Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(251,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.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: | \(2.87461447277\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.2580992.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + x^{4} + 2x^{2} - 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.6 | ||
Root | \(-1.06244 + 0.933389i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 360.251 |
Dual form | 360.2.b.c.251.5 |
$q$-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 \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.06244 | + | 0.933389i | 0.751260 | + | 0.660006i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.257569 | + | 1.98335i | 0.128785 | + | 0.991673i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.41421i | 0.534522i | 0.963624 | + | 0.267261i | \(0.0861187\pi\) | ||||
−0.963624 | + | 0.267261i | \(0.913881\pi\) | |||||||
\(8\) | −1.57758 | + | 2.34760i | −0.557759 | + | 0.830003i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.06244 | − | 0.933389i | −0.335974 | − | 0.295164i | ||||
\(11\) | 2.31934i | 0.699308i | 0.936879 | + | 0.349654i | \(0.113701\pi\) | ||||
−0.936879 | + | 0.349654i | \(0.886299\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.14777i | 1.42773i | 0.700281 | + | 0.713867i | \(0.253058\pi\) | ||||
−0.700281 | + | 0.713867i | \(0.746942\pi\) | |||||||
\(14\) | −1.32001 | + | 1.50252i | −0.352788 | + | 0.401566i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.86732 | + | 1.02170i | −0.966829 | + | 0.255424i | ||||
\(17\) | − | 5.10495i | − | 1.23813i | −0.785339 | − | 0.619067i | \(-0.787511\pi\) | ||
0.785339 | − | 0.619067i | \(-0.212489\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.24977 | 1.89263 | 0.946314 | − | 0.323250i | \(-0.104775\pi\) | ||||
0.946314 | + | 0.323250i | \(0.104775\pi\) | |||||||
\(20\) | −0.257569 | − | 1.98335i | −0.0575942 | − | 0.443489i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.16485 | + | 2.46417i | −0.461548 | + | 0.525363i | ||||
\(23\) | −0.969724 | −0.202201 | −0.101101 | − | 0.994876i | \(-0.532236\pi\) | ||||
−0.101101 | + | 0.994876i | \(0.532236\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.80487 | + | 5.46921i | −0.942313 | + | 1.07260i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.80487 | + | 0.364258i | −0.530071 | + | 0.0688382i | ||||
\(29\) | −3.28005 | −0.609089 | −0.304545 | − | 0.952498i | \(-0.598504\pi\) | ||||
−0.304545 | + | 0.952498i | \(0.598504\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.10495i | − | 0.916877i | −0.888726 | − | 0.458438i | \(-0.848409\pi\) | ||
0.888726 | − | 0.458438i | \(-0.151591\pi\) | |||||||
\(32\) | −5.06244 | − | 2.52422i | −0.894922 | − | 0.446223i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.76491 | − | 5.42372i | 0.817175 | − | 0.930160i | ||||
\(35\) | − | 1.41421i | − | 0.239046i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.69074i | − | 0.606754i | −0.952871 | − | 0.303377i | \(-0.901886\pi\) | ||
0.952871 | − | 0.303377i | \(-0.0981141\pi\) | |||||||
\(38\) | 8.76491 | + | 7.70025i | 1.42186 | + | 1.24915i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.57758 | − | 2.34760i | 0.249437 | − | 0.371189i | ||||
\(41\) | − | 4.59587i | − | 0.717754i | −0.933385 | − | 0.358877i | \(-0.883160\pi\) | ||
0.933385 | − | 0.358877i | \(-0.116840\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.21949 | 0.490968 | 0.245484 | − | 0.969401i | \(-0.421053\pi\) | ||||
0.245484 | + | 0.969401i | \(0.421053\pi\) | |||||||
\(44\) | −4.60006 | + | 0.597391i | −0.693485 | + | 0.0900601i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.03028 | − | 0.905130i | −0.151906 | − | 0.133454i | ||||
\(47\) | 9.52982 | 1.39007 | 0.695033 | − | 0.718977i | \(-0.255390\pi\) | ||||
0.695033 | + | 0.718977i | \(0.255390\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | 1.06244 | + | 0.933389i | 0.150252 | + | 0.132001i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −10.2098 | + | 1.32591i | −1.41585 | + | 0.183870i | ||||
\(53\) | −7.21949 | −0.991674 | −0.495837 | − | 0.868416i | \(-0.665139\pi\) | ||||
−0.495837 | + | 0.868416i | \(0.665139\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.31934i | − | 0.312740i | ||||||
\(56\) | −3.32001 | − | 2.23104i | −0.443655 | − | 0.298135i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.48486 | − | 3.06156i | −0.457585 | − | 0.402003i | ||||
\(59\) | 0.862313i | 0.112264i | 0.998423 | + | 0.0561318i | \(0.0178767\pi\) | ||||
−0.998423 | + | 0.0561318i | \(0.982123\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.63869i | 0.593923i | 0.954889 | + | 0.296961i | \(0.0959733\pi\) | ||||
−0.954889 | + | 0.296961i | \(0.904027\pi\) | |||||||
\(62\) | 4.76491 | − | 5.42372i | 0.605144 | − | 0.688813i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.02248 | − | 7.40707i | −0.377810 | − | 0.925883i | ||||
\(65\) | − | 5.14777i | − | 0.638502i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.28005 | 0.645060 | 0.322530 | − | 0.946559i | \(-0.395467\pi\) | ||||
0.322530 | + | 0.946559i | \(0.395467\pi\) | |||||||
\(68\) | 10.1249 | − | 1.31488i | 1.22782 | − | 0.159452i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.32001 | − | 1.50252i | 0.157772 | − | 0.179586i | ||||
\(71\) | 13.2800 | 1.57605 | 0.788026 | − | 0.615642i | \(-0.211103\pi\) | ||||
0.788026 | + | 0.615642i | \(0.211103\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.5601 | −1.47005 | −0.735024 | − | 0.678041i | \(-0.762829\pi\) | ||||
−0.735024 | + | 0.678041i | \(0.762829\pi\) | |||||||
\(74\) | 3.44490 | − | 3.92120i | 0.400461 | − | 0.455830i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.12489 | + | 16.3621i | 0.243741 | + | 1.87687i | ||||
\(77\) | −3.28005 | −0.373796 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 8.01901i | − | 0.902210i | −0.892471 | − | 0.451105i | \(-0.851030\pi\) | ||
0.892471 | − | 0.451105i | \(-0.148970\pi\) | |||||||
\(80\) | 3.86732 | − | 1.02170i | 0.432379 | − | 0.114229i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.28974 | − | 4.88285i | 0.473722 | − | 0.539220i | ||||
\(83\) | 7.38148i | 0.810223i | 0.914267 | + | 0.405111i | \(0.132767\pi\) | ||||
−0.914267 | + | 0.405111i | \(0.867233\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.10495i | 0.553710i | ||||||||
\(86\) | 3.42053 | + | 3.00504i | 0.368845 | + | 0.324042i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.44490 | − | 3.65895i | −0.580428 | − | 0.390046i | ||||
\(89\) | − | 10.2527i | − | 1.08679i | −0.839478 | − | 0.543393i | \(-0.817139\pi\) | ||
0.839478 | − | 0.543393i | \(-0.182861\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.28005 | −0.763156 | ||||||||
\(92\) | −0.249771 | − | 1.92330i | −0.0260404 | − | 0.200518i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.1249 | + | 8.89503i | 1.04430 | + | 0.917452i | ||||
\(95\) | −8.24977 | −0.846409 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.7796 | −1.60217 | −0.801087 | − | 0.598548i | \(-0.795745\pi\) | ||||
−0.801087 | + | 0.598548i | \(0.795745\pi\) | |||||||
\(98\) | 5.31221 | + | 4.66695i | 0.536615 | + | 0.471433i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.257569 | + | 1.98335i | 0.0257569 | + | 0.198335i | ||||
\(101\) | 16.4390 | 1.63574 | 0.817870 | − | 0.575403i | \(-0.195155\pi\) | ||||
0.817870 | + | 0.575403i | \(0.195155\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.9096i | 1.56762i | 0.621002 | + | 0.783809i | \(0.286726\pi\) | ||||
−0.621002 | + | 0.783809i | \(0.713274\pi\) | |||||||
\(104\) | −12.0849 | − | 8.12102i | −1.18502 | − | 0.796332i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.67030 | − | 6.73860i | −0.745005 | − | 0.654511i | ||||
\(107\) | − | 2.82843i | − | 0.273434i | −0.990610 | − | 0.136717i | \(-0.956345\pi\) | ||
0.990610 | − | 0.136717i | \(-0.0436552\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 10.2955i | − | 0.986134i | −0.869991 | − | 0.493067i | \(-0.835876\pi\) | ||
