Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,3,Mod(19,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.92371580679\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + 1408 x^{6} + 3584 x^{5} + 2560 x^{4} - 4096 x^{3} - 24576 x^{2} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 91.5 | ||
Root | \(0.125358 + 1.99607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.91 |
Dual form | 144.3.m.c.19.5 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.125358 | − | 1.99607i | 0.0626788 | − | 0.998034i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.96857 | − | 0.500444i | −0.992143 | − | 0.125111i | ||||
\(5\) | −3.32679 | − | 3.32679i | −0.665359 | − | 0.665359i | 0.291279 | − | 0.956638i | \(-0.405919\pi\) |
−0.956638 | + | 0.291279i | \(0.905919\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.04088 | −0.577269 | −0.288635 | − | 0.957439i | \(-0.593201\pi\) | ||||
−0.288635 | + | 0.957439i | \(0.593201\pi\) | |||||||
\(8\) | −1.49641 | + | 7.85880i | −0.187051 | + | 0.982350i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.05755 | + | 6.22347i | −0.705755 | + | 0.622347i | ||||
\(11\) | −6.82458 | + | 6.82458i | −0.620416 | + | 0.620416i | −0.945638 | − | 0.325222i | \(-0.894561\pi\) |
0.325222 | + | 0.945638i | \(0.394561\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.29091 | − | 4.29091i | 0.330070 | − | 0.330070i | −0.522543 | − | 0.852613i | \(-0.675017\pi\) |
0.852613 | + | 0.522543i | \(0.175017\pi\) | |||||||
\(14\) | −0.506555 | + | 8.06588i | −0.0361825 | + | 0.576134i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 15.4991 | + | 3.97210i | 0.968694 | + | 0.248256i | ||||
\(17\) | −30.1192 | −1.77172 | −0.885859 | − | 0.463954i | \(-0.846430\pi\) | ||||
−0.885859 | + | 0.463954i | \(0.846430\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.7548 | − | 19.7548i | −1.03973 | − | 1.03973i | −0.999177 | − | 0.0405505i | \(-0.987089\pi\) |
−0.0405505 | − | 0.999177i | \(-0.512911\pi\) | |||||||
\(20\) | 11.5377 | + | 14.8675i | 0.576887 | + | 0.743375i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 12.7668 | + | 14.4778i | 0.580309 | + | 0.658083i | ||||
\(23\) | 28.2345 | 1.22759 | 0.613794 | − | 0.789466i | \(-0.289642\pi\) | ||||
0.613794 | + | 0.789466i | \(0.289642\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 2.86488i | − | 0.114595i | ||||||
\(26\) | −8.02705 | − | 9.10285i | −0.308733 | − | 0.350109i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 16.0365 | + | 2.02224i | 0.572733 | + | 0.0722227i | ||||
\(29\) | 21.3607 | − | 21.3607i | 0.736575 | − | 0.736575i | −0.235338 | − | 0.971914i | \(-0.575620\pi\) |
0.971914 | + | 0.235338i | \(0.0756198\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 38.0396i | 1.22708i | 0.789662 | + | 0.613541i | \(0.210256\pi\) | ||||
−0.789662 | + | 0.613541i | \(0.789744\pi\) | |||||||
\(32\) | 9.87151 | − | 30.4393i | 0.308485 | − | 0.951229i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.77567 | + | 60.1200i | −0.111049 | + | 1.76823i | ||||
\(35\) | 13.4432 | + | 13.4432i | 0.384091 | + | 0.384091i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −42.8916 | − | 42.8916i | −1.15923 | − | 1.15923i | −0.984641 | − | 0.174590i | \(-0.944140\pi\) |
−0.174590 | − | 0.984641i | \(-0.555860\pi\) | |||||||
\(38\) | −41.9084 | + | 36.9556i | −1.10285 | + | 0.972515i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 31.1229 | − | 21.1664i | 0.778072 | − | 0.529159i | ||||
\(41\) | − | 48.2343i | − | 1.17645i | −0.808699 | − | 0.588223i | \(-0.799828\pi\) | ||
0.808699 | − | 0.588223i | \(-0.200172\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 32.6765 | − | 32.6765i | 0.759918 | − | 0.759918i | −0.216389 | − | 0.976307i | \(-0.569428\pi\) |
0.976307 | + | 0.216389i | \(0.0694281\pi\) | |||||||
\(44\) | 30.4991 | − | 23.6685i | 0.693162 | − | 0.537921i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.53941 | − | 56.3580i | 0.0769437 | − | 1.22517i | ||||
\(47\) | 15.8305i | 0.336818i | 0.985717 | + | 0.168409i | \(0.0538630\pi\) | ||||
−0.985717 | + | 0.168409i | \(0.946137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −32.6713 | −0.666760 | ||||||||
\(50\) | −5.71849 | − | 0.359134i | −0.114370 | − | 0.00718268i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −19.1761 | + | 14.8814i | −0.368772 | + | 0.286181i | ||||
\(53\) | 0.476870 | + | 0.476870i | 0.00899755 | + | 0.00899755i | 0.711591 | − | 0.702594i | \(-0.247975\pi\) |
−0.702594 | + | 0.711591i | \(0.747975\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 45.4079 | 0.825599 | ||||||||
\(56\) | 6.04682 | − | 31.7565i | 0.107979 | − | 0.567080i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −39.9596 | − | 45.3151i | −0.688959 | − | 0.781295i | ||||
\(59\) | −9.97719 | + | 9.97719i | −0.169105 | + | 0.169105i | −0.786586 | − | 0.617481i | \(-0.788153\pi\) |
0.617481 | + | 0.786586i | \(0.288153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 37.9455 | − | 37.9455i | 0.622057 | − | 0.622057i | −0.324000 | − | 0.946057i | \(-0.605028\pi\) |
0.946057 | + | 0.324000i | \(0.105028\pi\) | |||||||
\(62\) | 75.9296 | + | 4.76855i | 1.22467 | + | 0.0769121i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −59.5215 | − | 23.5200i | −0.930024 | − | 0.367500i | ||||
\(65\) | −28.5500 | −0.439230 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 20.0705 | + | 20.0705i | 0.299559 | + | 0.299559i | 0.840841 | − | 0.541282i | \(-0.182061\pi\) |
−0.541282 | + | 0.840841i | \(0.682061\pi\) | |||||||
\(68\) | 119.530 | + | 15.0730i | 1.75780 | + | 0.221662i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 28.5187 | − | 25.1483i | 0.407410 | − | 0.359261i | ||||
\(71\) | −40.0818 | −0.564532 | −0.282266 | − | 0.959336i | \(-0.591086\pi\) | ||||
−0.282266 | + | 0.959336i | \(0.591086\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 30.8095i | 0.422049i | 0.977481 | + | 0.211024i | \(0.0676799\pi\) | ||||
