Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [56,2,Mod(9,56)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(56, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("56.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 56 = 2^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 56.i (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: | \(0.447162251319\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 25.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 56.25 |
Dual form | 56.2.i.a.9.1 |
$q$-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 \(\left(\mathbb{Z}/56\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) | \(29\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.50000 | + | 2.59808i | −0.866025 | + | 1.50000i | 1.00000i | \(0.5\pi\) | ||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | 0.955901 | − | 0.293691i | \(-0.0948835\pi\) |
−0.732294 | + | 0.680989i | \(0.761550\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | − | 1.73205i | 0.755929 | − | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | − | 5.19615i | −1.00000 | − | 1.73205i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | −0.780750 | − | 0.624844i | \(-0.785163\pi\) |
0.931505 | + | 0.363727i | \(0.118496\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.00000 | −0.774597 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.50000 | + | 2.59808i | −0.363803 | + | 0.630126i | −0.988583 | − | 0.150675i | \(-0.951855\pi\) |
0.624780 | + | 0.780801i | \(0.285189\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.50000 | − | 4.33013i | −0.573539 | − | 0.993399i | −0.996199 | − | 0.0871106i | \(-0.972237\pi\) |
0.422659 | − | 0.906289i | \(-0.361097\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.50000 | + | 7.79423i | 0.327327 | + | 1.70084i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.50000 | + | 2.59808i | 0.312772 | + | 0.541736i | 0.978961 | − | 0.204046i | \(-0.0654092\pi\) |
−0.666190 | + | 0.745782i | \(0.732076\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | − | 3.46410i | 0.400000 | − | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.00000 | 1.73205 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.500000 | − | 0.866025i | 0.0898027 | − | 0.155543i | −0.817625 | − | 0.575751i | \(-0.804710\pi\) |
0.907428 | + | 0.420208i | \(0.138043\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.50000 | + | 2.59808i | 0.261116 | + | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.50000 | + | 0.866025i | 0.422577 | + | 0.146385i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.50000 | + | 4.33013i | 0.410997 | + | 0.711868i | 0.994999 | − | 0.0998840i | \(-0.0318472\pi\) |
−0.584002 | + | 0.811752i | \(0.698514\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.00000 | + | 5.19615i | −0.480384 | + | 0.832050i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.0000 | −1.56174 | −0.780869 | − | 0.624695i | \(-0.785223\pi\) | ||||
−0.780869 | + | 0.624695i | \(0.785223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.00000 | − | 5.19615i | 0.447214 | − | 0.774597i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.500000 | − | 0.866025i | −0.0729325 | − | 0.126323i | 0.827253 | − | 0.561830i | \(-0.189902\pi\) |
−0.900185 | + | 0.435507i | \(0.856569\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.50000 | − | 7.79423i | −0.630126 | − | 1.09141i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.50000 | − | 7.79423i | 0.618123 | − | 1.07062i | −0.371706 | − | 0.928351i | \(-0.621227\pi\) |
0.989828 | − | 0.142269i | \(-0.0454398\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 15.0000 | 1.98680 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.50000 | + | 2.59808i | −0.195283 | + | 0.338241i | −0.946993 | − | 0.321253i | \(-0.895896\pi\) |
0.751710 | + | 0.659494i | \(0.229229\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.50000 | − | 2.59808i | −0.192055 | − | 0.332650i | 0.753876 | − | 0.657017i | \(-0.228182\pi\) |
−0.945931 | + | 0.324367i | \(0.894849\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −15.0000 | − | 5.19615i | −1.88982 | − | 0.654654i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | + | 1.73205i | 0.124035 | + | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.50000 | + | 9.52628i | −0.671932 | + | 1.16382i | 0.305424 | + | 0.952217i | \(0.401202\pi\) |
−0.977356 | + | 0.211604i | \(0.932131\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.00000 | −1.08347 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.0000 | 1.89885 | 0.949425 | − | 0.313993i | \(-0.101667\pi\) | ||||
0.949425 | + | 0.313993i | \(0.101667\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.50000 | + | 6.06218i | −0.409644 | + | 0.709524i | −0.994850 | − | 0.101361i | \(-0.967680\pi\) |
0.585206 | + | 0.810885i | \(0.301014\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.00000 | + | 10.3923i | 0.692820 | + | 1.20000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.500000 | − | 2.59808i | −0.0569803 | − | 0.296078i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.50000 | + | 9.52628i | 0.618798 | + | 1.07179i | 0.989705 | + | 0.143120i | \(0.0457135\pi\) |
−0.370907 | + | 0.928670i | \(0.620953\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.00000 | −0.439057 | −0.219529 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219529 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.00000 | −0.325396 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.00000 | − | 15.5885i | 0.964901 | − | 1.67126i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.50000 | + | 7.79423i | 0.476999 | + | 0.826187i | 0.999653 | − | 0.0263586i | \(-0.00839118\pi\) |
−0.522654 | + | 0.852545i | \(0.675058\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | − | 3.46410i | 0.419314 | − | 0.363137i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.50000 | + | 2.59808i | 0.155543 | + | 0.269408i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.50000 | − | 4.33013i | 0.256495 | − | 0.444262i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000 | 0.609208 | 0.304604 | − | 0.952479i | \(-0.401476\pi\) | ||||
0.304604 | + | 0.952479i | \(0.401476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.00000 | −0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.50000 | − | 11.2583i | 0.646774 | − | 1.12025i | −0.337115 | − | 0.941464i | \(-0.609451\pi\) |
0.983889 | − | 0.178782i | \(-0.0572157\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.50000 | − | 4.33013i | −0.246332 | − | 0.426660i | 0.716173 | − | 0.697923i | \(-0.245892\pi\) |
−0.962505 | + | 0.271263i | \(0.912559\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.00000 | + | 5.19615i | −0.585540 | + | 0.507093i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.50000 | + | 2.59808i | 0.145010 | + | 0.251166i | 0.929377 | − | 0.369132i | \(-0.120345\pi\) |
−0.784366 | + | 0.620298i | \(0.787012\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.50000 | + | 9.52628i | −0.526804 | + | 0.912452i | 0.472708 | + | 0.881219i | \(0.343277\pi\) |
−0.999512 | + | 0.0312328i | \(0.990057\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.0000 | −1.42374 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.0000 | −0.940721 | −0.470360 | − | 0.882474i | \(-0.655876\pi\) | ||||
