||||||
\(95\) | 1.58579 | 0.162698 | ||||||||
\(96\) | 1.91421 | − | 3.31552i | 0.195369 | − | 0.338388i | ||||
\(97\) | 10.8284 | 1.09946 | 0.549730 | − | 0.835342i | \(-0.314731\pi\) | ||||
0.549730 | + | 0.835342i | \(0.314731\pi\) | |||||||
\(98\) | −1.41421 | − | 2.44949i | −0.142857 | − | 0.247436i | ||||
\(99\) | 7.41421 | − | 12.8418i | 0.745157 | − | 1.29065i | ||||
\(100\) | 7.65685 | − | 13.2621i | 0.765685 | − | 1.32621i | ||||
\(101\) | 8.48528 | 0.844317 | 0.422159 | − | 0.906522i | \(-0.361273\pi\) | ||||
0.422159 | + | 0.906522i | \(0.361273\pi\) | |||||||
\(102\) | 0.500000 | + | 0.866025i | 0.0495074 | + | 0.0857493i | ||||
\(103\) | 6.03553 | + | 10.4539i | 0.594699 | + | 1.03005i | 0.993589 | + | 0.113050i | \(0.0360620\pi\) |
−0.398890 | + | 0.916999i | \(0.630605\pi\) | |||||||
\(104\) | 4.03553 | + | 6.98975i | 0.395717 | + | 0.685401i | ||||
\(105\) | 2.91421 | − | 5.04757i | 0.284398 | − | 0.492592i | ||||
\(106\) | 0.207107 | + | 0.358719i | 0.0201160 | + | 0.0348419i | ||||
\(107\) | −4.79289 | + | 8.30153i | −0.463346 | + | 0.802540i | −0.999125 | − | 0.0418188i | \(-0.986685\pi\) |
0.535779 | + | 0.844358i | \(0.320018\pi\) | |||||||
\(108\) | 1.58579 | 0.152592 | ||||||||
\(109\) | −5.17157 | −0.495347 | −0.247673 | − | 0.968844i | \(-0.579666\pi\) | ||||
−0.247673 | + | 0.968844i | \(0.579666\pi\) | |||||||
\(110\) | −6.32843 | + | 10.9612i | −0.603392 | + | 1.04511i | ||||
\(111\) | 1.20711 | + | 2.09077i | 0.114574 | + | 0.198447i | ||||
\(112\) | −3.62132 | + | 6.27231i | −0.342183 | + | 0.592678i | ||||
\(113\) | −2.67157 | − | 4.62730i | −0.251320 | − | 0.435300i | 0.712569 | − | 0.701602i | \(-0.247531\pi\) |
−0.963890 | + | 0.266302i | \(0.914198\pi\) | |||||||
\(114\) | −4.62132 | − | 8.00436i | −0.432826 | − | 0.749677i | ||||
\(115\) | 2.00000 | + | 3.46410i | 0.186501 | + | 0.323029i | ||||
\(116\) | −4.48528 | −0.416448 | ||||||||
\(117\) | −2.58579 | + | 4.47871i | −0.239056 | + | 0.414057i | ||||
\(118\) | −12.1569 | + | 21.0563i | −1.11913 | + | 1.93839i | ||||
\(119\) | 0.207107 | + | 0.358719i | 0.0189854 | + | 0.0328838i | ||||
\(120\) | 10.6569 | 0.972833 | ||||||||
\(121\) | −8.24264 | + | 14.2767i | −0.749331 | + | 1.29788i | ||||
\(122\) | −6.82843 | −0.618217 | ||||||||
\(123\) | −22.8995 | −2.06478 | ||||||||
\(124\) | −19.1421 | − | 9.37769i | −1.71901 | − | 0.842142i | ||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | −16.4853 | −1.46863 | ||||||||
\(127\) | 5.44975 | − | 9.43924i | 0.483587 | − | 0.837597i | −0.516235 | − | 0.856447i | \(-0.672667\pi\) |
0.999822 | + | 0.0188496i | \(0.00600039\pi\) | |||||||
\(128\) | 20.5563 | 1.81694 | ||||||||
\(129\) | 10.7426 | + | 18.6068i | 0.945837 | + | 1.63824i | ||||
\(130\) | 2.20711 | − | 3.82282i | 0.193576 | − | 0.335284i | ||||
\(131\) | 2.37868 | − | 4.11999i | 0.207826 | − | 0.359966i | −0.743203 | − | 0.669066i | \(-0.766694\pi\) |
0.951030 | + | 0.309100i | \(0.100028\pi\) | |||||||
\(132\) | 48.4558 | 4.21754 | ||||||||
\(133\) | −1.91421 | − | 3.31552i | −0.165983 | − | 0.287492i | ||||
\(134\) | −6.32843 | − | 10.9612i | −0.546693 | − | 0.946900i | ||||
\(135\) | −0.207107 | − | 0.358719i | −0.0178249 | − | 0.0308737i | ||||
\(136\) | −0.378680 | + | 0.655892i | −0.0324715 | + | 0.0562423i | ||||
\(137\) | 3.74264 | + | 6.48244i | 0.319755 | + | 0.553833i | 0.980437 | − | 0.196834i | \(-0.0630659\pi\) |
−0.660681 | + | 0.750666i | \(0.729733\pi\) | |||||||
\(138\) | 11.6569 | − | 20.1903i | 0.992297 | − | 1.71871i | ||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 9.24264 | 0.781146 | ||||||||
\(141\) | −2.00000 | + | 3.46410i | −0.168430 | + | 0.291730i | ||||
\(142\) | −16.9853 | − | 29.4194i | −1.42537 | − | 2.46882i | ||||
\(143\) | 4.79289 | − | 8.30153i | 0.400802 | − | 0.694209i | ||||
\(144\) | −4.24264 | − | 7.34847i | −0.353553 | − | 0.612372i | ||||
\(145\) | 0.585786 | + | 1.01461i | 0.0486469 | + | 0.0842589i | ||||
\(146\) | 4.62132 | + | 8.00436i | 0.382463 | + | 0.662446i | ||||
\(147\) | 2.82843 | 0.233285 | ||||||||
\(148\) | −1.91421 | + | 3.31552i | −0.157347 | + | 0.272534i | ||||
\(149\) | −0.500000 | + | 0.866025i | −0.0409616 | + | 0.0709476i | −0.885779 | − | 0.464107i | \(-0.846375\pi\) |
0.844818 | + | 0.535054i | \(0.179709\pi\) | |||||||
\(150\) | 11.6569 | + | 20.1903i | 0.951778 | + | 1.64853i | ||||
\(151\) | −17.3137 | −1.40897 | −0.704485 | − | 0.709719i | \(-0.748822\pi\) | ||||
−0.704485 | + | 0.709719i | \(0.748822\pi\) | |||||||
\(152\) | 3.50000 | − | 6.06218i | 0.283887 | − | 0.491708i | ||||
\(153\) | −0.485281 | −0.0392327 | ||||||||
\(154\) | 30.5563 | 2.46230 | ||||||||
\(155\) | 0.378680 | + | 5.55487i | 0.0304163 | + | 0.446178i | ||||
\(156\) | −16.8995 | −1.35304 | ||||||||
\(157\) | 14.8284 | 1.18344 | 0.591719 | − | 0.806145i | \(-0.298450\pi\) | ||||
0.591719 | + | 0.806145i | \(0.298450\pi\) | |||||||
\(158\) | −18.3995 | + | 31.8689i | −1.46379 | + | 2.53535i | ||||
\(159\) | −0.414214 | −0.0328493 | ||||||||
\(160\) | −0.792893 | − | 1.37333i | −0.0626837 | − | 0.108571i | ||||
\(161\) | 4.82843 | − | 8.36308i | 0.380533 | − | 0.659103i | ||||
\(162\) | −11.4497 | + | 19.8315i | −0.899577 | + | 1.55811i | ||||
\(163\) | −12.9706 | −1.01593 | −0.507966 | − | 0.861377i | \(-0.669603\pi\) | ||||
−0.507966 | + | 0.861377i | \(0.669603\pi\) | |||||||
\(164\) | −18.1569 | − | 31.4486i | −1.41781 | − | 2.45572i | ||||
\(165\) | −6.32843 | − | 10.9612i | −0.492667 | − | 0.853325i | ||||
\(166\) | 4.91421 | + | 8.51167i | 0.381417 | + | 0.660634i | ||||
\(167\) | 4.27817 | − | 7.41002i | 0.331055 | − | 0.573404i | −0.651664 | − | 0.758508i | \(-0.725929\pi\) |
0.982719 | + | 0.185104i | \(0.0592621\pi\) | |||||||
\(168\) | −12.8640 | − | 22.2810i | −0.992476 | − | 1.71902i | ||||
\(169\) | 4.82843 | − | 8.36308i | 0.371417 | − | 0.643314i | ||||
\(170\) | 0.414214 | 0.0317687 | ||||||||
\(171\) | 4.48528 | 0.342998 | ||||||||
\(172\) | −17.0355 | + | 29.5064i | −1.29895 | + | 2.24984i | ||||
\(173\) | 7.15685 | + | 12.3960i | 0.544126 | + | 0.942453i | 0.998661 | + | 0.0517246i | \(0.0164718\pi\) |
−0.454536 | + | 0.890728i | \(0.650195\pi\) | |||||||
\(174\) | 3.41421 | − | 5.91359i | 0.258831 | − | 0.448308i | ||||
\(175\) | 4.82843 | + | 8.36308i | 0.364995 | + | 0.632190i | ||||
\(176\) | 7.86396 | + | 13.6208i | 0.592768 | + | 1.02670i | ||||
\(177\) | −12.1569 | − | 21.0563i | −0.913765 | − | 1.58269i | ||||
\(178\) | 30.1421 | 2.25925 | ||||||||
\(179\) | 3.37868 | − | 5.85204i | 0.252534 | − | 0.437402i | −0.711689 | − | 0.702495i | \(-0.752069\pi\) |
0.964223 | + | 0.265093i | \(0.0854026\pi\) | |||||||
\(180\) | −5.41421 | + | 9.37769i | −0.403552 | + | 0.698972i | ||||
\(181\) | 5.15685 | + | 8.93193i | 0.383306 | + | 0.663905i | 0.991533 | − | 0.129858i | \(-0.0414522\pi\) |
−0.608227 | + | 0.793763i | \(0.708119\pi\) | |||||||
\(182\) | −10.6569 | −0.789939 | ||||||||
\(183\) | 3.41421 | − | 5.91359i | 0.252386 | − | 0.437145i | ||||
\(184\) | 17.6569 | 1.30168 | ||||||||
\(185\) | 1.00000 | 0.0735215 | ||||||||
\(186\) | 26.9350 | − | 18.0995i | 1.97497 | − | 1.32712i | ||||
\(187\) | 0.899495 | 0.0657776 | ||||||||
\(188\) | −6.34315 | −0.462621 | ||||||||
\(189\) | −0.500000 | + | 0.866025i | −0.0363696 | + | 0.0629941i | ||||
\(190\) | −3.82843 | −0.277743 | ||||||||
\(191\) | 0.550253 | + | 0.953065i | 0.0398149 | + | 0.0689614i | 0.885246 | − | 0.465123i | \(-0.153990\pi\) |
−0.845431 | + | 0.534084i | \(0.820657\pi\) | |||||||
\(192\) | −11.8640 | + | 20.5490i | −0.856208 | + | 1.48300i | ||||
\(193\) | 10.5711 | − | 18.3096i | 0.760922 | − | 1.31796i | −0.181454 | − | 0.983399i | \(-0.558080\pi\) |
0.942376 | − | 0.334556i | \(-0.108586\pi\) | |||||||
\(194\) | −26.1421 | −1.87690 | ||||||||
\(195\) | 2.20711 | + | 3.82282i | 0.158054 | + | 0.273758i | ||||
\(196\) | 2.24264 | + | 3.88437i | 0.160189 | + | 0.277455i | ||||
\(197\) | −1.74264 | − | 3.01834i | −0.124158 | − | 0.215048i | 0.797245 | − | 0.603655i | \(-0.206290\pi\) |
−0.921404 | + | 0.388607i | \(0.872956\pi\) | |||||||
\(198\) | −17.8995 | + | 31.0028i | −1.27206 | + | 2.20328i | ||||
\(199\) | −7.79289 | − | 13.4977i | −0.552424 | − | 0.956826i | −0.998099 | − | 0.0616310i | \(-0.980370\pi\) |
0.445675 | − | 0.895195i | \(-0.352964\pi\) | |||||||
\(200\) | −8.82843 | + | 15.2913i | −0.624264 | + | 1.08126i | ||||
\(201\) | 12.6569 | 0.892746 | ||||||||
\(202\) | −20.4853 | −1.44134 | ||||||||