−0.977481 | + | 0.211024i | \(0.932320\pi\) | |||||||
\(74\) | −90.9912 | + | 80.2377i | −1.22961 | + | 1.08429i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 68.5123 | + | 88.2846i | 0.901477 | + | 1.16164i | ||||
\(77\) | 27.5773 | − | 27.5773i | 0.358147 | − | 0.358147i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 130.125i | 1.64716i | 0.567203 | + | 0.823578i | \(0.308025\pi\) | ||||
−0.567203 | + | 0.823578i | \(0.691975\pi\) | |||||||
\(80\) | −38.3480 | − | 64.7767i | −0.479350 | − | 0.809709i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −96.2789 | − | 6.04653i | −1.17413 | − | 0.0737382i | ||||
\(83\) | 2.26155 | + | 2.26155i | 0.0272476 | + | 0.0272476i | 0.720599 | − | 0.693352i | \(-0.243867\pi\) |
−0.693352 | + | 0.720599i | \(0.743867\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 100.200 | + | 100.200i | 1.17883 | + | 1.17883i | ||||
\(86\) | −61.1282 | − | 69.3207i | −0.710793 | − | 0.806054i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −43.4206 | − | 63.8454i | −0.493416 | − | 0.725516i | ||||
\(89\) | 72.2232i | 0.811496i | 0.913985 | + | 0.405748i | \(0.132989\pi\) | ||||
−0.913985 | + | 0.405748i | \(0.867011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.3391 | + | 17.3391i | −0.190539 | + | 0.190539i | ||||
\(92\) | −112.051 | − | 14.1298i | −1.21794 | − | 0.153585i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 31.5986 | + | 1.98447i | 0.336156 | + | 0.0211113i | ||||
\(95\) | 131.441i | 1.38358i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −112.343 | −1.15817 | −0.579085 | − | 0.815267i | \(-0.696590\pi\) | ||||
−0.579085 | + | 0.815267i | \(0.696590\pi\) | |||||||
\(98\) | −4.09559 | + | 65.2140i | −0.0417917 | + | 0.665449i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.43371 | + | 11.3695i | −0.0143371 | + | 0.113695i | ||||
\(101\) | 1.61933 | + | 1.61933i | 0.0160330 | + | 0.0160330i | 0.715078 | − | 0.699045i | \(-0.246391\pi\) |
−0.699045 | + | 0.715078i | \(0.746391\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 27.9974 | 0.271819 | 0.135910 | − | 0.990721i | \(-0.456604\pi\) | ||||
0.135910 | + | 0.990721i | \(0.456604\pi\) | |||||||
\(104\) | 27.3005 | + | 40.1424i | 0.262504 | + | 0.385984i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.01164 | − | 0.892086i | 0.00954381 | − | 0.00841590i | ||||
\(107\) | 40.3835 | − | 40.3835i | 0.377416 | − | 0.377416i | −0.492753 | − | 0.870169i | \(-0.664010\pi\) |
0.870169 | + | 0.492753i | \(0.164010\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 36.8336 | − | 36.8336i | 0.337923 | − | 0.337923i | −0.517662 | − | 0.855585i | \(-0.673198\pi\) |
0.855585 | + | 0.517662i | \(0.173198\pi\) | |||||||
\(110\) | 5.69223 | − | 90.6373i | 0.0517475 | − | 0.823976i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −62.6301 | − | 16.0508i | −0.559197 | − | 0.143311i | ||||
\(113\) | 55.5952 | 0.491993 | 0.245997 | − | 0.969271i | \(-0.420885\pi\) | ||||
0.245997 | + | 0.969271i | \(0.420885\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −93.9305 | − | 93.9305i | −0.816787 | − | 0.816787i | ||||
\(116\) | −95.4612 | + | 74.0815i | −0.822941 | + | 0.638634i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 18.6644 | + | 21.1659i | 0.158173 | + | 0.179372i | ||||
\(119\) | 121.708 | 1.02276 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 27.8503i | 0.230167i | ||||||||
\(122\) | −70.9850 | − | 80.4985i | −0.581844 | − | 0.659824i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 19.0367 | − | 150.963i | 0.153522 | − | 1.21744i | ||||
\(125\) | −92.7007 | + | 92.7007i | −0.741606 | + | 0.741606i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 109.927i | − | 0.865569i | −0.901497 | − | 0.432785i | \(-0.857531\pi\) | ||
0.901497 | − | 0.432785i | \(-0.142469\pi\) | |||||||
\(128\) | −54.4090 | + | 115.861i | −0.425070 | + | 0.905160i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.57895 | + | 56.9876i | −0.0275304 | + | 0.438367i | ||||
\(131\) | −75.6795 | − | 75.6795i | −0.577706 | − | 0.577706i | 0.356565 | − | 0.934271i | \(-0.383948\pi\) |
−0.934271 | + | 0.356565i | \(0.883948\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 79.8270 | + | 79.8270i | 0.600203 | + | 0.600203i | ||||
\(134\) | 42.5780 | − | 37.5460i | 0.317746 | − | 0.280194i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 45.0707 | − | 236.701i | 0.331402 | − | 1.74045i | ||||
\(137\) | 2.14751i | 0.0156752i | 0.999969 | + | 0.00783762i | \(0.00249482\pi\) | ||||
−0.999969 | + | 0.00783762i | \(0.997505\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −109.246 | + | 109.246i | −0.785941 | + | 0.785941i | −0.980826 | − | 0.194885i | \(-0.937567\pi\) |
0.194885 | + | 0.980826i | \(0.437567\pi\) | |||||||
\(140\) | −46.6227 | − | 60.0778i | −0.333019 | − | 0.429127i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.02455 | + | 80.0059i | −0.0353842 | + | 0.563422i | ||||
\(143\) | 58.5673i | 0.409562i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −142.125 | −0.980174 | ||||||||
\(146\) | 61.4979 | + | 3.86221i | 0.421219 | + | 0.0264535i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 148.753 | + | 191.683i | 1.00509 | + | 1.29516i | ||||
\(149\) | −79.6950 | − | 79.6950i | −0.534866 | − | 0.534866i | 0.387151 | − | 0.922016i | \(-0.373459\pi\) |
−0.922016 | + | 0.387151i | \(0.873459\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 105.546 | 0.698982 | 0.349491 | − | 0.936940i | \(-0.386355\pi\) | ||||
0.349491 | + | 0.936940i | \(0.386355\pi\) | |||||||
\(152\) | 184.811 | − | 125.688i | 1.21586 | − | 0.826894i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −51.5892 | − | 58.5032i | −0.334995 | − | 0.379891i | ||||
\(155\) | 126.550 | − | 126.550i | 0.816451 | − | 0.816451i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 190.060 | − | 190.060i | 1.21057 | − | 1.21057i | 0.239733 | − | 0.970839i | \(-0.422940\pi\) |