−0.470360 | + | 0.882474i | \(0.655876\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.50000 | + | 2.59808i | −0.139876 | + | 0.242272i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.00000 | − | 10.3923i | −0.554700 | − | 0.960769i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.50000 | + | 7.79423i | 0.137505 | + | 0.714496i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | + | 8.66025i | 0.454545 | + | 0.787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.0000 | − | 25.9808i | 1.35250 | − | 2.34261i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.00000 | − | 10.3923i | 0.528271 | − | 0.914991i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.50000 | − | 14.7224i | −0.742648 | − | 1.28630i | −0.951285 | − | 0.308312i | \(-0.900236\pi\) |
0.208637 | − | 0.977993i | \(-0.433097\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.5000 | − | 4.33013i | −1.08389 | − | 0.375470i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.50000 | + | 7.79423i | 0.387298 | + | 0.670820i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.50000 | + | 2.59808i | −0.128154 | + | 0.221969i | −0.922961 | − | 0.384893i | \(-0.874238\pi\) |
0.794808 | + | 0.606861i | \(0.207572\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | 0.252646 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | − | 1.73205i | 0.0836242 | − | 0.144841i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.00000 | − | 5.19615i | −0.249136 | − | 0.431517i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 16.5000 | + | 12.9904i | 1.36090 | + | 1.07143i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.50000 | − | 12.9904i | −0.614424 | − | 1.06421i | −0.990485 | − | 0.137619i | \(-0.956055\pi\) |
0.376061 | − | 0.926595i | \(-0.377278\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.50000 | + | 12.9904i | −0.610341 | + | 1.05714i | 0.380841 | + | 0.924640i | \(0.375634\pi\) |
−0.991183 | + | 0.132502i | \(0.957699\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18.0000 | 1.45521 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.00000 | 0.0803219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.50000 | + | 12.9904i | −0.598565 | + | 1.03675i | 0.394468 | + | 0.918910i | \(0.370929\pi\) |
−0.993033 | + | 0.117836i | \(0.962404\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.5000 | + | 23.3827i | 1.07062 | + | 1.85437i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.50000 | + | 2.59808i | 0.591083 | + | 0.204757i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.50000 | − | 7.79423i | −0.352467 | − | 0.610491i | 0.634214 | − | 0.773158i | \(-0.281324\pi\) |
−0.986681 | + | 0.162667i | \(0.947991\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.50000 | + | 2.59808i | −0.116775 | + | 0.202260i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.0000 | −1.54765 | −0.773823 | − | 0.633402i | \(-0.781658\pi\) | ||||
−0.773823 | + | 0.633402i | \(0.781658\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −15.0000 | + | 25.9808i | −1.14708 | + | 1.98680i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.5000 | + | 18.1865i | 0.798300 | + | 1.38270i | 0.920722 | + | 0.390218i | \(0.127601\pi\) |
−0.122422 | + | 0.992478i | \(0.539066\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00000 | − | 10.3923i | −0.151186 | − | 0.785584i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.50000 | − | 7.79423i | −0.338241 | − | 0.585850i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.500000 | − | 0.866025i | 0.0373718 | − | 0.0647298i | −0.846735 | − | 0.532016i | \(-0.821435\pi\) |
0.884106 | + | 0.467286i | \(0.154768\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.0000 | 1.63525 | 0.817624 | − | 0.575753i | \(-0.195291\pi\) | ||||
0.817624 | + | 0.575753i | \(0.195291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.00000 | 0.665299 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.50000 | + | 4.33013i | −0.183804 | + | 0.318357i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.50000 | + | 2.59808i | 0.109691 | + | 0.189990i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18.0000 | − | 15.5885i | 1.30931 | − | 1.13389i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.50000 | − | 14.7224i | −0.615038 | − | 1.06528i | −0.990378 | − | 0.138390i | \(-0.955807\pi\) |
0.375339 | − | 0.926887i | \(-0.377526\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.50000 | − | 4.33013i | 0.179954 | − | 0.311689i | −0.761911 | − | 0.647682i | \(-0.775738\pi\) |
0.941865 | + | 0.335993i | \(0.109072\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.00000 | −0.429669 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.50000 | − | 7.79423i | 0.318997 | − | 0.552518i | −0.661282 | − | 0.750137i | \(-0.729987\pi\) |
0.980279 | + | 0.197619i | \(0.0633208\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.5000 | − | 28.5788i | −1.16382 | − | 2.01580i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.0000 | + | 10.3923i | −0.842235 | + | 0.729397i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.00000 | − | 8.66025i | −0.349215 | − | 0.604858i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.00000 | − | 15.5885i | 0.625543 | − | 1.08347i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.00000 | −0.345857 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −24.0000 | + | 41.5692i | −1.64445 | + | 2.84828i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.00000 | − | 3.46410i | −0.136399 | − | 0.236250i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.500000 | − | 2.59808i | −0.0339422 | − | 0.176369i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.5000 | − | 18.1865i | −0.709524 | − | 1.22893i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | + | 5.19615i | −0.201802 | + | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.0000 | 1.60716 | 0.803579 | − | 0.595198i | \(-0.202926\pi\) | ||||
0.803579 | + | 0.595198i | \(0.202926\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −24.0000 | −1.60000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.50000 | + | 6.06218i | −0.232303 | + | 0.402361i | −0.958485 | − | 0.285141i | \(-0.907959\pi\) |
0.726182 | + | 0.687502i | \(0.241293\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.50000 | − | 6.06218i | −0.231287 | − | 0.400600i | 0.726900 | − | 0.686743i | \(-0.240960\pi\) |
−0.958187 | + | 0.286143i | \(0.907627\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.50000 | + | 2.59808i | 0.493464 | + | 0.170941i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.50000 | + | 11.2583i | 0.425829 | + | 0.737558i | 0.996497 | − | 0.0836229i | \(-0.0266491\pi\) |
−0.570668 | + | 0.821181i | \(0.693316\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.500000 | − | 0.866025i | 0.0326164 | − | 0.0564933i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −33.0000 | −2.14358 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.00000 | −0.258738 | −0.129369 | − | 0.991596i | \(-0.541295\pi\) | ||||
−0.129369 | + | 0.991596i | \(0.541295\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.50000 | − | 14.7224i | 0.547533 | − | 0.948355i | −0.450910 | − | 0.892570i | \(-0.648900\pi\) |