\(203\) | 1.41421 | − | 2.44949i | 0.0992583 | − | 0.171920i | ||||
\(204\) | −0.792893 | − | 1.37333i | −0.0555136 | − | 0.0961524i | ||||
\(205\) | −4.74264 | + | 8.21449i | −0.331240 | + | 0.573725i | ||||
\(206\) | −14.5711 | − | 25.2378i | −1.01521 | − | 1.75840i | ||||
\(207\) | 5.65685 | + | 9.79796i | 0.393179 | + | 0.681005i | ||||
\(208\) | −2.74264 | − | 4.75039i | −0.190168 | − | 0.329380i | ||||
\(209\) | −8.31371 | −0.575071 | ||||||||
\(210\) | −7.03553 | + | 12.1859i | −0.485498 | + | 0.840907i | ||||
\(211\) | −3.79289 | + | 6.56948i | −0.261114 | + | 0.452262i | −0.966538 | − | 0.256523i | \(-0.917423\pi\) |
0.705425 | + | 0.708785i | \(0.250756\pi\) | |||||||
\(212\) | −0.328427 | − | 0.568852i | −0.0225565 | − | 0.0390689i | ||||
\(213\) | 33.9706 | 2.32762 | ||||||||
\(214\) | 11.5711 | − | 20.0417i | 0.790982 | − | 1.37002i | ||||
\(215\) | 8.89949 | 0.606941 | ||||||||
\(216\) | −1.82843 | −0.124409 | ||||||||
\(217\) | 11.1569 | − | 7.49706i | 0.757377 | − | 0.508933i | ||||
\(218\) | 12.4853 | 0.845610 | ||||||||
\(219\) | −9.24264 | −0.624560 | ||||||||
\(220\) | 10.0355 | − | 17.3821i | 0.676596 | − | 1.17190i | ||||
\(221\) | −0.313708 | −0.0211023 | ||||||||
\(222\) | −2.91421 | − | 5.04757i | −0.195589 | − | 0.338770i | ||||
\(223\) | −0.863961 | + | 1.49642i | −0.0578551 | + | 0.100208i | −0.893502 | − | 0.449059i | \(-0.851759\pi\) |
0.835647 | + | 0.549266i | \(0.185093\pi\) | |||||||
\(224\) | −1.91421 | + | 3.31552i | −0.127899 | + | 0.221527i | ||||
\(225\) | −11.3137 | −0.754247 | ||||||||
\(226\) | 6.44975 | + | 11.1713i | 0.429031 | + | 0.743103i | ||||
\(227\) | 7.79289 | + | 13.4977i | 0.517232 | + | 0.895873i | 0.999800 | + | 0.0200140i | \(0.00637108\pi\) |
−0.482567 | + | 0.875859i | \(0.660296\pi\) | |||||||
\(228\) | 7.32843 | + | 12.6932i | 0.485337 | + | 0.840628i | ||||
\(229\) | −5.74264 | + | 9.94655i | −0.379484 | + | 0.657286i | −0.990987 | − | 0.133956i | \(-0.957232\pi\) |
0.611503 | + | 0.791242i | \(0.290565\pi\) | |||||||
\(230\) | −4.82843 | − | 8.36308i | −0.318377 | − | 0.551445i | ||||
\(231\) | −15.2782 | + | 26.4626i | −1.00523 | + | 1.74111i | ||||
\(232\) | 5.17157 | 0.339530 | ||||||||
\(233\) | −14.8284 | −0.971443 | −0.485721 | − | 0.874114i | \(-0.661443\pi\) | ||||
−0.485721 | + | 0.874114i | \(0.661443\pi\) | |||||||
\(234\) | 6.24264 | − | 10.8126i | 0.408094 | − | 0.706840i | ||||
\(235\) | 0.828427 | + | 1.43488i | 0.0540406 | + | 0.0936011i | ||||
\(236\) | 19.2782 | − | 33.3908i | 1.25490 | − | 2.17355i | ||||
\(237\) | −18.3995 | − | 31.8689i | −1.19518 | − | 2.07010i | ||||
\(238\) | −0.500000 | − | 0.866025i | −0.0324102 | − | 0.0561361i | ||||
\(239\) | 6.37868 | + | 11.0482i | 0.412602 | + | 0.714648i | 0.995173 | − | 0.0981314i | \(-0.0312865\pi\) |
−0.582571 | + | 0.812780i | \(0.697953\pi\) | |||||||
\(240\) | −7.24264 | −0.467510 | ||||||||
\(241\) | −12.3284 | + | 21.3535i | −0.794144 | + | 1.37550i | 0.129238 | + | 0.991614i | \(0.458747\pi\) |
−0.923381 | + | 0.383884i | \(0.874586\pi\) | |||||||
\(242\) | 19.8995 | − | 34.4669i | 1.27919 | − | 2.21562i | ||||
\(243\) | −10.8284 | − | 18.7554i | −0.694644 | − | 1.20316i | ||||
\(244\) | 10.8284 | 0.693219 | ||||||||
\(245\) | 0.585786 | − | 1.01461i | 0.0374245 | − | 0.0648212i | ||||
\(246\) | 55.2843 | 3.52480 | ||||||||
\(247\) | 2.89949 | 0.184490 | ||||||||
\(248\) | 22.0711 | + | 10.8126i | 1.40151 | + | 0.686599i | ||||
\(249\) | −9.82843 | −0.622851 | ||||||||
\(250\) | 21.7279 | 1.37419 | ||||||||
\(251\) | −1.79289 | + | 3.10538i | −0.113166 | + | 0.196010i | −0.917045 | − | 0.398783i | \(-0.869433\pi\) |
0.803879 | + | 0.594793i | \(0.202766\pi\) | |||||||
\(252\) | 26.1421 | 1.64680 | ||||||||
\(253\) | −10.4853 | − | 18.1610i | −0.659204 | − | 1.14177i | ||||
\(254\) | −13.1569 | + | 22.7883i | −0.825534 | + | 1.42987i | ||||
\(255\) | −0.207107 | + | 0.358719i | −0.0129695 | + | 0.0224639i | ||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 0.156854 | + | 0.271680i | 0.00978430 | + | 0.0169469i | 0.870876 | − | 0.491503i | \(-0.163552\pi\) |
−0.861092 | + | 0.508450i | \(0.830219\pi\) | |||||||
\(258\) | −25.9350 | − | 44.9208i | −1.61464 | − | 2.79665i | ||||
\(259\) | −1.20711 | − | 2.09077i | −0.0750060 | − | 0.129914i | ||||
\(260\) | −3.50000 | + | 6.06218i | −0.217061 | + | 0.375960i | ||||
\(261\) | 1.65685 | + | 2.86976i | 0.102557 | + | 0.177633i | ||||
\(262\) | −5.74264 | + | 9.94655i | −0.354782 | + | 0.614500i | ||||
\(263\) | −0.686292 | −0.0423185 | −0.0211593 | − | 0.999776i | \(-0.506736\pi\) | ||||
−0.0211593 | + | 0.999776i | \(0.506736\pi\) | |||||||
\(264\) | −55.8701 | −3.43856 | ||||||||
\(265\) | −0.0857864 | + | 0.148586i | −0.00526982 | + | 0.00912759i | ||||
\(266\) | 4.62132 | + | 8.00436i | 0.283351 | + | 0.490779i | ||||
\(267\) | −15.0711 | + | 26.1039i | −0.922334 | + | 1.59753i | ||||
\(268\) | 10.0355 | + | 17.3821i | 0.613018 | + | 1.06178i | ||||
\(269\) | 15.9142 | + | 27.5642i | 0.970307 | + | 1.68062i | 0.694626 | + | 0.719371i | \(0.255570\pi\) |
0.275681 | + | 0.961249i | \(0.411097\pi\) | |||||||
\(270\) | 0.500000 | + | 0.866025i | 0.0304290 | + | 0.0527046i | ||||
\(271\) | −23.3137 | −1.41621 | −0.708103 | − | 0.706109i | \(-0.750449\pi\) | ||||
−0.708103 | + | 0.706109i | \(0.750449\pi\) | |||||||
\(272\) | 0.257359 | − | 0.445759i | 0.0156047 | − | 0.0270281i | ||||
\(273\) | 5.32843 | − | 9.22911i | 0.322491 | − | 0.558571i | ||||
\(274\) | −9.03553 | − | 15.6500i | −0.545857 | − | 0.945451i | ||||
\(275\) | 20.9706 | 1.26457 | ||||||||
\(276\) | −18.4853 | + | 32.0174i | −1.11268 | + | 1.92722i | ||||
\(277\) | −14.1421 | −0.849719 | −0.424859 | − | 0.905259i | \(-0.639676\pi\) | ||||
−0.424859 | + | 0.905259i | \(0.639676\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.07107 | + | 15.7116i | 0.0641232 | + | 0.940626i | ||||
\(280\) | −10.6569 | −0.636869 | ||||||||
\(281\) | 2.00000 | 0.119310 | 0.0596550 | − | 0.998219i | \(-0.481000\pi\) | ||||
0.0596550 | + | 0.998219i | \(0.481000\pi\) | |||||||
\(282\) | 4.82843 | − | 8.36308i | 0.287529 | − | 0.498014i | ||||
\(283\) | −2.34315 | −0.139286 | −0.0696428 | − | 0.997572i | \(-0.522186\pi\) | ||||
−0.0696428 | + | 0.997572i | \(0.522186\pi\) | |||||||
\(284\) | 26.9350 | + | 46.6528i | 1.59830 | + | 2.76834i | ||||
\(285\) | 1.91421 | − | 3.31552i | 0.113388 | − | 0.196394i | ||||
\(286\) | −11.5711 | + | 20.0417i | −0.684212 | + | 1.18509i | ||||
\(287\) | 22.8995 | 1.35171 | ||||||||
\(288\) | −2.24264 | − | 3.88437i | −0.132149 | − | 0.228889i | ||||
\(289\) | 8.48528 | + | 14.6969i | 0.499134 | + | 0.864526i | ||||
\(290\) | −1.41421 | − | 2.44949i | −0.0830455 | − | 0.143839i | ||||
\(291\) | 13.0711 | − | 22.6398i | 0.766240 | − | 1.32717i | ||||
\(292\) | −7.32843 | − | 12.6932i | −0.428864 | − | 0.742814i | ||||
\(293\) | 12.3995 | − | 21.4766i | 0.724386 | − | 1.25467i | −0.234840 | − | 0.972034i | \(-0.575457\pi\) |
0.959226 | − | 0.282640i | \(-0.0912101\pi\) | |||||||
\(294\) | −6.82843 | −0.398242 | ||||||||
\(295\) | −10.0711 | −0.586360 | ||||||||
\(296\) | 2.20711 | − | 3.82282i | 0.128285 | − | 0.222197i | ||||
\(297\) | 1.08579 | + | 1.88064i | 0.0630037 | + | 0.109126i | ||||
\(298\) | 1.20711 | − | 2.09077i | 0.0699258 | − | 0.121115i | ||||
\(299\) | 3.65685 | + | 6.33386i | 0.211481 | + | 0.366296i | ||||
\(300\) | −18.4853 | − | 32.0174i | −1.06725 | − | 1.84853i | ||||
\(301\) | −10.7426 | − | 18.6068i | −0.619196 | − | 1.07248i | ||||
\(302\) | 41.7990 | 2.40526 | ||||||||
\(303\) | 10.2426 | − | 17.7408i | 0.588424 | − | 1.01918i | ||||
\(304\) | −2.37868 | + | 4.11999i | −0.136427 | + | 0.236298i | ||||
\(305\) | −1.41421 | − | 2.44949i | −0.0809776 | − | 0.140257i | ||||
\(306\) | 1.17157 | 0.0669744 | ||||||||
\(307\) | 1.37868 | − | 2.38794i | 0.0786854 | − | 0.136287i | −0.823998 | − | 0.566593i | \(-0.808261\pi\) |
0.902683 | + | 0.430306i | \(0.141594\pi\) | |||||||
\(308\) | −48.4558 | −2.76103 | ||||||||
\(309\) | 29.1421 | 1.65784 | ||||||||
\(310\) | −0.914214 | − | 13.4106i | −0.0519238 | − | 0.761674i | ||||
\(311\) | −11.3137 | −0.641542 | −0.320771 | − | 0.947157i | \(-0.603942\pi\) | ||||
−0.320771 | + | 0.947157i | \(0.603942\pi\) | |||||||
\(312\) | 19.4853 | 1.10314 | ||||||||
\(313\) | −1.91421 | + | 3.31552i | −0.108198 | + | 0.187404i | −0.915040 | − | 0.403363i | \(-0.867841\pi\) |
0.806842 | + | 0.590767i | \(0.201175\pi\) | |||||||
