Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [66,2,Mod(65,66)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(66, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("66.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 66 = 2 \cdot 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 66.b (of order \(2\), degree \(1\), 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: | \(0.527012653340\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-2}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 65.1 | ||
Root | \(-1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 66.65 |
Dual form | 66.2.b.a.65.2 |
$q$-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 \(\left(\mathbb{Z}/66\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | − | 1.41421i | −0.577350 | − | 0.816497i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | − | 1.41421i | − | 0.632456i | −0.948683 | − | 0.316228i | \(-0.897584\pi\) | ||
0.948683 | − | 0.316228i | \(-0.102416\pi\) | |||||||
\(6\) | 1.00000 | + | 1.41421i | 0.408248 | + | 0.577350i | ||||
\(7\) | − | 4.24264i | − | 1.60357i | −0.597614 | − | 0.801784i | \(-0.703885\pi\) | ||
0.597614 | − | 0.801784i | \(-0.296115\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.00000 | + | 2.82843i | −0.333333 | + | 0.942809i | ||||
\(10\) | 1.41421i | 0.447214i | ||||||||
\(11\) | 3.00000 | + | 1.41421i | 0.904534 | + | 0.426401i | ||||
\(12\) | −1.00000 | − | 1.41421i | −0.288675 | − | 0.408248i | ||||
\(13\) | 4.24264i | 1.17670i | 0.808608 | + | 0.588348i | \(0.200222\pi\) | ||||
−0.808608 | + | 0.588348i | \(0.799778\pi\) | |||||||
\(14\) | 4.24264i | 1.13389i | ||||||||
\(15\) | −2.00000 | + | 1.41421i | −0.516398 | + | 0.365148i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 1.00000 | − | 2.82843i | 0.235702 | − | 0.666667i | ||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | − | 1.41421i | − | 0.316228i | ||||||
\(21\) | −6.00000 | + | 4.24264i | −1.30931 | + | 0.925820i | ||||
\(22\) | −3.00000 | − | 1.41421i | −0.639602 | − | 0.301511i | ||||
\(23\) | − | 1.41421i | − | 0.294884i | −0.989071 | − | 0.147442i | \(-0.952896\pi\) | ||
0.989071 | − | 0.147442i | \(-0.0471040\pi\) | |||||||
\(24\) | 1.00000 | + | 1.41421i | 0.204124 | + | 0.288675i | ||||
\(25\) | 3.00000 | 0.600000 | ||||||||
\(26\) | − | 4.24264i | − | 0.832050i | ||||||
\(27\) | 5.00000 | − | 1.41421i | 0.962250 | − | 0.272166i | ||||
\(28\) | − | 4.24264i | − | 0.801784i | ||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 2.00000 | − | 1.41421i | 0.365148 | − | 0.258199i | ||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.00000 | − | 5.65685i | −0.174078 | − | 0.984732i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.00000 | −1.01419 | ||||||||
\(36\) | −1.00000 | + | 2.82843i | −0.166667 | + | 0.471405i | ||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.00000 | − | 4.24264i | 0.960769 | − | 0.679366i | ||||
\(40\) | 1.41421i | 0.223607i | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 6.00000 | − | 4.24264i | 0.925820 | − | 0.654654i | ||||
\(43\) | 8.48528i | 1.29399i | 0.762493 | + | 0.646997i | \(0.223975\pi\) | ||||
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | 3.00000 | + | 1.41421i | 0.452267 | + | 0.213201i | ||||
\(45\) | 4.00000 | + | 1.41421i | 0.596285 | + | 0.210819i | ||||
\(46\) | 1.41421i | 0.208514i | ||||||||
\(47\) | − | 9.89949i | − | 1.44399i | −0.691898 | − | 0.721995i | \(-0.743225\pi\) | ||
0.691898 | − | 0.721995i | \(-0.256775\pi\) | |||||||
\(48\) | −1.00000 | − | 1.41421i | −0.144338 | − | 0.204124i | ||||
\(49\) | −11.0000 | −1.57143 | ||||||||
\(50\) | −3.00000 | −0.424264 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.24264i | 0.588348i | ||||||||
\(53\) | 7.07107i | 0.971286i | 0.874157 | + | 0.485643i | \(0.161414\pi\) | ||||
−0.874157 | + | 0.485643i | \(0.838586\pi\) | |||||||
\(54\) | −5.00000 | + | 1.41421i | −0.680414 | + | 0.192450i | ||||
\(55\) | 2.00000 | − | 4.24264i | 0.269680 | − | 0.572078i | ||||
\(56\) | 4.24264i | 0.566947i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.00000 | −0.787839 | ||||||||
\(59\) | 11.3137i | 1.47292i | 0.676481 | + | 0.736460i | \(0.263504\pi\) | ||||
−0.676481 | + | 0.736460i | \(0.736496\pi\) | |||||||
\(60\) | −2.00000 | + | 1.41421i | −0.258199 | + | 0.182574i | ||||
\(61\) | − | 4.24264i | − | 0.543214i | −0.962408 | − | 0.271607i | \(-0.912445\pi\) | ||
0.962408 | − | 0.271607i | \(-0.0875552\pi\) | |||||||
\(62\) | 4.00000 | 0.508001 | ||||||||
\(63\) | 12.0000 | + | 4.24264i | 1.51186 | + | 0.534522i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.00000 | 0.744208 | ||||||||
\(66\) | 1.00000 | + | 5.65685i | 0.123091 | + | 0.696311i | ||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.00000 | + | 1.41421i | −0.240772 | + | 0.170251i | ||||
\(70\) | 6.00000 | 0.717137 | ||||||||
\(71\) | 7.07107i | 0.839181i | 0.907713 | + | 0.419591i | \(0.137826\pi\) | ||||
−0.907713 | + | 0.419591i | \(0.862174\pi\) | |||||||
\(72\) | 1.00000 | − | 2.82843i | 0.117851 | − | 0.333333i | ||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | −2.00000 | −0.232495 | ||||||||
\(75\) | −3.00000 | − | 4.24264i | −0.346410 | − | 0.489898i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.00000 | − | 12.7279i | 0.683763 | − | 1.45048i | ||||
\(78\) | −6.00000 | + | 4.24264i | −0.679366 | + | 0.480384i | ||||
\(79\) | − | 4.24264i | − | 0.477334i | −0.971101 | − | 0.238667i | \(-0.923290\pi\) | ||
0.971101 | − | 0.238667i | \(-0.0767105\pi\) | |||||||
\(80\) | − | 1.41421i | − | 0.158114i | ||||||
\(81\) | −7.00000 | − | 5.65685i | −0.777778 | − | 0.628539i | ||||
\(82\) | 6.00000 | 0.662589 | ||||||||
\(83\) | −12.0000 | −1.31717 | −0.658586 | − | 0.752506i | \(-0.728845\pi\) | ||||
−0.658586 | + | 0.752506i | \(0.728845\pi\) | |||||||
\(84\) | −6.00000 | + | 4.24264i | −0.654654 | + | 0.462910i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 8.48528i | − | 0.914991i | ||||||
\(87\) | −6.00000 | − | 8.48528i | −0.643268 | − | 0.909718i | ||||
\(88\) | −3.00000 | − | 1.41421i | −0.319801 | − | 0.150756i | ||||
\(89\) | − | 5.65685i | − | 0.599625i | −0.953998 | − | 0.299813i | \(-0.903076\pi\) | ||
0.953998 | − | 0.299813i | \(-0.0969242\pi\) | |||||||
\(90\) | −4.00000 | − | 1.41421i | −0.421637 | − | 0.149071i | ||||
\(91\) | 18.0000 | 1.88691 | ||||||||
\(92\) | − | 1.41421i | − | 0.147442i | ||||||
\(93\) | 4.00000 | + | 5.65685i | 0.414781 | + | 0.586588i | ||||
\(94\) | 9.89949i | 1.02105i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | + | 1.41421i | 0.102062 | + | 0.144338i | ||||
\(97\) | 8.00000 | 0.812277 | 0.406138 | − | 0.913812i | \(-0.366875\pi\) | ||||
0.406138 | + | 0.913812i | \(0.366875\pi\) | |||||||
\(98\) | 11.0000 | 1.11117 | ||||||||
\(99\) | −7.00000 | + | 7.07107i | −0.703526 | + | 0.710669i | ||||
\(100\) | 3.00000 | 0.300000 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | − | 4.24264i | − | 0.416025i | ||||||
\(105\) | 6.00000 | + | 8.48528i | 0.585540 | + | 0.828079i | ||||
\(106\) | − | 7.07107i | − | 0.686803i | ||||||
\(107\) | −18.0000 | −1.74013 | −0.870063 | − | 0.492941i | \(-0.835922\pi\) | ||||
−0.870063 | + | 0.492941i | \(0.835922\pi\) | |||||||
\(108\) | 5.00000 | − | 1.41421i | 0.481125 | − | 0.136083i | ||||
\(109\) | − | 12.7279i | − | 1.21911i | −0.792742 | − | 0.609557i | \(-0.791347\pi\) | ||
0.792742 | − | 0.609557i | \(-0.208653\pi\) | |||||||
\(110\) | −2.00000 | + | 4.24264i | −0.190693 | + | 0.404520i | ||||
\(111\) | −2.00000 | − | 2.82843i | −0.189832 | − | 0.268462i | ||||
\(112\) | − | 4.24264i | − | 0.400892i | ||||||
\(113\) | 11.3137i | 1.06430i | 0.846649 | + | 0.532152i | \(0.178617\pi\) | ||||
−0.846649 | + | 0.532152i | \(0.821383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.00000 | −0.186501 | ||||||||
\(116\) | 6.00000 | 0.557086 | ||||||||
\(117\) | −12.0000 | − | 4.24264i | −1.10940 | − | 0.392232i | ||||