0.998443 | − | 0.0557856i | \(-0.0177663\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.50000 | − | 2.59808i | 0.415270 | − | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.00000 | − | 8.66025i | −0.318142 | − | 0.551039i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.00000 | − | 10.3923i | 0.380235 | − | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.0000 | 1.51487 | 0.757433 | − | 0.652913i | \(-0.226453\pi\) | ||||
0.757433 | + | 0.652913i | \(0.226453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.00000 | 0.188608 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.50000 | − | 7.79423i | 0.281801 | − | 0.488094i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.50000 | + | 11.2583i | 0.405459 | + | 0.702275i | 0.994375 | − | 0.105919i | \(-0.0337784\pi\) |
−0.588916 | + | 0.808194i | \(0.700445\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.5000 | + | 4.33013i | 0.776712 | + | 0.269061i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.0000 | + | 31.1769i | 1.11417 | + | 1.92980i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.50000 | + | 2.59808i | −0.0924940 | + | 0.160204i | −0.908560 | − | 0.417755i | \(-0.862817\pi\) |
0.816066 | + | 0.577959i | \(0.196151\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.00000 | 0.552866 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −27.0000 | −1.65237 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.50000 | − | 14.7224i | 0.518254 | − | 0.897643i | −0.481521 | − | 0.876435i | \(-0.659915\pi\) |
0.999775 | − | 0.0212079i | \(-0.00675120\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.50000 | + | 2.59808i | 0.0911185 | + | 0.157822i | 0.907982 | − | 0.419009i | \(-0.137622\pi\) |
−0.816864 | + | 0.576831i | \(0.804289\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.00000 | + | 15.5885i | 0.181568 | + | 0.943456i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.00000 | − | 3.46410i | −0.120605 | − | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.50000 | + | 6.06218i | −0.210295 | + | 0.364241i | −0.951807 | − | 0.306699i | \(-0.900776\pi\) |
0.741512 | + | 0.670940i | \(0.234109\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.00000 | −0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0000 | −1.07379 | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.50000 | − | 14.7224i | 0.505273 | − | 0.875158i | −0.494709 | − | 0.869059i | \(-0.664725\pi\) |
0.999981 | − | 0.00609896i | \(-0.00194137\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.50000 | + | 12.9904i | 0.444262 | + | 0.769484i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.0000 | + | 17.3205i | −1.18056 | + | 1.02240i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.00000 | + | 15.5885i | −0.527589 | + | 0.913812i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.00000 | −0.174667 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.50000 | − | 7.79423i | 0.261116 | − | 0.452267i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.00000 | + | 5.19615i | 0.173494 | + | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.00000 | + | 6.92820i | −0.461112 | + | 0.399335i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.5000 | + | 33.7750i | 1.12025 | + | 1.94032i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.50000 | − | 2.59808i | 0.0858898 | − | 0.148765i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.00000 | 0.228292 | 0.114146 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114146 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.0000 | 0.853320 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.50000 | + | 9.52628i | −0.311876 | + | 0.540186i | −0.978769 | − | 0.204968i | \(-0.934291\pi\) |
0.666892 | + | 0.745154i | \(0.267624\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.5000 | − | 26.8468i | −0.876112 | − | 1.51747i | −0.855574 | − | 0.517681i | \(-0.826795\pi\) |
−0.0205381 | − | 0.999789i | \(-0.506538\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.00000 | − | 15.5885i | −0.169031 | − | 0.878310i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.5000 | − | 23.3827i | −0.758236 | − | 1.31330i | −0.943750 | − | 0.330661i | \(-0.892728\pi\) |
0.185514 | − | 0.982642i | \(-0.440605\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.00000 | + | 5.19615i | −0.167968 | + | 0.290929i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.00000 | −0.502331 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.0000 | 0.834622 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.00000 | − | 6.92820i | 0.221880 | − | 0.384308i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.5000 | − | 28.5788i | −0.912452 | − | 1.58041i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.50000 | − | 0.866025i | −0.137829 | − | 0.0477455i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.50000 | + | 6.06218i | 0.192377 | + | 0.333207i | 0.946038 | − | 0.324057i | \(-0.105047\pi\) |
−0.753660 | + | 0.657264i | \(0.771714\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.0000 | − | 25.9808i | 0.821995 | − | 1.42374i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.0000 | −0.600994 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.0000 | − | 25.9808i | 0.814688 | − | 1.41108i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.500000 | − | 0.866025i | −0.0270765 | − | 0.0468979i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.50000 | − | 7.79423i | −0.242272 | − | 0.419627i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.50000 | + | 2.59808i | −0.0805242 | + | 0.139472i | −0.903475 | − | 0.428640i | \(-0.858993\pi\) |
0.822951 | + | 0.568112i | \(0.192326\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.00000 | −0.321173 | −0.160586 | − | 0.987022i | \(-0.551338\pi\) | ||||
−0.160586 | + | 0.987022i | \(0.551338\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.0000 | 0.960769 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.50000 | − | 4.33013i | 0.133062 | − | 0.230469i | −0.791794 | − | 0.610789i | \(-0.790853\pi\) |
0.924855 | + | 0.380319i | \(0.124186\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.00000 | + | 13.8564i | 0.424596 | + | 0.735422i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −22.5000 | − | 7.79423i | −1.19083 | − | 0.412514i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.50000 | + | 12.9904i | 0.395835 | + | 0.685606i | 0.993207 | − | 0.116358i | \(-0.0371219\pi\) |
−0.597372 | + | 0.801964i | \(0.703789\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | + | 5.19615i | −0.157895 | + | 0.273482i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −30.0000 | −1.57459 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.00000 | −0.366397 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.50000 | + | 16.4545i | −0.495896 | + | 0.858917i | −0.999989 | − | 0.00473247i | \(-0.998494\pi\) |
0.504093 | + | 0.863649i | \(0.331827\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 30.0000 | + | 51.9615i | 1.56174 | + | 2.70501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.50000 | − | 23.3827i | −0.233628 | − | 1.21397i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.50000 | − | 16.4545i | −0.491891 | − | 0.851981i | 0.508065 | − | 0.861319i | \(-0.330361\pi\) |