\(314\) | −35.7990 | −2.02025 | ||||||||
\(315\) | −3.41421 | − | 5.91359i | −0.192369 | − | 0.333193i | ||||
\(316\) | 29.1777 | − | 50.5372i | 1.64137 | − | 2.84294i | ||||
\(317\) | 1.08579 | − | 1.88064i | 0.0609838 | − | 0.105627i | −0.833922 | − | 0.551883i | \(-0.813910\pi\) |
0.894905 | + | 0.446256i | \(0.147243\pi\) | |||||||
\(318\) | 1.00000 | 0.0560772 | ||||||||
\(319\) | −3.07107 | − | 5.31925i | −0.171947 | − | 0.297821i | ||||
\(320\) | 4.91421 | + | 8.51167i | 0.274713 | + | 0.475817i | ||||
\(321\) | 11.5711 | + | 20.0417i | 0.645834 | + | 1.11862i | ||||
\(322\) | −11.6569 | + | 20.1903i | −0.649611 | + | 1.12516i | ||||
\(323\) | 0.136039 | + | 0.235626i | 0.00756941 | + | 0.0131106i | ||||
\(324\) | 18.1569 | − | 31.4486i | 1.00871 | − | 1.74714i | ||||
\(325\) | −7.31371 | −0.405692 | ||||||||
\(326\) | 31.3137 | 1.73431 | ||||||||
\(327\) | −6.24264 | + | 10.8126i | −0.345219 | + | 0.597937i | ||||
\(328\) | 20.9350 | + | 36.2605i | 1.15594 | + | 2.00215i | ||||
\(329\) | 2.00000 | − | 3.46410i | 0.110264 | − | 0.190982i | ||||
\(330\) | 15.2782 | + | 26.4626i | 0.841036 | + | 1.45672i | ||||
\(331\) | −0.378680 | − | 0.655892i | −0.0208141 | − | 0.0360511i | 0.855431 | − | 0.517917i | \(-0.173292\pi\) |
−0.876245 | + | 0.481866i | \(0.839959\pi\) | |||||||
\(332\) | −7.79289 | − | 13.4977i | −0.427691 | − | 0.740782i | ||||
\(333\) | 2.82843 | 0.154997 | ||||||||
\(334\) | −10.3284 | + | 17.8894i | −0.565146 | + | 0.978862i | ||||
\(335\) | 2.62132 | − | 4.54026i | 0.143218 | − | 0.248061i | ||||
\(336\) | 8.74264 | + | 15.1427i | 0.476950 | + | 0.826102i | ||||
\(337\) | −13.3137 | −0.725244 | −0.362622 | − | 0.931936i | \(-0.618118\pi\) | ||||
−0.362622 | + | 0.931936i | \(0.618118\pi\) | |||||||
\(338\) | −11.6569 | + | 20.1903i | −0.634049 | + | 1.09821i | ||||
\(339\) | −12.8995 | −0.700604 | ||||||||
\(340\) | −0.656854 | −0.0356229 | ||||||||
\(341\) | −1.98528 | − | 29.1222i | −0.107509 | − | 1.57706i | ||||
\(342\) | −10.8284 | −0.585534 | ||||||||
\(343\) | −19.7279 | −1.06521 | ||||||||
\(344\) | 19.6421 | − | 34.0212i | 1.05903 | − | 1.83430i | ||||
\(345\) | 9.65685 | 0.519908 | ||||||||
\(346\) | −17.2782 | − | 29.9267i | −0.928880 | − | 1.60887i | ||||
\(347\) | −11.2782 | + | 19.5344i | −0.605444 | + | 1.04866i | 0.386537 | + | 0.922274i | \(0.373671\pi\) |
−0.991981 | + | 0.126386i | \(0.959662\pi\) | |||||||
\(348\) | −5.41421 | + | 9.37769i | −0.290232 | + | 0.502697i | ||||
\(349\) | 35.1127 | 1.87954 | 0.939770 | − | 0.341808i | \(-0.111039\pi\) | ||||
0.939770 | + | 0.341808i | \(0.111039\pi\) | |||||||
\(350\) | −11.6569 | − | 20.1903i | −0.623085 | − | 1.07921i | ||||
\(351\) | −0.378680 | − | 0.655892i | −0.0202124 | − | 0.0350089i | ||||
\(352\) | 4.15685 | + | 7.19988i | 0.221561 | + | 0.383755i | ||||
\(353\) | −1.50000 | + | 2.59808i | −0.0798369 | + | 0.138282i | −0.903179 | − | 0.429263i | \(-0.858773\pi\) |
0.823343 | + | 0.567545i | \(0.192107\pi\) | |||||||
\(354\) | 29.3492 | + | 50.8344i | 1.55989 | + | 2.70182i | ||||
\(355\) | 7.03553 | − | 12.1859i | 0.373407 | − | 0.646761i | ||||
\(356\) | −47.7990 | −2.53334 | ||||||||
\(357\) | 1.00000 | 0.0529256 | ||||||||
\(358\) | −8.15685 | + | 14.1281i | −0.431103 | + | 0.746693i | ||||
\(359\) | −13.4497 | − | 23.2956i | −0.709851 | − | 1.22950i | −0.964912 | − | 0.262572i | \(-0.915429\pi\) |
0.255062 | − | 0.966925i | \(-0.417904\pi\) | |||||||
\(360\) | 6.24264 | − | 10.8126i | 0.329016 | − | 0.569873i | ||||
\(361\) | 8.24264 | + | 14.2767i | 0.433823 | + | 0.751404i | ||||
\(362\) | −12.4497 | − | 21.5636i | −0.654344 | − | 1.13336i | ||||
\(363\) | 19.8995 | + | 34.4669i | 1.04445 | + | 1.80904i | ||||
\(364\) | 16.8995 | 0.885774 | ||||||||
\(365\) | −1.91421 | + | 3.31552i | −0.100195 | + | 0.173542i | ||||
\(366\) | −8.24264 | + | 14.2767i | −0.430850 | + | 0.746254i | ||||
\(367\) | −9.10660 | − | 15.7731i | −0.475361 | − | 0.823349i | 0.524241 | − | 0.851570i | \(-0.324349\pi\) |
−0.999602 | + | 0.0282210i | \(0.991016\pi\) | |||||||
\(368\) | −12.0000 | −0.625543 | ||||||||
\(369\) | −13.4142 | + | 23.2341i | −0.698316 | + | 1.20952i | ||||
\(370\) | −2.41421 | −0.125509 | ||||||||
\(371\) | 0.414214 | 0.0215049 | ||||||||
\(372\) | −42.7132 | + | 28.7019i | −2.21458 | + | 1.48813i | ||||
\(373\) | 10.0000 | 0.517780 | 0.258890 | − | 0.965907i | \(-0.416643\pi\) | ||||
0.258890 | + | 0.965907i | \(0.416643\pi\) | |||||||
\(374\) | −2.17157 | −0.112289 | ||||||||
\(375\) | −10.8640 | + | 18.8169i | −0.561013 | + | 0.971702i | ||||
\(376\) | 7.31371 | 0.377176 | ||||||||
\(377\) | 1.07107 | + | 1.85514i | 0.0551628 | + | 0.0955448i | ||||
\(378\) | 1.20711 | − | 2.09077i | 0.0620869 | − | 0.107538i | ||||
\(379\) | 14.6924 | − | 25.4480i | 0.754697 | − | 1.30717i | −0.190827 | − | 0.981624i | \(-0.561117\pi\) |
0.945525 | − | 0.325550i | \(-0.105550\pi\) | |||||||
\(380\) | 6.07107 | 0.311439 | ||||||||
\(381\) | −13.1569 | − | 22.7883i | −0.674046 | − | 1.16748i | ||||
\(382\) | −1.32843 | − | 2.30090i | −0.0679682 | − | 0.117724i | ||||
\(383\) | −12.4497 | − | 21.5636i | −0.636152 | − | 1.10185i | −0.986270 | − | 0.165142i | \(-0.947192\pi\) |
0.350117 | − | 0.936706i | \(-0.386142\pi\) | |||||||
\(384\) | 24.8137 | − | 42.9786i | 1.26627 | − | 2.19324i | ||||
\(385\) | 6.32843 | + | 10.9612i | 0.322527 | + | 0.558632i | ||||
\(386\) | −25.5208 | + | 44.2033i | −1.29898 | + | 2.24989i | ||||
\(387\) | 25.1716 | 1.27954 | ||||||||
\(388\) | 41.4558 | 2.10460 | ||||||||
\(389\) | −8.57107 | + | 14.8455i | −0.434570 | + | 0.752698i | −0.997260 | − | 0.0739699i | \(-0.976433\pi\) |
0.562690 | + | 0.826668i | \(0.309766\pi\) | |||||||
\(390\) | −5.32843 | − | 9.22911i | −0.269815 | − | 0.467334i | ||||
\(391\) | −0.343146 | + | 0.594346i | −0.0173536 | + | 0.0300574i | ||||
\(392\) | −2.58579 | − | 4.47871i | −0.130602 | − | 0.226209i | ||||
\(393\) | −5.74264 | − | 9.94655i | −0.289678 | − | 0.501737i | ||||
\(394\) | 4.20711 | + | 7.28692i | 0.211951 | + | 0.367110i | ||||
\(395\) | −15.2426 | −0.766940 | ||||||||
\(396\) | 28.3848 | − | 49.1639i | 1.42639 | − | 2.47058i | ||||
\(397\) | 8.25736 | − | 14.3022i | 0.414425 | − | 0.717805i | −0.580943 | − | 0.813944i | \(-0.697316\pi\) |
0.995368 | + | 0.0961392i | \(0.0306494\pi\) | |||||||
\(398\) | 18.8137 | + | 32.5863i | 0.943046 | + | 1.63340i | ||||
\(399\) | −9.24264 | −0.462711 | ||||||||
\(400\) | 6.00000 | − | 10.3923i | 0.300000 | − | 0.519615i | ||||
\(401\) | −21.1716 | −1.05726 | −0.528629 | − | 0.848853i | \(-0.677294\pi\) | ||||
−0.528629 | + | 0.848853i | \(0.677294\pi\) | |||||||
\(402\) | −30.5563 | −1.52401 | ||||||||
\(403\) | 0.692388 | + | 10.1567i | 0.0344903 | + | 0.505940i | ||||
\(404\) | 32.4853 | 1.61620 | ||||||||
\(405\) | −9.48528 | −0.471327 | ||||||||
\(406\) | −3.41421 | + | 5.91359i | −0.169445 | + | 0.293487i | ||||
\(407\) | −5.24264 | −0.259868 | ||||||||
\(408\) | 0.914214 | + | 1.58346i | 0.0452603 | + | 0.0783932i | ||||
\(409\) | −4.67157 | + | 8.09140i | −0.230994 | + | 0.400094i | −0.958101 | − | 0.286431i | \(-0.907531\pi\) |
0.727107 | + | 0.686525i | \(0.240865\pi\) | |||||||
\(410\) | 11.4497 | − | 19.8315i | 0.565463 | − | 0.979410i | ||||
\(411\) | 18.0711 | 0.891380 | ||||||||
\(412\) | 23.1066 | + | 40.0218i | 1.13838 | + | 1.97173i | ||||
\(413\) | 12.1569 | + | 21.0563i | 0.598200 | + | 1.03611i | ||||
\(414\) | −13.6569 | − | 23.6544i | −0.671198 | − | 1.16255i | ||||
\(415\) | −2.03553 | + | 3.52565i | −0.0999204 | + | 0.173067i | ||||
\(416\) | −1.44975 | − | 2.51104i | −0.0710797 | − | 0.123114i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 20.0711 | 0.981708 | ||||||||
\(419\) | 28.0000 | 1.36789 | 0.683945 | − | 0.729534i | \(-0.260263\pi\) | ||||
0.683945 | + | 0.729534i | \(0.260263\pi\) | |||||||
\(420\) | 11.1569 | − | 19.3242i | 0.544399 | − | 0.942926i | ||||
\(421\) | 1.42893 | + | 2.47498i | 0.0696419 | + | 0.120623i | 0.898744 | − | 0.438474i | \(-0.144481\pi\) |
−0.829102 | + | 0.559098i | \(0.811148\pi\) | |||||||
\(422\) | 9.15685 | − | 15.8601i | 0.445749 | − | 0.772059i | ||||
\(423\) | 2.34315 | + | 4.05845i | 0.113928 | + | 0.197328i | ||||
\(424\) | 0.378680 | + | 0.655892i | 0.0183903 | + | 0.0318530i | ||||
\(425\) | −0.343146 | − | 0.594346i | −0.0166450 | − | 0.0288300i | ||||
\(426\) | −82.0122 | −3.97350 | ||||||||
\(427\) | −3.41421 | + | 5.91359i | −0.165225 | + | 0.286179i | ||||