\(118\) | − | 11.3137i | − | 1.04151i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.00000 | − | 1.41421i | 0.182574 | − | 0.129099i | ||||
\(121\) | 7.00000 | + | 8.48528i | 0.636364 | + | 0.771389i | ||||
\(122\) | 4.24264i | 0.384111i | ||||||||
\(123\) | 6.00000 | + | 8.48528i | 0.541002 | + | 0.765092i | ||||
\(124\) | −4.00000 | −0.359211 | ||||||||
\(125\) | − | 11.3137i | − | 1.01193i | ||||||
\(126\) | −12.0000 | − | 4.24264i | −1.06904 | − | 0.377964i | ||||
\(127\) | 12.7279i | 1.12942i | 0.825289 | + | 0.564710i | \(0.191012\pi\) | ||||
−0.825289 | + | 0.564710i | \(0.808988\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 12.0000 | − | 8.48528i | 1.05654 | − | 0.747087i | ||||
\(130\) | −6.00000 | −0.526235 | ||||||||
\(131\) | 12.0000 | 1.04844 | 0.524222 | − | 0.851581i | \(-0.324356\pi\) | ||||
0.524222 | + | 0.851581i | \(0.324356\pi\) | |||||||
\(132\) | −1.00000 | − | 5.65685i | −0.0870388 | − | 0.492366i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.00000 | 0.345547 | ||||||||
\(135\) | −2.00000 | − | 7.07107i | −0.172133 | − | 0.608581i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.82843i | 0.241649i | 0.992674 | + | 0.120824i | \(0.0385538\pi\) | ||||
−0.992674 | + | 0.120824i | \(0.961446\pi\) | |||||||
\(138\) | 2.00000 | − | 1.41421i | 0.170251 | − | 0.120386i | ||||
\(139\) | 16.9706i | 1.43942i | 0.694273 | + | 0.719712i | \(0.255726\pi\) | ||||
−0.694273 | + | 0.719712i | \(0.744274\pi\) | |||||||
\(140\) | −6.00000 | −0.507093 | ||||||||
\(141\) | −14.0000 | + | 9.89949i | −1.17901 | + | 0.833688i | ||||
\(142\) | − | 7.07107i | − | 0.593391i | ||||||
\(143\) | −6.00000 | + | 12.7279i | −0.501745 | + | 1.06436i | ||||
\(144\) | −1.00000 | + | 2.82843i | −0.0833333 | + | 0.235702i | ||||
\(145\) | − | 8.48528i | − | 0.704664i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.0000 | + | 15.5563i | 0.907265 | + | 1.28307i | ||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | −6.00000 | −0.491539 | −0.245770 | − | 0.969328i | \(-0.579041\pi\) | ||||
−0.245770 | + | 0.969328i | \(0.579041\pi\) | |||||||
\(150\) | 3.00000 | + | 4.24264i | 0.244949 | + | 0.346410i | ||||
\(151\) | − | 4.24264i | − | 0.345261i | −0.984987 | − | 0.172631i | \(-0.944773\pi\) | ||
0.984987 | − | 0.172631i | \(-0.0552267\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.00000 | + | 12.7279i | −0.483494 | + | 1.02565i | ||||
\(155\) | 5.65685i | 0.454369i | ||||||||
\(156\) | 6.00000 | − | 4.24264i | 0.480384 | − | 0.339683i | ||||
\(157\) | −22.0000 | −1.75579 | −0.877896 | − | 0.478852i | \(-0.841053\pi\) | ||||
−0.877896 | + | 0.478852i | \(0.841053\pi\) | |||||||
\(158\) | 4.24264i | 0.337526i | ||||||||
\(159\) | 10.0000 | − | 7.07107i | 0.793052 | − | 0.560772i | ||||
\(160\) | 1.41421i | 0.111803i | ||||||||
\(161\) | −6.00000 | −0.472866 | ||||||||
\(162\) | 7.00000 | + | 5.65685i | 0.549972 | + | 0.444444i | ||||
\(163\) | 2.00000 | 0.156652 | 0.0783260 | − | 0.996928i | \(-0.475042\pi\) | ||||
0.0783260 | + | 0.996928i | \(0.475042\pi\) | |||||||
\(164\) | −6.00000 | −0.468521 | ||||||||
\(165\) | −8.00000 | + | 1.41421i | −0.622799 | + | 0.110096i | ||||
\(166\) | 12.0000 | 0.931381 | ||||||||
\(167\) | 12.0000 | 0.928588 | 0.464294 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464294 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(168\) | 6.00000 | − | 4.24264i | 0.462910 | − | 0.327327i | ||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.48528i | 0.646997i | ||||||||
\(173\) | 6.00000 | 0.456172 | 0.228086 | − | 0.973641i | \(-0.426753\pi\) | ||||
0.228086 | + | 0.973641i | \(0.426753\pi\) | |||||||
\(174\) | 6.00000 | + | 8.48528i | 0.454859 | + | 0.643268i | ||||
\(175\) | − | 12.7279i | − | 0.962140i | ||||||
\(176\) | 3.00000 | + | 1.41421i | 0.226134 | + | 0.106600i | ||||
\(177\) | 16.0000 | − | 11.3137i | 1.20263 | − | 0.850390i | ||||
\(178\) | 5.65685i | 0.423999i | ||||||||
\(179\) | − | 5.65685i | − | 0.422813i | −0.977398 | − | 0.211407i | \(-0.932196\pi\) | ||
0.977398 | − | 0.211407i | \(-0.0678044\pi\) | |||||||
\(180\) | 4.00000 | + | 1.41421i | 0.298142 | + | 0.105409i | ||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | −18.0000 | −1.33425 | ||||||||
\(183\) | −6.00000 | + | 4.24264i | −0.443533 | + | 0.313625i | ||||
\(184\) | 1.41421i | 0.104257i | ||||||||
\(185\) | − | 2.82843i | − | 0.207950i | ||||||
\(186\) | −4.00000 | − | 5.65685i | −0.293294 | − | 0.414781i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 9.89949i | − | 0.721995i | ||||||
\(189\) | −6.00000 | − | 21.2132i | −0.436436 | − | 1.54303i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 9.89949i | − | 0.716302i | −0.933664 | − | 0.358151i | \(-0.883407\pi\) | ||
0.933664 | − | 0.358151i | \(-0.116593\pi\) | |||||||
\(192\) | −1.00000 | − | 1.41421i | −0.0721688 | − | 0.102062i | ||||
\(193\) | − | 8.48528i | − | 0.610784i | −0.952227 | − | 0.305392i | \(-0.901213\pi\) | ||
0.952227 | − | 0.305392i | \(-0.0987875\pi\) | |||||||
\(194\) | −8.00000 | −0.574367 | ||||||||
\(195\) | −6.00000 | − | 8.48528i | −0.429669 | − | 0.607644i | ||||
\(196\) | −11.0000 | −0.785714 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 7.00000 | − | 7.07107i | 0.497468 | − | 0.502519i | ||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | −3.00000 | −0.212132 | ||||||||
\(201\) | 4.00000 | + | 5.65685i | 0.282138 | + | 0.399004i | ||||
\(202\) | −6.00000 | −0.422159 | ||||||||
\(203\) | − | 25.4558i | − | 1.78665i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.48528i | 0.592638i | ||||||||
\(206\) | 4.00000 | 0.278693 | ||||||||
\(207\) | 4.00000 | + | 1.41421i | 0.278019 | + | 0.0982946i | ||||
\(208\) | 4.24264i | 0.294174i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −6.00000 | − | 8.48528i | −0.414039 | − | 0.585540i | ||||
\(211\) | − | 8.48528i | − | 0.584151i | −0.956395 | − | 0.292075i | \(-0.905654\pi\) | ||
0.956395 | − | 0.292075i | \(-0.0943458\pi\) | |||||||
\(212\) | 7.07107i | 0.485643i | ||||||||
\(213\) | 10.0000 | − | 7.07107i | 0.685189 | − | 0.484502i | ||||
\(214\) | 18.0000 | 1.23045 | ||||||||
\(215\) | 12.0000 | 0.818393 | ||||||||
\(216\) | −5.00000 | + | 1.41421i | −0.340207 | + | 0.0962250i | ||||
\(217\) | 16.9706i | 1.15204i | ||||||||
\(218\) | 12.7279i | 0.862044i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.00000 | − | 4.24264i | 0.134840 | − | 0.286039i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.00000 | + | 2.82843i | 0.134231 | + | 0.189832i | ||||
\(223\) | 8.00000 | 0.535720 | 0.267860 | − | 0.963458i | \(-0.413684\pi\) | ||||
0.267860 | + | 0.963458i | \(0.413684\pi\) | |||||||
\(224\) | 4.24264i | 0.283473i | ||||||||
\(225\) | −3.00000 | + | 8.48528i | −0.200000 | + | 0.565685i | ||||
\(226\) | − | 11.3137i | − | 0.752577i | ||||||
\(227\) | 6.00000 | 0.398234 | 0.199117 | − | 0.979976i | \(-0.436193\pi\) | ||||
0.199117 | + | 0.979976i | \(0.436193\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0000 | 0.925146 | 0.462573 | − | 0.886581i | \(-0.346926\pi\) | ||||
0.462573 | + | 0.886581i | \(0.346926\pi\) | |||||||
\(230\) | 2.00000 | 0.131876 | ||||||||
\(231\) | −24.0000 | + | 4.24264i | −1.57908 | + | 0.279145i | ||||
\(232\) | −6.00000 | −0.393919 | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 12.0000 | + | 4.24264i | 0.784465 | + | 0.277350i | ||||
\(235\) | −14.0000 | −0.913259 | ||||||||
\(236\) | 11.3137i | 0.736460i | ||||||||
\(237\) | −6.00000 | + | 4.24264i | −0.389742 | + | 0.275589i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | −2.00000 | + | 1.41421i | −0.129099 | + | 0.0912871i | ||||
\(241\) | 8.48528i | 0.546585i | 0.961931 | + | 0.273293i | \(0.0881127\pi\) | ||||
−0.961931 | + | 0.273293i | \(0.911887\pi\) | |||||||
\(242\) | −7.00000 | − | 8.48528i | −0.449977 | − | 0.545455i | ||||
\(243\) | −1.00000 | + | 15.5563i | −0.0641500 | + | 0.997940i | ||||
\(244\) | − | 4.24264i | − | 0.271607i | ||||||
\(245\) | 15.5563i | 0.993859i | ||||||||
\(246\) | −6.00000 | − | 8.48528i | −0.382546 | − | 0.541002i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.00000 | 0.254000 | ||||||||