−0.999956 | + | 0.00933789i | \(0.997028\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.5000 | + | 23.3827i | −0.697137 | + | 1.20748i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.0000 | −0.821865 | −0.410932 | − | 0.911666i | \(-0.634797\pi\) | ||||
−0.410932 | + | 0.911666i | \(0.634797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.0000 | − | 20.7846i | 0.614779 | − | 1.06483i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.50000 | − | 7.79423i | −0.229939 | − | 0.398266i | 0.727851 | − | 0.685736i | \(-0.240519\pi\) |
−0.957790 | + | 0.287469i | \(0.907186\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.00000 | − | 1.73205i | 0.101929 | − | 0.0882735i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.0000 | + | 20.7846i | 0.609994 | + | 1.05654i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.50000 | + | 16.4545i | −0.481669 | + | 0.834275i | −0.999779 | − | 0.0210389i | \(-0.993303\pi\) |
0.518110 | + | 0.855314i | \(0.326636\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | −0.455150 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 51.0000 | 2.57261 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.50000 | + | 9.52628i | −0.276735 | + | 0.479319i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.50000 | + | 14.7224i | 0.426603 | + | 0.738898i | 0.996569 | − | 0.0827707i | \(-0.0263769\pi\) |
−0.569966 | + | 0.821668i | \(0.693044\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 30.0000 | − | 25.9808i | 1.50188 | − | 1.30066i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.50000 | − | 2.59808i | −0.0749064 | − | 0.129742i | 0.826139 | − | 0.563466i | \(-0.190532\pi\) |
−0.901046 | + | 0.433724i | \(0.857199\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.00000 | − | 1.73205i | 0.0498135 | − | 0.0862796i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.00000 | −0.447214 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.00000 | 0.247841 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.50000 | + | 16.4545i | −0.469745 | + | 0.813622i | −0.999402 | − | 0.0345902i | \(-0.988987\pi\) |
0.529657 | + | 0.848212i | \(0.322321\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.50000 | − | 7.79423i | −0.221969 | − | 0.384461i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.50000 | + | 7.79423i | 0.0738102 | + | 0.383529i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.00000 | − | 3.46410i | −0.0981761 | − | 0.170046i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.00000 | + | 10.3923i | −0.293821 | + | 0.508913i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.0000 | 0.977064 | 0.488532 | − | 0.872546i | \(-0.337533\pi\) | ||||
0.488532 | + | 0.872546i | \(0.337533\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.00000 | + | 5.19615i | −0.145865 | + | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.00000 | + | 10.3923i | 0.291043 | + | 0.504101i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.50000 | − | 2.59808i | −0.362950 | − | 0.125730i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.00000 | + | 5.19615i | 0.144841 | + | 0.250873i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.5000 | − | 35.5070i | 0.987450 | − | 1.71031i | 0.356953 | − | 0.934122i | \(-0.383815\pi\) |
0.630497 | − | 0.776192i | \(-0.282851\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.0000 | −1.24948 | −0.624740 | − | 0.780833i | \(-0.714795\pi\) | ||||
−0.624740 | + | 0.780833i | \(0.714795\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 18.0000 | 0.863034 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.50000 | − | 12.9904i | 0.358774 | − | 0.621414i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.50000 | + | 12.9904i | 0.357955 | + | 0.619997i | 0.987619 | − | 0.156871i | \(-0.0501406\pi\) |
−0.629664 | + | 0.776868i | \(0.716807\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −39.0000 | + | 15.5885i | −1.85714 | + | 0.742307i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.5000 | + | 23.3827i | 0.641404 | + | 1.11094i | 0.985119 | + | 0.171871i | \(0.0549812\pi\) |
−0.343715 | + | 0.939074i | \(0.611685\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.50000 | + | 7.79423i | −0.213320 | + | 0.369482i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 45.0000 | 2.12843 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.00000 | −0.0943858 | −0.0471929 | − | 0.998886i | \(-0.515028\pi\) | ||||
−0.0471929 | + | 0.998886i | \(0.515028\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.00000 | + | 8.66025i | −0.235441 | + | 0.407795i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.5000 | − | 38.9711i | −1.05714 | − | 1.83102i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.00000 | + | 1.73205i | 0.234404 | + | 0.0811998i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.50000 | + | 14.7224i | 0.397613 | + | 0.688686i | 0.993431 | − | 0.114433i | \(-0.0365053\pi\) |
−0.595818 | + | 0.803120i | \(0.703172\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.5000 | + | 23.3827i | −0.630126 | + | 1.09141i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.00000 | −0.279448 | −0.139724 | − | 0.990190i | \(-0.544622\pi\) | ||||
−0.139724 | + | 0.990190i | \(0.544622\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.50000 | + | 2.59808i | −0.0695608 | + | 0.120483i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.5000 | − | 21.6506i | −0.578431 | − | 1.00187i | −0.995660 | − | 0.0930703i | \(-0.970332\pi\) |
0.417229 | − | 0.908802i | \(-0.363001\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.50000 | + | 28.5788i | 0.253966 | + | 1.31965i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.5000 | − | 38.9711i | −1.03675 | − | 1.79570i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.00000 | + | 3.46410i | −0.0919601 | + | 0.159280i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.0000 | −0.917663 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −54.0000 | −2.47249 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.5000 | − | 18.1865i | 0.479757 | − | 0.830964i | −0.519973 | − | 0.854183i | \(-0.674058\pi\) |
0.999730 | + | 0.0232187i | \(0.00739140\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.00000 | + | 8.66025i | 0.227980 | + | 0.394874i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −18.0000 | + | 15.5885i | −0.819028 | + | 0.709299i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.00000 | + | 5.19615i | 0.136223 | + | 0.235945i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.50000 | − | 11.2583i | 0.294543 | − | 0.510164i | −0.680335 | − | 0.732901i | \(-0.738166\pi\) |
0.974879 | + | 0.222737i | \(0.0714992\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 27.0000 | 1.22098 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.00000 | − | 15.5885i | 0.405340 | − | 0.702069i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.00000 | − | 5.19615i | −0.134840 | − | 0.233550i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 32.0000 | − | 27.7128i | 1.43540 | − | 1.24309i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.50000 | + | 6.06218i | 0.156682 | + | 0.271380i | 0.933670 | − | 0.358134i | \(-0.116587\pi\) |