0.869991 | − | 0.493067i | \(-0.164124\pi\) | |||||||
\(110\) | 2.16485 | − | 2.46417i | 0.206410 | − | 0.234949i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.44490 | − | 5.46921i | −0.136530 | − | 0.516792i | ||||
\(113\) | 0.466267i | 0.0438627i | 0.999759 | + | 0.0219313i | \(0.00698152\pi\) | ||||
−0.999759 | + | 0.0219313i | \(0.993018\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.969724 | 0.0904272 | ||||||||
\(116\) | −0.844838 | − | 6.50547i | −0.0784413 | − | 0.604017i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.804874 | + | 0.916158i | −0.0740946 | + | 0.0843392i | ||||
\(119\) | 7.21949 | 0.661810 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.62065 | 0.510968 | ||||||||
\(122\) | −4.32970 | + | 4.92834i | −0.391993 | + | 0.446191i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.1249 | − | 1.31488i | 0.909242 | − | 0.118080i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.71784i | − | 0.596112i | −0.954548 | − | 0.298056i | \(-0.903662\pi\) | ||
0.954548 | − | 0.298056i | \(-0.0963382\pi\) | |||||||
\(128\) | 3.70247 | − | 10.6907i | 0.327255 | − | 0.944936i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.80487 | − | 5.46921i | 0.421415 | − | 0.479682i | ||||
\(131\) | 21.1002i | 1.84353i | 0.387749 | + | 0.921765i | \(0.373253\pi\) | ||||
−0.387749 | + | 0.921765i | \(0.626747\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.6669i | 1.01165i | ||||||||
\(134\) | 5.60975 | + | 4.92834i | 0.484608 | + | 0.425744i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.9844 | + | 8.05348i | 1.02765 | + | 0.690580i | ||||
\(137\) | 21.0573i | 1.79905i | 0.436869 | + | 0.899525i | \(0.356087\pi\) | ||||
−0.436869 | + | 0.899525i | \(0.643913\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.90917 | −0.246753 | −0.123376 | − | 0.992360i | \(-0.539372\pi\) | ||||
−0.123376 | + | 0.992360i | \(0.539372\pi\) | |||||||
\(140\) | 2.80487 | − | 0.364258i | 0.237055 | − | 0.0307854i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 14.1093 | + | 12.3955i | 1.18403 | + | 1.04020i | ||||
\(143\) | −11.9394 | −0.998427 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.28005 | 0.272393 | ||||||||
\(146\) | −13.3444 | − | 11.7235i | −1.10439 | − | 0.970240i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.32001 | − | 0.950620i | 0.601701 | − | 0.0781405i | ||||
\(149\) | −11.2800 | −0.924097 | −0.462049 | − | 0.886855i | \(-0.652885\pi\) | ||||
−0.462049 | + | 0.886855i | \(0.652885\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 21.7638i | − | 1.77111i | −0.464531 | − | 0.885557i | \(-0.653777\pi\) | ||
0.464531 | − | 0.885557i | \(-0.346223\pi\) | |||||||
\(152\) | −13.0147 | + | 19.3672i | −1.05563 | + | 1.57089i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.48486 | − | 3.06156i | −0.280818 | − | 0.246708i | ||||
\(155\) | 5.10495i | 0.410040i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 8.32943i | − | 0.664761i | −0.943145 | − | 0.332380i | \(-0.892148\pi\) | ||
0.943145 | − | 0.332380i | \(-0.107852\pi\) | |||||||
\(158\) | 7.48486 | − | 8.51974i | 0.595464 | − | 0.677794i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.06244 | + | 2.52422i | 0.400221 | + | 0.199557i | ||||
\(161\) | − | 1.37140i | − | 0.108081i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.4995 | −1.60565 | −0.802824 | − | 0.596216i | \(-0.796670\pi\) | ||||
−0.802824 | + | 0.596216i | \(0.796670\pi\) | |||||||
\(164\) | 9.11520 | − | 1.18375i | 0.711777 | − | 0.0924356i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.88979 | + | 7.84240i | −0.534752 | + | 0.608688i | ||||
\(167\) | 6.90917 | 0.534648 | 0.267324 | − | 0.963607i | \(-0.413861\pi\) | ||||
0.267324 | + | 0.963607i | \(0.413861\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.4995 | −1.03843 | ||||||||
\(170\) | −4.76491 | + | 5.42372i | −0.365452 | + | 0.415980i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.829242 | + | 6.38537i | 0.0632291 | + | 0.486880i | ||||
\(173\) | −19.2195 | −1.46123 | −0.730616 | − | 0.682789i | \(-0.760767\pi\) | ||||
−0.730616 | + | 0.682789i | \(0.760767\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.41421i | 0.106904i | ||||||||
\(176\) | −2.36967 | − | 8.96963i | −0.178620 | − | 0.676112i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.56978 | − | 10.8929i | 0.717286 | − | 0.816460i | ||||
\(179\) | − | 12.5293i | − | 0.936480i | −0.883601 | − | 0.468240i | \(-0.844888\pi\) | ||
0.883601 | − | 0.468240i | \(-0.155112\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.53489i | 0.262746i | 0.991333 | + | 0.131373i | \(0.0419386\pi\) | ||||
−0.991333 | + | 0.131373i | \(0.958061\pi\) | |||||||
\(182\) | −7.73463 | − | 6.79512i | −0.573329 | − | 0.503688i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.52982 | − | 2.27653i | 0.112780 | − | 0.167828i | ||||
\(185\) | 3.69074i | 0.271349i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.8401 | 0.865837 | ||||||||
\(188\) | 2.45459 | + | 18.9009i | 0.179019 | + | 1.37849i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.76491 | − | 7.70025i | −0.635873 | − | 0.558635i | ||||
\(191\) | −25.1202 | −1.81763 | −0.908816 | − | 0.417196i | \(-0.863013\pi\) | ||||
−0.908816 | + | 0.417196i | \(0.863013\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.77959 | 0.559987 | 0.279994 | − | 0.960002i | \(-0.409668\pi\) | ||||
0.279994 | + | 0.960002i | \(0.409668\pi\) | |||||||
\(194\) | −16.7649 | − | 14.7285i | −1.20365 | − | 1.05744i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.28785 | + | 9.91673i | 0.0919889 | + | 0.708338i | ||||
\(197\) | −2.49954 | −0.178085 | −0.0890425 | − | 0.996028i | \(-0.528381\pi\) | ||||
−0.0890425 | + | 0.996028i | \(0.528381\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.0573i | 1.49272i | 0.665545 | + | 0.746358i | \(0.268199\pi\) | ||||
−0.665545 | + | 0.746358i | \(0.731801\pi\) | |||||||
\(200\) | −1.57758 | + | 2.34760i | −0.111552 | + | 0.166001i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 17.4655 | + | 15.3440i | 1.22887 | + | 1.07960i | ||||
\(203\) | − | 4.63869i | − | 0.325572i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.59587i | 0.320989i | ||||||||
\(206\) | −14.8498 | + | 16.9030i | −1.03464 | + | 1.17769i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.25946 | − | 19.9081i | −0.364678 | − | 1.38038i | ||||
\(209\) | 19.1341i | 1.32353i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0294 | −1.10351 | −0.551753 | − | 0.834007i | \(-0.686041\pi\) | ||||
−0.551753 | + | 0.834007i | \(0.686041\pi\) | |||||||
\(212\) | −1.85952 | − | 14.3188i | −0.127712 | − | 0.983416i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.64002 | − | 3.00504i | 0.180468 | − | 0.205420i | ||||
\(215\) | −3.21949 | −0.219568 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.21949 | 0.490091 | ||||||||
\(218\) | 9.60975 | − | 10.9384i | 0.650854 | − | 0.740843i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.60006 | − | 0.597391i | 0.310136 | − | 0.0402761i | ||||
\(221\) | 26.2791 | 1.76773 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.310412i | 0.0207868i | 0.999946 | + | 0.0103934i | \(0.00330837\pi\) | ||||
−0.999946 | + | 0.0103934i | \(0.996692\pi\) | |||||||
\(224\) | 3.56978 | − | 7.15938i | 0.238516 | − | 0.478356i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.435208 | + | 0.495382i | −0.0289496 | + | 0.0329523i | ||||
\(227\) | 3.84659i | 0.255307i | 0.991819 | + | 0.127654i | \(0.0407446\pi\) | ||||
−0.991819 | + | 0.127654i | \(0.959255\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 6.36331i | − | 0.420500i | −0.977648 | − | 0.210250i | \(-0.932572\pi\) | ||
0.977648 | − | 0.210250i | \(-0.0674277\pi\) | |||||||
\(230\) | 1.03028 | + | 0.905130i | 0.0679344 | + | 0.0596825i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.17454 | − | 7.70025i | 0.339725 | − | 0.505546i | ||||