0.970839 | − | 0.239733i | \(-0.0770598\pi\) | |||||||
\(158\) | 259.739 | + | 16.3122i | 1.64392 | + | 0.103242i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −134.106 | + | 68.4250i | −0.838162 | + | 0.427656i | ||||
\(161\) | −114.092 | −0.708649 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −59.4130 | − | 59.4130i | −0.364497 | − | 0.364497i | 0.500969 | − | 0.865465i | \(-0.332977\pi\) |
−0.865465 | + | 0.500969i | \(0.832977\pi\) | |||||||
\(164\) | −24.1386 | + | 191.421i | −0.147186 | + | 1.16720i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.79772 | − | 4.23071i | 0.0289019 | − | 0.0254862i | ||||
\(167\) | −65.3894 | −0.391553 | −0.195777 | − | 0.980649i | \(-0.562723\pi\) | ||||
−0.195777 | + | 0.980649i | \(0.562723\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 132.176i | 0.782107i | ||||||||
\(170\) | 212.568 | − | 187.446i | 1.25040 | − | 1.10262i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −146.032 | + | 113.326i | −0.849021 | + | 0.658873i | ||||
\(173\) | 212.939 | − | 212.939i | 1.23086 | − | 1.23086i | 0.267228 | − | 0.963633i | \(-0.413892\pi\) |
0.963633 | − | 0.267228i | \(-0.0861077\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.5766i | 0.0661522i | ||||||||
\(176\) | −132.883 | + | 78.6670i | −0.755016 | + | 0.446972i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 144.162 | + | 9.05372i | 0.809901 | + | 0.0508636i | ||||
\(179\) | −196.852 | − | 196.852i | −1.09973 | − | 1.09973i | −0.994442 | − | 0.105289i | \(-0.966423\pi\) |
−0.105289 | − | 0.994442i | \(-0.533577\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −27.4330 | − | 27.4330i | −0.151564 | − | 0.151564i | 0.627252 | − | 0.778816i | \(-0.284179\pi\) |
−0.778816 | + | 0.627252i | \(0.784179\pi\) | |||||||
\(182\) | 32.4364 | + | 36.7835i | 0.178222 | + | 0.202107i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −42.2505 | + | 221.890i | −0.229622 | + | 1.20592i | ||||
\(185\) | 285.383i | 1.54261i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 205.551 | − | 205.551i | 1.09920 | − | 1.09920i | ||||
\(188\) | 7.92226 | − | 62.8243i | 0.0421397 | − | 0.334172i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 262.364 | + | 16.4771i | 1.38086 | + | 0.0867214i | ||||
\(191\) | − | 244.409i | − | 1.27963i | −0.768530 | − | 0.639814i | \(-0.779011\pi\) | ||
0.768530 | − | 0.639814i | \(-0.220989\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 255.040 | 1.32145 | 0.660726 | − | 0.750627i | \(-0.270249\pi\) | ||||
0.660726 | + | 0.750627i | \(0.270249\pi\) | |||||||
\(194\) | −14.0830 | + | 224.243i | −0.0725927 | + | 1.15589i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 129.658 | + | 16.3501i | 0.661522 | + | 0.0834191i | ||||
\(197\) | 194.229 | + | 194.229i | 0.985936 | + | 0.985936i | 0.999902 | − | 0.0139666i | \(-0.00444586\pi\) |
−0.0139666 | + | 0.999902i | \(0.504446\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −169.797 | −0.853252 | −0.426626 | − | 0.904428i | \(-0.640298\pi\) | ||||
−0.426626 | + | 0.904428i | \(0.640298\pi\) | |||||||
\(200\) | 22.5145 | + | 4.28703i | 0.112573 | + | 0.0214352i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.43529 | − | 3.02930i | 0.0170064 | − | 0.0149965i | ||||
\(203\) | −86.3160 | + | 86.3160i | −0.425202 | + | 0.425202i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −160.466 | + | 160.466i | −0.782759 | + | 0.782759i | ||||
\(206\) | 3.50969 | − | 55.8847i | 0.0170373 | − | 0.271285i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 83.5492 | − | 49.4614i | 0.401679 | − | 0.237795i | ||||
\(209\) | 269.637 | 1.29013 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −132.691 | − | 132.691i | −0.628868 | − | 0.628868i | 0.318915 | − | 0.947783i | \(-0.396681\pi\) |
−0.947783 | + | 0.318915i | \(0.896681\pi\) | |||||||
\(212\) | −1.65385 | − | 2.13114i | −0.00780116 | − | 0.0100525i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −75.5458 | − | 85.6705i | −0.353018 | − | 0.400330i | ||||
\(215\) | −217.416 | −1.01124 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 153.713i | − | 0.708357i | ||||||
\(218\) | −68.9050 | − | 78.1398i | −0.316078 | − | 0.358439i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −180.205 | − | 22.7241i | −0.819112 | − | 0.103292i | ||||
\(221\) | −129.239 | + | 129.239i | −0.584791 | + | 0.584791i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 26.3436i | − | 0.118133i | −0.998254 | − | 0.0590664i | \(-0.981188\pi\) | ||
0.998254 | − | 0.0590664i | \(-0.0188124\pi\) | |||||||
\(224\) | −39.8896 | + | 123.002i | −0.178079 | + | 0.549115i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.96928 | − | 110.972i | 0.0308375 | − | 0.491026i | ||||
\(227\) | 70.3362 | + | 70.3362i | 0.309851 | + | 0.309851i | 0.844852 | − | 0.535001i | \(-0.179689\pi\) |
−0.535001 | + | 0.844852i | \(0.679689\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −215.607 | − | 215.607i | −0.941516 | − | 0.941516i | 0.0568658 | − | 0.998382i | \(-0.481889\pi\) |
−0.998382 | + | 0.0568658i | \(0.981889\pi\) | |||||||
\(230\) | −199.266 | + | 175.717i | −0.866376 | + | 0.763986i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 135.905 | + | 199.834i | 0.585797 | + | 0.861352i | ||||
\(233\) | − | 183.853i | − | 0.789069i | −0.918881 | − | 0.394534i | \(-0.870906\pi\) | ||
0.918881 | − | 0.394534i | \(-0.129094\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 52.6647 | − | 52.6647i | 0.224105 | − | 0.224105i | ||||
\(236\) | 44.5882 | − | 34.6021i | 0.188933 | − | 0.146619i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 15.2570 | − | 242.938i | 0.0641052 | − | 1.02075i | ||||
\(239\) | − | 315.183i | − | 1.31876i | −0.751811 | − | 0.659379i | \(-0.770819\pi\) | ||
0.751811 | − | 0.659379i | \(-0.229181\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −327.804 | −1.36018 | −0.680090 | − | 0.733128i | \(-0.738059\pi\) | ||||