−0.776989 | + | 0.629515i | \(0.783254\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 30.0000 | − | 51.9615i | 1.34030 | − | 2.32147i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.0000 | 0.713405 | 0.356702 | − | 0.934218i | \(-0.383901\pi\) | ||||
0.356702 | + | 0.934218i | \(0.383901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.0000 | 0.578492 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.5000 | − | 23.3827i | 0.599556 | − | 1.03846i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.50000 | − | 6.06218i | −0.155135 | − | 0.268701i | 0.777973 | − | 0.628297i | \(-0.216248\pi\) |
−0.933108 | + | 0.359596i | \(0.882915\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.50000 | + | 18.1865i | 0.154831 | + | 0.804525i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −22.5000 | − | 38.9711i | −0.993399 | − | 1.72062i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.50000 | − | 4.33013i | 0.110163 | − | 0.190808i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.00000 | −0.0439799 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −63.0000 | −2.76539 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.50000 | + | 12.9904i | −0.328581 | + | 0.569119i | −0.982231 | − | 0.187678i | \(-0.939904\pi\) |
0.653650 | + | 0.756797i | \(0.273237\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.50000 | − | 11.2583i | −0.284225 | − | 0.492292i | 0.688196 | − | 0.725525i | \(-0.258403\pi\) |
−0.972421 | + | 0.233233i | \(0.925070\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 30.0000 | + | 10.3923i | 1.30931 | + | 0.453557i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.50000 | + | 2.59808i | 0.0653410 | + | 0.113174i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | − | 12.1244i | 0.304348 | − | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.0000 | 0.781133 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20.0000 | −0.866296 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.50000 | + | 2.59808i | −0.0648507 | + | 0.112325i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.50000 | + | 2.59808i | 0.0647298 | + | 0.112115i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.50000 | − | 4.33013i | −0.236902 | − | 0.186512i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.5000 | + | 21.6506i | 0.537417 | + | 0.930834i | 0.999042 | + | 0.0437584i | \(0.0139332\pi\) |
−0.461625 | + | 0.887075i | \(0.652733\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −33.0000 | + | 57.1577i | −1.41617 | + | 2.45287i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.0000 | −0.471188 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.00000 | + | 15.5885i | −0.384111 | + | 0.665299i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.0000 | + | 25.9808i | 0.639021 | + | 1.10682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27.5000 | + | 9.52628i | 1.16942 | + | 0.405099i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.50000 | − | 12.9904i | −0.318357 | − | 0.551411i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.50000 | + | 9.52628i | −0.233042 | + | 0.403641i | −0.958702 | − | 0.284413i | \(-0.908201\pi\) |
0.725660 | + | 0.688054i | \(0.241535\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.00000 | −0.379980 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.50000 | + | 9.52628i | −0.231797 | + | 0.401485i | −0.958337 | − | 0.285640i | \(-0.907794\pi\) |
0.726540 | + | 0.687124i | \(0.241127\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.00000 | − | 8.66025i | −0.210352 | − | 0.364340i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.50000 | + | 23.3827i | 0.188982 | + | 0.981981i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.500000 | + | 0.866025i | 0.0209611 | + | 0.0363057i | 0.876316 | − | 0.481737i | \(-0.159994\pi\) |
−0.855355 | + | 0.518043i | \(0.826661\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.50000 | − | 14.7224i | 0.355714 | − | 0.616115i | −0.631526 | − | 0.775355i | \(-0.717571\pi\) |
0.987240 | + | 0.159240i | \(0.0509044\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 51.0000 | 2.13056 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.0000 | 0.500435 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.5000 | + | 26.8468i | −0.645273 | + | 1.11765i | 0.338965 | + | 0.940799i | \(0.389923\pi\) |
−0.984238 | + | 0.176847i | \(0.943410\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.50000 | + | 12.9904i | 0.311689 | + | 0.539862i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.00000 | + | 6.92820i | −0.331896 | + | 0.287430i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.50000 | − | 7.79423i | −0.186371 | − | 0.322804i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.00000 | − | 10.3923i | 0.248069 | − | 0.429669i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.0000 | 0.495293 | 0.247647 | − | 0.968850i | \(-0.420343\pi\) | ||||
0.247647 | + | 0.968850i | \(0.420343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.00000 | −0.206021 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.0000 | + | 46.7654i | −1.11063 | + | 1.92367i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.5000 | − | 37.2391i | −0.882899 | − | 1.52923i | −0.848103 | − | 0.529832i | \(-0.822255\pi\) |
−0.0347964 | − | 0.999394i | \(-0.511078\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.00000 | + | 5.19615i | −0.245976 | + | 0.213021i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.5000 | + | 23.3827i | 0.552518 | + | 0.956990i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.5000 | − | 18.1865i | 0.429018 | − | 0.743082i | −0.567768 | − | 0.823189i | \(-0.692193\pi\) |
0.996786 | + | 0.0801071i | \(0.0255262\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.0000 | −1.38689 | −0.693444 | − | 0.720510i | \(-0.743908\pi\) | ||||
−0.693444 | + | 0.720510i | \(0.743908\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 66.0000 | 2.68773 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.00000 | + | 8.66025i | −0.203279 | + | 0.352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.50000 | + | 6.06218i | 0.142061 | + | 0.246056i | 0.928272 | − | 0.371901i | \(-0.121294\pi\) |
−0.786212 | + | 0.617957i | \(0.787961\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.00000 | − | 46.7654i | −0.364698 | − | 1.89503i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.00000 | − | 1.73205i | −0.0404557 | − | 0.0700713i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.5000 | − | 18.1865i | 0.424091 | − | 0.734547i | −0.572244 | − | 0.820083i | \(-0.693927\pi\) |
0.996335 | + | 0.0855362i | \(0.0272603\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 30.0000 | 1.20972 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.0000 | 0.885687 | 0.442843 | − | 0.896599i | \(-0.353970\pi\) | ||||
0.442843 | + | 0.896599i | \(0.353970\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.50000 | − | 4.33013i | 0.100483 | − | 0.174042i | −0.811400 | − | 0.584491i | \(-0.801294\pi\) |