\(249\) | 12.0000 | + | 16.9706i | 0.760469 | + | 1.07547i | ||||
\(250\) | 11.3137i | 0.715542i | ||||||||
\(251\) | − | 5.65685i | − | 0.357057i | −0.983935 | − | 0.178529i | \(-0.942866\pi\) | ||
0.983935 | − | 0.178529i | \(-0.0571337\pi\) | |||||||
\(252\) | 12.0000 | + | 4.24264i | 0.755929 | + | 0.267261i | ||||
\(253\) | 2.00000 | − | 4.24264i | 0.125739 | − | 0.266733i | ||||
\(254\) | − | 12.7279i | − | 0.798621i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.3137i | 0.705730i | 0.935674 | + | 0.352865i | \(0.114792\pi\) | ||||
−0.935674 | + | 0.352865i | \(0.885208\pi\) | |||||||
\(258\) | −12.0000 | + | 8.48528i | −0.747087 | + | 0.528271i | ||||
\(259\) | − | 8.48528i | − | 0.527250i | ||||||
\(260\) | 6.00000 | 0.372104 | ||||||||
\(261\) | −6.00000 | + | 16.9706i | −0.371391 | + | 1.05045i | ||||
\(262\) | −12.0000 | −0.741362 | ||||||||
\(263\) | −12.0000 | −0.739952 | −0.369976 | − | 0.929041i | \(-0.620634\pi\) | ||||
−0.369976 | + | 0.929041i | \(0.620634\pi\) | |||||||
\(264\) | 1.00000 | + | 5.65685i | 0.0615457 | + | 0.348155i | ||||
\(265\) | 10.0000 | 0.614295 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.00000 | + | 5.65685i | −0.489592 | + | 0.346194i | ||||
\(268\) | −4.00000 | −0.244339 | ||||||||
\(269\) | 7.07107i | 0.431131i | 0.976489 | + | 0.215565i | \(0.0691594\pi\) | ||||
−0.976489 | + | 0.215565i | \(0.930841\pi\) | |||||||
\(270\) | 2.00000 | + | 7.07107i | 0.121716 | + | 0.430331i | ||||
\(271\) | − | 12.7279i | − | 0.773166i | −0.922255 | − | 0.386583i | \(-0.873655\pi\) | ||
0.922255 | − | 0.386583i | \(-0.126345\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −18.0000 | − | 25.4558i | −1.08941 | − | 1.54066i | ||||
\(274\) | − | 2.82843i | − | 0.170872i | ||||||
\(275\) | 9.00000 | + | 4.24264i | 0.542720 | + | 0.255841i | ||||
\(276\) | −2.00000 | + | 1.41421i | −0.120386 | + | 0.0851257i | ||||
\(277\) | 21.2132i | 1.27458i | 0.770625 | + | 0.637289i | \(0.219944\pi\) | ||||
−0.770625 | + | 0.637289i | \(0.780056\pi\) | |||||||
\(278\) | − | 16.9706i | − | 1.01783i | ||||||
\(279\) | 4.00000 | − | 11.3137i | 0.239474 | − | 0.677334i | ||||
\(280\) | 6.00000 | 0.358569 | ||||||||
\(281\) | −12.0000 | −0.715860 | −0.357930 | − | 0.933748i | \(-0.616517\pi\) | ||||
−0.357930 | + | 0.933748i | \(0.616517\pi\) | |||||||
\(282\) | 14.0000 | − | 9.89949i | 0.833688 | − | 0.589506i | ||||
\(283\) | − | 8.48528i | − | 0.504398i | −0.967675 | − | 0.252199i | \(-0.918846\pi\) | ||
0.967675 | − | 0.252199i | \(-0.0811537\pi\) | |||||||
\(284\) | 7.07107i | 0.419591i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.00000 | − | 12.7279i | 0.354787 | − | 0.752618i | ||||
\(287\) | 25.4558i | 1.50261i | ||||||||
\(288\) | 1.00000 | − | 2.82843i | 0.0589256 | − | 0.166667i | ||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 8.48528i | 0.498273i | ||||||||
\(291\) | −8.00000 | − | 11.3137i | −0.468968 | − | 0.663221i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.00000 | −0.350524 | −0.175262 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175262 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(294\) | −11.0000 | − | 15.5563i | −0.641533 | − | 0.907265i | ||||
\(295\) | 16.0000 | 0.931556 | ||||||||
\(296\) | −2.00000 | −0.116248 | ||||||||
\(297\) | 17.0000 | + | 2.82843i | 0.986440 | + | 0.164122i | ||||
\(298\) | 6.00000 | 0.347571 | ||||||||
\(299\) | 6.00000 | 0.346989 | ||||||||
\(300\) | −3.00000 | − | 4.24264i | −0.173205 | − | 0.244949i | ||||
\(301\) | 36.0000 | 2.07501 | ||||||||
\(302\) | 4.24264i | 0.244137i | ||||||||
\(303\) | −6.00000 | − | 8.48528i | −0.344691 | − | 0.487467i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.00000 | −0.343559 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 6.00000 | − | 12.7279i | 0.341882 | − | 0.725241i | ||||
\(309\) | 4.00000 | + | 5.65685i | 0.227552 | + | 0.321807i | ||||
\(310\) | − | 5.65685i | − | 0.321288i | ||||||
\(311\) | − | 26.8701i | − | 1.52366i | −0.647776 | − | 0.761831i | \(-0.724301\pi\) | ||
0.647776 | − | 0.761831i | \(-0.275699\pi\) | |||||||
\(312\) | −6.00000 | + | 4.24264i | −0.339683 | + | 0.240192i | ||||
\(313\) | −10.0000 | −0.565233 | −0.282617 | − | 0.959233i | \(-0.591202\pi\) | ||||
−0.282617 | + | 0.959233i | \(0.591202\pi\) | |||||||
\(314\) | 22.0000 | 1.24153 | ||||||||
\(315\) | 6.00000 | − | 16.9706i | 0.338062 | − | 0.956183i | ||||
\(316\) | − | 4.24264i | − | 0.238667i | ||||||
\(317\) | − | 9.89949i | − | 0.556011i | −0.960579 | − | 0.278006i | \(-0.910327\pi\) | ||
0.960579 | − | 0.278006i | \(-0.0896734\pi\) | |||||||
\(318\) | −10.0000 | + | 7.07107i | −0.560772 | + | 0.396526i | ||||
\(319\) | 18.0000 | + | 8.48528i | 1.00781 | + | 0.475085i | ||||
\(320\) | − | 1.41421i | − | 0.0790569i | ||||||
\(321\) | 18.0000 | + | 25.4558i | 1.00466 | + | 1.42081i | ||||
\(322\) | 6.00000 | 0.334367 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −7.00000 | − | 5.65685i | −0.388889 | − | 0.314270i | ||||
\(325\) | 12.7279i | 0.706018i | ||||||||
\(326\) | −2.00000 | −0.110770 | ||||||||
\(327\) | −18.0000 | + | 12.7279i | −0.995402 | + | 0.703856i | ||||
\(328\) | 6.00000 | 0.331295 | ||||||||
\(329\) | −42.0000 | −2.31553 | ||||||||
\(330\) | 8.00000 | − | 1.41421i | 0.440386 | − | 0.0778499i | ||||
\(331\) | −10.0000 | −0.549650 | −0.274825 | − | 0.961494i | \(-0.588620\pi\) | ||||
−0.274825 | + | 0.961494i | \(0.588620\pi\) | |||||||
\(332\) | −12.0000 | −0.658586 | ||||||||
\(333\) | −2.00000 | + | 5.65685i | −0.109599 | + | 0.309994i | ||||
\(334\) | −12.0000 | −0.656611 | ||||||||
\(335\) | 5.65685i | 0.309067i | ||||||||
\(336\) | −6.00000 | + | 4.24264i | −0.327327 | + | 0.231455i | ||||
\(337\) | − | 33.9411i | − | 1.84889i | −0.381314 | − | 0.924445i | \(-0.624528\pi\) | ||
0.381314 | − | 0.924445i | \(-0.375472\pi\) | |||||||
\(338\) | 5.00000 | 0.271964 | ||||||||
\(339\) | 16.0000 | − | 11.3137i | 0.869001 | − | 0.614476i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.0000 | − | 5.65685i | −0.649836 | − | 0.306336i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706i | 0.916324i | ||||||||
\(344\) | − | 8.48528i | − | 0.457496i | ||||||
\(345\) | 2.00000 | + | 2.82843i | 0.107676 | + | 0.152277i | ||||
\(346\) | −6.00000 | −0.322562 | ||||||||
\(347\) | 12.0000 | 0.644194 | 0.322097 | − | 0.946707i | \(-0.395612\pi\) | ||||
0.322097 | + | 0.946707i | \(0.395612\pi\) | |||||||
\(348\) | −6.00000 | − | 8.48528i | −0.321634 | − | 0.454859i | ||||
\(349\) | − | 29.6985i | − | 1.58972i | −0.606791 | − | 0.794862i | \(-0.707543\pi\) | ||
0.606791 | − | 0.794862i | \(-0.292457\pi\) | |||||||
\(350\) | 12.7279i | 0.680336i | ||||||||
\(351\) | 6.00000 | + | 21.2132i | 0.320256 | + | 1.13228i | ||||
\(352\) | −3.00000 | − | 1.41421i | −0.159901 | − | 0.0753778i | ||||
\(353\) | − | 22.6274i | − | 1.20434i | −0.798369 | − | 0.602168i | \(-0.794304\pi\) | ||
0.798369 | − | 0.602168i | \(-0.205696\pi\) | |||||||
\(354\) | −16.0000 | + | 11.3137i | −0.850390 | + | 0.601317i | ||||
\(355\) | 10.0000 | 0.530745 | ||||||||
\(356\) | − | 5.65685i | − | 0.299813i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.65685i | 0.298974i | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | −4.00000 | − | 1.41421i | −0.210819 | − | 0.0745356i | ||||
\(361\) | 19.0000 | 1.00000 | ||||||||
\(362\) | −2.00000 | −0.105118 | ||||||||
\(363\) | 5.00000 | − | 18.3848i | 0.262432 | − | 0.964951i | ||||
\(364\) | 18.0000 | 0.943456 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.00000 | − | 4.24264i | 0.313625 | − | 0.221766i | ||||
\(367\) | −28.0000 | −1.46159 | −0.730794 | − | 0.682598i | \(-0.760850\pi\) | ||||
−0.730794 | + | 0.682598i | \(0.760850\pi\) | |||||||
\(368\) | − | 1.41421i | − | 0.0737210i | ||||||
\(369\) | 6.00000 | − | 16.9706i | 0.312348 | − | 0.883452i | ||||
\(370\) | 2.82843i | 0.147043i | ||||||||
\(371\) | 30.0000 | 1.55752 | ||||||||