−0.680090 | + | 0.733128i | \(0.738059\pi\) | |||||||
\(242\) | 55.5910 | + | 3.49124i | 0.229715 | + | 0.0144266i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −169.579 | + | 131.600i | −0.694996 | + | 0.539343i | ||||
\(245\) | 108.691 | + | 108.691i | 0.443635 | + | 0.443635i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −169.532 | −0.686366 | ||||||||
\(248\) | −298.945 | − | 56.9228i | −1.20543 | − | 0.229528i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 173.416 | + | 196.658i | 0.693665 | + | 0.786631i | ||||
\(251\) | −219.813 | + | 219.813i | −0.875747 | + | 0.875747i | −0.993091 | − | 0.117344i | \(-0.962562\pi\) |
0.117344 | + | 0.993091i | \(0.462562\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −192.689 | + | 192.689i | −0.761616 | + | 0.761616i | ||||
\(254\) | −219.422 | − | 13.7802i | −0.863867 | − | 0.0542528i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 224.445 | + | 123.128i | 0.876738 | + | 0.480969i | ||||
\(257\) | −150.042 | −0.583823 | −0.291911 | − | 0.956445i | \(-0.594291\pi\) | ||||
−0.291911 | + | 0.956445i | \(0.594291\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 173.320 | + | 173.320i | 0.669188 | + | 0.669188i | ||||
\(260\) | 113.303 | + | 14.2877i | 0.435779 | + | 0.0549526i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −160.548 | + | 141.574i | −0.612780 | + | 0.540360i | ||||
\(263\) | −14.8922 | −0.0566242 | −0.0283121 | − | 0.999599i | \(-0.509013\pi\) | ||||
−0.0283121 | + | 0.999599i | \(0.509013\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3.17290i | − | 0.0119732i | ||||||
\(266\) | 169.347 | − | 149.333i | 0.636643 | − | 0.561403i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −69.6069 | − | 89.6952i | −0.259727 | − | 0.334684i | ||||
\(269\) | −95.4169 | + | 95.4169i | −0.354710 | + | 0.354710i | −0.861858 | − | 0.507149i | \(-0.830699\pi\) |
0.507149 | + | 0.861858i | \(0.330699\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 46.4991i | − | 0.171583i | −0.996313 | − | 0.0857917i | \(-0.972658\pi\) | ||
0.996313 | − | 0.0857917i | \(-0.0273420\pi\) | |||||||
\(272\) | −466.821 | − | 119.636i | −1.71625 | − | 0.439840i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.28657 | + | 0.269206i | 0.0156444 | + | 0.000982505i | ||||
\(275\) | 19.5516 | + | 19.5516i | 0.0710967 | + | 0.0710967i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.5071 | + | 30.5071i | 0.110134 | + | 0.110134i | 0.760026 | − | 0.649892i | \(-0.225186\pi\) |
−0.649892 | + | 0.760026i | \(0.725186\pi\) | |||||||
\(278\) | 204.367 | + | 231.757i | 0.735134 | + | 0.833657i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −125.764 | + | 85.5308i | −0.449157 | + | 0.305467i | ||||
\(281\) | − | 217.239i | − | 0.773093i | −0.922270 | − | 0.386547i | \(-0.873668\pi\) | ||
0.922270 | − | 0.386547i | \(-0.126332\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −136.055 | + | 136.055i | −0.480760 | + | 0.480760i | −0.905374 | − | 0.424614i | \(-0.860410\pi\) |
0.424614 | + | 0.905374i | \(0.360410\pi\) | |||||||
\(284\) | 159.067 | + | 20.0587i | 0.560096 | + | 0.0706292i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 116.904 | + | 7.34186i | 0.408756 | + | 0.0256708i | ||||
\(287\) | 194.909i | 0.679126i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 618.167 | 2.13898 | ||||||||
\(290\) | −17.8165 | + | 283.691i | −0.0614361 | + | 0.978246i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 15.4185 | − | 122.270i | 0.0528030 | − | 0.418732i | ||||
\(293\) | 56.8362 | + | 56.8362i | 0.193980 | + | 0.193980i | 0.797414 | − | 0.603433i | \(-0.206201\pi\) |
−0.603433 | + | 0.797414i | \(0.706201\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 66.3841 | 0.225031 | ||||||||
\(296\) | 401.260 | − | 272.893i | 1.35561 | − | 0.921935i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −169.067 | + | 149.086i | −0.567339 | + | 0.500289i | ||||
\(299\) | 121.152 | − | 121.152i | 0.405190 | − | 0.405190i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −132.042 | + | 132.042i | −0.438677 | + | 0.438677i | ||||
\(302\) | 13.2310 | − | 210.677i | 0.0438113 | − | 0.697608i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −227.714 | − | 384.650i | −0.749060 | − | 1.26530i | ||||
\(305\) | −252.474 | −0.827782 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 245.927 | + | 245.927i | 0.801067 | + | 0.801067i | 0.983262 | − | 0.182196i | \(-0.0583205\pi\) |
−0.182196 | + | 0.983262i | \(0.558320\pi\) | |||||||
\(308\) | −123.243 | + | 95.6416i | −0.400141 | + | 0.310525i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −236.738 | − | 268.466i | −0.763671 | − | 0.866019i | ||||
\(311\) | 359.964 | 1.15744 | 0.578721 | − | 0.815526i | \(-0.303552\pi\) | ||||
0.578721 | + | 0.815526i | \(0.303552\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 131.023i | − | 0.418605i | −0.977851 | − | 0.209303i | \(-0.932881\pi\) | ||
0.977851 | − | 0.209303i | \(-0.0671194\pi\) | |||||||
\(314\) | −355.547 | − | 403.198i | −1.13231 | − | 1.28407i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 65.1205 | − | 516.412i | 0.206077 | − | 1.63421i | ||||
\(317\) | −89.0470 | + | 89.0470i | −0.280905 | + | 0.280905i | −0.833470 | − | 0.552565i | \(-0.813649\pi\) |
0.552565 | + | 0.833470i | \(0.313649\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 291.555i | 0.913966i | ||||||||
\(320\) | 119.770 | + | 276.262i | 0.374280 | + | 0.863319i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −14.3024 | + | 227.736i | −0.0444172 | + | 0.707255i | ||||
\(323\) | 595.000 | + | 595.000i | 1.84210 | + | 1.84210i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.2929 | − | 12.2929i | −0.0378244 | − | 0.0378244i | ||||
\(326\) | −126.040 | + | 111.144i | −0.386626 | + | 0.340934i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 379.064 | + | 72.1783i | 1.15568 | + | 0.220056i | ||||