\(233\) | 1.25836i | 0.0824379i | 0.999150 | + | 0.0412189i | \(0.0131241\pi\) | ||||
−0.999150 | + | 0.0412189i | \(0.986876\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.52982 | −0.621657 | ||||||||
\(236\) | −1.71026 | + | 0.222105i | −0.111329 | + | 0.0144578i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.67030 | + | 6.73860i | 0.497192 | + | 0.436798i | ||||
\(239\) | 0.499542 | 0.0323127 | 0.0161563 | − | 0.999869i | \(-0.494857\pi\) | ||||
0.0161563 | + | 0.999869i | \(0.494857\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.06055 | 0.390394 | 0.195197 | − | 0.980764i | \(-0.437465\pi\) | ||||
0.195197 | + | 0.980764i | \(0.437465\pi\) | |||||||
\(242\) | 5.97161 | + | 5.24625i | 0.383870 | + | 0.337242i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9.20012 | + | 1.19478i | −0.588977 | + | 0.0764881i | ||||
\(245\) | −5.00000 | −0.319438 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 42.4679i | 2.70217i | ||||||||
\(248\) | 11.9844 | + | 8.05348i | 0.761010 | + | 0.511396i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.06244 | − | 0.933389i | −0.0671948 | − | 0.0590327i | ||||
\(251\) | − | 12.0904i | − | 0.763139i | −0.924340 | − | 0.381569i | \(-0.875384\pi\) | ||
0.924340 | − | 0.381569i | \(-0.124616\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.24912i | − | 0.141401i | ||||||
\(254\) | 6.27036 | − | 7.13732i | 0.393437 | − | 0.447835i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.9123 | − | 7.90245i | 0.869517 | − | 0.493903i | ||||
\(257\) | 11.5539i | 0.720712i | 0.932815 | + | 0.360356i | \(0.117345\pi\) | ||||
−0.932815 | + | 0.360356i | \(0.882655\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.21949 | 0.324324 | ||||||||
\(260\) | 10.2098 | − | 1.32591i | 0.633185 | − | 0.0822292i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −19.6947 | + | 22.4177i | −1.21674 | + | 1.38497i | ||||
\(263\) | −7.52982 | −0.464308 | −0.232154 | − | 0.972679i | \(-0.574577\pi\) | ||||
−0.232154 | + | 0.972679i | \(0.574577\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.21949 | 0.443490 | ||||||||
\(266\) | −10.8898 | + | 12.3955i | −0.667696 | + | 0.760014i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.35998 | + | 10.4722i | 0.0830738 | + | 0.639689i | ||||
\(269\) | 25.8401 | 1.57550 | 0.787751 | − | 0.615994i | \(-0.211246\pi\) | ||||
0.787751 | + | 0.615994i | \(0.211246\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 23.8001i | − | 1.44576i | −0.690976 | − | 0.722878i | \(-0.742819\pi\) | ||
0.690976 | − | 0.722878i | \(-0.257181\pi\) | |||||||
\(272\) | 5.21571 | + | 19.7425i | 0.316249 | + | 1.19706i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.6547 | + | 22.3722i | −1.18738 | + | 1.35156i | ||||
\(275\) | 2.31934i | 0.139862i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 24.1962i | − | 1.45381i | −0.686739 | − | 0.726904i | \(-0.740958\pi\) | ||
0.686739 | − | 0.726904i | \(-0.259042\pi\) | |||||||
\(278\) | −3.09083 | − | 2.71539i | −0.185376 | − | 0.162858i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.32001 | + | 2.23104i | 0.198409 | + | 0.133330i | ||||
\(281\) | − | 8.96696i | − | 0.534924i | −0.963568 | − | 0.267462i | \(-0.913815\pi\) | ||
0.963568 | − | 0.267462i | \(-0.0861850\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.7200 | 0.875010 | 0.437505 | − | 0.899216i | \(-0.355862\pi\) | ||||
0.437505 | + | 0.899216i | \(0.355862\pi\) | |||||||
\(284\) | 3.42053 | + | 26.3389i | 0.202971 | + | 1.56293i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.6850 | − | 11.1442i | −0.750079 | − | 0.658968i | ||||
\(287\) | 6.49954 | 0.383656 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.06055 | −0.532974 | ||||||||
\(290\) | 3.48486 | + | 3.06156i | 0.204638 | + | 0.179781i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.23509 | − | 24.9110i | −0.189319 | − | 1.45781i | ||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 0.862313i | − | 0.0502058i | ||||||
\(296\) | 8.66439 | + | 5.82244i | 0.503608 | + | 0.338422i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −11.9844 | − | 10.5287i | −0.694238 | − | 0.609910i | ||||
\(299\) | − | 4.99192i | − | 0.288690i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.55305i | 0.262434i | ||||||||
\(302\) | 20.3141 | − | 23.1228i | 1.16895 | − | 1.33057i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −31.9045 | + | 8.42876i | −1.82985 | + | 0.483423i | ||||
\(305\) | − | 4.63869i | − | 0.265610i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.0606 | 0.574186 | 0.287093 | − | 0.957903i | \(-0.407311\pi\) | ||||
0.287093 | + | 0.957903i | \(0.407311\pi\) | |||||||
\(308\) | −0.844838 | − | 6.50547i | −0.0481391 | − | 0.370683i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.76491 | + | 5.42372i | −0.270629 | + | 0.308047i | ||||
\(311\) | 11.5005 | 0.652131 | 0.326066 | − | 0.945347i | \(-0.394277\pi\) | ||||
0.326066 | + | 0.945347i | \(0.394277\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.65940 | 0.376412 | 0.188206 | − | 0.982130i | \(-0.439733\pi\) | ||||
0.188206 | + | 0.982130i | \(0.439733\pi\) | |||||||
\(314\) | 7.77460 | − | 8.84954i | 0.438746 | − | 0.499408i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.9045 | − | 2.06545i | 0.894697 | − | 0.116191i | ||||
\(317\) | 4.06055 | 0.228063 | 0.114032 | − | 0.993477i | \(-0.463623\pi\) | ||||
0.114032 | + | 0.993477i | \(0.463623\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 7.60756i | − | 0.425941i | ||||||
\(320\) | 3.02248 | + | 7.40707i | 0.168962 | + | 0.414068i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.28005 | − | 1.45703i | 0.0713342 | − | 0.0811971i | ||||
\(323\) | − | 42.1147i | − | 2.34332i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.14777i | 0.285547i | ||||||||
\(326\) | −21.7796 | − | 19.1341i | −1.20626 | − | 1.05974i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10.7893 | + | 7.25036i | 0.595738 | + | 0.400334i | ||||
\(329\) | 13.4772i | 0.743022i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.3103 | −0.566707 | −0.283353 | − | 0.959016i | \(-0.591447\pi\) | ||||
−0.283353 | + | 0.959016i | \(0.591447\pi\) | |||||||
\(332\) | −14.6400 | + | 1.90124i | −0.803476 | + | 0.104344i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.34060 | + | 6.44895i | 0.401660 | + | 0.352871i | ||||
\(335\) | −5.28005 | −0.288480 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.12110 | −0.115544 | −0.0577720 | − | 0.998330i | \(-0.518400\pi\) | ||||
−0.0577720 | + | 0.998330i | \(0.518400\pi\) | |||||||
\(338\) | −14.3425 | − | 12.6003i | −0.780129 | − | 0.685367i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −10.1249 | + | 1.31488i | −0.549099 | + | 0.0713093i | ||||
\(341\) | 11.8401 | 0.641180 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706i | 0.916324i | ||||||||
\(344\) | −5.07901 | + | 7.55809i | −0.273842 | + | 0.407505i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.4196 | − | 17.9393i | −1.09777 | − | 0.964421i | ||||
\(347\) | − | 32.6112i | − | 1.75066i | −0.483523 | − | 0.875332i | \(-0.660643\pi\) | ||
0.483523 | − | 0.875332i | \(-0.339357\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.55275i | 0.404289i | 0.979356 | + | 0.202145i | \(0.0647911\pi\) | ||||
−0.979356 | + | 0.202145i | \(0.935209\pi\) | |||||||
\(350\) | −1.32001 | + | 1.50252i | −0.0705576 | + | 0.0803131i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.85453 | − | 11.7415i | 0.312047 | − | 0.625826i | ||||
\(353\) | − | 8.01901i | − | 0.426809i | −0.976964 | − | 0.213405i | \(-0.931545\pi\) | ||
0.976964 | − | 0.213405i | \(-0.0684552\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.2800 | −0.704832 | ||||||||
\(356\) | 20.3347 | − | 2.64078i | 1.07774 | − | 0.139961i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.6947 | − | 13.3116i | 0.618082 | − | 0.703541i | ||||