\(372\) | 4.00000 | + | 5.65685i | 0.207390 | + | 0.293294i | ||||
\(373\) | 29.6985i | 1.53773i | 0.639412 | + | 0.768865i | \(0.279178\pi\) | ||||
−0.639412 | + | 0.768865i | \(0.720822\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −16.0000 | + | 11.3137i | −0.826236 | + | 0.584237i | ||||
\(376\) | 9.89949i | 0.510527i | ||||||||
\(377\) | 25.4558i | 1.31104i | ||||||||
\(378\) | 6.00000 | + | 21.2132i | 0.308607 | + | 1.09109i | ||||
\(379\) | 2.00000 | 0.102733 | 0.0513665 | − | 0.998680i | \(-0.483642\pi\) | ||||
0.0513665 | + | 0.998680i | \(0.483642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.0000 | − | 12.7279i | 0.922168 | − | 0.652071i | ||||
\(382\) | 9.89949i | 0.506502i | ||||||||
\(383\) | − | 1.41421i | − | 0.0722629i | −0.999347 | − | 0.0361315i | \(-0.988496\pi\) | ||
0.999347 | − | 0.0361315i | \(-0.0115035\pi\) | |||||||
\(384\) | 1.00000 | + | 1.41421i | 0.0510310 | + | 0.0721688i | ||||
\(385\) | −18.0000 | − | 8.48528i | −0.917365 | − | 0.432450i | ||||
\(386\) | 8.48528i | 0.431889i | ||||||||
\(387\) | −24.0000 | − | 8.48528i | −1.21999 | − | 0.431331i | ||||
\(388\) | 8.00000 | 0.406138 | ||||||||
\(389\) | − | 9.89949i | − | 0.501924i | −0.967997 | − | 0.250962i | \(-0.919253\pi\) | ||
0.967997 | − | 0.250962i | \(-0.0807470\pi\) | |||||||
\(390\) | 6.00000 | + | 8.48528i | 0.303822 | + | 0.429669i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 11.0000 | 0.555584 | ||||||||
\(393\) | −12.0000 | − | 16.9706i | −0.605320 | − | 0.856052i | ||||
\(394\) | −18.0000 | −0.906827 | ||||||||
\(395\) | −6.00000 | −0.301893 | ||||||||
\(396\) | −7.00000 | + | 7.07107i | −0.351763 | + | 0.355335i | ||||
\(397\) | −34.0000 | −1.70641 | −0.853206 | − | 0.521575i | \(-0.825345\pi\) | ||||
−0.853206 | + | 0.521575i | \(0.825345\pi\) | |||||||
\(398\) | 16.0000 | 0.802008 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | 0.150000 | ||||||||
\(401\) | 36.7696i | 1.83618i | 0.396368 | + | 0.918092i | \(0.370271\pi\) | ||||
−0.396368 | + | 0.918092i | \(0.629729\pi\) | |||||||
\(402\) | −4.00000 | − | 5.65685i | −0.199502 | − | 0.282138i | ||||
\(403\) | − | 16.9706i | − | 0.845364i | ||||||
\(404\) | 6.00000 | 0.298511 | ||||||||
\(405\) | −8.00000 | + | 9.89949i | −0.397523 | + | 0.491910i | ||||
\(406\) | 25.4558i | 1.26335i | ||||||||
\(407\) | 6.00000 | + | 2.82843i | 0.297409 | + | 0.140200i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 8.48528i | − | 0.419570i | −0.977748 | − | 0.209785i | \(-0.932724\pi\) | ||
0.977748 | − | 0.209785i | \(-0.0672764\pi\) | |||||||
\(410\) | − | 8.48528i | − | 0.419058i | ||||||
\(411\) | 4.00000 | − | 2.82843i | 0.197305 | − | 0.139516i | ||||
\(412\) | −4.00000 | −0.197066 | ||||||||
\(413\) | 48.0000 | 2.36193 | ||||||||
\(414\) | −4.00000 | − | 1.41421i | −0.196589 | − | 0.0695048i | ||||
\(415\) | 16.9706i | 0.833052i | ||||||||
\(416\) | − | 4.24264i | − | 0.208013i | ||||||
\(417\) | 24.0000 | − | 16.9706i | 1.17529 | − | 0.831052i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.3137i | 0.552711i | 0.961056 | + | 0.276355i | \(0.0891267\pi\) | ||||
−0.961056 | + | 0.276355i | \(0.910873\pi\) | |||||||
\(420\) | 6.00000 | + | 8.48528i | 0.292770 | + | 0.414039i | ||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 8.48528i | 0.413057i | ||||||||
\(423\) | 28.0000 | + | 9.89949i | 1.36141 | + | 0.481330i | ||||
\(424\) | − | 7.07107i | − | 0.343401i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −10.0000 | + | 7.07107i | −0.484502 | + | 0.342594i | ||||
\(427\) | −18.0000 | −0.871081 | ||||||||
\(428\) | −18.0000 | −0.870063 | ||||||||
\(429\) | 24.0000 | − | 4.24264i | 1.15873 | − | 0.204837i | ||||
\(430\) | −12.0000 | −0.578691 | ||||||||
\(431\) | −36.0000 | −1.73406 | −0.867029 | − | 0.498257i | \(-0.833974\pi\) | ||||
−0.867029 | + | 0.498257i | \(0.833974\pi\) | |||||||
\(432\) | 5.00000 | − | 1.41421i | 0.240563 | − | 0.0680414i | ||||
\(433\) | 2.00000 | 0.0961139 | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480569 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(434\) | − | 16.9706i | − | 0.814613i | ||||||
\(435\) | −12.0000 | + | 8.48528i | −0.575356 | + | 0.406838i | ||||
\(436\) | − | 12.7279i | − | 0.609557i | ||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.2132i | 1.01245i | 0.862401 | + | 0.506225i | \(0.168960\pi\) | ||||
−0.862401 | + | 0.506225i | \(0.831040\pi\) | |||||||
\(440\) | −2.00000 | + | 4.24264i | −0.0953463 | + | 0.202260i | ||||
\(441\) | 11.0000 | − | 31.1127i | 0.523810 | − | 1.48156i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.2843i | 1.34383i | 0.740630 | + | 0.671913i | \(0.234527\pi\) | ||||
−0.740630 | + | 0.671913i | \(0.765473\pi\) | |||||||
\(444\) | −2.00000 | − | 2.82843i | −0.0949158 | − | 0.134231i | ||||
\(445\) | −8.00000 | −0.379236 | ||||||||
\(446\) | −8.00000 | −0.378811 | ||||||||
\(447\) | 6.00000 | + | 8.48528i | 0.283790 | + | 0.401340i | ||||
\(448\) | − | 4.24264i | − | 0.200446i | ||||||
\(449\) | − | 31.1127i | − | 1.46830i | −0.678988 | − | 0.734150i | \(-0.737581\pi\) | ||
0.678988 | − | 0.734150i | \(-0.262419\pi\) | |||||||
\(450\) | 3.00000 | − | 8.48528i | 0.141421 | − | 0.400000i | ||||
\(451\) | −18.0000 | − | 8.48528i | −0.847587 | − | 0.399556i | ||||
\(452\) | 11.3137i | 0.532152i | ||||||||
\(453\) | −6.00000 | + | 4.24264i | −0.281905 | + | 0.199337i | ||||
\(454\) | −6.00000 | −0.281594 | ||||||||
\(455\) | − | 25.4558i | − | 1.19339i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.48528i | 0.396925i | 0.980109 | + | 0.198462i | \(0.0635948\pi\) | ||||
−0.980109 | + | 0.198462i | \(0.936405\pi\) | |||||||
\(458\) | −14.0000 | −0.654177 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.00000 | −0.0932505 | ||||||||
\(461\) | −30.0000 | −1.39724 | −0.698620 | − | 0.715493i | \(-0.746202\pi\) | ||||
−0.698620 | + | 0.715493i | \(0.746202\pi\) | |||||||
\(462\) | 24.0000 | − | 4.24264i | 1.11658 | − | 0.197386i | ||||
\(463\) | 32.0000 | 1.48717 | 0.743583 | − | 0.668644i | \(-0.233125\pi\) | ||||
0.743583 | + | 0.668644i | \(0.233125\pi\) | |||||||
\(464\) | 6.00000 | 0.278543 | ||||||||
\(465\) | 8.00000 | − | 5.65685i | 0.370991 | − | 0.262330i | ||||
\(466\) | 18.0000 | 0.833834 | ||||||||
\(467\) | − | 31.1127i | − | 1.43972i | −0.694117 | − | 0.719862i | \(-0.744205\pi\) | ||
0.694117 | − | 0.719862i | \(-0.255795\pi\) | |||||||
\(468\) | −12.0000 | − | 4.24264i | −0.554700 | − | 0.196116i | ||||
\(469\) | 16.9706i | 0.783628i | ||||||||
\(470\) | 14.0000 | 0.645772 | ||||||||
\(471\) | 22.0000 | + | 31.1127i | 1.01371 | + | 1.43360i | ||||
\(472\) | − | 11.3137i | − | 0.520756i | ||||||
\(473\) | −12.0000 | + | 25.4558i | −0.551761 | + | 1.17046i | ||||
\(474\) | 6.00000 | − | 4.24264i | 0.275589 | − | 0.194871i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −20.0000 | − | 7.07107i | −0.915737 | − | 0.323762i | ||||
\(478\) | −12.0000 | −0.548867 | ||||||||
\(479\) | −12.0000 | −0.548294 | −0.274147 | − | 0.961688i | \(-0.588395\pi\) | ||||
−0.274147 | + | 0.961688i | \(0.588395\pi\) | |||||||
\(480\) | 2.00000 | − | 1.41421i | 0.0912871 | − | 0.0645497i | ||||
\(481\) | 8.48528i | 0.386896i | ||||||||
\(482\) | − | 8.48528i | − | 0.386494i | ||||||
\(483\) | 6.00000 | + | 8.48528i | 0.273009 | + | 0.386094i | ||||
\(484\) | 7.00000 | + | 8.48528i | 0.318182 | + | 0.385695i | ||||
\(485\) | − | 11.3137i | − | 0.513729i | ||||||
\(486\) | 1.00000 | − | 15.5563i | 0.0453609 | − | 0.705650i | ||||
\(487\) | 20.0000 | 0.906287 | 0.453143 | − | 0.891438i | \(-0.350303\pi\) | ||||
0.453143 | + | 0.891438i | \(0.350303\pi\) | |||||||
\(488\) | 4.24264i | 0.192055i | ||||||||
\(489\) | −2.00000 | − | 2.82843i | −0.0904431 | − | 0.127906i | ||||
\(490\) | − | 15.5563i | − | 0.702764i | ||||||
\(491\) | −6.00000 | −0.270776 | −0.135388 | − | 0.990793i | \(-0.543228\pi\) | ||||
−0.135388 | + | 0.990793i | \(0.543228\pi\) | |||||||