\(329\) | − | 63.9690i | − | 0.194435i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 95.5992 | − | 95.5992i | 0.288819 | − | 0.288819i | −0.547794 | − | 0.836613i | \(-0.684532\pi\) |
0.836613 | + | 0.547794i | \(0.184532\pi\) | |||||||
\(332\) | −7.84336 | − | 10.1069i | −0.0236246 | − | 0.0304425i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.19706 | + | 130.522i | −0.0245421 | + | 0.390783i | ||||
\(335\) | − | 133.541i | − | 0.398629i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 583.717 | 1.73210 | 0.866050 | − | 0.499958i | \(-0.166651\pi\) | ||||
0.866050 | + | 0.499958i | \(0.166651\pi\) | |||||||
\(338\) | 263.833 | + | 16.5693i | 0.780570 | + | 0.0490215i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −347.508 | − | 447.797i | −1.02208 | − | 1.31705i | ||||
\(341\) | −259.604 | − | 259.604i | −0.761302 | − | 0.761302i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 330.024 | 0.962169 | ||||||||
\(344\) | 207.900 | + | 305.695i | 0.604362 | + | 0.888649i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −398.347 | − | 451.734i | −1.15129 | − | 1.30559i | ||||
\(347\) | −191.655 | + | 191.655i | −0.552320 | + | 0.552320i | −0.927110 | − | 0.374790i | \(-0.877715\pi\) |
0.374790 | + | 0.927110i | \(0.377715\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.4781 | + | 19.4781i | −0.0558112 | + | 0.0558112i | −0.734462 | − | 0.678650i | \(-0.762565\pi\) |
0.678650 | + | 0.734462i | \(0.262565\pi\) | |||||||
\(350\) | 23.1077 | + | 1.45122i | 0.0660221 | + | 0.00414634i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 140.367 | + | 275.105i | 0.398769 | + | 0.781547i | ||||
\(353\) | 82.9610 | 0.235017 | 0.117509 | − | 0.993072i | \(-0.462509\pi\) | ||||
0.117509 | + | 0.993072i | \(0.462509\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 133.344 | + | 133.344i | 0.375616 | + | 0.375616i | ||||
\(356\) | 36.1437 | − | 286.623i | 0.101527 | − | 0.805120i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −417.606 | + | 368.253i | −1.16650 | + | 1.02864i | ||||
\(359\) | −357.792 | −0.996634 | −0.498317 | − | 0.866995i | \(-0.666048\pi\) | ||||
−0.498317 | + | 0.866995i | \(0.666048\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 419.507i | 1.16207i | ||||||||
\(362\) | −58.1971 | + | 51.3193i | −0.160766 | + | 0.141766i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 77.4886 | − | 60.1341i | 0.212881 | − | 0.165204i | ||||
\(365\) | 102.497 | − | 102.497i | 0.280814 | − | 0.280814i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 651.729i | − | 1.77583i | −0.460010 | − | 0.887914i | \(-0.652154\pi\) | ||
0.460010 | − | 0.887914i | \(-0.347846\pi\) | |||||||
\(368\) | 437.610 | + | 112.150i | 1.18916 | + | 0.304756i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 569.643 | + | 35.7749i | 1.53958 | + | 0.0966889i | ||||
\(371\) | −1.92698 | − | 1.92698i | −0.00519401 | − | 0.00519401i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 199.720 | + | 199.720i | 0.535442 | + | 0.535442i | 0.922187 | − | 0.386745i | \(-0.126401\pi\) |
−0.386745 | + | 0.922187i | \(0.626401\pi\) | |||||||
\(374\) | −384.526 | − | 436.061i | −1.02814 | − | 1.16594i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −124.408 | − | 23.6889i | −0.330873 | − | 0.0630023i | ||||
\(377\) | − | 183.314i | − | 0.486243i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −330.204 | + | 330.204i | −0.871251 | + | 0.871251i | −0.992609 | − | 0.121358i | \(-0.961275\pi\) |
0.121358 | + | 0.992609i | \(0.461275\pi\) | |||||||
\(380\) | 65.7787 | − | 521.631i | 0.173102 | − | 1.37271i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −487.857 | − | 30.6385i | −1.27711 | − | 0.0802055i | ||||
\(383\) | 174.284i | 0.455049i | 0.973772 | + | 0.227524i | \(0.0730631\pi\) | ||||
−0.973772 | + | 0.227524i | \(0.926937\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −183.488 | −0.476593 | ||||||||
\(386\) | 31.9712 | − | 509.077i | 0.0828270 | − | 1.31885i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 445.839 | + | 56.2212i | 1.14907 | + | 0.144900i | ||||
\(389\) | −207.835 | − | 207.835i | −0.534279 | − | 0.534279i | 0.387564 | − | 0.921843i | \(-0.373317\pi\) |
−0.921843 | + | 0.387564i | \(0.873317\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −850.402 | −2.17494 | ||||||||
\(392\) | 48.8896 | − | 256.757i | 0.124718 | − | 0.654992i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 412.043 | − | 363.347i | 1.04579 | − | 0.922200i | ||||
\(395\) | 432.900 | − | 432.900i | 1.09595 | − | 1.09595i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −37.2994 | + | 37.2994i | −0.0939533 | + | 0.0939533i | −0.752521 | − | 0.658568i | \(-0.771162\pi\) |
0.658568 | + | 0.752521i | \(0.271162\pi\) | |||||||
\(398\) | −21.2854 | + | 338.927i | −0.0534808 | + | 0.851574i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.3796 | − | 44.4031i | 0.0284489 | − | 0.111008i | ||||
\(401\) | 524.704 | 1.30849 | 0.654244 | − | 0.756284i | \(-0.272987\pi\) | ||||
0.654244 | + | 0.756284i | \(0.272987\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 163.224 | + | 163.224i | 0.405023 | + | 0.405023i | ||||
\(404\) | −5.61605 | − | 7.23682i | −0.0139011 | − | 0.0179129i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 161.472 | + | 183.113i | 0.397715 | + | 0.451017i | ||||
\(407\) | 585.434 | 1.43841 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 787.357i | − | 1.92508i | −0.271141 | − | 0.962540i | \(-0.587401\pi\) | ||
0.271141 | − | 0.962540i | \(-0.412599\pi\) | |||||||
\(410\) | 300.184 | + | 340.416i | 0.732157 | + | 0.830282i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −111.110 | − | 14.0111i | −0.269684 | − | 0.0340076i | ||||
\(413\) | 40.3166 | − | 40.3166i | 0.0976190 | − | 0.0976190i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 15.0475i | − | 0.0362589i | ||||||