\(359\) | −3.71904 | −0.196283 | −0.0981416 | − | 0.995172i | \(-0.531290\pi\) | ||||
−0.0981416 | + | 0.995172i | \(0.531290\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 49.0587 | 2.58204 | ||||||||
\(362\) | −3.29942 | + | 3.75561i | −0.173414 | + | 0.197391i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.87511 | − | 14.4388i | −0.0982827 | − | 0.756801i | ||||
\(365\) | 12.5601 | 0.657425 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 14.1850i | − | 0.740448i | −0.928942 | − | 0.370224i | \(-0.879281\pi\) | ||
0.928942 | − | 0.370224i | \(-0.120719\pi\) | |||||||
\(368\) | 3.75023 | − | 0.990764i | 0.195494 | − | 0.0516471i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.44490 | + | 3.92120i | −0.179092 | + | 0.203853i | ||||
\(371\) | − | 10.2099i | − | 0.530072i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 35.5955i | − | 1.84307i | −0.388299 | − | 0.921533i | \(-0.626937\pi\) | ||
0.388299 | − | 0.921533i | \(-0.373063\pi\) | |||||||
\(374\) | 12.5795 | + | 11.0515i | 0.650469 | + | 0.571457i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −15.0341 | + | 22.3722i | −0.775322 | + | 1.15376i | ||||
\(377\) | − | 16.8849i | − | 0.869618i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.59037 | −0.492624 | −0.246312 | − | 0.969191i | \(-0.579219\pi\) | ||||
−0.246312 | + | 0.969191i | \(0.579219\pi\) | |||||||
\(380\) | −2.12489 | − | 16.3621i | −0.109004 | − | 0.839360i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −26.6888 | − | 23.4469i | −1.36552 | − | 1.19965i | ||||
\(383\) | −19.5904 | −1.00102 | −0.500511 | − | 0.865730i | \(-0.666854\pi\) | ||||
−0.500511 | + | 0.865730i | \(0.666854\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.28005 | 0.167167 | ||||||||
\(386\) | 8.26537 | + | 7.26138i | 0.420696 | + | 0.369595i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.06433 | − | 31.2964i | −0.206335 | − | 1.58883i | ||||
\(389\) | 2.12110 | 0.107544 | 0.0537721 | − | 0.998553i | \(-0.482876\pi\) | ||||
0.0537721 | + | 0.998553i | \(0.482876\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.95040i | 0.250352i | ||||||||
\(392\) | −7.88790 | + | 11.7380i | −0.398399 | + | 0.592859i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.65562 | − | 2.33305i | −0.133788 | − | 0.117537i | ||||
\(395\) | 8.01901i | 0.403480i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 27.3778i | − | 1.37405i | −0.726632 | − | 0.687027i | \(-0.758915\pi\) | ||
0.726632 | − | 0.687027i | \(-0.241085\pi\) | |||||||
\(398\) | −19.6547 | + | 22.3722i | −0.985201 | + | 1.12142i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.86732 | + | 1.02170i | −0.193366 | + | 0.0510848i | ||||
\(401\) | 2.78561i | 0.139107i | 0.997578 | + | 0.0695534i | \(0.0221574\pi\) | ||||
−0.997578 | + | 0.0695534i | \(0.977843\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.2791 | 1.30906 | ||||||||
\(404\) | 4.23417 | + | 32.6042i | 0.210658 | + | 1.62212i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.32970 | − | 4.92834i | 0.214879 | − | 0.244589i | ||||
\(407\) | 8.56009 | 0.424308 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.4390 | 0.615068 | 0.307534 | − | 0.951537i | \(-0.400496\pi\) | ||||
0.307534 | + | 0.951537i | \(0.400496\pi\) | |||||||
\(410\) | −4.28974 | + | 4.88285i | −0.211855 | + | 0.241147i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −31.5542 | + | 4.09781i | −1.55456 | + | 0.201885i | ||||
\(413\) | −1.21949 | −0.0600074 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 7.38148i | − | 0.362343i | ||||||
\(416\) | 12.9941 | − | 26.0603i | 0.637088 | − | 1.27771i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −17.8595 | + | 20.3288i | −0.873538 | + | 0.994316i | ||||
\(419\) | 9.34759i | 0.456660i | 0.973584 | + | 0.228330i | \(0.0733265\pi\) | ||||
−0.973584 | + | 0.228330i | \(0.926674\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.3339i | 1.13722i | 0.822606 | + | 0.568612i | \(0.192519\pi\) | ||||
−0.822606 | + | 0.568612i | \(0.807481\pi\) | |||||||
\(422\) | −17.0303 | − | 14.9616i | −0.829021 | − | 0.728321i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.3893 | − | 16.9485i | 0.553115 | − | 0.823092i | ||||
\(425\) | − | 5.10495i | − | 0.247627i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.56009 | −0.317465 | ||||||||
\(428\) | 5.60975 | − | 0.728515i | 0.271157 | − | 0.0352141i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.42053 | − | 3.00504i | −0.164953 | − | 0.144916i | ||||
\(431\) | −23.7190 | −1.14251 | −0.571253 | − | 0.820774i | \(-0.693542\pi\) | ||||
−0.571253 | + | 0.820774i | \(0.693542\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.5601 | 0.795827 | 0.397914 | − | 0.917423i | \(-0.369734\pi\) | ||||
0.397914 | + | 0.917423i | \(0.369734\pi\) | |||||||
\(434\) | 7.67030 | + | 6.73860i | 0.368186 | + | 0.323463i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 20.4196 | − | 2.65181i | 0.977922 | − | 0.126999i | ||||
\(437\) | −8.00000 | −0.382692 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.3711i | 1.54499i | 0.635023 | + | 0.772493i | \(0.280991\pi\) | ||||
−0.635023 | + | 0.772493i | \(0.719009\pi\) | |||||||
\(440\) | 5.44490 | + | 3.65895i | 0.259575 | + | 0.174434i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 27.9201 | + | 24.5287i | 1.32802 | + | 1.16671i | ||||
\(443\) | 30.0945i | 1.42983i | 0.699209 | + | 0.714917i | \(0.253536\pi\) | ||||
−0.699209 | + | 0.714917i | \(0.746464\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.2527i | 0.486026i | ||||||||
\(446\) | −0.289736 | + | 0.329795i | −0.0137194 | + | 0.0156163i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 10.4752 | − | 4.27443i | 0.494905 | − | 0.201948i | ||||
\(449\) | − | 4.24264i | − | 0.200223i | −0.994976 | − | 0.100111i | \(-0.968080\pi\) | ||
0.994976 | − | 0.100111i | \(-0.0319199\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.6594 | 0.501932 | ||||||||
\(452\) | −0.924768 | + | 0.120096i | −0.0434974 | + | 0.00564884i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.59037 | + | 4.08679i | −0.168504 | + | 0.191802i | ||||
\(455\) | 7.28005 | 0.341294 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.2186 | −1.22645 | −0.613227 | − | 0.789907i | \(-0.710129\pi\) | ||||
−0.613227 | + | 0.789907i | \(0.710129\pi\) | |||||||
\(458\) | 5.93945 | − | 6.76066i | 0.277532 | − | 0.315905i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.249771 | + | 1.92330i | 0.0116456 | + | 0.0896742i | ||||
\(461\) | −15.4012 | −0.717303 | −0.358652 | − | 0.933472i | \(-0.616763\pi\) | ||||
−0.358652 | + | 0.933472i | \(0.616763\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 25.4130i | − | 1.18104i | −0.807022 | − | 0.590522i | \(-0.798922\pi\) | ||
0.807022 | − | 0.590522i | \(-0.201078\pi\) | |||||||
\(464\) | 12.6850 | − | 3.35121i | 0.588885 | − | 0.155576i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.17454 | + | 1.33693i | −0.0544095 | + | 0.0619323i | ||||
\(467\) | − | 26.1623i | − | 1.21065i | −0.795980 | − | 0.605323i | \(-0.793044\pi\) | ||
0.795980 | − | 0.605323i | \(-0.206956\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.46711i | 0.344799i | ||||||||
\(470\) | −10.1249 | − | 8.89503i | −0.467026 | − | 0.410297i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.02437 | − | 1.36037i | −0.0931791 | − | 0.0626160i | ||||
\(473\) | 7.46711i | 0.343338i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.24977 | 0.378525 | ||||||||
\(476\) | 1.85952 | + | 14.3188i | 0.0852309 | + | 0.656299i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.530734 | + | 0.466267i | 0.0242752 | + | 0.0213265i | ||||
\(479\) | 7.84014 | 0.358225 | 0.179113 | − | 0.983829i | \(-0.442677\pi\) | ||||
0.179113 | + | 0.983829i | \(0.442677\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.9991 | 0.866284 | ||||||||
\(482\) | 6.43899 | + | 5.65685i | 0.293288 | + | 0.257663i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.44770 | + | 11.1477i | 0.0658047 | + | 0.506713i | ||||