\(492\) | 6.00000 | + | 8.48528i | 0.270501 | + | 0.382546i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.0000 | + | 9.89949i | 0.449467 | + | 0.444949i | ||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 30.0000 | 1.34568 | ||||||||
\(498\) | −12.0000 | − | 16.9706i | −0.537733 | − | 0.760469i | ||||
\(499\) | 14.0000 | 0.626726 | 0.313363 | − | 0.949633i | \(-0.398544\pi\) | ||||
0.313363 | + | 0.949633i | \(0.398544\pi\) | |||||||
\(500\) | − | 11.3137i | − | 0.505964i | ||||||
\(501\) | −12.0000 | − | 16.9706i | −0.536120 | − | 0.758189i | ||||
\(502\) | 5.65685i | 0.252478i | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | −12.0000 | − | 4.24264i | −0.534522 | − | 0.188982i | ||||
\(505\) | − | 8.48528i | − | 0.377590i | ||||||
\(506\) | −2.00000 | + | 4.24264i | −0.0889108 | + | 0.188608i | ||||
\(507\) | 5.00000 | + | 7.07107i | 0.222058 | + | 0.314037i | ||||
\(508\) | 12.7279i | 0.564710i | ||||||||
\(509\) | − | 1.41421i | − | 0.0626839i | −0.999509 | − | 0.0313420i | \(-0.990022\pi\) | ||
0.999509 | − | 0.0313420i | \(-0.00997809\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 11.3137i | − | 0.499026i | ||||||
\(515\) | 5.65685i | 0.249271i | ||||||||
\(516\) | 12.0000 | − | 8.48528i | 0.528271 | − | 0.373544i | ||||
\(517\) | 14.0000 | − | 29.6985i | 0.615719 | − | 1.30614i | ||||
\(518\) | 8.48528i | 0.372822i | ||||||||
\(519\) | −6.00000 | − | 8.48528i | −0.263371 | − | 0.372463i | ||||
\(520\) | −6.00000 | −0.263117 | ||||||||
\(521\) | 19.7990i | 0.867409i | 0.901055 | + | 0.433705i | \(0.142794\pi\) | ||||
−0.901055 | + | 0.433705i | \(0.857206\pi\) | |||||||
\(522\) | 6.00000 | − | 16.9706i | 0.262613 | − | 0.742781i | ||||
\(523\) | − | 25.4558i | − | 1.11311i | −0.830812 | − | 0.556553i | \(-0.812124\pi\) | ||
0.830812 | − | 0.556553i | \(-0.187876\pi\) | |||||||
\(524\) | 12.0000 | 0.524222 | ||||||||
\(525\) | −18.0000 | + | 12.7279i | −0.785584 | + | 0.555492i | ||||
\(526\) | 12.0000 | 0.523225 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.00000 | − | 5.65685i | −0.0435194 | − | 0.246183i | ||||
\(529\) | 21.0000 | 0.913043 | ||||||||
\(530\) | −10.0000 | −0.434372 | ||||||||
\(531\) | −32.0000 | − | 11.3137i | −1.38868 | − | 0.490973i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 25.4558i | − | 1.10262i | ||||||
\(534\) | 8.00000 | − | 5.65685i | 0.346194 | − | 0.244796i | ||||
\(535\) | 25.4558i | 1.10055i | ||||||||
\(536\) | 4.00000 | 0.172774 | ||||||||
\(537\) | −8.00000 | + | 5.65685i | −0.345225 | + | 0.244111i | ||||
\(538\) | − | 7.07107i | − | 0.304855i | ||||||
\(539\) | −33.0000 | − | 15.5563i | −1.42141 | − | 0.670059i | ||||
\(540\) | −2.00000 | − | 7.07107i | −0.0860663 | − | 0.304290i | ||||
\(541\) | − | 12.7279i | − | 0.547216i | −0.961841 | − | 0.273608i | \(-0.911783\pi\) | ||
0.961841 | − | 0.273608i | \(-0.0882171\pi\) | |||||||
\(542\) | 12.7279i | 0.546711i | ||||||||
\(543\) | −2.00000 | − | 2.82843i | −0.0858282 | − | 0.121379i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.0000 | −0.771035 | ||||||||
\(546\) | 18.0000 | + | 25.4558i | 0.770329 | + | 1.08941i | ||||
\(547\) | 33.9411i | 1.45122i | 0.688107 | + | 0.725609i | \(0.258442\pi\) | ||||
−0.688107 | + | 0.725609i | \(0.741558\pi\) | |||||||
\(548\) | 2.82843i | 0.120824i | ||||||||
\(549\) | 12.0000 | + | 4.24264i | 0.512148 | + | 0.181071i | ||||
\(550\) | −9.00000 | − | 4.24264i | −0.383761 | − | 0.180907i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 2.00000 | − | 1.41421i | 0.0851257 | − | 0.0601929i | ||||
\(553\) | −18.0000 | −0.765438 | ||||||||
\(554\) | − | 21.2132i | − | 0.901263i | ||||||
\(555\) | −4.00000 | + | 2.82843i | −0.169791 | + | 0.120060i | ||||
\(556\) | 16.9706i | 0.719712i | ||||||||
\(557\) | 18.0000 | 0.762684 | 0.381342 | − | 0.924434i | \(-0.375462\pi\) | ||||
0.381342 | + | 0.924434i | \(0.375462\pi\) | |||||||
\(558\) | −4.00000 | + | 11.3137i | −0.169334 | + | 0.478947i | ||||
\(559\) | −36.0000 | −1.52264 | ||||||||
\(560\) | −6.00000 | −0.253546 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.0000 | 0.506189 | ||||||||
\(563\) | 30.0000 | 1.26435 | 0.632175 | − | 0.774826i | \(-0.282163\pi\) | ||||
0.632175 | + | 0.774826i | \(0.282163\pi\) | |||||||
\(564\) | −14.0000 | + | 9.89949i | −0.589506 | + | 0.416844i | ||||
\(565\) | 16.0000 | 0.673125 | ||||||||
\(566\) | 8.48528i | 0.356663i | ||||||||
\(567\) | −24.0000 | + | 29.6985i | −1.00791 | + | 1.24722i | ||||
\(568\) | − | 7.07107i | − | 0.296695i | ||||||
\(569\) | 24.0000 | 1.00613 | 0.503066 | − | 0.864248i | \(-0.332205\pi\) | ||||
0.503066 | + | 0.864248i | \(0.332205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 33.9411i | − | 1.42039i | −0.704004 | − | 0.710196i | \(-0.748606\pi\) | ||
0.704004 | − | 0.710196i | \(-0.251394\pi\) | |||||||
\(572\) | −6.00000 | + | 12.7279i | −0.250873 | + | 0.532181i | ||||
\(573\) | −14.0000 | + | 9.89949i | −0.584858 | + | 0.413557i | ||||
\(574\) | − | 25.4558i | − | 1.06251i | ||||||
\(575\) | − | 4.24264i | − | 0.176930i | ||||||
\(576\) | −1.00000 | + | 2.82843i | −0.0416667 | + | 0.117851i | ||||
\(577\) | 20.0000 | 0.832611 | 0.416305 | − | 0.909225i | \(-0.363325\pi\) | ||||
0.416305 | + | 0.909225i | \(0.363325\pi\) | |||||||
\(578\) | 17.0000 | 0.707107 | ||||||||
\(579\) | −12.0000 | + | 8.48528i | −0.498703 | + | 0.352636i | ||||
\(580\) | − | 8.48528i | − | 0.352332i | ||||||
\(581\) | 50.9117i | 2.11217i | ||||||||
\(582\) | 8.00000 | + | 11.3137i | 0.331611 | + | 0.468968i | ||||
\(583\) | −10.0000 | + | 21.2132i | −0.414158 | + | 0.878561i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.00000 | + | 16.9706i | −0.248069 | + | 0.701646i | ||||
\(586\) | 6.00000 | 0.247858 | ||||||||
\(587\) | 28.2843i | 1.16742i | 0.811963 | + | 0.583708i | \(0.198399\pi\) | ||||
−0.811963 | + | 0.583708i | \(0.801601\pi\) | |||||||
\(588\) | 11.0000 | + | 15.5563i | 0.453632 | + | 0.641533i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −16.0000 | −0.658710 | ||||||||
\(591\) | −18.0000 | − | 25.4558i | −0.740421 | − | 1.04711i | ||||
\(592\) | 2.00000 | 0.0821995 | ||||||||
\(593\) | 36.0000 | 1.47834 | 0.739171 | − | 0.673517i | \(-0.235217\pi\) | ||||
0.739171 | + | 0.673517i | \(0.235217\pi\) | |||||||
\(594\) | −17.0000 | − | 2.82843i | −0.697518 | − | 0.116052i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | 16.0000 | + | 22.6274i | 0.654836 | + | 0.926079i | ||||
\(598\) | −6.00000 | −0.245358 | ||||||||
\(599\) | 24.0416i | 0.982314i | 0.871071 | + | 0.491157i | \(0.163426\pi\) | ||||
−0.871071 | + | 0.491157i | \(0.836574\pi\) | |||||||
\(600\) | 3.00000 | + | 4.24264i | 0.122474 | + | 0.173205i | ||||
\(601\) | 33.9411i | 1.38449i | 0.721664 | + | 0.692244i | \(0.243378\pi\) | ||||
−0.721664 | + | 0.692244i | \(0.756622\pi\) | |||||||
\(602\) | −36.0000 | −1.46725 | ||||||||
\(603\) | 4.00000 | − | 11.3137i | 0.162893 | − | 0.460730i | ||||
\(604\) | − | 4.24264i | − | 0.172631i | ||||||
\(605\) | 12.0000 | − | 9.89949i | 0.487869 | − | 0.402472i | ||||
\(606\) | 6.00000 | + | 8.48528i | 0.243733 | + | 0.344691i | ||||
\(607\) | 4.24264i | 0.172203i | 0.996286 | + | 0.0861017i | \(0.0274410\pi\) | ||||
−0.996286 | + | 0.0861017i | \(0.972559\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −36.0000 | + | 25.4558i | −1.45879 | + | 1.03152i | ||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | 42.0000 | 1.69914 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 12.7279i | − | 0.514076i | −0.966401 | − | 0.257038i | \(-0.917253\pi\) | ||
0.966401 | − | 0.257038i | \(-0.0827465\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.0000 | − | 8.48528i | 0.483887 | − | 0.342160i | ||||
\(616\) | −6.00000 | + | 12.7279i | −0.241747 | + | 0.512823i | ||||
\(617\) | − | 39.5980i | − | 1.59415i | −0.603877 | − | 0.797077i | \(-0.706378\pi\) | ||
0.603877 | − | 0.797077i | \(-0.293622\pi\) | |||||||
\(618\) | −4.00000 | − | 5.65685i | −0.160904 | − | 0.227552i | ||||
\(619\) | 44.0000 | 1.76851 | 0.884255 | − | 0.467005i | \(-0.154667\pi\) | ||||
0.884255 | + | 0.467005i | \(0.154667\pi\) | |||||||