0.911884 | + | 0.410448i | \(0.134628\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.5000 | + | 23.3827i | 0.541736 | + | 0.938315i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.5000 | + | 7.79423i | 0.901443 | + | 0.312269i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.50000 | − | 12.9904i | 0.299521 | − | 0.518786i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.0000 | −0.598089 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.0000 | + | 31.1769i | −0.715436 | + | 1.23917i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.00000 | − | 6.92820i | −0.158735 | − | 0.274937i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.00000 | − | 13.8564i | 0.0792429 | − | 0.549011i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −48.0000 | − | 83.1384i | −1.89885 | − | 3.28891i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.50000 | + | 12.9904i | −0.296232 | + | 0.513089i | −0.975271 | − | 0.221013i | \(-0.929064\pi\) |
0.679039 | + | 0.734103i | \(0.262397\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −44.0000 | −1.73519 | −0.867595 | − | 0.497271i | \(-0.834335\pi\) | ||||
−0.867595 | + | 0.497271i | \(0.834335\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.0000 | 0.472500 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.5000 | + | 37.2391i | −0.845252 | + | 1.46402i | 0.0401498 | + | 0.999194i | \(0.487216\pi\) |
−0.885402 | + | 0.464826i | \(0.846117\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.50000 | + | 2.59808i | 0.0588802 | + | 0.101983i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.50000 | + | 2.59808i | 0.293948 | + | 0.101827i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.50000 | + | 4.33013i | 0.0978326 | + | 0.169451i | 0.910787 | − | 0.412876i | \(-0.135476\pi\) |
−0.812955 | + | 0.582327i | \(0.802142\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.50000 | − | 14.7224i | 0.332122 | − | 0.575253i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 42.0000 | 1.63858 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.0000 | −1.40236 | −0.701180 | − | 0.712984i | \(-0.747343\pi\) | ||||
−0.701180 | + | 0.712984i | \(0.747343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.500000 | − | 0.866025i | 0.0194477 | − | 0.0336845i | −0.856138 | − | 0.516748i | \(-0.827143\pi\) |
0.875585 | + | 0.483063i | \(0.160476\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.00000 | − | 15.5885i | −0.349531 | − | 0.605406i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.50000 | − | 12.9904i | −0.0969458 | − | 0.503745i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.00000 | − | 15.5885i | −0.348481 | − | 0.603587i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −36.0000 | + | 62.3538i | −1.39184 | + | 2.41074i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.00000 | −0.115814 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.00000 | −0.0770943 | −0.0385472 | − | 0.999257i | \(-0.512273\pi\) | ||||
−0.0385472 | + | 0.999257i | \(0.512273\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18.0000 | − | 31.1769i | 0.692820 | − | 1.20000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.50000 | + | 7.79423i | 0.172949 | + | 0.299557i | 0.939450 | − | 0.342687i | \(-0.111337\pi\) |
−0.766501 | + | 0.642244i | \(0.778004\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.0000 | − | 10.3923i | 0.460518 | − | 0.398820i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.5000 | − | 18.1865i | −0.402361 | − | 0.696909i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.5000 | + | 33.7750i | −0.746147 | + | 1.29236i | 0.203510 | + | 0.979073i | \(0.434765\pi\) |
−0.949657 | + | 0.313291i | \(0.898568\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.00000 | −0.114624 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.0000 | 0.801200 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.00000 | − | 15.5885i | 0.342873 | − | 0.593873i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.5000 | + | 40.7032i | 0.893982 | + | 1.54842i | 0.835059 | + | 0.550160i | \(0.185433\pi\) |
0.0589228 | + | 0.998263i | \(0.481233\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.0000 | + | 10.3923i | −0.455842 | + | 0.394771i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.00000 | + | 3.46410i | 0.0758643 | + | 0.131401i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.0000 | − | 25.9808i | 0.568166 | − | 0.984092i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −39.0000 | −1.47512 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.0000 | −0.679851 | −0.339925 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.5000 | − | 21.6506i | 0.471446 | − | 0.816569i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.50000 | + | 2.59808i | 0.0564933 | + | 0.0978492i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.50000 | − | 33.7750i | −0.244458 | − | 1.27024i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.5000 | − | 23.3827i | −0.507003 | − | 0.878155i | −0.999967 | − | 0.00810550i | \(-0.997420\pi\) |
0.492964 | − | 0.870050i | \(-0.335913\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 33.0000 | − | 57.1577i | 1.23760 | − | 2.14358i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.00000 | 0.112351 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.00000 | 0.0747958 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.00000 | − | 10.3923i | 0.224074 | − | 0.388108i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.5000 | − | 25.1147i | −0.540759 | − | 0.936622i | −0.998861 | − | 0.0477220i | \(-0.984804\pi\) |
0.458102 | − | 0.888900i | \(-0.348529\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.5000 | − | 4.33013i | −0.465524 | − | 0.161262i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25.5000 | + | 44.1673i | 0.948355 | + | 1.64260i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.0000 | + | 20.7846i | −0.445669 | + | 0.771921i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.0000 | 0.593407 | 0.296704 | − | 0.954970i | \(-0.404113\pi\) | ||||
0.296704 | + | 0.954970i | \(0.404113\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.00000 | − | 10.3923i | 0.221918 | − | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.50000 | − | 9.52628i | −0.203147 | − | 0.351861i | 0.746394 | − | 0.665505i | \(-0.231784\pi\) |
−0.949541 | + | 0.313644i | \(0.898450\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.00000 | + | 20.7846i | −0.110657 | + | 0.766652i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.50000 | + | 9.52628i | 0.202595 | + | 0.350905i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.5000 | − | 35.5070i | 0.754105 | − | 1.30615i | −0.191714 | − | 0.981451i | \(-0.561404\pi\) |
0.945818 | − | 0.324697i | \(-0.105262\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 30.0000 | 1.10208 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.0000 | 1.17397 | 0.586983 | − | 0.809599i | \(-0.300316\pi\) | ||||
0.586983 | + | 0.809599i | \(0.300316\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.50000 | − | 12.9904i | 0.274779 | − | 0.475931i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.0000 | + | 20.7846i | 0.439057 | + | 0.760469i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.50000 | + | 2.59808i | 0.274044 | + | 0.0949316i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.5000 | + | 40.7032i | 0.857527 | + | 1.48528i | 0.874281 | + | 0.485421i | \(0.161334\pi\) |