\(485\) | 15.7796 | 0.716514 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.1668i | 0.596644i | 0.954465 | + | 0.298322i | \(0.0964269\pi\) | ||||
−0.954465 | + | 0.298322i | \(0.903573\pi\) | |||||||
\(488\) | −10.8898 | − | 7.31790i | −0.492958 | − | 0.331266i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.31221 | − | 4.66695i | −0.239981 | − | 0.210831i | ||||
\(491\) | 12.8825i | 0.581378i | 0.956818 | + | 0.290689i | \(0.0938845\pi\) | ||||
−0.956818 | + | 0.290689i | \(0.906115\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.7445i | 0.754134i | ||||||||
\(494\) | −39.6391 | + | 45.1197i | −1.78345 | + | 2.03003i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.21571 | + | 19.7425i | 0.234192 | + | 0.886463i | ||||
\(497\) | 18.7808i | 0.842435i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.1287 | −0.542954 | −0.271477 | − | 0.962445i | \(-0.587512\pi\) | ||||
−0.271477 | + | 0.962445i | \(0.587512\pi\) | |||||||
\(500\) | −0.257569 | − | 1.98335i | −0.0115188 | − | 0.0886979i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.2850 | − | 12.8453i | 0.503676 | − | 0.573316i | ||||
\(503\) | 29.4087 | 1.31127 | 0.655635 | − | 0.755078i | \(-0.272401\pi\) | ||||
0.655635 | + | 0.755078i | \(0.272401\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.4390 | −0.731525 | ||||||||
\(506\) | 2.09931 | − | 2.38956i | 0.0933256 | − | 0.106229i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.3238 | − | 1.73031i | 0.591148 | − | 0.0767700i | ||||
\(509\) | −25.5592 | −1.13289 | −0.566445 | − | 0.824099i | \(-0.691682\pi\) | ||||
−0.566445 | + | 0.824099i | \(0.691682\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 17.7627i | − | 0.785774i | ||||||
\(512\) | 22.1571 | + | 4.58967i | 0.979213 | + | 0.202837i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.7843 | + | 12.2754i | −0.475674 | + | 0.541443i | ||||
\(515\) | − | 15.9096i | − | 0.701060i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.1029i | 0.972085i | ||||||||
\(518\) | 5.54541 | + | 4.87182i | 0.243652 | + | 0.214055i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12.0849 | + | 8.12102i | 0.529959 | + | 0.356130i | ||||
\(521\) | − | 19.0912i | − | 0.836402i | −0.908354 | − | 0.418201i | \(-0.862661\pi\) | ||
0.908354 | − | 0.418201i | \(-0.137339\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.12110 | 0.355111 | 0.177556 | − | 0.984111i | \(-0.443181\pi\) | ||||
0.177556 | + | 0.984111i | \(0.443181\pi\) | |||||||
\(524\) | −41.8489 | + | 5.43475i | −1.82818 | + | 0.237418i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.00000 | − | 7.02825i | −0.348817 | − | 0.306446i | ||||
\(527\) | −26.0606 | −1.13522 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0596 | −0.959115 | ||||||||
\(530\) | 7.67030 | + | 6.73860i | 0.333177 | + | 0.292706i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −23.1396 | + | 3.00504i | −1.00323 | + | 0.130285i | ||||
\(533\) | 23.6585 | 1.02476 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.82843i | 0.122284i | ||||||||
\(536\) | −8.32970 | + | 12.3955i | −0.359788 | + | 0.535402i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 27.4537 | + | 24.1189i | 1.18361 | + | 1.03984i | ||||
\(539\) | 11.5967i | 0.499506i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.5914i | 0.756313i | 0.925742 | + | 0.378156i | \(0.123442\pi\) | ||||
−0.925742 | + | 0.378156i | \(0.876558\pi\) | |||||||
\(542\) | 22.2148 | − | 25.2863i | 0.954207 | − | 1.08614i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −12.8860 | + | 25.8435i | −0.552483 | + | 1.10803i | ||||
\(545\) | 10.2955i | 0.441013i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.3397 | 0.869662 | 0.434831 | − | 0.900512i | \(-0.356808\pi\) | ||||
0.434831 | + | 0.900512i | \(0.356808\pi\) | |||||||
\(548\) | −41.7640 | + | 5.42372i | −1.78407 | + | 0.231690i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.16485 | + | 2.46417i | −0.0923095 | + | 0.105073i | ||||
\(551\) | −27.0596 | −1.15278 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.3406 | 0.482251 | ||||||||
\(554\) | 22.5845 | − | 25.7071i | 0.959522 | − | 1.09219i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.749313 | − | 5.76989i | −0.0317779 | − | 0.244698i | ||||
\(557\) | −25.7796 | −1.09232 | −0.546158 | − | 0.837682i | \(-0.683910\pi\) | ||||
−0.546158 | + | 0.837682i | \(0.683910\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.5732i | 0.700973i | ||||||||
\(560\) | 1.44490 | + | 5.46921i | 0.0610580 | + | 0.231116i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.36967 | − | 9.52688i | 0.353053 | − | 0.401867i | ||||
\(563\) | − | 2.03633i | − | 0.0858213i | −0.999079 | − | 0.0429106i | \(-0.986337\pi\) | ||
0.999079 | − | 0.0429106i | \(-0.0136631\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 0.466267i | − | 0.0196160i | ||||||
\(566\) | 15.6391 | + | 13.7394i | 0.657361 | + | 0.577512i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −20.9503 | + | 31.1763i | −0.879057 | + | 1.30813i | ||||
\(569\) | 34.6904i | 1.45430i | 0.686480 | + | 0.727149i | \(0.259155\pi\) | ||||
−0.686480 | + | 0.727149i | \(0.740845\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.3094 | −1.47765 | −0.738826 | − | 0.673896i | \(-0.764620\pi\) | ||||
−0.738826 | + | 0.673896i | \(0.764620\pi\) | |||||||
\(572\) | −3.07523 | − | 23.6800i | −0.128582 | − | 0.990112i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.90539 | + | 6.06660i | 0.288225 | + | 0.253215i | ||||
\(575\) | −0.969724 | −0.0404403 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.21949 | −0.0507682 | −0.0253841 | − | 0.999678i | \(-0.508081\pi\) | ||||
−0.0253841 | + | 0.999678i | \(0.508081\pi\) | |||||||
\(578\) | −9.62632 | − | 8.45702i | −0.400402 | − | 0.351766i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.844838 | + | 6.50547i | 0.0350800 | + | 0.270125i | ||||
\(581\) | −10.4390 | −0.433082 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 16.7445i | − | 0.693486i | ||||||
\(584\) | 19.8146 | − | 29.4861i | 0.819932 | − | 1.22014i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.37466 | + | 5.60034i | 0.263335 | + | 0.231348i | ||||
\(587\) | 24.1260i | 0.995785i | 0.867239 | + | 0.497893i | \(0.165893\pi\) | ||||
−0.867239 | + | 0.497893i | \(0.834107\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 42.1147i | − | 1.73531i | ||||||
\(590\) | 0.804874 | − | 0.916158i | 0.0331361 | − | 0.0377176i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.77082 | + | 14.2733i | 0.154980 | + | 0.586627i | ||||
\(593\) | 8.10465i | 0.332818i | 0.986057 | + | 0.166409i | \(0.0532172\pi\) | ||||
−0.986057 | + | 0.166409i | \(0.946783\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.21949 | −0.295970 | ||||||||
\(596\) | −2.90539 | − | 22.3722i | −0.119009 | − | 0.916402i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.65940 | − | 5.30362i | 0.190537 | − | 0.216881i | ||||
\(599\) | 31.7190 | 1.29600 | 0.648002 | − | 0.761638i | \(-0.275605\pi\) | ||||
0.648002 | + | 0.761638i | \(0.275605\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.4381 | −1.60871 | −0.804356 | − | 0.594147i | \(-0.797490\pi\) | ||||
−0.804356 | + | 0.594147i | \(0.797490\pi\) | |||||||
\(602\) | −4.24977 | + | 4.83736i | −0.173208 | + | 0.197156i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 43.1651 | − | 5.60568i | 1.75636 | − | 0.228092i | ||||
\(605\) | −5.62065 | −0.228512 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.5203i | 0.427007i | 0.976942 | + | 0.213503i | \(0.0684874\pi\) | ||||
−0.976942 | + | 0.213503i | \(0.931513\pi\) | |||||||
\(608\) | −41.7640 | − | 20.8242i | −1.69375 | − | 0.844533i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.32970 | − | 4.92834i | 0.175304 | − | 0.199543i | ||||
\(611\) | 49.0573i | 1.98465i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.25157i | 0.252499i | 0.991999 | + | 0.126249i | \(0.0402939\pi\) | ||||