\(428\) | −18.3492 | + | 31.7818i | −0.886944 | + | 1.53623i | ||||
\(429\) | −11.5711 | − | 20.0417i | −0.558656 | − | 0.967621i | ||||
\(430\) | −21.4853 | −1.03611 | ||||||||
\(431\) | 12.6213 | − | 21.8608i | 0.607948 | − | 1.05300i | −0.383631 | − | 0.923487i | \(-0.625326\pi\) |
0.991578 | − | 0.129510i | \(-0.0413403\pi\) | |||||||
\(432\) | 1.24264 | 0.0597866 | ||||||||
\(433\) | −35.1127 | −1.68741 | −0.843704 | − | 0.536808i | \(-0.819630\pi\) | ||||
−0.843704 | + | 0.536808i | \(0.819630\pi\) | |||||||
\(434\) | −26.9350 | + | 18.0995i | −1.29292 | + | 0.868803i | ||||
\(435\) | 2.82843 | 0.135613 | ||||||||
\(436\) | −19.7990 | −0.948200 | ||||||||
\(437\) | 3.17157 | − | 5.49333i | 0.151717 | − | 0.262781i | ||||
\(438\) | 22.3137 | 1.06619 | ||||||||
\(439\) | 6.03553 | + | 10.4539i | 0.288060 | + | 0.498935i | 0.973347 | − | 0.229339i | \(-0.0736563\pi\) |
−0.685286 | + | 0.728274i | \(0.740323\pi\) | |||||||
\(440\) | −11.5711 | + | 20.0417i | −0.551629 | + | 0.955449i | ||||
\(441\) | 1.65685 | − | 2.86976i | 0.0788978 | − | 0.136655i | ||||
\(442\) | 0.757359 | 0.0360239 | ||||||||
\(443\) | 6.62132 | + | 11.4685i | 0.314588 | + | 0.544883i | 0.979350 | − | 0.202173i | \(-0.0648002\pi\) |
−0.664761 | + | 0.747056i | \(0.731467\pi\) | |||||||
\(444\) | 4.62132 | + | 8.00436i | 0.219318 | + | 0.379870i | ||||
\(445\) | 6.24264 | + | 10.8126i | 0.295930 | + | 0.512565i | ||||
\(446\) | 2.08579 | − | 3.61269i | 0.0987649 | − | 0.171066i | ||||
\(447\) | 1.20711 | + | 2.09077i | 0.0570942 | + | 0.0988900i | ||||
\(448\) | 11.8640 | − | 20.5490i | 0.560519 | − | 0.970848i | ||||
\(449\) | 4.62742 | 0.218381 | 0.109191 | − | 0.994021i | \(-0.465174\pi\) | ||||
0.109191 | + | 0.994021i | \(0.465174\pi\) | |||||||
\(450\) | 27.3137 | 1.28758 | ||||||||
\(451\) | 24.8640 | − | 43.0656i | 1.17080 | − | 2.02788i | ||||
\(452\) | −10.2279 | − | 17.7153i | −0.481081 | − | 0.833257i | ||||
\(453\) | −20.8995 | + | 36.1990i | −0.981944 | + | 1.70078i | ||||
\(454\) | −18.8137 | − | 32.5863i | −0.882971 | − | 1.52935i | ||||
\(455\) | −2.20711 | − | 3.82282i | −0.103471 | − | 0.179217i | ||||
\(456\) | −8.44975 | − | 14.6354i | −0.395696 | − | 0.685365i | ||||
\(457\) | 31.1127 | 1.45539 | 0.727695 | − | 0.685901i | \(-0.240591\pi\) | ||||
0.727695 | + | 0.685901i | \(0.240591\pi\) | |||||||
\(458\) | 13.8640 | − | 24.0131i | 0.647820 | − | 1.12206i | ||||
\(459\) | 0.0355339 | − | 0.0615465i | 0.00165858 | − | 0.00287275i | ||||
\(460\) | 7.65685 | + | 13.2621i | 0.357003 | + | 0.618347i | ||||
\(461\) | 26.1421 | 1.21756 | 0.608780 | − | 0.793339i | \(-0.291659\pi\) | ||||
0.608780 | + | 0.793339i | \(0.291659\pi\) | |||||||
\(462\) | 36.8848 | − | 63.8863i | 1.71604 | − | 2.97226i | ||||
\(463\) | 24.9706 | 1.16048 | 0.580240 | − | 0.814445i | \(-0.302959\pi\) | ||||
0.580240 | + | 0.814445i | \(0.302959\pi\) | |||||||
\(464\) | −3.51472 | −0.163167 | ||||||||
\(465\) | 12.0711 | + | 5.91359i | 0.559782 | + | 0.274236i | ||||
\(466\) | 35.7990 | 1.65836 | ||||||||
\(467\) | −8.00000 | −0.370196 | −0.185098 | − | 0.982720i | \(-0.559260\pi\) | ||||
−0.185098 | + | 0.982720i | \(0.559260\pi\) | |||||||
\(468\) | −9.89949 | + | 17.1464i | −0.457604 | + | 0.792594i | ||||
\(469\) | −12.6569 | −0.584439 | ||||||||
\(470\) | −2.00000 | − | 3.46410i | −0.0922531 | − | 0.159787i | ||||
\(471\) | 17.8995 | − | 31.0028i | 0.824765 | − | 1.42854i | ||||
\(472\) | −22.2279 | + | 38.4999i | −1.02312 | + | 1.77210i | ||||
\(473\) | −46.6569 | −2.14528 | ||||||||
\(474\) | 44.4203 | + | 76.9382i | 2.04029 | + | 3.53389i | ||||
\(475\) | 3.17157 | + | 5.49333i | 0.145522 | + | 0.252051i | ||||
\(476\) | 0.792893 | + | 1.37333i | 0.0363422 | + | 0.0629465i | ||||
\(477\) | −0.242641 | + | 0.420266i | −0.0111098 | + | 0.0192427i | ||||
\(478\) | −15.3995 | − | 26.6727i | −0.704357 | − | 1.21998i | ||||
\(479\) | −4.86396 | + | 8.42463i | −0.222240 | + | 0.384931i | −0.955488 | − | 0.295030i | \(-0.904670\pi\) |
0.733248 | + | 0.679962i | \(0.238004\pi\) | |||||||
\(480\) | −3.82843 | −0.174743 | ||||||||
\(481\) | 1.82843 | 0.0833691 | ||||||||
\(482\) | 29.7635 | − | 51.5518i | 1.35569 | − | 2.34812i | ||||
\(483\) | −11.6569 | − | 20.1903i | −0.530405 | − | 0.918689i | ||||
\(484\) | −31.5563 | + | 54.6572i | −1.43438 | + | 2.48442i | ||||
\(485\) | −5.41421 | − | 9.37769i | −0.245847 | − | 0.425819i | ||||
\(486\) | 26.1421 | + | 45.2795i | 1.18583 | + | 2.05392i | ||||
\(487\) | 8.69239 | + | 15.0557i | 0.393890 | + | 0.682237i | 0.992959 | − | 0.118460i | \(-0.0377959\pi\) |
−0.599069 | + | 0.800697i | \(0.704463\pi\) | |||||||
\(488\) | −12.4853 | −0.565182 | ||||||||
\(489\) | −15.6569 | + | 27.1185i | −0.708027 | + | 1.22634i | ||||
\(490\) | −1.41421 | + | 2.44949i | −0.0638877 | + | 0.110657i | ||||
\(491\) | −2.20711 | − | 3.82282i | −0.0996053 | − | 0.172522i | 0.811916 | − | 0.583774i | \(-0.198425\pi\) |
−0.911521 | + | 0.411253i | \(0.865091\pi\) | |||||||
\(492\) | −87.6690 | −3.95243 | ||||||||
\(493\) | −0.100505 | + | 0.174080i | −0.00452652 | + | 0.00784016i | ||||
\(494\) | −7.00000 | −0.314945 | ||||||||
\(495\) | −14.8284 | −0.666488 | ||||||||
\(496\) | −15.0000 | − | 7.34847i | −0.673520 | − | 0.329956i | ||||
\(497\) | −33.9706 | −1.52379 | ||||||||
\(498\) | 23.7279 | 1.06327 | ||||||||
\(499\) | −20.1066 | + | 34.8257i | −0.900095 | + | 1.55901i | −0.0727259 | + | 0.997352i | \(0.523170\pi\) |
−0.827369 | + | 0.561659i | \(0.810163\pi\) | |||||||
\(500\) | −34.4558 | −1.54091 | ||||||||
\(501\) | −10.3284 | − | 17.8894i | −0.461440 | − | 0.799238i | ||||
\(502\) | 4.32843 | − | 7.49706i | 0.193187 | − | 0.334610i | ||||
\(503\) | −11.6924 | + | 20.2518i | −0.521338 | + | 0.902984i | 0.478354 | + | 0.878167i | \(0.341234\pi\) |
−0.999692 | + | 0.0248166i | \(0.992100\pi\) | |||||||
\(504\) | −30.1421 | −1.34264 | ||||||||
\(505\) | −4.24264 | − | 7.34847i | −0.188795 | − | 0.327003i | ||||
\(506\) | 25.3137 | + | 43.8446i | 1.12533 | + | 1.94913i | ||||
\(507\) | −11.6569 | − | 20.1903i | −0.517699 | − | 0.896681i | ||||
\(508\) | 20.8640 | − | 36.1374i | 0.925689 | − | 1.60334i | ||||
\(509\) | −3.39949 | − | 5.88810i | −0.150680 | − | 0.260985i | 0.780798 | − | 0.624784i | \(-0.214813\pi\) |
−0.931478 | + | 0.363799i | \(0.881480\pi\) | |||||||
\(510\) | 0.500000 | − | 0.866025i | 0.0221404 | − | 0.0383482i | ||||
\(511\) | 9.24264 | 0.408870 | ||||||||
\(512\) | 31.2426 | 1.38074 | ||||||||
\(513\) | −0.328427 | + | 0.568852i | −0.0145004 | + | 0.0251154i | ||||
\(514\) | −0.378680 | − | 0.655892i | −0.0167028 | − | 0.0289302i | ||||
\(515\) | 6.03553 | − | 10.4539i | 0.265957 | − | 0.460652i | ||||
\(516\) | 41.1274 | + | 71.2348i | 1.81053 | + | 3.13594i | ||||
\(517\) | −4.34315 | − | 7.52255i | −0.191011 | − | 0.330841i | ||||
\(518\) | 2.91421 | + | 5.04757i | 0.128043 | + | 0.221777i | ||||
\(519\) | 34.5563 | 1.51686 | ||||||||
\(520\) | 4.03553 | − | 6.98975i | 0.176970 | − | 0.306521i | ||||
\(521\) | −15.2279 | + | 26.3755i | −0.667147 | + | 1.15553i | 0.311551 | + | 0.950229i | \(0.399152\pi\) |
−0.978698 | + | 0.205304i | \(0.934182\pi\) | |||||||
\(522\) | −4.00000 | − | 6.92820i | −0.175075 | − | 0.303239i | ||||
\(523\) | −8.00000 | −0.349816 | −0.174908 | − | 0.984585i | \(-0.555963\pi\) | ||||
−0.174908 | + | 0.984585i | \(0.555963\pi\) | |||||||
\(524\) | 9.10660 | − | 15.7731i | 0.397824 | − | 0.689051i | ||||
\(525\) | 23.3137 | 1.01749 | ||||||||
\(526\) | 1.65685 | 0.0722423 | ||||||||
\(527\) | −0.792893 | + | 0.532799i | −0.0345390 | + | 0.0232091i | ||||
\(528\) | 37.9706 | 1.65246 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0.207107 | − | 0.358719i | 0.00899614 | − | 0.0155818i | ||||
\(531\) | −28.4853 | −1.23616 | ||||||||
\(532\) | −7.32843 | − | 12.6932i | −0.317728 | − | 0.550320i | ||||
\(533\) | −8.67157 | + | 15.0196i | −0.375608 | + | 0.650571i | ||||
\(534\) | 36.3848 | − | 63.0203i | 1.57452 | − | 2.72715i | ||||
\(535\) | 9.58579 | 0.414430 | ||||||||
\(536\) | −11.5711 | − | 20.0417i | −0.499794 | − | 0.865669i | ||||
\(537\) | −8.15685 | − | 14.1281i | −0.351994 | − | 0.609672i | ||||
\(538\) | −38.4203 | − | 66.5459i | −1.65642 | − | 2.86900i | ||||
\(539\) | −3.07107 | + | 5.31925i | −0.132280 | + | 0.229116i | ||||
\(540\) | −0.792893 | − | 1.37333i | −0.0341207 | − | 0.0590988i | ||||
\(541\) | −12.6421 | + | 21.8968i | −0.543528 | + | 0.941418i | 0.455170 | + | 0.890405i | \(0.349578\pi\) |