\(620\) | 5.65685i | 0.227185i | ||||||||
\(621\) | −2.00000 | − | 7.07107i | −0.0802572 | − | 0.283752i | ||||
\(622\) | 26.8701i | 1.07739i | ||||||||
\(623\) | −24.0000 | −0.961540 | ||||||||
\(624\) | 6.00000 | − | 4.24264i | 0.240192 | − | 0.169842i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 10.0000 | 0.399680 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −22.0000 | −0.877896 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −6.00000 | + | 16.9706i | −0.239046 | + | 0.676123i | ||||
\(631\) | 20.0000 | 0.796187 | 0.398094 | − | 0.917345i | \(-0.369672\pi\) | ||||
0.398094 | + | 0.917345i | \(0.369672\pi\) | |||||||
\(632\) | 4.24264i | 0.168763i | ||||||||
\(633\) | −12.0000 | + | 8.48528i | −0.476957 | + | 0.337260i | ||||
\(634\) | 9.89949i | 0.393159i | ||||||||
\(635\) | 18.0000 | 0.714308 | ||||||||
\(636\) | 10.0000 | − | 7.07107i | 0.396526 | − | 0.280386i | ||||
\(637\) | − | 46.6690i | − | 1.84909i | ||||||
\(638\) | −18.0000 | − | 8.48528i | −0.712627 | − | 0.335936i | ||||
\(639\) | −20.0000 | − | 7.07107i | −0.791188 | − | 0.279727i | ||||
\(640\) | 1.41421i | 0.0559017i | ||||||||
\(641\) | − | 48.0833i | − | 1.89917i | −0.313503 | − | 0.949587i | \(-0.601502\pi\) | ||
0.313503 | − | 0.949587i | \(-0.398498\pi\) | |||||||
\(642\) | −18.0000 | − | 25.4558i | −0.710403 | − | 1.00466i | ||||
\(643\) | −4.00000 | −0.157745 | −0.0788723 | − | 0.996885i | \(-0.525132\pi\) | ||||
−0.0788723 | + | 0.996885i | \(0.525132\pi\) | |||||||
\(644\) | −6.00000 | −0.236433 | ||||||||
\(645\) | −12.0000 | − | 16.9706i | −0.472500 | − | 0.668215i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.07107i | 0.277992i | 0.990293 | + | 0.138996i | \(0.0443876\pi\) | ||||
−0.990293 | + | 0.138996i | \(0.955612\pi\) | |||||||
\(648\) | 7.00000 | + | 5.65685i | 0.274986 | + | 0.222222i | ||||
\(649\) | −16.0000 | + | 33.9411i | −0.628055 | + | 1.33231i | ||||
\(650\) | − | 12.7279i | − | 0.499230i | ||||||
\(651\) | 24.0000 | − | 16.9706i | 0.940634 | − | 0.665129i | ||||
\(652\) | 2.00000 | 0.0783260 | ||||||||
\(653\) | − | 26.8701i | − | 1.05151i | −0.850637 | − | 0.525753i | \(-0.823784\pi\) | ||
0.850637 | − | 0.525753i | \(-0.176216\pi\) | |||||||
\(654\) | 18.0000 | − | 12.7279i | 0.703856 | − | 0.497701i | ||||
\(655\) | − | 16.9706i | − | 0.663095i | ||||||
\(656\) | −6.00000 | −0.234261 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 42.0000 | 1.63733 | ||||||||
\(659\) | −30.0000 | −1.16863 | −0.584317 | − | 0.811525i | \(-0.698638\pi\) | ||||
−0.584317 | + | 0.811525i | \(0.698638\pi\) | |||||||
\(660\) | −8.00000 | + | 1.41421i | −0.311400 | + | 0.0550482i | ||||
\(661\) | −22.0000 | −0.855701 | −0.427850 | − | 0.903850i | \(-0.640729\pi\) | ||||
−0.427850 | + | 0.903850i | \(0.640729\pi\) | |||||||
\(662\) | 10.0000 | 0.388661 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.0000 | 0.465690 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.00000 | − | 5.65685i | 0.0774984 | − | 0.219199i | ||||
\(667\) | − | 8.48528i | − | 0.328551i | ||||||
\(668\) | 12.0000 | 0.464294 | ||||||||
\(669\) | −8.00000 | − | 11.3137i | −0.309298 | − | 0.437413i | ||||
\(670\) | − | 5.65685i | − | 0.218543i | ||||||
\(671\) | 6.00000 | − | 12.7279i | 0.231627 | − | 0.491356i | ||||
\(672\) | 6.00000 | − | 4.24264i | 0.231455 | − | 0.163663i | ||||
\(673\) | − | 42.4264i | − | 1.63542i | −0.575632 | − | 0.817709i | \(-0.695244\pi\) | ||
0.575632 | − | 0.817709i | \(-0.304756\pi\) | |||||||
\(674\) | 33.9411i | 1.30736i | ||||||||
\(675\) | 15.0000 | − | 4.24264i | 0.577350 | − | 0.163299i | ||||
\(676\) | −5.00000 | −0.192308 | ||||||||
\(677\) | −30.0000 | −1.15299 | −0.576497 | − | 0.817099i | \(-0.695581\pi\) | ||||
−0.576497 | + | 0.817099i | \(0.695581\pi\) | |||||||
\(678\) | −16.0000 | + | 11.3137i | −0.614476 | + | 0.434500i | ||||
\(679\) | − | 33.9411i | − | 1.30254i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.00000 | − | 8.48528i | −0.229920 | − | 0.325157i | ||||
\(682\) | 12.0000 | + | 5.65685i | 0.459504 | + | 0.216612i | ||||
\(683\) | − | 5.65685i | − | 0.216454i | −0.994126 | − | 0.108227i | \(-0.965483\pi\) | ||
0.994126 | − | 0.108227i | \(-0.0345173\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.00000 | 0.152832 | ||||||||
\(686\) | − | 16.9706i | − | 0.647939i | ||||||
\(687\) | −14.0000 | − | 19.7990i | −0.534133 | − | 0.755379i | ||||
\(688\) | 8.48528i | 0.323498i | ||||||||
\(689\) | −30.0000 | −1.14291 | ||||||||
\(690\) | −2.00000 | − | 2.82843i | −0.0761387 | − | 0.107676i | ||||
\(691\) | −28.0000 | −1.06517 | −0.532585 | − | 0.846376i | \(-0.678779\pi\) | ||||
−0.532585 | + | 0.846376i | \(0.678779\pi\) | |||||||
\(692\) | 6.00000 | 0.228086 | ||||||||
\(693\) | 30.0000 | + | 29.6985i | 1.13961 | + | 1.12815i | ||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | 24.0000 | 0.910372 | ||||||||
\(696\) | 6.00000 | + | 8.48528i | 0.227429 | + | 0.321634i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 29.6985i | 1.12410i | ||||||||
\(699\) | 18.0000 | + | 25.4558i | 0.680823 | + | 0.962828i | ||||
\(700\) | − | 12.7279i | − | 0.481070i | ||||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | −6.00000 | − | 21.2132i | −0.226455 | − | 0.800641i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 3.00000 | + | 1.41421i | 0.113067 | + | 0.0533002i | ||||
\(705\) | 14.0000 | + | 19.7990i | 0.527271 | + | 0.745673i | ||||
\(706\) | 22.6274i | 0.851594i | ||||||||
\(707\) | − | 25.4558i | − | 0.957366i | ||||||
\(708\) | 16.0000 | − | 11.3137i | 0.601317 | − | 0.425195i | ||||
\(709\) | −10.0000 | −0.375558 | −0.187779 | − | 0.982211i | \(-0.560129\pi\) | ||||
−0.187779 | + | 0.982211i | \(0.560129\pi\) | |||||||
\(710\) | −10.0000 | −0.375293 | ||||||||
\(711\) | 12.0000 | + | 4.24264i | 0.450035 | + | 0.159111i | ||||
\(712\) | 5.65685i | 0.212000i | ||||||||
\(713\) | 5.65685i | 0.211851i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.0000 | + | 8.48528i | 0.673162 | + | 0.317332i | ||||
\(716\) | − | 5.65685i | − | 0.211407i | ||||||
\(717\) | −12.0000 | − | 16.9706i | −0.448148 | − | 0.633777i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.5269i | 1.21305i | 0.795065 | + | 0.606525i | \(0.207437\pi\) | ||||
−0.795065 | + | 0.606525i | \(0.792563\pi\) | |||||||
\(720\) | 4.00000 | + | 1.41421i | 0.149071 | + | 0.0527046i | ||||
\(721\) | 16.9706i | 0.632017i | ||||||||
\(722\) | −19.0000 | −0.707107 | ||||||||
\(723\) | 12.0000 | − | 8.48528i | 0.446285 | − | 0.315571i | ||||
\(724\) | 2.00000 | 0.0743294 | ||||||||
\(725\) | 18.0000 | 0.668503 | ||||||||
\(726\) | −5.00000 | + | 18.3848i | −0.185567 | + | 0.682323i | ||||
\(727\) | 44.0000 | 1.63187 | 0.815935 | − | 0.578144i | \(-0.196223\pi\) | ||||
0.815935 | + | 0.578144i | \(0.196223\pi\) | |||||||
\(728\) | −18.0000 | −0.667124 | ||||||||
\(729\) | 23.0000 | − | 14.1421i | 0.851852 | − | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −6.00000 | + | 4.24264i | −0.221766 | + | 0.156813i | ||||
\(733\) | 4.24264i | 0.156706i | 0.996926 | + | 0.0783528i | \(0.0249660\pi\) | ||||
−0.996926 | + | 0.0783528i | \(0.975034\pi\) | |||||||
\(734\) | 28.0000 | 1.03350 | ||||||||
\(735\) | 22.0000 | − | 15.5563i | 0.811482 | − | 0.573805i | ||||
\(736\) | 1.41421i | 0.0521286i | ||||||||
\(737\) | −12.0000 | − | 5.65685i | −0.442026 | − | 0.208373i | ||||
\(738\) | −6.00000 | + | 16.9706i | −0.220863 | + | 0.624695i | ||||
\(739\) | 25.4558i | 0.936408i | 0.883620 | + | 0.468204i | \(0.155099\pi\) | ||||
−0.883620 | + | 0.468204i | \(0.844901\pi\) | |||||||
\(740\) | − | 2.82843i | − | 0.103975i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −30.0000 | −1.10133 | ||||||||
\(743\) | −24.0000 | −0.880475 | −0.440237 | − | 0.897881i | \(-0.645106\pi\) | ||||
−0.440237 | + | 0.897881i | \(0.645106\pi\) | |||||||
\(744\) | −4.00000 | − | 5.65685i | −0.146647 | − | 0.207390i | ||||
\(745\) | 8.48528i | 0.310877i | ||||||||
\(746\) | − | 29.6985i | − | 1.08734i | ||||||