−0.991999 | + | 0.126249i | \(0.959706\pi\) | |||||||
\(614\) | 10.6888 | + | 9.39041i | 0.431363 | + | 0.378966i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.17454 | − | 7.70025i | 0.208488 | − | 0.310252i | ||||
\(617\) | − | 11.6395i | − | 0.468590i | −0.972166 | − | 0.234295i | \(-0.924722\pi\) | ||
0.972166 | − | 0.234295i | \(-0.0752782\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.0284 | 1.32753 | 0.663763 | − | 0.747943i | \(-0.268959\pi\) | ||||
0.663763 | + | 0.747943i | \(0.268959\pi\) | |||||||
\(620\) | −10.1249 | + | 1.31488i | −0.406625 | + | 0.0528068i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.2186 | + | 10.7344i | 0.489920 | + | 0.430410i | ||||
\(623\) | 14.4995 | 0.580912 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 7.07523 | + | 6.21581i | 0.282783 | + | 0.248434i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16.5201 | − | 2.14540i | 0.659225 | − | 0.0856109i | ||||
\(629\) | −18.8411 | −0.751242 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.7525i | 1.58252i | 0.611478 | + | 0.791262i | \(0.290575\pi\) | ||||
−0.611478 | + | 0.791262i | \(0.709425\pi\) | |||||||
\(632\) | 18.8255 | + | 12.6506i | 0.748837 | + | 0.503216i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.31410 | + | 3.79008i | 0.171335 | + | 0.150523i | ||||
\(635\) | 6.71784i | 0.266589i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25.7389i | 1.01981i | ||||||||
\(638\) | 7.10081 | − | 8.08259i | 0.281124 | − | 0.319993i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.70247 | + | 10.6907i | −0.146353 | + | 0.422588i | ||||
\(641\) | − | 37.9577i | − | 1.49924i | −0.661869 | − | 0.749619i | \(-0.730237\pi\) | ||
0.661869 | − | 0.749619i | \(-0.269763\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.4995 | −1.28166 | −0.640828 | − | 0.767684i | \(-0.721409\pi\) | ||||
−0.640828 | + | 0.767684i | \(0.721409\pi\) | |||||||
\(644\) | 2.71995 | − | 0.353229i | 0.107181 | − | 0.0139192i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 39.3094 | − | 44.7445i | 1.54661 | − | 1.76045i | ||||
\(647\) | 36.0899 | 1.41884 | 0.709420 | − | 0.704786i | \(-0.248957\pi\) | ||||
0.709420 | + | 0.704786i | \(0.248957\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.00000 | −0.0785069 | ||||||||
\(650\) | −4.80487 | + | 5.46921i | −0.188463 | + | 0.214520i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.28005 | − | 40.6577i | −0.206783 | − | 1.59228i | ||||
\(653\) | −4.18166 | −0.163641 | −0.0818204 | − | 0.996647i | \(-0.526073\pi\) | ||||
−0.0818204 | + | 0.996647i | \(0.526073\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 21.1002i | − | 0.824452i | ||||||
\(656\) | 4.69558 | + | 17.7737i | 0.183332 | + | 0.693946i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.5795 | + | 14.3188i | −0.490399 | + | 0.558203i | ||||
\(659\) | 16.6434i | 0.648336i | 0.945999 | + | 0.324168i | \(0.105084\pi\) | ||||
−0.945999 | + | 0.324168i | \(0.894916\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 19.7990i | − | 0.770091i | −0.922897 | − | 0.385046i | \(-0.874186\pi\) | ||
0.922897 | − | 0.385046i | \(-0.125814\pi\) | |||||||
\(662\) | −10.9541 | − | 9.62354i | −0.425744 | − | 0.374030i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −17.3288 | − | 11.6449i | −0.672487 | − | 0.451909i | ||||
\(665\) | − | 11.6669i | − | 0.452424i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.18074 | 0.123159 | ||||||||
\(668\) | 1.77959 | + | 13.7033i | 0.0688544 | + | 0.530196i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.60975 | − | 4.92834i | −0.216723 | − | 0.190398i | ||||
\(671\) | −10.7587 | −0.415335 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −43.9982 | −1.69600 | −0.848002 | − | 0.529992i | \(-0.822195\pi\) | ||||
−0.848002 | + | 0.529992i | \(0.822195\pi\) | |||||||
\(674\) | −2.25355 | − | 1.97982i | −0.0868036 | − | 0.0762597i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.47706 | − | 26.7743i | −0.133733 | − | 1.02978i | ||||
\(677\) | −2.49954 | −0.0960652 | −0.0480326 | − | 0.998846i | \(-0.515295\pi\) | ||||
−0.0480326 | + | 0.998846i | \(0.515295\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 22.3157i | − | 0.856398i | ||||||
\(680\) | −11.9844 | − | 8.05348i | −0.459581 | − | 0.308837i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.5795 | + | 11.0515i | 0.481693 | + | 0.423182i | ||||
\(683\) | 23.6456i | 0.904773i | 0.891822 | + | 0.452387i | \(0.149427\pi\) | ||||
−0.891822 | + | 0.452387i | \(0.850573\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 21.0573i | − | 0.804560i | ||||||
\(686\) | −15.8401 | + | 18.0303i | −0.604779 | + | 0.688398i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −12.4508 | + | 3.28935i | −0.474682 | + | 0.125405i | ||||
\(689\) | − | 37.1643i | − | 1.41585i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.6888 | 0.558787 | 0.279393 | − | 0.960177i | \(-0.409867\pi\) | ||||
0.279393 | + | 0.960177i | \(0.409867\pi\) | |||||||
\(692\) | −4.95035 | − | 38.1189i | −0.188184 | − | 1.44906i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.4390 | − | 34.6476i | 1.15545 | − | 1.31520i | ||||
\(695\) | 2.90917 | 0.110351 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23.4617 | −0.888675 | ||||||||
\(698\) | −7.04965 | + | 8.02436i | −0.266833 | + | 0.303727i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.80487 | + | 0.364258i | −0.106014 | + | 0.0137676i | ||||
\(701\) | −8.43899 | −0.318736 | −0.159368 | − | 0.987219i | \(-0.550946\pi\) | ||||
−0.159368 | + | 0.987219i | \(0.550946\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 30.4478i | − | 1.14836i | ||||||
\(704\) | 17.1795 | − | 7.01016i | 0.647478 | − | 0.264206i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.48486 | − | 8.51974i | 0.281696 | − | 0.320645i | ||||
\(707\) | 23.2482i | 0.874340i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.3904i | 1.40423i | 0.712066 | + | 0.702113i | \(0.247760\pi\) | ||||
−0.712066 | + | 0.702113i | \(0.752240\pi\) | |||||||
\(710\) | −14.1093 | − | 12.3955i | −0.529512 | − | 0.465193i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 24.0693 | + | 16.1745i | 0.902036 | + | 0.606165i | ||||
\(713\) | 4.95040i | 0.185394i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.9394 | 0.446510 | ||||||||
\(716\) | 24.8498 | − | 3.22715i | 0.928682 | − | 0.120604i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.95126 | − | 3.47131i | −0.147460 | − | 0.129548i | ||||
\(719\) | −40.3397 | −1.50442 | −0.752208 | − | 0.658926i | \(-0.771011\pi\) | ||||
−0.752208 | + | 0.658926i | \(0.771011\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.4995 | −0.837927 | ||||||||
\(722\) | 52.1221 | + | 45.7909i | 1.93978 | + | 1.70416i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.01090 | + | 0.910477i | −0.260558 | + | 0.0338376i | ||||
\(725\) | −3.28005 | −0.121818 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 11.1305i | − | 0.412806i | −0.978467 | − | 0.206403i | \(-0.933824\pi\) | ||
0.978467 | − | 0.206403i | \(-0.0661757\pi\) | |||||||
\(728\) | 11.4849 | − | 17.0907i | 0.425657 | − | 0.633422i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13.3444 | + | 11.7235i | 0.493898 | + | 0.433905i | ||||
\(731\) | − | 16.4354i | − | 0.607884i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 29.8530i | − | 1.10265i | −0.834291 | − | 0.551324i | \(-0.814123\pi\) | ||
0.834291 | − | 0.551324i | \(-0.185877\pi\) | |||||||
\(734\) | 13.2401 | − | 15.0707i | 0.488700 | − | 0.556270i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.90917 | + | 2.44779i | 0.180954 | + | 0.0902269i | ||||
\(737\) | 12.2462i | 0.451096i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.7493 | −0.616133 | −0.308067 | − | 0.951365i | \(-0.599682\pi\) | ||||
−0.308067 | + | 0.951365i | \(0.599682\pi\) | |||||||