\(416\) | −88.2548 | − | 172.970i | −0.212151 | − | 0.415794i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 33.8010 | − | 538.213i | 0.0808637 | − | 1.28759i | ||||
\(419\) | −30.1767 | − | 30.1767i | −0.0720209 | − | 0.0720209i | 0.670179 | − | 0.742200i | \(-0.266217\pi\) |
−0.742200 | + | 0.670179i | \(0.766217\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −261.021 | − | 261.021i | −0.620003 | − | 0.620003i | 0.325529 | − | 0.945532i | \(-0.394458\pi\) |
−0.945532 | + | 0.325529i | \(0.894458\pi\) | |||||||
\(422\) | −281.494 | + | 248.227i | −0.667048 | + | 0.588215i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.46122 | + | 3.03403i | −0.0105217 | + | 0.00715574i | ||||
\(425\) | 86.2878i | 0.203030i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −153.333 | + | 153.333i | −0.359094 | + | 0.359094i | ||||
\(428\) | −180.474 | + | 140.055i | −0.421669 | + | 0.327231i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −27.2547 | + | 433.977i | −0.0633830 | + | 1.00925i | ||||
\(431\) | 459.989i | 1.06726i | 0.845718 | + | 0.533630i | \(0.179172\pi\) | ||||
−0.845718 | + | 0.533630i | \(0.820828\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −445.246 | −1.02828 | −0.514140 | − | 0.857706i | \(-0.671889\pi\) | ||||
−0.514140 | + | 0.857706i | \(0.671889\pi\) | |||||||
\(434\) | −306.822 | − | 19.2691i | −0.706964 | − | 0.0443989i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −164.610 | + | 127.744i | −0.377546 | + | 0.292990i | ||||
\(437\) | −557.768 | − | 557.768i | −1.27636 | − | 1.27636i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 356.467 | 0.811998 | 0.405999 | − | 0.913874i | \(-0.366924\pi\) | ||||
0.405999 | + | 0.913874i | \(0.366924\pi\) | |||||||
\(440\) | −67.9489 | + | 356.852i | −0.154429 | + | 0.811027i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 241.768 | + | 274.171i | 0.546987 | + | 0.620295i | ||||
\(443\) | −358.752 | + | 358.752i | −0.809824 | + | 0.809824i | −0.984607 | − | 0.174783i | \(-0.944078\pi\) |
0.174783 | + | 0.984607i | \(0.444078\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 240.272 | − | 240.272i | 0.539936 | − | 0.539936i | ||||
\(446\) | −52.5837 | − | 3.30237i | −0.117901 | − | 0.00740442i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 240.519 | + | 95.0415i | 0.536874 | + | 0.212146i | ||||
\(449\) | 44.6564 | 0.0994576 | 0.0497288 | − | 0.998763i | \(-0.484164\pi\) | ||||
0.0497288 | + | 0.998763i | \(0.484164\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 329.179 | + | 329.179i | 0.729886 | + | 0.729886i | ||||
\(452\) | −220.634 | − | 27.8223i | −0.488128 | − | 0.0615538i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 149.213 | − | 131.579i | 0.328663 | − | 0.289821i | ||||
\(455\) | 115.367 | 0.253554 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 84.2332i | − | 0.184318i | −0.995744 | − | 0.0921589i | \(-0.970623\pi\) | ||
0.995744 | − | 0.0921589i | \(-0.0293768\pi\) | |||||||
\(458\) | −457.394 | + | 403.338i | −0.998678 | + | 0.880652i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 325.763 | + | 419.777i | 0.708180 | + | 0.912558i | ||||
\(461\) | −205.347 | + | 205.347i | −0.445438 | + | 0.445438i | −0.893835 | − | 0.448397i | \(-0.851995\pi\) |
0.448397 | + | 0.893835i | \(0.351995\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 270.647i | − | 0.584550i | −0.956334 | − | 0.292275i | \(-0.905588\pi\) | ||
0.956334 | − | 0.292275i | \(-0.0944123\pi\) | |||||||
\(464\) | 415.918 | − | 246.225i | 0.896376 | − | 0.530657i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −366.983 | − | 23.0474i | −0.787517 | − | 0.0494579i | ||||
\(467\) | −230.389 | − | 230.389i | −0.493338 | − | 0.493338i | 0.416018 | − | 0.909356i | \(-0.363425\pi\) |
−0.909356 | + | 0.416018i | \(0.863425\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −81.1024 | − | 81.1024i | −0.172926 | − | 0.172926i | ||||
\(470\) | −98.5203 | − | 111.724i | −0.209618 | − | 0.237711i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −63.4788 | − | 93.3387i | −0.134489 | − | 0.197751i | ||||
\(473\) | 446.006i | 0.942931i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −56.5952 | + | 56.5952i | −0.119148 | + | 0.119148i | ||||
\(476\) | −483.008 | − | 60.9082i | −1.01472 | − | 0.127958i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −629.127 | − | 39.5106i | −1.31616 | − | 0.0826581i | ||||
\(479\) | 575.911i | 1.20232i | 0.799129 | + | 0.601159i | \(0.205294\pi\) | ||||
−0.799129 | + | 0.601159i | \(0.794706\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −368.088 | −0.765255 | ||||||||
\(482\) | −41.0926 | + | 654.318i | −0.0852545 | + | 1.35751i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 13.9375 | − | 110.526i | 0.0287965 | − | 0.228359i | ||||
\(485\) | 373.740 | + | 373.740i | 0.770599 | + | 0.770599i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 600.355 | 1.23276 | 0.616381 | − | 0.787448i | \(-0.288598\pi\) | ||||
0.616381 | + | 0.787448i | \(0.288598\pi\) | |||||||
\(488\) | 241.424 | + | 354.988i | 0.494721 | + | 0.727434i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 230.579 | − | 203.329i | 0.470569 | − | 0.414956i | ||||
\(491\) | −79.7182 | + | 79.7182i | −0.162359 | + | 0.162359i | −0.783611 | − | 0.621252i | \(-0.786624\pi\) |
0.621252 | + | 0.783611i | \(0.286624\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −643.367 | + | 643.367i | −1.30500 | + | 1.30500i | ||||
\(494\) | −21.2522 | + | 338.398i | −0.0430206 | + | 0.685017i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −151.097 | + | 589.580i | −0.304631 | + | 1.18867i | ||||
\(497\) | 161.966 | 0.325887 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.4912 | − | 13.4912i | −0.0270365 | − | 0.0270365i | 0.693459 | − | 0.720496i | \(-0.256086\pi\) |
−0.720496 | + | 0.693459i | \(0.756086\pi\) | |||||||