−0.998698 | + | 0.0510134i | \(0.983755\pi\) | |||||||
\(542\) | 56.2843 | 2.41762 | ||||||||
\(543\) | 24.8995 | 1.06854 | ||||||||
\(544\) | 0.136039 | − | 0.235626i | 0.00583262 | − | 0.0101024i | ||||
\(545\) | 2.58579 | + | 4.47871i | 0.110763 | + | 0.191847i | ||||
\(546\) | −12.8640 | + | 22.2810i | −0.550527 | + | 0.953540i | ||||
\(547\) | −2.86396 | − | 4.96053i | −0.122454 | − | 0.212097i | 0.798281 | − | 0.602285i | \(-0.205743\pi\) |
−0.920735 | + | 0.390189i | \(0.872410\pi\) | |||||||
\(548\) | 14.3284 | + | 24.8176i | 0.612080 | + | 1.06015i | ||||
\(549\) | −4.00000 | − | 6.92820i | −0.170716 | − | 0.295689i | ||||
\(550\) | −50.6274 | −2.15876 | ||||||||
\(551\) | 0.928932 | − | 1.60896i | 0.0395738 | − | 0.0685439i | ||||
\(552\) | 21.3137 | − | 36.9164i | 0.907172 | − | 1.57127i | ||||
\(553\) | 18.3995 | + | 31.8689i | 0.782426 | + | 1.35520i | ||||
\(554\) | 34.1421 | 1.45056 | ||||||||
\(555\) | 1.20711 | − | 2.09077i | 0.0512388 | − | 0.0887483i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 44.4853 | 1.88490 | 0.942451 | − | 0.334344i | \(-0.108515\pi\) | ||||
0.942451 | + | 0.334344i | \(0.108515\pi\) | |||||||
\(558\) | −2.58579 | − | 37.9310i | −0.109465 | − | 1.60575i | ||||
\(559\) | 16.2721 | 0.688236 | ||||||||
\(560\) | 7.24264 | 0.306057 | ||||||||
\(561\) | 1.08579 | − | 1.88064i | 0.0458419 | − | 0.0794006i | ||||
\(562\) | −4.82843 | −0.203675 | ||||||||
\(563\) | −2.37868 | − | 4.11999i | −0.100249 | − | 0.173637i | 0.811538 | − | 0.584300i | \(-0.198631\pi\) |
−0.911787 | + | 0.410663i | \(0.865297\pi\) | |||||||
\(564\) | −7.65685 | + | 13.2621i | −0.322412 | + | 0.558433i | ||||
\(565\) | −2.67157 | + | 4.62730i | −0.112394 | + | 0.194672i | ||||
\(566\) | 5.65685 | 0.237775 | ||||||||
\(567\) | 11.4497 | + | 19.8315i | 0.480844 | + | 0.832847i | ||||
\(568\) | −31.0563 | − | 53.7912i | −1.30310 | − | 2.25703i | ||||
\(569\) | −7.57107 | − | 13.1135i | −0.317396 | − | 0.549745i | 0.662548 | − | 0.749019i | \(-0.269475\pi\) |
−0.979944 | + | 0.199274i | \(0.936142\pi\) | |||||||
\(570\) | −4.62132 | + | 8.00436i | −0.193566 | + | 0.335266i | ||||
\(571\) | 20.4497 | + | 35.4200i | 0.855795 | + | 1.48228i | 0.875905 | + | 0.482483i | \(0.160265\pi\) |
−0.0201099 | + | 0.999798i | \(0.506402\pi\) | |||||||
\(572\) | 18.3492 | − | 31.7818i | 0.767220 | − | 1.32886i | ||||
\(573\) | 2.65685 | 0.110992 | ||||||||
\(574\) | −55.2843 | −2.30752 | ||||||||
\(575\) | −8.00000 | + | 13.8564i | −0.333623 | + | 0.577852i | ||||
\(576\) | 13.8995 | + | 24.0746i | 0.579146 | + | 1.00311i | ||||
\(577\) | 16.9853 | − | 29.4194i | 0.707107 | − | 1.22474i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.965926 | − | 0.258819i | \(-0.0833332\pi\) | |||||||
\(578\) | −20.4853 | − | 35.4815i | −0.852075 | − | 1.47584i | ||||
\(579\) | −25.5208 | − | 44.2033i | −1.06061 | − | 1.83703i | ||||
\(580\) | 2.24264 | + | 3.88437i | 0.0931206 | + | 0.161290i | ||||
\(581\) | 9.82843 | 0.407752 | ||||||||
\(582\) | −31.5563 | + | 54.6572i | −1.30805 | + | 2.26561i | ||||
\(583\) | 0.449747 | − | 0.778985i | 0.0186266 | − | 0.0322623i | ||||
\(584\) | 8.44975 | + | 14.6354i | 0.349653 | + | 0.605617i | ||||
\(585\) | 5.17157 | 0.213818 | ||||||||
\(586\) | −29.9350 | + | 51.8490i | −1.23660 | + | 2.14186i | ||||
\(587\) | −20.3431 | −0.839651 | −0.419826 | − | 0.907605i | \(-0.637909\pi\) | ||||
−0.419826 | + | 0.907605i | \(0.637909\pi\) | |||||||
\(588\) | 10.8284 | 0.446557 | ||||||||
\(589\) | 7.32843 | − | 4.92447i | 0.301963 | − | 0.202909i | ||||
\(590\) | 24.3137 | 1.00098 | ||||||||
\(591\) | −8.41421 | −0.346114 | ||||||||
\(592\) | −1.50000 | + | 2.59808i | −0.0616496 | + | 0.106780i | ||||
\(593\) | 21.3137 | 0.875249 | 0.437625 | − | 0.899158i | \(-0.355820\pi\) | ||||
0.437625 | + | 0.899158i | \(0.355820\pi\) | |||||||
\(594\) | −2.62132 | − | 4.54026i | −0.107554 | − | 0.186289i | ||||
\(595\) | 0.207107 | − | 0.358719i | 0.00849055 | − | 0.0147061i | ||||
\(596\) | −1.91421 | + | 3.31552i | −0.0784092 | + | 0.135809i | ||||
\(597\) | −37.6274 | −1.53999 | ||||||||
\(598\) | −8.82843 | − | 15.2913i | −0.361021 | − | 0.625307i | ||||
\(599\) | −17.4497 | − | 30.2238i | −0.712977 | − | 1.23491i | −0.963734 | − | 0.266863i | \(-0.914013\pi\) |
0.250757 | − | 0.968050i | \(-0.419320\pi\) | |||||||
\(600\) | 21.3137 | + | 36.9164i | 0.870129 | + | 1.50711i | ||||
\(601\) | 11.7426 | − | 20.3389i | 0.478992 | − | 0.829639i | −0.520717 | − | 0.853729i | \(-0.674336\pi\) |
0.999710 | + | 0.0240900i | \(0.00766884\pi\) | |||||||
\(602\) | 25.9350 | + | 44.9208i | 1.05703 | + | 1.83083i | ||||
\(603\) | 7.41421 | − | 12.8418i | 0.301930 | − | 0.522958i | ||||
\(604\) | −66.2843 | −2.69707 | ||||||||
\(605\) | 16.4853 | 0.670222 | ||||||||
\(606\) | −24.7279 | + | 42.8300i | −1.00450 | + | 1.73985i | ||||
\(607\) | 2.20711 | + | 3.82282i | 0.0895837 | + | 0.155164i | 0.907335 | − | 0.420408i | \(-0.138113\pi\) |
−0.817752 | + | 0.575571i | \(0.804780\pi\) | |||||||
\(608\) | −1.25736 | + | 2.17781i | −0.0509927 | + | 0.0883219i | ||||
\(609\) | −3.41421 | − | 5.91359i | −0.138351 | − | 0.239631i | ||||
\(610\) | 3.41421 | + | 5.91359i | 0.138237 | + | 0.239434i | ||||
\(611\) | 1.51472 | + | 2.62357i | 0.0612790 | + | 0.106138i | ||||
\(612\) | −1.85786 | −0.0750997 | ||||||||
\(613\) | 5.15685 | − | 8.93193i | 0.208283 | − | 0.360757i | −0.742890 | − | 0.669413i | \(-0.766546\pi\) |
0.951174 | + | 0.308656i | \(0.0998790\pi\) | |||||||
\(614\) | −3.32843 | + | 5.76500i | −0.134324 | + | 0.232657i | ||||
\(615\) | 11.4497 | + | 19.8315i | 0.461698 | + | 0.799685i | ||||
\(616\) | 55.8701 | 2.25107 | ||||||||
\(617\) | −11.6421 | + | 20.1648i | −0.468695 | + | 0.811803i | −0.999360 | − | 0.0357786i | \(-0.988609\pi\) |
0.530665 | + | 0.847582i | \(0.321942\pi\) | |||||||
\(618\) | −70.3553 | −2.83011 | ||||||||
\(619\) | −31.6569 | −1.27240 | −0.636198 | − | 0.771526i | \(-0.719494\pi\) | ||||
−0.636198 | + | 0.771526i | \(0.719494\pi\) | |||||||
\(620\) | 1.44975 | + | 21.2664i | 0.0582233 | + | 0.854080i | ||||
\(621\) | −1.65685 | −0.0664873 | ||||||||
\(622\) | 27.3137 | 1.09518 | ||||||||
\(623\) | 15.0711 | − | 26.1039i | 0.603810 | − | 1.04583i | ||||
\(624\) | −13.2426 | −0.530130 | ||||||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | 4.62132 | − | 8.00436i | 0.184705 | − | 0.319919i | ||||
\(627\) | −10.0355 | + | 17.3821i | −0.400781 | + | 0.694172i | ||||
\(628\) | 56.7696 | 2.26535 | ||||||||
\(629\) | 0.0857864 | + | 0.148586i | 0.00342053 | + | 0.00592453i | ||||
\(630\) | 8.24264 | + | 14.2767i | 0.328395 | + | 0.568796i | ||||
\(631\) | 16.0061 | + | 27.7234i | 0.637193 | + | 1.10365i | 0.986046 | + | 0.166473i | \(0.0532378\pi\) |
−0.348853 | + | 0.937177i | \(0.613429\pi\) | |||||||
\(632\) | −33.6421 | + | 58.2699i | −1.33821 | + | 2.31785i | ||||
\(633\) | 9.15685 | + | 15.8601i | 0.363952 | + | 0.630384i | ||||
\(634\) | −2.62132 | + | 4.54026i | −0.104106 | + | 0.180317i | ||||
\(635\) | −10.8995 | −0.432533 | ||||||||
\(636\) | −1.58579 | −0.0628805 | ||||||||
\(637\) | 1.07107 | − | 1.85514i | 0.0424373 | − | 0.0735035i | ||||
\(638\) | 7.41421 | + | 12.8418i | 0.293532 | + | 0.508412i | ||||
\(639\) | 19.8995 | − | 34.4669i | 0.787212 | − | 1.36349i | ||||
\(640\) | −10.2782 | − | 17.8023i | −0.406281 | − | 0.703699i | ||||
\(641\) | −9.98528 | − | 17.2950i | −0.394395 | − | 0.683112i | 0.598629 | − | 0.801027i | \(-0.295712\pi\) |
−0.993024 | + | 0.117915i | \(0.962379\pi\) | |||||||
\(642\) | −27.9350 | − | 48.3849i | −1.10251 | − | 1.90960i | ||||
\(643\) | 12.6863 | 0.500298 | 0.250149 | − | 0.968207i | \(-0.419520\pi\) | ||||
0.250149 | + | 0.968207i | \(0.419520\pi\) | |||||||
\(644\) | 18.4853 | − | 32.0174i | 0.728422 | − | 1.26166i | ||||
\(645\) | 10.7426 | − | 18.6068i | 0.422991 | − | 0.732642i | ||||
\(646\) | −0.328427 | − | 0.568852i | −0.0129218 | − | 0.0223812i | ||||
\(647\) | −22.6863 | −0.891890 | −0.445945 | − | 0.895060i | \(-0.647132\pi\) | ||||
−0.445945 | + | 0.895060i | \(0.647132\pi\) | |||||||
\(648\) | −20.9350 | + | 36.2605i | −0.822406 | + | 1.42445i | ||||
\(649\) | 52.7990 | 2.07254 | ||||||||
\(650\) | 17.6569 | 0.692559 | ||||||||
\(651\) | −2.20711 | − | 32.3762i | −0.0865033 | − | 1.26892i | ||||
\(652\) | −49.6569 | −1.94471 | ||||||||
\(653\) | 22.1421 | 0.866489 | 0.433244 | − | 0.901276i | \(-0.357369\pi\) | ||||