−0.0167534 | + | 0.999860i | \(0.505333\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −36.0000 | + | 62.3538i | −1.31191 | + | 2.27230i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.0000 | −0.545906 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.0000 | 1.23575 | 0.617876 | − | 0.786276i | \(-0.287994\pi\) | ||||
0.617876 | + | 0.786276i | \(0.287994\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.50000 | + | 7.79423i | −0.163340 | + | 0.282913i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.5000 | − | 23.3827i | −0.489375 | − | 0.847622i | 0.510551 | − | 0.859848i | \(-0.329442\pi\) |
−0.999925 | + | 0.0122260i | \(0.996108\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.50000 | + | 28.5788i | 0.199113 | + | 1.03462i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.00000 | + | 15.5885i | 0.325396 | + | 0.563602i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.00000 | + | 5.19615i | −0.108324 | + | 0.187622i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −39.0000 | −1.40455 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.5000 | + | 30.3109i | −0.629431 | + | 1.09021i | 0.358235 | + | 0.933632i | \(0.383379\pi\) |
−0.987666 | + | 0.156575i | \(0.949955\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.00000 | − | 3.46410i | −0.0718421 | − | 0.124434i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −30.0000 | + | 25.9808i | −1.07624 | + | 0.932055i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.0000 | + | 43.3013i | 0.895718 | + | 1.55143i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.00000 | − | 13.8564i | 0.286263 | − | 0.495821i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −54.0000 | −1.92980 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.0000 | −0.535373 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.50000 | − | 11.2583i | 0.231700 | − | 0.401316i | −0.726609 | − | 0.687052i | \(-0.758905\pi\) |
0.958308 | + | 0.285736i | \(0.0922379\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.50000 | − | 7.79423i | −0.160204 | − | 0.277482i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.0000 | + | 17.3205i | −0.711118 | + | 0.615846i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.00000 | − | 5.19615i | −0.106533 | − | 0.184521i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.5000 | + | 23.3827i | −0.478796 | + | 0.829298i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.0000 | 1.48772 | 0.743858 | − | 0.668338i | \(-0.232994\pi\) | ||||
0.743858 | + | 0.668338i | \(0.232994\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.00000 | 0.106132 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 27.0000 | − | 46.7654i | 0.953998 | − | 1.65237i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.50000 | + | 6.06218i | 0.123512 | + | 0.213930i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.50000 | + | 7.79423i | 0.0528681 | + | 0.274710i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.5000 | + | 44.1673i | 0.897643 | + | 1.55476i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.5000 | − | 21.6506i | 0.439477 | − | 0.761196i | −0.558173 | − | 0.829725i | \(-0.688497\pi\) |
0.997649 | + | 0.0685291i | \(0.0218306\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.0000 | −0.702295 | −0.351147 | − | 0.936320i | \(-0.614208\pi\) | ||||
−0.351147 | + | 0.936320i | \(0.614208\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.00000 | −0.315644 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.50000 | − | 7.79423i | 0.157628 | − | 0.273020i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.0000 | + | 17.3205i | 0.349856 | + | 0.605968i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −30.0000 | − | 10.3923i | −1.04828 | − | 0.363137i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.5000 | + | 21.6506i | 0.436253 | + | 0.755612i | 0.997397 | − | 0.0721058i | \(-0.0229719\pi\) |
−0.561144 | + | 0.827718i | \(0.689639\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.5000 | − | 18.1865i | 0.366007 | − | 0.633943i | −0.622930 | − | 0.782277i | \(-0.714058\pi\) |
0.988937 | + | 0.148335i | \(0.0473913\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.0000 | 0.417786 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.00000 | −0.139094 | −0.0695468 | − | 0.997579i | \(-0.522155\pi\) | ||||
−0.0695468 | + | 0.997579i | \(0.522155\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.5000 | − | 32.0429i | 0.642532 | − | 1.11290i | −0.342334 | − | 0.939578i | \(-0.611217\pi\) |
0.984866 | − | 0.173319i | \(-0.0554492\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.5000 | − | 18.1865i | −0.364241 | − | 0.630884i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.5000 | + | 12.9904i | 0.571691 | + | 0.450090i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.0000 | − | 17.3205i | −0.346064 | − | 0.599401i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.50000 | − | 7.79423i | 0.155543 | − | 0.269408i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.0000 | −0.828572 | −0.414286 | − | 0.910147i | \(-0.635969\pi\) | ||||
−0.414286 | + | 0.910147i | \(0.635969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 27.0000 | − | 46.7654i | 0.929929 | − | 1.61068i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.50000 | − | 7.79423i | −0.154805 | − | 0.268130i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.0000 | + | 8.66025i | 0.859010 | + | 0.297570i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.5000 | + | 44.1673i | 0.875158 | + | 1.51582i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.50000 | + | 12.9904i | −0.257097 | + | 0.445305i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.0000 | −0.753266 | −0.376633 | − | 0.926363i | \(-0.622918\pi\) | ||||
−0.376633 | + | 0.926363i | \(0.622918\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −30.0000 | −1.02598 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.5000 | − | 49.3634i | 0.973541 | − | 1.68622i | 0.288875 | − | 0.957367i | \(-0.406719\pi\) |
0.684667 | − | 0.728856i | \(-0.259948\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.50000 | − | 4.33013i | −0.0852989 | − | 0.147742i | 0.820220 | − | 0.572049i | \(-0.193851\pi\) |
−0.905519 | + | 0.424307i | \(0.860518\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.0000 | − | 77.9423i | −0.511199 | − | 2.65627i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.5000 | − | 32.0429i | −0.629747 | − | 1.09075i | −0.987602 | − | 0.156977i | \(-0.949825\pi\) |
0.357855 | − | 0.933777i | \(-0.383508\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.5000 | + | 18.1865i | −0.357011 | + | 0.618361i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −24.0000 | −0.815083 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.0000 | 0.373149 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.0000 | + | 19.0526i | −0.372721 | + | 0.645571i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −18.0000 | − | 31.1769i | −0.609208 | − | 1.05518i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.0000 | − | 15.5885i | 0.608511 | − | 0.526986i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.5000 | − | 33.7750i | −0.658468 | − | 1.14050i | −0.981012 | − | 0.193946i | \(-0.937871\pi\) |