\(747\) | 12.0000 | − | 33.9411i | 0.439057 | − | 1.24184i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 76.3675i | 2.79041i | ||||||||
\(750\) | 16.0000 | − | 11.3137i | 0.584237 | − | 0.413118i | ||||
\(751\) | −40.0000 | −1.45962 | −0.729810 | − | 0.683650i | \(-0.760392\pi\) | ||||
−0.729810 | + | 0.683650i | \(0.760392\pi\) | |||||||
\(752\) | − | 9.89949i | − | 0.360997i | ||||||
\(753\) | −8.00000 | + | 5.65685i | −0.291536 | + | 0.206147i | ||||
\(754\) | − | 25.4558i | − | 0.927047i | ||||||
\(755\) | −6.00000 | −0.218362 | ||||||||
\(756\) | −6.00000 | − | 21.2132i | −0.218218 | − | 0.771517i | ||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | −2.00000 | −0.0726433 | ||||||||
\(759\) | −8.00000 | + | 1.41421i | −0.290382 | + | 0.0513327i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.0000 | −0.869999 | −0.435000 | − | 0.900431i | \(-0.643252\pi\) | ||||
−0.435000 | + | 0.900431i | \(0.643252\pi\) | |||||||
\(762\) | −18.0000 | + | 12.7279i | −0.652071 | + | 0.461084i | ||||
\(763\) | −54.0000 | −1.95493 | ||||||||
\(764\) | − | 9.89949i | − | 0.358151i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.41421i | 0.0510976i | ||||||||
\(767\) | −48.0000 | −1.73318 | ||||||||
\(768\) | −1.00000 | − | 1.41421i | −0.0360844 | − | 0.0510310i | ||||
\(769\) | 42.4264i | 1.52994i | 0.644069 | + | 0.764968i | \(0.277245\pi\) | ||||
−0.644069 | + | 0.764968i | \(0.722755\pi\) | |||||||
\(770\) | 18.0000 | + | 8.48528i | 0.648675 | + | 0.305788i | ||||
\(771\) | 16.0000 | − | 11.3137i | 0.576226 | − | 0.407453i | ||||
\(772\) | − | 8.48528i | − | 0.305392i | ||||||
\(773\) | − | 18.3848i | − | 0.661254i | −0.943761 | − | 0.330627i | \(-0.892740\pi\) | ||
0.943761 | − | 0.330627i | \(-0.107260\pi\) | |||||||
\(774\) | 24.0000 | + | 8.48528i | 0.862662 | + | 0.304997i | ||||
\(775\) | −12.0000 | −0.431053 | ||||||||
\(776\) | −8.00000 | −0.287183 | ||||||||
\(777\) | −12.0000 | + | 8.48528i | −0.430498 | + | 0.304408i | ||||
\(778\) | 9.89949i | 0.354914i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −6.00000 | − | 8.48528i | −0.214834 | − | 0.303822i | ||||
\(781\) | −10.0000 | + | 21.2132i | −0.357828 | + | 0.759068i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 30.0000 | − | 8.48528i | 1.07211 | − | 0.303239i | ||||
\(784\) | −11.0000 | −0.392857 | ||||||||
\(785\) | 31.1127i | 1.11046i | ||||||||
\(786\) | 12.0000 | + | 16.9706i | 0.428026 | + | 0.605320i | ||||
\(787\) | 42.4264i | 1.51234i | 0.654376 | + | 0.756169i | \(0.272931\pi\) | ||||
−0.654376 | + | 0.756169i | \(0.727069\pi\) | |||||||
\(788\) | 18.0000 | 0.641223 | ||||||||
\(789\) | 12.0000 | + | 16.9706i | 0.427211 | + | 0.604168i | ||||
\(790\) | 6.00000 | 0.213470 | ||||||||
\(791\) | 48.0000 | 1.70668 | ||||||||
\(792\) | 7.00000 | − | 7.07107i | 0.248734 | − | 0.251259i | ||||
\(793\) | 18.0000 | 0.639199 | ||||||||
\(794\) | 34.0000 | 1.20661 | ||||||||
\(795\) | −10.0000 | − | 14.1421i | −0.354663 | − | 0.501570i | ||||
\(796\) | −16.0000 | −0.567105 | ||||||||
\(797\) | − | 1.41421i | − | 0.0500940i | −0.999686 | − | 0.0250470i | \(-0.992026\pi\) | ||
0.999686 | − | 0.0250470i | \(-0.00797354\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −3.00000 | −0.106066 | ||||||||
\(801\) | 16.0000 | + | 5.65685i | 0.565332 | + | 0.199875i | ||||
\(802\) | − | 36.7696i | − | 1.29838i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 4.00000 | + | 5.65685i | 0.141069 | + | 0.199502i | ||||
\(805\) | 8.48528i | 0.299067i | ||||||||
\(806\) | 16.9706i | 0.597763i | ||||||||
\(807\) | 10.0000 | − | 7.07107i | 0.352017 | − | 0.248913i | ||||
\(808\) | −6.00000 | −0.211079 | ||||||||
\(809\) | 54.0000 | 1.89854 | 0.949269 | − | 0.314464i | \(-0.101825\pi\) | ||||
0.949269 | + | 0.314464i | \(0.101825\pi\) | |||||||
\(810\) | 8.00000 | − | 9.89949i | 0.281091 | − | 0.347833i | ||||
\(811\) | − | 25.4558i | − | 0.893876i | −0.894565 | − | 0.446938i | \(-0.852515\pi\) | ||
0.894565 | − | 0.446938i | \(-0.147485\pi\) | |||||||
\(812\) | − | 25.4558i | − | 0.893325i | ||||||
\(813\) | −18.0000 | + | 12.7279i | −0.631288 | + | 0.446388i | ||||
\(814\) | −6.00000 | − | 2.82843i | −0.210300 | − | 0.0991363i | ||||
\(815\) | − | 2.82843i | − | 0.0990755i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 8.48528i | 0.296681i | ||||||||
\(819\) | −18.0000 | + | 50.9117i | −0.628971 | + | 1.77900i | ||||
\(820\) | 8.48528i | 0.296319i | ||||||||
\(821\) | −30.0000 | −1.04701 | −0.523504 | − | 0.852023i | \(-0.675375\pi\) | ||||
−0.523504 | + | 0.852023i | \(0.675375\pi\) | |||||||
\(822\) | −4.00000 | + | 2.82843i | −0.139516 | + | 0.0986527i | ||||
\(823\) | −40.0000 | −1.39431 | −0.697156 | − | 0.716919i | \(-0.745552\pi\) | ||||
−0.697156 | + | 0.716919i | \(0.745552\pi\) | |||||||
\(824\) | 4.00000 | 0.139347 | ||||||||
\(825\) | −3.00000 | − | 16.9706i | −0.104447 | − | 0.590839i | ||||
\(826\) | −48.0000 | −1.67013 | ||||||||
\(827\) | −36.0000 | −1.25184 | −0.625921 | − | 0.779886i | \(-0.715277\pi\) | ||||
−0.625921 | + | 0.779886i | \(0.715277\pi\) | |||||||
\(828\) | 4.00000 | + | 1.41421i | 0.139010 | + | 0.0491473i | ||||
\(829\) | 2.00000 | 0.0694629 | 0.0347314 | − | 0.999397i | \(-0.488942\pi\) | ||||
0.0347314 | + | 0.999397i | \(0.488942\pi\) | |||||||
\(830\) | − | 16.9706i | − | 0.589057i | ||||||
\(831\) | 30.0000 | − | 21.2132i | 1.04069 | − | 0.735878i | ||||
\(832\) | 4.24264i | 0.147087i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −24.0000 | + | 16.9706i | −0.831052 | + | 0.587643i | ||||
\(835\) | − | 16.9706i | − | 0.587291i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −20.0000 | + | 5.65685i | −0.691301 | + | 0.195529i | ||||
\(838\) | − | 11.3137i | − | 0.390826i | ||||||
\(839\) | 15.5563i | 0.537065i | 0.963271 | + | 0.268532i | \(0.0865386\pi\) | ||||
−0.963271 | + | 0.268532i | \(0.913461\pi\) | |||||||
\(840\) | −6.00000 | − | 8.48528i | −0.207020 | − | 0.292770i | ||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 10.0000 | 0.344623 | ||||||||
\(843\) | 12.0000 | + | 16.9706i | 0.413302 | + | 0.584497i | ||||
\(844\) | − | 8.48528i | − | 0.292075i | ||||||
\(845\) | 7.07107i | 0.243252i | ||||||||
\(846\) | −28.0000 | − | 9.89949i | −0.962660 | − | 0.340352i | ||||
\(847\) | 36.0000 | − | 29.6985i | 1.23697 | − | 1.02045i | ||||
\(848\) | 7.07107i | 0.242821i | ||||||||
\(849\) | −12.0000 | + | 8.48528i | −0.411839 | + | 0.291214i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 2.82843i | − | 0.0969572i | ||||||
\(852\) | 10.0000 | − | 7.07107i | 0.342594 | − | 0.242251i | ||||
\(853\) | 21.2132i | 0.726326i | 0.931726 | + | 0.363163i | \(0.118303\pi\) | ||||
−0.931726 | + | 0.363163i | \(0.881697\pi\) | |||||||
\(854\) | 18.0000 | 0.615947 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.0000 | 0.615227 | ||||||||
\(857\) | 6.00000 | 0.204956 | 0.102478 | − | 0.994735i | \(-0.467323\pi\) | ||||
0.102478 | + | 0.994735i | \(0.467323\pi\) | |||||||
\(858\) | −24.0000 | + | 4.24264i | −0.819346 | + | 0.144841i | ||||
\(859\) | −22.0000 | −0.750630 | −0.375315 | − | 0.926897i | \(-0.622466\pi\) | ||||
−0.375315 | + | 0.926897i | \(0.622466\pi\) | |||||||
\(860\) | 12.0000 | 0.409197 | ||||||||
\(861\) | 36.0000 | − | 25.4558i | 1.22688 | − | 0.867533i | ||||
\(862\) | 36.0000 | 1.22616 | ||||||||
\(863\) | 7.07107i | 0.240702i | 0.992731 | + | 0.120351i | \(0.0384020\pi\) | ||||
−0.992731 | + | 0.120351i | \(0.961598\pi\) | |||||||
\(864\) | −5.00000 | + | 1.41421i | −0.170103 | + | 0.0481125i | ||||
\(865\) | − | 8.48528i | − | 0.288508i | ||||||
\(866\) | −2.00000 | −0.0679628 | ||||||||
\(867\) | 17.0000 | + | 24.0416i | 0.577350 | + | 0.816497i | ||||
\(868\) | 16.9706i | 0.576018i | ||||||||
\(869\) | 6.00000 | − | 12.7279i | 0.203536 | − | 0.431765i | ||||
\(870\) | 12.0000 | − | 8.48528i | 0.406838 | − | 0.287678i | ||||
\(871\) | − | 16.9706i | − | 0.575026i | ||||||
\(872\) | 12.7279i | 0.431022i | ||||||||