0.433244 | + | 0.901276i | \(0.357369\pi\) | |||||||
\(654\) | 15.0711 | − | 26.1039i | 0.589325 | − | 1.02074i | ||||
\(655\) | −4.75736 | −0.185885 | ||||||||
\(656\) | −14.2279 | − | 24.6435i | −0.555507 | − | 0.962166i | ||||
\(657\) | −5.41421 | + | 9.37769i | −0.211229 | + | 0.365859i | ||||
\(658\) | −4.82843 | + | 8.36308i | −0.188232 | + | 0.326027i | ||||
\(659\) | 9.65685 | 0.376178 | 0.188089 | − | 0.982152i | \(-0.439771\pi\) | ||||
0.188089 | + | 0.982152i | \(0.439771\pi\) | |||||||
\(660\) | −24.2279 | − | 41.9640i | −0.943071 | − | 1.63345i | ||||
\(661\) | −16.5711 | − | 28.7019i | −0.644540 | − | 1.11638i | −0.984408 | − | 0.175903i | \(-0.943716\pi\) |
0.339868 | − | 0.940473i | \(-0.389618\pi\) | |||||||
\(662\) | 0.914214 | + | 1.58346i | 0.0355319 | + | 0.0615431i | ||||
\(663\) | −0.378680 | + | 0.655892i | −0.0147067 | + | 0.0254728i | ||||
\(664\) | 8.98528 | + | 15.5630i | 0.348697 | + | 0.603960i | ||||
\(665\) | −1.91421 | + | 3.31552i | −0.0742300 | + | 0.128570i | ||||
\(666\) | −6.82843 | −0.264596 | ||||||||
\(667\) | 4.68629 | 0.181454 | ||||||||
\(668\) | 16.3787 | − | 28.3687i | 0.633710 | − | 1.09762i | ||||
\(669\) | 2.08579 | + | 3.61269i | 0.0806412 | + | 0.139675i | ||||
\(670\) | −6.32843 | + | 10.9612i | −0.244488 | + | 0.423466i | ||||
\(671\) | 7.41421 | + | 12.8418i | 0.286223 | + | 0.495752i | ||||
\(672\) | 4.62132 | + | 8.00436i | 0.178271 | + | 0.308775i | ||||
\(673\) | −10.3284 | − | 17.8894i | −0.398132 | − | 0.689584i | 0.595364 | − | 0.803456i | \(-0.297008\pi\) |
−0.993495 | + | 0.113872i | \(0.963675\pi\) | |||||||
\(674\) | 32.1421 | 1.23807 | ||||||||
\(675\) | 0.828427 | − | 1.43488i | 0.0318862 | − | 0.0552285i | ||||
\(676\) | 18.4853 | − | 32.0174i | 0.710972 | − | 1.23144i | ||||
\(677\) | −20.2990 | − | 35.1589i | −0.780154 | − | 1.35127i | −0.931852 | − | 0.362839i | \(-0.881808\pi\) |
0.151698 | − | 0.988427i | \(-0.451526\pi\) | |||||||
\(678\) | 31.1421 | 1.19601 | ||||||||
\(679\) | −13.0711 | + | 22.6398i | −0.501622 | + | 0.868834i | ||||
\(680\) | 0.757359 | 0.0290434 | ||||||||
\(681\) | 37.6274 | 1.44189 | ||||||||
\(682\) | 4.79289 | + | 70.3072i | 0.183529 | + | 2.69220i | ||||
\(683\) | −46.6274 | −1.78415 | −0.892074 | − | 0.451889i | \(-0.850750\pi\) | ||||
−0.892074 | + | 0.451889i | \(0.850750\pi\) | |||||||
\(684\) | 17.1716 | 0.656571 | ||||||||
\(685\) | 3.74264 | − | 6.48244i | 0.142999 | − | 0.247681i | ||||
\(686\) | 47.6274 | 1.81842 | ||||||||
\(687\) | 13.8640 | + | 24.0131i | 0.528943 | + | 0.916156i | ||||
\(688\) | −13.3492 | + | 23.1216i | −0.508935 | + | 0.881501i | ||||
\(689\) | −0.156854 | + | 0.271680i | −0.00597567 | + | 0.0103502i | ||||
\(690\) | −23.3137 | −0.887538 | ||||||||
\(691\) | −7.03553 | − | 12.1859i | −0.267644 | − | 0.463574i | 0.700609 | − | 0.713546i | \(-0.252912\pi\) |
−0.968253 | + | 0.249972i | \(0.919579\pi\) | |||||||
\(692\) | 27.3995 | + | 47.4573i | 1.04157 | + | 1.80406i | ||||
\(693\) | 17.8995 | + | 31.0028i | 0.679946 | + | 1.17770i | ||||
\(694\) | 27.2279 | − | 47.1601i | 1.03356 | − | 1.79017i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.24264 | − | 10.8126i | 0.236627 | − | 0.409849i | ||||
\(697\) | −1.62742 | −0.0616428 | ||||||||
\(698\) | −84.7696 | −3.20857 | ||||||||
\(699\) | −17.8995 | + | 31.0028i | −0.677021 | + | 1.17263i | ||||
\(700\) | 18.4853 | + | 32.0174i | 0.698678 | + | 1.21015i | ||||
\(701\) | −1.74264 | + | 3.01834i | −0.0658186 | + | 0.114001i | −0.897057 | − | 0.441915i | \(-0.854299\pi\) |
0.831238 | + | 0.555916i | \(0.187633\pi\) | |||||||
\(702\) | 0.914214 | + | 1.58346i | 0.0345048 | + | 0.0597640i | ||||
\(703\) | −0.792893 | − | 1.37333i | −0.0299045 | − | 0.0517962i | ||||
\(704\) | −25.7635 | − | 44.6236i | −0.970997 | − | 1.68182i | ||||
\(705\) | 4.00000 | 0.150649 | ||||||||
\(706\) | 3.62132 | − | 6.27231i | 0.136290 | − | 0.236062i | ||||
\(707\) | −10.2426 | + | 17.7408i | −0.385214 | + | 0.667210i | ||||
\(708\) | −46.5416 | − | 80.6125i | −1.74914 | − | 3.02960i | ||||
\(709\) | −5.31371 | −0.199561 | −0.0997803 | − | 0.995009i | \(-0.531814\pi\) | ||||
−0.0997803 | + | 0.995009i | \(0.531814\pi\) | |||||||
\(710\) | −16.9853 | + | 29.4194i | −0.637446 | + | 1.10409i | ||||
\(711\) | −43.1127 | −1.61685 | ||||||||
\(712\) | 55.1127 | 2.06544 | ||||||||
\(713\) | 20.0000 | + | 9.79796i | 0.749006 | + | 0.366936i | ||||
\(714\) | −2.41421 | −0.0903497 | ||||||||
\(715\) | −9.58579 | −0.358488 | ||||||||
\(716\) | 12.9350 | − | 22.4041i | 0.483405 | − | 0.837282i | ||||
\(717\) | 30.7990 | 1.15021 | ||||||||
\(718\) | 32.4706 | + | 56.2407i | 1.21179 | + | 2.09888i | ||||
\(719\) | −3.03553 | + | 5.25770i | −0.113206 | + | 0.196079i | −0.917061 | − | 0.398746i | \(-0.869445\pi\) |
0.803855 | + | 0.594825i | \(0.202779\pi\) | |||||||
\(720\) | −4.24264 | + | 7.34847i | −0.158114 | + | 0.273861i | ||||
\(721\) | −29.1421 | −1.08531 | ||||||||
\(722\) | −19.8995 | − | 34.4669i | −0.740583 | − | 1.28273i | ||||
\(723\) | 29.7635 | + | 51.5518i | 1.10691 | + | 1.91723i | ||||
\(724\) | 19.7426 | + | 34.1953i | 0.733729 | + | 1.27086i | ||||
\(725\) | −2.34315 | + | 4.05845i | −0.0870222 | + | 0.150727i | ||||
\(726\) | −48.0416 | − | 83.2105i | −1.78299 | − | 3.08823i | ||||
\(727\) | 23.4203 | − | 40.5652i | 0.868611 | − | 1.50448i | 0.00519502 | − | 0.999987i | \(-0.498346\pi\) |
0.863416 | − | 0.504492i | \(-0.168320\pi\) | |||||||
\(728\) | −19.4853 | −0.722173 | ||||||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | 4.62132 | − | 8.00436i | 0.171043 | − | 0.296255i | ||||
\(731\) | 0.763456 | + | 1.32234i | 0.0282374 | + | 0.0489087i | ||||
\(732\) | 13.0711 | − | 22.6398i | 0.483121 | − | 0.836789i | ||||
\(733\) | 14.8137 | + | 25.6581i | 0.547157 | + | 0.947703i | 0.998468 | + | 0.0553366i | \(0.0176232\pi\) |
−0.451311 | + | 0.892367i | \(0.649043\pi\) | |||||||
\(734\) | 21.9853 | + | 38.0796i | 0.811492 | + | 1.40554i | ||||
\(735\) | −1.41421 | − | 2.44949i | −0.0521641 | − | 0.0903508i | ||||
\(736\) | −6.34315 | −0.233811 | ||||||||
\(737\) | −13.7426 | + | 23.8030i | −0.506217 | + | 0.876793i | ||||
\(738\) | 32.3848 | − | 56.0921i | 1.19210 | − | 2.06478i | ||||
\(739\) | 3.93503 | + | 6.81567i | 0.144752 | + | 0.250718i | 0.929281 | − | 0.369375i | \(-0.120428\pi\) |
−0.784528 | + | 0.620093i | \(0.787095\pi\) | |||||||
\(740\) | 3.82843 | 0.140736 | ||||||||
\(741\) | 3.50000 | − | 6.06218i | 0.128576 | − | 0.222700i | ||||
\(742\) | −1.00000 | −0.0367112 | ||||||||
\(743\) | −5.65685 | −0.207530 | −0.103765 | − | 0.994602i | \(-0.533089\pi\) | ||||
−0.103765 | + | 0.994602i | \(0.533089\pi\) | |||||||
\(744\) | 49.2487 | − | 33.0936i | 1.80555 | − | 1.21327i | ||||
\(745\) | 1.00000 | 0.0366372 | ||||||||
\(746\) | −24.1421 | −0.883906 | ||||||||
\(747\) | −5.75736 | + | 9.97204i | −0.210651 | + | 0.364858i | ||||
\(748\) | 3.44365 | 0.125912 | ||||||||
\(749\) | −11.5711 | − | 20.0417i | −0.422798 | − | 0.732307i | ||||
\(750\) | 26.2279 | − | 45.4281i | 0.957708 | − | 1.65880i | ||||
\(751\) | 0.621320 | − | 1.07616i | 0.0226723 | − | 0.0392696i | −0.854467 | − | 0.519506i | \(-0.826116\pi\) |
0.877139 | + | 0.480237i | \(0.159449\pi\) | |||||||
\(752\) | −4.97056 | −0.181258 | ||||||||
\(753\) | 4.32843 | + | 7.49706i | 0.157737 | + | 0.273208i | ||||
\(754\) | −2.58579 | − | 4.47871i | −0.0941688 | − | 0.163105i | ||||
\(755\) | 8.65685 | + | 14.9941i | 0.315055 | + | 0.545692i | ||||
\(756\) | −1.91421 | + | 3.31552i | −0.0696193 | + | 0.120584i | ||||
\(757\) | −17.3284 | − | 30.0137i | −0.629812 | − | 1.09087i | −0.987589 | − | 0.157060i | \(-0.949798\pi\) |
0.357777 | − | 0.933807i | \(-0.383535\pi\) | |||||||
\(758\) | −35.4706 | + | 61.4368i | −1.28835 | + | 2.23149i | ||||
\(759\) | −50.6274 | −1.83766 | ||||||||
\(760\) | −7.00000 | −0.253917 | ||||||||
\(761\) | 10.2279 | − | 17.7153i | 0.370762 | − | 0.642178i | −0.618921 | − | 0.785453i | \(-0.712430\pi\) |
0.989683 | + | 0.143275i | \(0.0457633\pi\) | |||||||
\(762\) | 31.7635 | + | 55.0159i | 1.15067 | + | 1.99302i | ||||
\(763\) | 6.24264 | − | 10.8126i | 0.225999 | − | 0.391441i | ||||
\(764\) | 2.10660 | + | 3.64874i | 0.0762142 | + | 0.132007i | ||||
\(765\) | 0.242641 | + | 0.420266i | 0.00877269 | + | 0.0151947i | ||||
\(766\) | 30.0563 | + | 52.0591i | 1.08598 | + | 1.88097i | ||||
\(767\) | −18.4142 | −0.664899 | ||||||||
\(768\) | −36.1777 | + | 62.6616i | −1.30545 | + | 2.26110i | ||||