0.322544 | − | 0.946554i | \(-0.395462\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.00000 | + | 15.5885i | −0.303562 | + | 0.525786i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.0000 | 0.942275 | 0.471138 | − | 0.882060i | \(-0.343844\pi\) | ||||
0.471138 | + | 0.882060i | \(0.343844\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.50000 | − | 7.79423i | 0.151266 | − | 0.262000i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.5000 | + | 47.6314i | 0.923360 | + | 1.59931i | 0.794178 | + | 0.607685i | \(0.207902\pi\) |
0.129181 | + | 0.991621i | \(0.458765\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.0000 | + | 13.8564i | −0.536623 | + | 0.464729i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.50000 | + | 7.79423i | 0.150756 | + | 0.261116i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.50000 | + | 4.33013i | −0.0836593 | + | 0.144902i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.00000 | 0.0334263 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.0000 | −0.601003 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.00000 | + | 5.19615i | −0.100056 | + | 0.173301i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.5000 | + | 23.3827i | 0.449750 | + | 0.778990i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.00000 | − | 31.1769i | −0.199667 | − | 1.03750i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.0000 | + | 19.0526i | 0.365652 | + | 0.633328i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.50000 | − | 11.2583i | 0.215829 | − | 0.373827i | −0.737700 | − | 0.675129i | \(-0.764088\pi\) |
0.953529 | + | 0.301302i | \(0.0974213\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −78.0000 | −2.58710 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.0000 | −1.59031 | −0.795155 | − | 0.606406i | \(-0.792611\pi\) | ||||
−0.795155 | + | 0.606406i | \(0.792611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.00000 | + | 3.46410i | −0.0661903 | + | 0.114645i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.50000 | + | 7.79423i | 0.148765 | + | 0.257669i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −42.5000 | − | 14.7224i | −1.40347 | − | 0.486178i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.50000 | − | 14.7224i | −0.280389 | − | 0.485648i | 0.691091 | − | 0.722767i | \(-0.257130\pi\) |
−0.971481 | + | 0.237119i | \(0.923797\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.00000 | + | 10.3923i | −0.197707 | + | 0.342438i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 32.0000 | 1.05329 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.0000 | 0.657596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15.0000 | + | 25.9808i | −0.492665 | + | 0.853320i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.5000 | + | 35.5070i | 0.672583 | + | 1.16495i | 0.977169 | + | 0.212463i | \(0.0681486\pi\) |
−0.304586 | + | 0.952485i | \(0.598518\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.5000 | + | 12.9904i | −1.06514 | + | 0.425743i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.5000 | − | 28.5788i | −0.540186 | − | 0.935629i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.50000 | + | 2.59808i | −0.0490552 | + | 0.0849662i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.0000 | −1.24141 | −0.620703 | − | 0.784046i | \(-0.713153\pi\) | ||||
−0.620703 | + | 0.784046i | \(0.713153\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 93.0000 | 3.03494 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.5000 | + | 33.7750i | −0.635682 | + | 1.10103i | 0.350688 | + | 0.936492i | \(0.385948\pi\) |
−0.986370 | + | 0.164541i | \(0.947386\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.0000 | − | 25.9808i | −0.488467 | − | 0.846050i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 22.5000 | + | 7.79423i | 0.731925 | + | 0.253546i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.5000 | − | 42.4352i | −0.796143 | − | 1.37896i | −0.922111 | − | 0.386926i | \(-0.873537\pi\) |
0.125968 | − | 0.992034i | \(-0.459796\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.00000 | + | 12.1244i | −0.227230 | + | 0.393573i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 81.0000 | 2.62660 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.0000 | 0.971795 | 0.485898 | − | 0.874016i | \(-0.338493\pi\) | ||||
0.485898 | + | 0.874016i | \(0.338493\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.50000 | − | 14.7224i | 0.275054 | − | 0.476407i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.00000 | − | 15.5885i | −0.290929 | − | 0.503903i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.50000 | + | 7.79423i | 0.0484375 | + | 0.251689i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0000 | + | 25.9808i | 0.483871 | + | 0.838089i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.00000 | − | 15.5885i | 0.290021 | − | 0.502331i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.00000 | 0.160956 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.0000 | 1.02905 | 0.514525 | − | 0.857475i | \(-0.327968\pi\) | ||||
0.514525 | + | 0.857475i | \(0.327968\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22.5000 | + | 38.9711i | −0.722804 | + | 1.25193i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.5000 | − | 49.3634i | −0.914609 | − | 1.58415i | −0.807473 | − | 0.589904i | \(-0.799166\pi\) |
−0.107135 | − | 0.994244i | \(-0.534168\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.00000 | − | 6.92820i | 0.256468 | − | 0.222108i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.0000 | + | 20.7846i | 0.384308 | + | 0.665640i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.5000 | − | 32.0429i | 0.591867 | − | 1.02514i | −0.402113 | − | 0.915590i | \(-0.631724\pi\) |
0.993981 | − | 0.109555i | \(-0.0349424\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.00000 | 0.287641 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 66.0000 | 2.10722 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.5000 | − | 28.5788i | 0.526268 | − | 0.911523i | −0.473263 | − | 0.880921i | \(-0.656924\pi\) |
0.999532 | − | 0.0306024i | \(-0.00974257\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.00000 | + | 15.5885i | 0.286764 | + | 0.496690i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.00000 | − | 5.19615i | 0.190982 | − | 0.165395i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.00000 | − | 10.3923i | −0.190789 | − | 0.330456i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.5000 | + | 51.0955i | −0.937098 | + | 1.62310i | −0.166250 | + | 0.986084i | \(0.553166\pi\) |
−0.770849 | + | 0.637018i | \(0.780168\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −21.0000 | −0.666415 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.00000 | 0.285319 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.5000 | + | 26.8468i | −0.490890 | + | 0.850246i | −0.999945 | − | 0.0104877i | \(-0.996662\pi\) |
0.509055 | + | 0.860734i | \(0.329995\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 22.5000 | + | 38.9711i | 0.711868 | + | 1.23299i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))