\(873\) | −8.00000 | + | 22.6274i | −0.270759 | + | 0.765822i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −48.0000 | −1.62270 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.6985i | 1.00285i | 0.865202 | + | 0.501423i | \(0.167190\pi\) | ||||
−0.865202 | + | 0.501423i | \(0.832810\pi\) | |||||||
\(878\) | − | 21.2132i | − | 0.715911i | ||||||
\(879\) | 6.00000 | + | 8.48528i | 0.202375 | + | 0.286201i | ||||
\(880\) | 2.00000 | − | 4.24264i | 0.0674200 | − | 0.143019i | ||||
\(881\) | − | 5.65685i | − | 0.190584i | −0.995449 | − | 0.0952921i | \(-0.969621\pi\) | ||
0.995449 | − | 0.0952921i | \(-0.0303785\pi\) | |||||||
\(882\) | −11.0000 | + | 31.1127i | −0.370389 | + | 1.04762i | ||||
\(883\) | 20.0000 | 0.673054 | 0.336527 | − | 0.941674i | \(-0.390748\pi\) | ||||
0.336527 | + | 0.941674i | \(0.390748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16.0000 | − | 22.6274i | −0.537834 | − | 0.760612i | ||||
\(886\) | − | 28.2843i | − | 0.950229i | ||||||
\(887\) | 48.0000 | 1.61168 | 0.805841 | − | 0.592132i | \(-0.201714\pi\) | ||||
0.805841 | + | 0.592132i | \(0.201714\pi\) | |||||||
\(888\) | 2.00000 | + | 2.82843i | 0.0671156 | + | 0.0949158i | ||||
\(889\) | 54.0000 | 1.81110 | ||||||||
\(890\) | 8.00000 | 0.268161 | ||||||||
\(891\) | −13.0000 | − | 26.8701i | −0.435516 | − | 0.900181i | ||||
\(892\) | 8.00000 | 0.267860 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −6.00000 | − | 8.48528i | −0.200670 | − | 0.283790i | ||||
\(895\) | −8.00000 | −0.267411 | ||||||||
\(896\) | 4.24264i | 0.141737i | ||||||||
\(897\) | −6.00000 | − | 8.48528i | −0.200334 | − | 0.283315i | ||||
\(898\) | 31.1127i | 1.03824i | ||||||||
\(899\) | −24.0000 | −0.800445 | ||||||||
\(900\) | −3.00000 | + | 8.48528i | −0.100000 | + | 0.282843i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 18.0000 | + | 8.48528i | 0.599334 | + | 0.282529i | ||||
\(903\) | −36.0000 | − | 50.9117i | −1.19800 | − | 1.69423i | ||||
\(904\) | − | 11.3137i | − | 0.376288i | ||||||
\(905\) | − | 2.82843i | − | 0.0940201i | ||||||
\(906\) | 6.00000 | − | 4.24264i | 0.199337 | − | 0.140952i | ||||
\(907\) | 44.0000 | 1.46100 | 0.730498 | − | 0.682915i | \(-0.239288\pi\) | ||||
0.730498 | + | 0.682915i | \(0.239288\pi\) | |||||||
\(908\) | 6.00000 | 0.199117 | ||||||||
\(909\) | −6.00000 | + | 16.9706i | −0.199007 | + | 0.562878i | ||||
\(910\) | 25.4558i | 0.843853i | ||||||||
\(911\) | − | 9.89949i | − | 0.327985i | −0.986462 | − | 0.163992i | \(-0.947563\pi\) | ||
0.986462 | − | 0.163992i | \(-0.0524373\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36.0000 | − | 16.9706i | −1.19143 | − | 0.561644i | ||||
\(914\) | − | 8.48528i | − | 0.280668i | ||||||
\(915\) | 6.00000 | + | 8.48528i | 0.198354 | + | 0.280515i | ||||
\(916\) | 14.0000 | 0.462573 | ||||||||
\(917\) | − | 50.9117i | − | 1.68125i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 38.1838i | − | 1.25957i | −0.776771 | − | 0.629783i | \(-0.783144\pi\) | ||
0.776771 | − | 0.629783i | \(-0.216856\pi\) | |||||||
\(920\) | 2.00000 | 0.0659380 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 30.0000 | 0.987997 | ||||||||
\(923\) | −30.0000 | −0.987462 | ||||||||
\(924\) | −24.0000 | + | 4.24264i | −0.789542 | + | 0.139573i | ||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | −32.0000 | −1.05159 | ||||||||
\(927\) | 4.00000 | − | 11.3137i | 0.131377 | − | 0.371591i | ||||
\(928\) | −6.00000 | −0.196960 | ||||||||
\(929\) | 2.82843i | 0.0927977i | 0.998923 | + | 0.0463988i | \(0.0147745\pi\) | ||||
−0.998923 | + | 0.0463988i | \(0.985225\pi\) | |||||||
\(930\) | −8.00000 | + | 5.65685i | −0.262330 | + | 0.185496i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −18.0000 | −0.589610 | ||||||||
\(933\) | −38.0000 | + | 26.8701i | −1.24406 | + | 0.879686i | ||||
\(934\) | 31.1127i | 1.01804i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 12.0000 | + | 4.24264i | 0.392232 | + | 0.138675i | ||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | − | 16.9706i | − | 0.554109i | ||||||
\(939\) | 10.0000 | + | 14.1421i | 0.326338 | + | 0.461511i | ||||
\(940\) | −14.0000 | −0.456630 | ||||||||
\(941\) | −42.0000 | −1.36916 | −0.684580 | − | 0.728937i | \(-0.740015\pi\) | ||||
−0.684580 | + | 0.728937i | \(0.740015\pi\) | |||||||
\(942\) | −22.0000 | − | 31.1127i | −0.716799 | − | 1.01371i | ||||
\(943\) | 8.48528i | 0.276319i | ||||||||
\(944\) | 11.3137i | 0.368230i | ||||||||
\(945\) | −30.0000 | + | 8.48528i | −0.975900 | + | 0.276026i | ||||
\(946\) | 12.0000 | − | 25.4558i | 0.390154 | − | 0.827641i | ||||
\(947\) | − | 48.0833i | − | 1.56250i | −0.624221 | − | 0.781248i | \(-0.714583\pi\) | ||
0.624221 | − | 0.781248i | \(-0.285417\pi\) | |||||||
\(948\) | −6.00000 | + | 4.24264i | −0.194871 | + | 0.137795i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.0000 | + | 9.89949i | −0.453981 | + | 0.321013i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.0000 | 1.74923 | 0.874616 | − | 0.484817i | \(-0.161114\pi\) | ||||
0.874616 | + | 0.484817i | \(0.161114\pi\) | |||||||
\(954\) | 20.0000 | + | 7.07107i | 0.647524 | + | 0.228934i | ||||
\(955\) | −14.0000 | −0.453029 | ||||||||
\(956\) | 12.0000 | 0.388108 | ||||||||
\(957\) | −6.00000 | − | 33.9411i | −0.193952 | − | 1.09716i | ||||
\(958\) | 12.0000 | 0.387702 | ||||||||
\(959\) | 12.0000 | 0.387500 | ||||||||
\(960\) | −2.00000 | + | 1.41421i | −0.0645497 | + | 0.0456435i | ||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | − | 8.48528i | − | 0.273576i | ||||||
\(963\) | 18.0000 | − | 50.9117i | 0.580042 | − | 1.64061i | ||||
\(964\) | 8.48528i | 0.273293i | ||||||||
\(965\) | −12.0000 | −0.386294 | ||||||||
\(966\) | −6.00000 | − | 8.48528i | −0.193047 | − | 0.273009i | ||||
\(967\) | 4.24264i | 0.136434i | 0.997671 | + | 0.0682171i | \(0.0217310\pi\) | ||||
−0.997671 | + | 0.0682171i | \(0.978269\pi\) | |||||||
\(968\) | −7.00000 | − | 8.48528i | −0.224989 | − | 0.272727i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 11.3137i | 0.363261i | ||||||||
\(971\) | 45.2548i | 1.45230i | 0.687538 | + | 0.726148i | \(0.258691\pi\) | ||||
−0.687538 | + | 0.726148i | \(0.741309\pi\) | |||||||
\(972\) | −1.00000 | + | 15.5563i | −0.0320750 | + | 0.498970i | ||||
\(973\) | 72.0000 | 2.30821 | ||||||||
\(974\) | −20.0000 | −0.640841 | ||||||||
\(975\) | 18.0000 | − | 12.7279i | 0.576461 | − | 0.407620i | ||||
\(976\) | − | 4.24264i | − | 0.135804i | ||||||
\(977\) | − | 14.1421i | − | 0.452447i | −0.974075 | − | 0.226224i | \(-0.927362\pi\) | ||
0.974075 | − | 0.226224i | \(-0.0726380\pi\) | |||||||
\(978\) | 2.00000 | + | 2.82843i | 0.0639529 | + | 0.0904431i | ||||
\(979\) | 8.00000 | − | 16.9706i | 0.255681 | − | 0.542382i | ||||
\(980\) | 15.5563i | 0.496929i | ||||||||
\(981\) | 36.0000 | + | 12.7279i | 1.14939 | + | 0.406371i | ||||
\(982\) | 6.00000 | 0.191468 | ||||||||
\(983\) | − | 9.89949i | − | 0.315745i | −0.987460 | − | 0.157872i | \(-0.949537\pi\) | ||
0.987460 | − | 0.157872i | \(-0.0504635\pi\) | |||||||
\(984\) | −6.00000 | − | 8.48528i | −0.191273 | − | 0.270501i | ||||
\(985\) | − | 25.4558i | − | 0.811091i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 42.0000 | + | 59.3970i | 1.33687 | + | 1.89063i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.0000 | 0.381578 | ||||||||
\(990\) | −10.0000 | − | 9.89949i | −0.317821 | − | 0.314627i | ||||
\(991\) | 20.0000 | 0.635321 | 0.317660 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317660 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(992\) | 4.00000 | 0.127000 | ||||||||
\(993\) | 10.0000 | + | 14.1421i | 0.317340 | + | 0.448787i | ||||
\(994\) | −30.0000 | −0.951542 | ||||||||
\(995\) | 22.6274i | 0.717337i | ||||||||
\(996\) | 12.0000 | + | 16.9706i | 0.380235 | + | 0.537733i | ||||
\(997\) | − | 29.6985i | − | 0.940560i | −0.882517 | − | 0.470280i | \(-0.844153\pi\) | ||
0.882517 | − | 0.470280i | \(-0.155847\pi\) | |||||||
\(998\) | −14.0000 | −0.443162 | ||||||||
\(999\) | 10.0000 | − | 2.82843i | 0.316386 | − | 0.0894875i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))