\(769\) | 13.0563 | − | 22.6143i | 0.470824 | − | 0.815491i | −0.528619 | − | 0.848859i | \(-0.677290\pi\) |
0.999443 | + | 0.0333680i | \(0.0106233\pi\) | |||||||
\(770\) | −15.2782 | − | 26.4626i | −0.550587 | − | 0.953645i | ||||
\(771\) | 0.757359 | 0.0272756 | ||||||||
\(772\) | 40.4706 | − | 70.0971i | 1.45657 | − | 2.52285i | ||||
\(773\) | 18.0000 | 0.647415 | 0.323708 | − | 0.946157i | \(-0.395071\pi\) | ||||
0.323708 | + | 0.946157i | \(0.395071\pi\) | |||||||
\(774\) | −60.7696 | −2.18432 | ||||||||
\(775\) | −18.4853 | + | 12.4215i | −0.664011 | + | 0.446194i | ||||
\(776\) | −47.7990 | −1.71588 | ||||||||
\(777\) | −5.82843 | −0.209094 | ||||||||
\(778\) | 20.6924 | − | 35.8403i | 0.741858 | − | 1.28494i | ||||
\(779\) | 15.0416 | 0.538922 | ||||||||
\(780\) | 8.44975 | + | 14.6354i | 0.302549 | + | 0.524031i | ||||
\(781\) | −36.8848 | + | 63.8863i | −1.31984 | + | 2.28603i | ||||
\(782\) | 0.828427 | − | 1.43488i | 0.0296245 | − | 0.0513111i | ||||
\(783\) | −0.485281 | −0.0173425 | ||||||||
\(784\) | 1.75736 | + | 3.04384i | 0.0627628 | + | 0.108708i | ||||
\(785\) | −7.41421 | − | 12.8418i | −0.264625 | − | 0.458343i | ||||
\(786\) | 13.8640 | + | 24.0131i | 0.494511 | + | 0.856518i | ||||
\(787\) | −19.7929 | + | 34.2823i | −0.705540 | + | 1.22203i | 0.260956 | + | 0.965351i | \(0.415962\pi\) |
−0.966496 | + | 0.256681i | \(0.917371\pi\) | |||||||
\(788\) | −6.67157 | − | 11.5555i | −0.237665 | − | 0.411648i | ||||
\(789\) | −0.828427 | + | 1.43488i | −0.0294928 | + | 0.0510830i | ||||
\(790\) | 36.7990 | 1.30925 | ||||||||
\(791\) | 12.8995 | 0.458653 | ||||||||
\(792\) | −32.7279 | + | 56.6864i | −1.16294 | + | 2.01426i | ||||
\(793\) | −2.58579 | − | 4.47871i | −0.0918240 | − | 0.159044i | ||||
\(794\) | −19.9350 | + | 34.5285i | −0.707468 | + | 1.22537i | ||||
\(795\) | 0.207107 | + | 0.358719i | 0.00734532 | + | 0.0127225i | ||||
\(796\) | −29.8345 | − | 51.6749i | −1.05746 | − | 1.83157i | ||||
\(797\) | 11.2279 | + | 19.4473i | 0.397713 | + | 0.688860i | 0.993443 | − | 0.114325i | \(-0.0364705\pi\) |
−0.595730 | + | 0.803185i | \(0.703137\pi\) | |||||||
\(798\) | 22.3137 | 0.789897 | ||||||||
\(799\) | −0.142136 | + | 0.246186i | −0.00502840 | + | 0.00870944i | ||||
\(800\) | 3.17157 | − | 5.49333i | 0.112132 | − | 0.194218i | ||||
\(801\) | 17.6569 | + | 30.5826i | 0.623874 | + | 1.08058i | ||||
\(802\) | 51.1127 | 1.80485 | ||||||||
\(803\) | 10.0355 | − | 17.3821i | 0.354146 | − | 0.613399i | ||||
\(804\) | 48.4558 | 1.70891 | ||||||||
\(805\) | −9.65685 | −0.340359 | ||||||||
\(806\) | −1.67157 | − | 24.5204i | −0.0588786 | − | 0.863694i | ||||
\(807\) | 76.8406 | 2.70492 | ||||||||
\(808\) | −37.4558 | −1.31769 | ||||||||
\(809\) | 22.9853 | − | 39.8117i | 0.808119 | − | 1.39970i | −0.106045 | − | 0.994361i | \(-0.533819\pi\) |
0.914165 | − | 0.405343i | \(-0.132848\pi\) | |||||||
\(810\) | 22.8995 | 0.804606 | ||||||||
\(811\) | −5.86396 | − | 10.1567i | −0.205912 | − | 0.356649i | 0.744511 | − | 0.667610i | \(-0.232683\pi\) |
−0.950423 | + | 0.310961i | \(0.899349\pi\) | |||||||
\(812\) | 5.41421 | − | 9.37769i | 0.190002 | − | 0.329093i | ||||
\(813\) | −28.1421 | + | 48.7436i | −0.986988 | + | 1.70951i | ||||
\(814\) | 12.6569 | 0.443623 | ||||||||
\(815\) | 6.48528 | + | 11.2328i | 0.227169 | + | 0.393469i | ||||
\(816\) | −0.621320 | − | 1.07616i | −0.0217506 | − | 0.0376731i | ||||
\(817\) | −7.05635 | − | 12.2220i | −0.246870 | − | 0.427592i | ||||
\(818\) | 11.2782 | − | 19.5344i | 0.394332 | − | 0.683003i | ||||
\(819\) | −6.24264 | − | 10.8126i | −0.218136 | − | 0.377822i | ||||
\(820\) | −18.1569 | + | 31.4486i | −0.634065 | + | 1.09823i | ||||
\(821\) | −8.48528 | −0.296138 | −0.148069 | − | 0.988977i | \(-0.547306\pi\) | ||||
−0.148069 | + | 0.988977i | \(0.547306\pi\) | |||||||
\(822\) | −43.6274 | −1.52168 | ||||||||
\(823\) | 3.10660 | − | 5.38079i | 0.108289 | − | 0.187563i | −0.806788 | − | 0.590841i | \(-0.798796\pi\) |
0.915077 | + | 0.403278i | \(0.132129\pi\) | |||||||
\(824\) | −26.6421 | − | 46.1455i | −0.928123 | − | 1.60756i | ||||
\(825\) | 25.3137 | − | 43.8446i | 0.881310 | − | 1.52647i | ||||
\(826\) | −29.3492 | − | 50.8344i | −1.02119 | − | 1.76875i | ||||
\(827\) | −8.55025 | − | 14.8095i | −0.297321 | − | 0.514976i | 0.678201 | − | 0.734877i | \(-0.262760\pi\) |
−0.975522 | + | 0.219901i | \(0.929427\pi\) | |||||||
\(828\) | 21.6569 | + | 37.5108i | 0.752628 | + | 1.30359i | ||||
\(829\) | −46.4264 | −1.61246 | −0.806228 | − | 0.591605i | \(-0.798494\pi\) | ||||
−0.806228 | + | 0.591605i | \(0.798494\pi\) | |||||||
\(830\) | 4.91421 | − | 8.51167i | 0.170575 | − | 0.295444i | ||||
\(831\) | −17.0711 | + | 29.5680i | −0.592189 | + | 1.02570i | ||||
\(832\) | 8.98528 | + | 15.5630i | 0.311509 | + | 0.539549i | ||||
\(833\) | 0.201010 | 0.00696459 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.55635 | −0.296105 | ||||||||
\(836\) | −31.8284 | −1.10081 | ||||||||
\(837\) | −2.07107 | − | 1.01461i | −0.0715866 | − | 0.0350701i | ||||
\(838\) | −67.5980 | −2.33513 | ||||||||
\(839\) | 30.6274 | 1.05738 | 0.528688 | − | 0.848816i | \(-0.322684\pi\) | ||||
0.528688 | + | 0.848816i | \(0.322684\pi\) | |||||||
\(840\) | −12.8640 | + | 22.2810i | −0.443849 | + | 0.768769i | ||||
\(841\) | −27.6274 | −0.952670 | ||||||||
\(842\) | −3.44975 | − | 5.97514i | −0.118886 | − | 0.205917i | ||||
\(843\) | 2.41421 | − | 4.18154i | 0.0831499 | − | 0.144020i | ||||
\(844\) | −14.5208 | + | 25.1508i | −0.499827 | + | 0.865726i | ||||
\(845\) | −9.65685 | −0.332206 | ||||||||
\(846\) | −5.65685 | − | 9.79796i | −0.194487 | − | 0.336861i | ||||
\(847\) | −19.8995 | − | 34.4669i | −0.683755 | − | 1.18430i | ||||
\(848\) | −0.257359 | − | 0.445759i | −0.00883776 | − | 0.0153074i | ||||
\(849\) | −2.82843 | + | 4.89898i | −0.0970714 | + | 0.168133i | ||||
\(850\) | 0.828427 | + | 1.43488i | 0.0284148 | + | 0.0492159i | ||||
\(851\) | 2.00000 | − | 3.46410i | 0.0685591 | − | 0.118748i | ||||
\(852\) | 130.054 | 4.45557 | ||||||||
\(853\) | −32.4853 | −1.11227 | −0.556137 | − | 0.831090i | \(-0.687717\pi\) | ||||
−0.556137 | + | 0.831090i | \(0.687717\pi\) | |||||||
\(854\) | 8.24264 | − | 14.2767i | 0.282057 | − | 0.488538i | ||||
\(855\) | −2.24264 | − | 3.88437i | −0.0766967 | − | 0.132843i | ||||
\(856\) | 21.1569 | − | 36.6447i | 0.723126 | − | 1.25249i | ||||
\(857\) | 1.25736 | + | 2.17781i | 0.0429506 | + | 0.0743926i | 0.886702 | − | 0.462342i | \(-0.152991\pi\) |
−0.843751 | + | 0.536735i | \(0.819658\pi\) | |||||||
\(858\) | 27.9350 | + | 48.3849i | 0.953686 | + | 1.65183i | ||||
\(859\) | 6.30761 | + | 10.9251i | 0.215213 | + | 0.372760i | 0.953338 | − | 0.301904i | \(-0.0976221\pi\) |
−0.738125 | + | 0.674663i | \(0.764289\pi\) | |||||||
\(860\) | 34.0711 | 1.16181 | ||||||||
\(861\) | 27.6421 | − | 47.8776i | 0.942041 | − | 1.63166i | ||||
\(862\) | −30.4706 | + | 52.7766i | −1.03783 | + | 1.79758i | ||||
\(863\) | 19.6924 | + | 34.1082i | 0.670337 | + | 1.16106i | 0.977809 | + | 0.209500i | \(0.0671836\pi\) |
−0.307472 | + | 0.951557i | \(0.599483\pi\) | |||||||
\(864\) | 0.656854 | 0.0223466 | ||||||||
\(865\) | 7.15685 | − | 12.3960i | 0.243340 | − | 0.421478i | ||||
\(866\) | 84.7696 | 2.88059 | ||||||||
\(867\) | 40.9706 | 1.39143 | ||||||||
\(868\) | 42.7132 | − | 28.7019i | 1.44978 | − | 0.974207i | ||||
\(869\) | 79.9117 | 2.71082 | ||||||||
\(870\) | −6.82843 | −0.231505 | ||||||||
\(871\) | 4.79289 | − | 8.30153i | 0.162401 | − | 0.281287i | ||||
\(872\) | 22.8284 | 0.773068 | ||||||||
\(873\) | −15.3137 | − | 26.5241i | −0.518291 | − | 0.897705i | ||||
\(874\) | −7.65685 | + | 13.2621i | −0.258997 | + | 0.448596i | ||||
\(875\) | 10.8640 | − | 18.8169i | 0.367269 | − | 0.636128i | ||||
\(876\) | −35.3848 | −1.19554 | ||||||||
\(877\) | −24.0858 | − | 41.7178i | −0.813319 | − | 1.40871i | −0.910529 | − | 0.413446i | \(-0.864325\pi\) |
0.0972093 | − | 0.995264i | \(-0.469008\pi\) | |||||||
\(878\) | −14.5711 | − | 25.2378i | −0.491750 | − | 0.851735i | ||||
\(879\) | −29.9350 | − | 51.8490i | −1.00968 | − | 1.74882i | ||||
\(880\) | 7.86396 | − | 13.6208i | 0.265094 | − | 0.459156i | ||||
\(881\) | −17.1569 | − | 29.7165i | −0.578029 | − | 1.00118i | −0.995705 | − | 0.0925798i | \(-0.970489\pi\) |
0.417676 | − | 0.908596i | \(-0.362845\pi\) | |||||||
\(882\) | −4.00000 | + | 6.92820i | −0.134687 | + | 0.233285i | ||||
\(883\) | 26.2843 | 0.884536 | 0.442268 | − | 0.896883i | \(-0.354174\pi\) | ||||