\(740\) | −7.32001 | + | 0.950620i | −0.269089 | + | 0.0349455i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.52982 | − | 10.8474i | 0.349851 | − | 0.398222i | ||||
\(743\) | 44.0899 | 1.61750 | 0.808751 | − | 0.588151i | \(-0.200144\pi\) | ||||
0.808751 | + | 0.588151i | \(0.200144\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.2800 | 0.413269 | ||||||||
\(746\) | 33.2245 | − | 37.8182i | 1.21643 | − | 1.38462i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.04965 | + | 23.4831i | 0.111506 | + | 0.858627i | ||||
\(749\) | 4.00000 | 0.146157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 24.9896i | − | 0.911883i | −0.890010 | − | 0.455941i | \(-0.849303\pi\) | ||
0.890010 | − | 0.455941i | \(-0.150697\pi\) | |||||||
\(752\) | −36.8548 | + | 9.73658i | −1.34396 | + | 0.355057i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 15.7602 | − | 17.9393i | 0.573953 | − | 0.653310i | ||||
\(755\) | 21.7638i | 0.792066i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 22.7833i | − | 0.828072i | −0.910260 | − | 0.414036i | \(-0.864119\pi\) | ||
0.910260 | − | 0.414036i | \(-0.135881\pi\) | |||||||
\(758\) | −10.1892 | − | 8.95155i | −0.370089 | − | 0.325135i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.0147 | − | 19.3672i | 0.472092 | − | 0.702522i | ||||
\(761\) | 30.4049i | 1.10218i | 0.834446 | + | 0.551089i | \(0.185788\pi\) | ||||
−0.834446 | + | 0.551089i | \(0.814212\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.5601 | 0.527111 | ||||||||
\(764\) | −6.47018 | − | 49.8220i | −0.234083 | − | 1.80250i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20.8136 | − | 18.2854i | −0.752028 | − | 0.660680i | ||||
\(767\) | −4.43899 | −0.160283 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.3179 | −0.372072 | −0.186036 | − | 0.982543i | \(-0.559564\pi\) | ||||
−0.186036 | + | 0.982543i | \(0.559564\pi\) | |||||||
\(770\) | 3.48486 | + | 3.06156i | 0.125586 | + | 0.110331i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.00378 | + | 15.4296i | 0.0721177 | + | 0.555324i | ||||
\(773\) | 2.94036 | 0.105758 | 0.0528788 | − | 0.998601i | \(-0.483160\pi\) | ||||
0.0528788 | + | 0.998601i | \(0.483160\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 5.10495i | − | 0.183375i | ||||||
\(776\) | 24.8936 | − | 37.0442i | 0.893627 | − | 1.32981i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.25355 | + | 1.97982i | 0.0807937 | + | 0.0709798i | ||||
\(779\) | − | 37.9149i | − | 1.35844i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.8010i | 1.10215i | ||||||||
\(782\) | −4.62065 | + | 5.25951i | −0.165234 | + | 0.188080i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −19.3366 | + | 5.10848i | −0.690592 | + | 0.182446i | ||||
\(785\) | 8.32943i | 0.297290i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.2413 | −0.899755 | −0.449877 | − | 0.893090i | \(-0.648532\pi\) | ||||
−0.449877 | + | 0.893090i | \(0.648532\pi\) | |||||||
\(788\) | −0.643805 | − | 4.95745i | −0.0229346 | − | 0.176602i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.48486 | + | 8.51974i | −0.266299 | + | 0.303119i | ||||
\(791\) | −0.659401 | −0.0234456 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.8789 | −0.847964 | ||||||||
\(794\) | 25.5542 | − | 29.0874i | 0.906884 | − | 1.03227i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −41.7640 | + | 5.42372i | −1.48029 | + | 0.192239i | ||||
\(797\) | −13.7796 | −0.488098 | −0.244049 | − | 0.969763i | \(-0.578476\pi\) | ||||
−0.244049 | + | 0.969763i | \(0.578476\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 48.6493i | − | 1.72109i | ||||||
\(800\) | −5.06244 | − | 2.52422i | −0.178984 | − | 0.0892446i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.60006 | + | 2.95955i | −0.0918113 | + | 0.104505i | ||||
\(803\) | − | 29.1312i | − | 1.02802i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.37140i | 0.0483354i | ||||||||
\(806\) | 27.9201 | + | 24.5287i | 0.983443 | + | 0.863985i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −25.9338 | + | 38.5922i | −0.912349 | + | 1.35767i | ||||
\(809\) | − | 32.3865i | − | 1.13865i | −0.822113 | − | 0.569324i | \(-0.807205\pi\) | ||
0.822113 | − | 0.569324i | \(-0.192795\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.4702 | −0.437887 | −0.218944 | − | 0.975738i | \(-0.570261\pi\) | ||||
−0.218944 | + | 0.975738i | \(0.570261\pi\) | |||||||
\(812\) | 9.20012 | − | 1.19478i | 0.322861 | − | 0.0419286i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.09461 | + | 7.98990i | 0.318766 | + | 0.280046i | ||||
\(815\) | 20.4995 | 0.718068 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.5601 | 0.929220 | ||||||||
\(818\) | 13.2157 | + | 11.6104i | 0.462077 | + | 0.405949i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.11520 | + | 1.18375i | −0.318316 | + | 0.0413385i | ||||
\(821\) | −41.8401 | −1.46023 | −0.730115 | − | 0.683324i | \(-0.760534\pi\) | ||||
−0.730115 | + | 0.683324i | \(0.760534\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.39574i | 0.118368i | 0.998247 | + | 0.0591840i | \(0.0188499\pi\) | ||||
−0.998247 | + | 0.0591840i | \(0.981150\pi\) | |||||||
\(824\) | −37.3494 | − | 25.0986i | −1.30113 | − | 0.874353i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.29564 | − | 1.13826i | −0.0450812 | − | 0.0396052i | ||||
\(827\) | 4.38179i | 0.152370i | 0.997094 | + | 0.0761848i | \(0.0242739\pi\) | ||||
−0.997094 | + | 0.0761848i | \(0.975726\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.8757i | 1.59333i | 0.604423 | + | 0.796664i | \(0.293404\pi\) | ||||
−0.604423 | + | 0.796664i | \(0.706596\pi\) | |||||||
\(830\) | 6.88979 | − | 7.84240i | 0.239148 | − | 0.272214i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 38.1299 | − | 15.5590i | 1.32192 | − | 0.539412i | ||||
\(833\) | − | 25.5248i | − | 0.884381i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.90917 | −0.239102 | ||||||||
\(836\) | −37.9494 | + | 4.92834i | −1.31251 | + | 0.170450i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.72494 | + | 9.93128i | −0.301398 | + | 0.343070i | ||||
\(839\) | 24.8392 | 0.857545 | 0.428773 | − | 0.903412i | \(-0.358946\pi\) | ||||
0.428773 | + | 0.903412i | \(0.358946\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.2413 | −0.629010 | ||||||||
\(842\) | −21.7796 | + | 24.7909i | −0.750574 | + | 0.854351i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.12867 | − | 31.7918i | −0.142115 | − | 1.09432i | ||||
\(845\) | 13.4995 | 0.464398 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.94879i | 0.273124i | ||||||||
\(848\) | 27.9201 | − | 7.37613i | 0.958779 | − | 0.253297i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.76491 | − | 5.42372i | 0.163435 | − | 0.186032i | ||||
\(851\) | 3.57900i | 0.122687i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 10.0125i | − | 0.342823i | −0.985200 | − | 0.171411i | \(-0.945167\pi\) | ||
0.985200 | − | 0.171411i | \(-0.0548327\pi\) | |||||||
\(854\) | −6.96972 | − | 6.12312i | −0.238499 | − | 0.209529i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.64002 | + | 4.46207i | 0.226951 | + | 0.152510i | ||||
\(857\) | − | 26.6286i | − | 0.909615i | −0.890590 | − | 0.454807i | \(-0.849708\pi\) | ||
0.890590 | − | 0.454807i | \(-0.150292\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.4096 | 0.491650 | 0.245825 | − | 0.969314i | \(-0.420941\pi\) | ||||
0.245825 | + | 0.969314i | \(0.420941\pi\) | |||||||
\(860\) | −0.829242 | − | 6.38537i | −0.0282769 | − | 0.217739i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −25.2001 | − | 22.1391i | −0.858319 | − | 0.754061i | ||||
\(863\) | 49.5280 | 1.68595 | 0.842976 | − | 0.537951i | \(-0.180801\pi\) | ||||
0.842976 | + | 0.537951i | \(0.180801\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.2195 | 0.653482 | ||||||||
\(866\) | 17.5942 | + | 15.4570i | 0.597874 | + | 0.525251i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.85952 | + | 14.3188i | 0.0631162 | + | 0.486010i | ||||