\(500\) | 414.281 | − | 321.498i | 0.828562 | − | 0.642996i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 411.205 | + | 466.316i | 0.819134 | + | 0.928916i | ||||
\(503\) | −892.196 | −1.77375 | −0.886875 | − | 0.462009i | \(-0.847129\pi\) | ||||
−0.886875 | + | 0.462009i | \(0.847129\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 10.7744i | − | 0.0213354i | ||||||
\(506\) | 360.465 | + | 408.775i | 0.712381 | + | 0.807855i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −55.0125 | + | 436.254i | −0.108292 | + | 0.858768i | ||||
\(509\) | 44.9128 | − | 44.9128i | 0.0882374 | − | 0.0882374i | −0.661610 | − | 0.749848i | \(-0.730127\pi\) |
0.749848 | + | 0.661610i | \(0.230127\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 124.498i | − | 0.243636i | ||||||
\(512\) | 273.908 | − | 432.572i | 0.534976 | − | 0.844867i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.8090 | + | 299.495i | −0.0365933 | + | 0.582675i | ||||
\(515\) | −93.1416 | − | 93.1416i | −0.180857 | − | 0.180857i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −108.036 | − | 108.036i | −0.208967 | − | 0.208967i | ||||
\(518\) | 367.685 | − | 324.231i | 0.709816 | − | 0.625929i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 42.7225 | − | 224.368i | 0.0821586 | − | 0.431478i | ||||
\(521\) | − | 866.038i | − | 1.66226i | −0.556078 | − | 0.831130i | \(-0.687694\pi\) | ||
0.556078 | − | 0.831130i | \(-0.312306\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 359.579 | − | 359.579i | 0.687531 | − | 0.687531i | −0.274155 | − | 0.961686i | \(-0.588398\pi\) |
0.961686 | + | 0.274155i | \(0.0883981\pi\) | |||||||
\(524\) | 262.466 | + | 338.213i | 0.500889 | + | 0.645444i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.86684 | + | 29.7257i | −0.00354913 | + | 0.0565128i | ||||
\(527\) | − | 1145.72i | − | 2.17405i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 268.189 | 0.506973 | ||||||||
\(530\) | −6.33332 | − | 0.397747i | −0.0119497 | − | 0.000750466i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −276.850 | − | 356.748i | −0.520395 | − | 0.670579i | ||||
\(533\) | −206.969 | − | 206.969i | −0.388310 | − | 0.388310i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −268.695 | −0.502234 | ||||||||
\(536\) | −187.764 | + | 127.696i | −0.350305 | + | 0.238239i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 178.497 | + | 202.420i | 0.331779 | + | 0.376245i | ||||
\(539\) | 222.968 | − | 222.968i | 0.413669 | − | 0.413669i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.41176 | + | 9.41176i | −0.0173970 | + | 0.0173970i | −0.715752 | − | 0.698355i | \(-0.753916\pi\) |
0.698355 | + | 0.715752i | \(0.253916\pi\) | |||||||
\(542\) | −92.8154 | − | 5.82902i | −0.171246 | − | 0.0107546i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −297.322 | + | 916.809i | −0.546548 | + | 1.68531i | ||||
\(545\) | −245.076 | −0.449680 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.6377 | − | 37.6377i | −0.0688075 | − | 0.0688075i | 0.671866 | − | 0.740673i | \(-0.265493\pi\) |
−0.740673 | + | 0.671866i | \(0.765493\pi\) | |||||||
\(548\) | 1.07471 | − | 8.52253i | 0.00196115 | − | 0.0155521i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 41.4772 | − | 36.5753i | 0.0754131 | − | 0.0665006i | ||||
\(551\) | −843.953 | −1.53168 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 525.821i | − | 0.950852i | ||||||
\(554\) | 64.7186 | − | 57.0700i | 0.116821 | − | 0.103014i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 488.221 | − | 378.878i | 0.878096 | − | 0.681436i | ||||
\(557\) | −369.172 | + | 369.172i | −0.662786 | + | 0.662786i | −0.956036 | − | 0.293250i | \(-0.905263\pi\) |
0.293250 | + | 0.956036i | \(0.405263\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 280.424i | − | 0.501652i | ||||||
\(560\) | 154.960 | + | 261.755i | 0.276714 | + | 0.467420i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −433.624 | − | 27.2326i | −0.771573 | − | 0.0484565i | ||||
\(563\) | 141.210 | + | 141.210i | 0.250817 | + | 0.250817i | 0.821306 | − | 0.570489i | \(-0.193246\pi\) |
−0.570489 | + | 0.821306i | \(0.693246\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −184.954 | − | 184.954i | −0.327352 | − | 0.327352i | ||||
\(566\) | 254.520 | + | 288.631i | 0.449682 | + | 0.509949i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 59.9788 | − | 314.995i | 0.105596 | − | 0.554568i | ||||
\(569\) | 134.928i | 0.237131i | 0.992946 | + | 0.118566i | \(0.0378296\pi\) | ||||
−0.992946 | + | 0.118566i | \(0.962170\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −486.485 | + | 486.485i | −0.851988 | + | 0.851988i | −0.990378 | − | 0.138390i | \(-0.955807\pi\) |
0.138390 | + | 0.990378i | \(0.455807\pi\) | |||||||
\(572\) | 29.3097 | − | 232.429i | 0.0512407 | − | 0.406344i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 389.052 | + | 24.4333i | 0.677790 | + | 0.0425668i | ||||
\(575\) | − | 80.8885i | − | 0.140676i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −310.050 | −0.537349 | −0.268674 | − | 0.963231i | \(-0.586586\pi\) | ||||
−0.268674 | + | 0.963231i | \(0.586586\pi\) | |||||||
\(578\) | 77.4919 | − | 1233.90i | 0.134069 | − | 2.13478i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 564.034 | + | 71.1257i | 0.972472 | + | 0.122631i | ||||
\(581\) | −9.13868 | − | 9.13868i | −0.0157292 | − | 0.0157292i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.50888 | −0.0111645 | ||||||||
\(584\) | −242.126 | − | 46.1037i | −0.414599 | − | 0.0789448i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 120.574 | − | 106.324i | 0.205757 | − | 0.181440i | ||||
\(587\) | 301.021 | − | 301.021i | 0.512812 | − | 0.512812i | −0.402575 | − | 0.915387i | \(-0.631885\pi\) |
0.915387 | + | 0.402575i | \(0.131885\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 751.465 | − | 751.465i | 1.27583 | − | 1.27583i | ||||