0.442268 | + | 0.896883i | \(0.354174\pi\) | |||||||
\(884\) | −1.20101 | −0.0403943 | ||||||||
\(885\) | −12.1569 | + | 21.0563i | −0.408648 | + | 0.707799i | ||||
\(886\) | −15.9853 | − | 27.6873i | −0.537036 | − | 0.930174i | ||||
\(887\) | −26.6630 | + | 46.1816i | −0.895254 | + | 1.55063i | −0.0617647 | + | 0.998091i | \(0.519673\pi\) |
−0.833490 | + | 0.552535i | \(0.813661\pi\) | |||||||
\(888\) | −5.32843 | − | 9.22911i | −0.178810 | − | 0.309709i | ||||
\(889\) | 13.1569 | + | 22.7883i | 0.441267 | + | 0.764296i | ||||
\(890\) | −15.0711 | − | 26.1039i | −0.505183 | − | 0.875003i | ||||
\(891\) | 49.7279 | 1.66595 | ||||||||
\(892\) | −3.30761 | + | 5.72895i | −0.110747 | + | 0.191819i | ||||
\(893\) | 1.31371 | − | 2.27541i | 0.0439616 | − | 0.0761437i | ||||
\(894\) | −2.91421 | − | 5.04757i | −0.0974659 | − | 0.168816i | ||||
\(895\) | −6.75736 | −0.225874 | ||||||||
\(896\) | −24.8137 | + | 42.9786i | −0.828968 | + | 1.43581i | ||||
\(897\) | 17.6569 | 0.589545 | ||||||||
\(898\) | −11.1716 | −0.372800 | ||||||||
\(899\) | 5.85786 | + | 2.86976i | 0.195371 | + | 0.0957117i | ||||
\(900\) | −43.3137 | −1.44379 | ||||||||
\(901\) | −0.0294373 | −0.000980697 | ||||||||
\(902\) | −60.0269 | + | 103.970i | −1.99868 | + | 3.46181i | ||||
\(903\) | −51.8701 | −1.72613 | ||||||||
\(904\) | 11.7929 | + | 20.4259i | 0.392226 | + | 0.679355i | ||||
\(905\) | 5.15685 | − | 8.93193i | 0.171420 | − | 0.296908i | ||||
\(906\) | 50.4558 | − | 87.3921i | 1.67628 | − | 2.90341i | ||||
\(907\) | 55.3137 | 1.83666 | 0.918331 | − | 0.395814i | \(-0.129537\pi\) | ||||
0.918331 | + | 0.395814i | \(0.129537\pi\) | |||||||
\(908\) | 29.8345 | + | 51.6749i | 0.990093 | + | 1.71489i | ||||
\(909\) | −12.0000 | − | 20.7846i | −0.398015 | − | 0.689382i | ||||
\(910\) | 5.32843 | + | 9.22911i | 0.176636 | + | 0.305942i | ||||
\(911\) | −24.5208 | + | 42.4713i | −0.812411 | + | 1.40714i | 0.0987614 | + | 0.995111i | \(0.468512\pi\) |
−0.911172 | + | 0.412026i | \(0.864821\pi\) | |||||||
\(912\) | 5.74264 | + | 9.94655i | 0.190158 | + | 0.329363i | ||||
\(913\) | 10.6716 | − | 18.4837i | 0.353178 | − | 0.611721i | ||||
\(914\) | −75.1127 | −2.48451 | ||||||||
\(915\) | −6.82843 | −0.225741 | ||||||||
\(916\) | −21.9853 | + | 38.0796i | −0.726414 | + | 1.25819i | ||||
\(917\) | 5.74264 | + | 9.94655i | 0.189639 | + | 0.328464i | ||||
\(918\) | −0.0857864 | + | 0.148586i | −0.00283137 | + | 0.00490408i | ||||
\(919\) | 7.55025 | + | 13.0774i | 0.249060 | + | 0.431384i | 0.963265 | − | 0.268552i | \(-0.0865451\pi\) |
−0.714205 | + | 0.699936i | \(0.753212\pi\) | |||||||
\(920\) | −8.82843 | − | 15.2913i | −0.291065 | − | 0.504139i | ||||
\(921\) | −3.32843 | − | 5.76500i | −0.109675 | − | 0.189963i | ||||
\(922\) | −63.1127 | −2.07851 | ||||||||
\(923\) | 12.8640 | − | 22.2810i | 0.423422 | − | 0.733389i | ||||
\(924\) | −58.4914 | + | 101.310i | −1.92423 | + | 3.33286i | ||||
\(925\) | 2.00000 | + | 3.46410i | 0.0657596 | + | 0.113899i | ||||
\(926\) | −60.2843 | −1.98106 | ||||||||
\(927\) | 17.0711 | − | 29.5680i | 0.560687 | − | 0.971139i | ||||
\(928\) | −1.85786 | −0.0609874 | ||||||||
\(929\) | 24.4853 | 0.803336 | 0.401668 | − | 0.915785i | \(-0.368431\pi\) | ||||
0.401668 | + | 0.915785i | \(0.368431\pi\) | |||||||
\(930\) | −29.1421 | − | 14.2767i | −0.955608 | − | 0.468151i | ||||
\(931\) | −1.85786 | −0.0608890 | ||||||||
\(932\) | −56.7696 | −1.85955 | ||||||||
\(933\) | −13.6569 | + | 23.6544i | −0.447105 | + | 0.774409i | ||||
\(934\) | 19.3137 | 0.631964 | ||||||||
\(935\) | −0.449747 | − | 0.778985i | −0.0147083 | − | 0.0254755i | ||||
\(936\) | 11.4142 | − | 19.7700i | 0.373085 | − | 0.646203i | ||||
\(937\) | −19.1569 | + | 33.1806i | −0.625827 | + | 1.08396i | 0.362553 | + | 0.931963i | \(0.381905\pi\) |
−0.988380 | + | 0.152001i | \(0.951428\pi\) | |||||||
\(938\) | 30.5563 | 0.997700 | ||||||||
\(939\) | 4.62132 | + | 8.00436i | 0.150811 | + | 0.261212i | ||||
\(940\) | 3.17157 | + | 5.49333i | 0.103445 | + | 0.179173i | ||||
\(941\) | 17.5000 | + | 30.3109i | 0.570484 | + | 0.988107i | 0.996516 | + | 0.0833989i | \(0.0265776\pi\) |
−0.426033 | + | 0.904708i | \(0.640089\pi\) | |||||||
\(942\) | −43.2132 | + | 74.8475i | −1.40796 | + | 2.43866i | ||||
\(943\) | 18.9706 | + | 32.8580i | 0.617767 | + | 1.07000i | ||||
\(944\) | 15.1066 | − | 26.1654i | 0.491678 | − | 0.851611i | ||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | 112.640 | 3.66223 | ||||||||
\(947\) | −19.4497 | + | 33.6880i | −0.632032 | + | 1.09471i | 0.355104 | + | 0.934827i | \(0.384445\pi\) |
−0.987136 | + | 0.159884i | \(0.948888\pi\) | |||||||
\(948\) | −70.4411 | − | 122.008i | −2.28782 | − | 3.96262i | ||||
\(949\) | −3.50000 | + | 6.06218i | −0.113615 | + | 0.196787i | ||||
\(950\) | −7.65685 | − | 13.2621i | −0.248421 | − | 0.430278i | ||||
\(951\) | −2.62132 | − | 4.54026i | −0.0850021 | − | 0.147228i | ||||
\(952\) | −0.914214 | − | 1.58346i | −0.0296298 | − | 0.0513204i | ||||
\(953\) | 20.4853 | 0.663583 | 0.331792 | − | 0.943353i | \(-0.392347\pi\) | ||||
0.331792 | + | 0.943353i | \(0.392347\pi\) | |||||||
\(954\) | 0.585786 | − | 1.01461i | 0.0189655 | − | 0.0328493i | ||||
\(955\) | 0.550253 | − | 0.953065i | 0.0178058 | − | 0.0308405i | ||||
\(956\) | 24.4203 | + | 42.2972i | 0.789809 | + | 1.36799i | ||||
\(957\) | −14.8284 | −0.479335 | ||||||||
\(958\) | 11.7426 | − | 20.3389i | 0.379387 | − | 0.657118i | ||||
\(959\) | −18.0711 | −0.583545 | ||||||||
\(960\) | 23.7279 | 0.765815 | ||||||||
\(961\) | 19.0000 | + | 24.4949i | 0.612903 | + | 0.790158i | ||||
\(962\) | −4.41421 | −0.142320 | ||||||||
\(963\) | 27.1127 | 0.873694 | ||||||||
\(964\) | −47.1985 | + | 81.7502i | −1.52016 | + | 2.63300i | ||||
\(965\) | −21.1421 | −0.680589 | ||||||||
\(966\) | 28.1421 | + | 48.7436i | 0.905458 | + | 1.56830i | ||||
\(967\) | 23.2782 | − | 40.3190i | 0.748576 | − | 1.29657i | −0.199930 | − | 0.979810i | \(-0.564071\pi\) |
0.948505 | − | 0.316761i | \(-0.102595\pi\) | |||||||
\(968\) | 36.3848 | − | 63.0203i | 1.16945 | − | 2.02555i | ||||
\(969\) | 0.656854 | 0.0211012 | ||||||||
\(970\) | 13.0711 | + | 22.6398i | 0.419687 | + | 0.726919i | ||||
\(971\) | −29.3492 | − | 50.8344i | −0.941862 | − | 1.63135i | −0.761915 | − | 0.647676i | \(-0.775741\pi\) |
−0.179947 | − | 0.983676i | \(-0.557592\pi\) | |||||||
\(972\) | −41.4558 | − | 71.8036i | −1.32970 | − | 2.30310i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −20.9853 | − | 36.3476i | −0.672412 | − | 1.16465i | ||||
\(975\) | −8.82843 | + | 15.2913i | −0.282736 | + | 0.489713i | ||||
\(976\) | 8.48528 | 0.271607 | ||||||||
\(977\) | 16.4853 | 0.527411 | 0.263705 | − | 0.964603i | \(-0.415055\pi\) | ||||
0.263705 | + | 0.964603i | \(0.415055\pi\) | |||||||
\(978\) | 37.7990 | − | 65.4698i | 1.20868 | − | 2.09349i | ||||
\(979\) | −32.7279 | − | 56.6864i | −1.04599 | − | 1.81171i | ||||
\(980\) | 2.24264 | − | 3.88437i | 0.0716385 | − | 0.124082i | ||||
\(981\) | 7.31371 | + | 12.6677i | 0.233509 | + | 0.404449i | ||||
\(982\) | 5.32843 | + | 9.22911i | 0.170037 | + | 0.294513i | ||||
\(983\) | −24.4203 | − | 42.2972i | −0.778887 | − | 1.34907i | −0.932584 | − | 0.360954i | \(-0.882451\pi\) |
0.153697 | − | 0.988118i | \(-0.450882\pi\) | |||||||
\(984\) | 101.083 | 3.22242 | ||||||||
\(985\) | −1.74264 | + | 3.01834i | −0.0555251 | + | 0.0961724i | ||||
\(986\) | 0.242641 | − | 0.420266i | 0.00772725 | − | 0.0133840i | ||||
\(987\) | −4.82843 | − | 8.36308i | −0.153691 | − | 0.266200i | ||||
\(988\) | 11.1005 | 0.353154 | ||||||||
\(989\) | 17.7990 | − | 30.8288i | 0.565975 | − | 0.980297i | ||||
\(990\) | 35.7990 | 1.13777 | ||||||||
\(991\) | −19.9411 | −0.633451 | −0.316725 | − | 0.948517i | \(-0.602583\pi\) | ||||
−0.316725 | + | 0.948517i | \(0.602583\pi\) | |||||||
\(992\) | −7.92893 | − | 3.88437i | −0.251744 | − | 0.123329i | ||||
\(993\) | −1.82843 | −0.0580234 | ||||||||
\(994\) | 82.0122 | 2.60127 | ||||||||
\(995\) | −7.79289 | + | 13.4977i | −0.247051 | + | 0.427905i | ||||
\(996\) | −37.6274 | −1.19227 | ||||||||
\(997\) | 23.2990 | + | 40.3550i | 0.737886 | + | 1.27806i | 0.953445 | + | 0.301566i | \(0.0975093\pi\) |
−0.215559 | + | 0.976491i | \(0.569157\pi\) | |||||||
\(998\) | 48.5416 | − | 84.0766i | 1.53656 | − | 2.66140i | ||||
\(999\) | −0.207107 | + | 0.358719i | −0.00655257 | + | 0.0113494i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))