\(869\) | 18.5988 | 0.630923 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.1805i | 0.920975i | ||||||||
\(872\) | 24.1698 | + | 16.2420i | 0.818494 | + | 0.550025i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8.49954 | − | 7.46711i | −0.287501 | − | 0.252579i | ||||
\(875\) | − | 1.41421i | − | 0.0478091i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.0924i | 0.779775i | 0.920863 | + | 0.389887i | \(0.127486\pi\) | ||||
−0.920863 | + | 0.389887i | \(0.872514\pi\) | |||||||
\(878\) | −30.2148 | + | 34.3924i | −1.01970 | + | 1.16069i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.36967 | + | 8.96963i | 0.0798814 | + | 0.302366i | ||||
\(881\) | 24.3092i | 0.818999i | 0.912310 | + | 0.409499i | \(0.134297\pi\) | ||||
−0.912310 | + | 0.409499i | \(0.865703\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.0606 | −0.473175 | −0.236588 | − | 0.971610i | \(-0.576029\pi\) | ||||
−0.236588 | + | 0.971610i | \(0.576029\pi\) | |||||||
\(884\) | 6.76869 | + | 52.1206i | 0.227656 | + | 1.75301i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −28.0899 | + | 31.9737i | −0.943699 | + | 1.07418i | ||||
\(887\) | −5.96881 | −0.200413 | −0.100206 | − | 0.994967i | \(-0.531950\pi\) | ||||
−0.100206 | + | 0.994967i | \(0.531950\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.50046 | 0.318635 | ||||||||
\(890\) | −9.56978 | + | 10.8929i | −0.320780 | + | 0.365132i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.615655 | + | 0.0799526i | −0.0206137 | + | 0.00267701i | ||||
\(893\) | 78.6188 | 2.63088 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.5293i | 0.418807i | ||||||||
\(896\) | 15.1190 | + | 5.23608i | 0.505090 | + | 0.174925i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.96004 | − | 4.50756i | 0.132148 | − | 0.150419i | ||||
\(899\) | 16.7445i | 0.558460i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.8552i | 1.22782i | ||||||||
\(902\) | 11.3250 | + | 9.94937i | 0.377081 | + | 0.331278i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.09461 | − | 0.735574i | −0.0364062 | − | 0.0244648i | ||||
\(905\) | − | 3.53489i | − | 0.117504i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.96125 | −0.264349 | −0.132174 | − | 0.991226i | \(-0.542196\pi\) | ||||
−0.132174 | + | 0.991226i | \(0.542196\pi\) | |||||||
\(908\) | −7.62912 | + | 0.990764i | −0.253181 | + | 0.0328796i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.73463 | + | 6.79512i | 0.256401 | + | 0.225256i | ||||
\(911\) | 40.4995 | 1.34181 | 0.670905 | − | 0.741543i | \(-0.265906\pi\) | ||||
0.670905 | + | 0.741543i | \(0.265906\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.1202 | −0.566596 | ||||||||
\(914\) | −27.8557 | − | 24.4721i | −0.921386 | − | 0.809466i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.6206 | − | 1.63899i | 0.416998 | − | 0.0541538i | ||||
\(917\) | −29.8401 | −0.985408 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 11.6395i | − | 0.383953i | −0.981400 | − | 0.191976i | \(-0.938510\pi\) | ||
0.981400 | − | 0.191976i | \(-0.0614897\pi\) | |||||||
\(920\) | −1.52982 | + | 2.27653i | −0.0504366 | + | 0.0750549i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16.3628 | − | 14.3753i | −0.538881 | − | 0.473424i | ||||
\(923\) | 68.3626i | 2.25018i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 3.69074i | − | 0.121351i | ||||||
\(926\) | 23.7202 | − | 26.9999i | 0.779496 | − | 0.887271i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 16.6050 | + | 8.27955i | 0.545087 | + | 0.271790i | ||||
\(929\) | − | 23.9560i | − | 0.785971i | −0.919545 | − | 0.392985i | \(-0.871442\pi\) | ||
0.919545 | − | 0.392985i | \(-0.128558\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 41.2489 | 1.35188 | ||||||||
\(932\) | −2.49576 | + | 0.324114i | −0.0817514 | + | 0.0106167i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 24.4196 | − | 27.7959i | 0.799034 | − | 0.909511i | ||||
\(935\) | −11.8401 | −0.387214 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.1211 | 0.330642 | 0.165321 | − | 0.986240i | \(-0.447134\pi\) | ||||
0.165321 | + | 0.986240i | \(0.447134\pi\) | |||||||
\(938\) | −6.96972 | + | 7.93338i | −0.227570 | + | 0.259034i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.45459 | − | 18.9009i | −0.0800598 | − | 0.616480i | ||||
\(941\) | −28.3179 | −0.923137 | −0.461568 | − | 0.887105i | \(-0.652713\pi\) | ||||
−0.461568 | + | 0.887105i | \(0.652713\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.45673i | 0.145131i | ||||||||
\(944\) | −0.881022 | − | 3.33484i | −0.0286748 | − | 0.108540i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.96972 | + | 7.93338i | −0.226605 | + | 0.257936i | ||||
\(947\) | 53.4284i | 1.73619i | 0.496398 | + | 0.868095i | \(0.334656\pi\) | ||||
−0.496398 | + | 0.868095i | \(0.665344\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 64.6565i | − | 2.09884i | ||||||
\(950\) | 8.76491 | + | 7.70025i | 0.284371 | + | 0.249829i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −11.3893 | + | 16.9485i | −0.369130 | + | 0.549304i | ||||
\(953\) | 4.48413i | 0.145255i | 0.997359 | + | 0.0726276i | \(0.0231385\pi\) | ||||
−0.997359 | + | 0.0726276i | \(0.976862\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.1202 | 0.812870 | ||||||||
\(956\) | 0.128666 | + | 0.990764i | 0.00416137 | + | 0.0320436i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.32970 | + | 7.31790i | 0.269120 | + | 0.236431i | ||||
\(959\) | −29.7796 | −0.961633 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.93945 | 0.159337 | ||||||||
\(962\) | 20.1854 | + | 17.7335i | 0.650805 | + | 0.571752i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.56101 | + | 12.0202i | 0.0502768 | + | 0.387144i | ||||
\(965\) | −7.77959 | −0.250434 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.5748i | 0.436537i | 0.975889 | + | 0.218268i | \(0.0700408\pi\) | ||||
−0.975889 | + | 0.218268i | \(0.929959\pi\) | |||||||
\(968\) | −8.86702 | + | 13.1950i | −0.284997 | + | 0.424105i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 16.7649 | + | 14.7285i | 0.538289 | + | 0.472904i | ||||
\(971\) | − | 54.2907i | − | 1.74227i | −0.491042 | − | 0.871136i | \(-0.663384\pi\) | ||
0.491042 | − | 0.871136i | \(-0.336616\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 4.11419i | − | 0.131895i | ||||||
\(974\) | −12.2897 | + | 13.9890i | −0.393789 | + | 0.448235i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.73933 | − | 17.9393i | −0.151702 | − | 0.574222i | ||||
\(977\) | − | 15.7122i | − | 0.502678i | −0.967899 | − | 0.251339i | \(-0.919129\pi\) | ||
0.967899 | − | 0.251339i | \(-0.0808709\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.7796 | 0.759999 | ||||||||
\(980\) | −1.28785 | − | 9.91673i | −0.0411387 | − | 0.316778i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12.0244 | + | 13.6869i | −0.383713 | + | 0.436766i | ||||
\(983\) | −13.4087 | −0.427672 | −0.213836 | − | 0.976870i | \(-0.568596\pi\) | ||||
−0.213836 | + | 0.976870i | \(0.568596\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.49954 | 0.0796420 | ||||||||
\(986\) | −15.6291 | + | 17.7901i | −0.497733 | + | 0.566551i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −84.2286 | + | 10.9384i | −2.67967 | + | 0.347998i | ||||
\(989\) | −3.12202 | −0.0992745 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.1433i | 0.576341i | 0.957579 | + | 0.288170i | \(0.0930469\pi\) | ||||
−0.957579 | + | 0.288170i | \(0.906953\pi\) | |||||||
\(992\) | −12.8860 | + | 25.8435i | −0.409131 | + | 0.820533i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −17.5298 | + | 19.9535i | −0.556012 | + | 0.632888i | ||||
\(995\) | − | 21.0573i | − | 0.667563i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.7385i | 0.910159i | 0.890451 | + | 0.455079i | \(0.150389\pi\) | ||||
−0.890451 | + | 0.455079i | \(0.849611\pi\) | |||||||
\(998\) | −12.8860 | − | 11.3208i | −0.407900 | − | 0.358353i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))