\(590\) | 8.32175 | − | 132.507i | 0.0141047 | − | 0.224588i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −494.412 | − | 835.150i | −0.835155 | − | 1.41073i | ||||
\(593\) | −6.08782 | −0.0102661 | −0.00513307 | − | 0.999987i | \(-0.501634\pi\) | ||||
−0.00513307 | + | 0.999987i | \(0.501634\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −404.898 | − | 404.898i | −0.680501 | − | 0.680501i | ||||
\(596\) | 276.392 | + | 356.158i | 0.463746 | + | 0.597581i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −226.640 | − | 257.015i | −0.378997 | − | 0.429790i | ||||
\(599\) | 756.472 | 1.26289 | 0.631446 | − | 0.775420i | \(-0.282462\pi\) | ||||
0.631446 | + | 0.775420i | \(0.282462\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 753.072i | 1.25303i | 0.779409 | + | 0.626516i | \(0.215520\pi\) | ||||
−0.779409 | + | 0.626516i | \(0.784480\pi\) | |||||||
\(602\) | 247.012 | + | 280.117i | 0.410319 | + | 0.465310i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −418.868 | − | 52.8200i | −0.693490 | − | 0.0874504i | ||||
\(605\) | 92.6521 | − | 92.6521i | 0.153144 | − | 0.153144i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 47.1200i | − | 0.0776277i | −0.999246 | − | 0.0388139i | \(-0.987642\pi\) | ||
0.999246 | − | 0.0388139i | \(-0.0123579\pi\) | |||||||
\(608\) | −796.334 | + | 406.314i | −1.30976 | + | 0.668280i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −31.6495 | + | 503.954i | −0.0518844 | + | 0.826155i | ||||
\(611\) | 67.9271 | + | 67.9271i | 0.111174 | + | 0.111174i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 637.192 | + | 637.192i | 1.03947 | + | 1.03947i | 0.999189 | + | 0.0402769i | \(0.0128240\pi\) |
0.0402769 | + | 0.999189i | \(0.487176\pi\) | |||||||
\(614\) | 521.717 | − | 460.059i | 0.849701 | − | 0.749282i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 175.458 | + | 257.992i | 0.284834 | + | 0.418818i | ||||
\(617\) | 514.635i | 0.834092i | 0.908885 | + | 0.417046i | \(0.136935\pi\) | ||||
−0.908885 | + | 0.417046i | \(0.863065\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 313.704 | − | 313.704i | 0.506791 | − | 0.506791i | −0.406749 | − | 0.913540i | \(-0.633338\pi\) |
0.913540 | + | 0.406749i | \(0.133338\pi\) | |||||||
\(620\) | −565.553 | + | 438.891i | −0.912182 | + | 0.707888i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 45.1243 | − | 718.513i | 0.0725471 | − | 1.15517i | ||||
\(623\) | − | 291.845i | − | 0.468452i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 545.171 | 0.872273 | ||||||||
\(626\) | −261.532 | − | 16.4248i | −0.417782 | − | 0.0262377i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −849.380 | + | 659.151i | −1.35252 | + | 1.04960i | ||||
\(629\) | 1291.86 | + | 1291.86i | 2.05383 | + | 2.05383i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1226.20 | −1.94326 | −0.971631 | − | 0.236502i | \(-0.923999\pi\) | ||||
−0.971631 | + | 0.236502i | \(0.923999\pi\) | |||||||
\(632\) | −1022.63 | − | 194.721i | −1.61808 | − | 0.308103i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 166.581 | + | 188.906i | 0.262746 | + | 0.297960i | ||||
\(635\) | −365.706 | + | 365.706i | −0.575914 | + | 0.575914i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −140.189 | + | 140.189i | −0.220078 | + | 0.220078i | ||||
\(638\) | 581.964 | + | 36.5487i | 0.912169 | + | 0.0572863i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 566.452 | − | 204.437i | 0.885081 | − | 0.319432i | ||||
\(641\) | −241.218 | −0.376314 | −0.188157 | − | 0.982139i | \(-0.560251\pi\) | ||||
−0.188157 | + | 0.982139i | \(0.560251\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −736.141 | − | 736.141i | −1.14485 | − | 1.14485i | −0.987550 | − | 0.157304i | \(-0.949720\pi\) |
−0.157304 | − | 0.987550i | \(-0.550280\pi\) | |||||||
\(644\) | 452.784 | + | 57.0969i | 0.703081 | + | 0.0886598i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1262.25 | − | 1113.07i | 1.95394 | − | 1.72302i | ||||
\(647\) | 680.082 | 1.05113 | 0.525565 | − | 0.850753i | \(-0.323854\pi\) | ||||
0.525565 | + | 0.850753i | \(0.323854\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 136.180i | − | 0.209831i | ||||||
\(650\) | −26.0785 | + | 22.9965i | −0.0401208 | + | 0.0353793i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 206.052 | + | 265.518i | 0.316030 | + | 0.407235i | ||||
\(653\) | 716.929 | − | 716.929i | 1.09790 | − | 1.09790i | 0.103244 | − | 0.994656i | \(-0.467078\pi\) |
0.994656 | − | 0.103244i | \(-0.0329224\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 503.540i | 0.768763i | ||||||||
\(656\) | 191.591 | − | 747.589i | 0.292060 | − | 1.13962i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −127.686 | − | 8.01900i | −0.194052 | − | 0.0121869i | ||||
\(659\) | −276.868 | − | 276.868i | −0.420133 | − | 0.420133i | 0.465116 | − | 0.885250i | \(-0.346012\pi\) |
−0.885250 | + | 0.465116i | \(0.846012\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 251.780 | + | 251.780i | 0.380907 | + | 0.380907i | 0.871429 | − | 0.490522i | \(-0.163194\pi\) |
−0.490522 | + | 0.871429i | \(0.663194\pi\) | |||||||
\(662\) | −178.838 | − | 202.807i | −0.270149 | − | 0.306354i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −21.1573 | + | 14.3889i | −0.0318634 | + | 0.0216700i | ||||
\(665\) | − | 531.136i | − | 0.798700i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 603.109 | − | 603.109i | 0.904211 | − | 0.904211i | ||||
\(668\) | 259.502 | + | 32.7238i | 0.388477 | + | 0.0489877i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −266.556 | − | 16.7403i | −0.397845 | − | 0.0249856i | ||||
\(671\) | 517.924i | 0.771869i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 674.332 | 1.00198 | 0.500990 | − | 0.865453i | \(-0.332969\pi\) | ||||
0.500990 | + | 0.865453i | \(0.332969\pi\) | |||||||
\(674\) | 73.1734 | − | 1165.14i | 0.108566 | − | 1.72869i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 66.1468 | − | 524.550i | 0.0978503 | − | 0.775962i | ||||
\(677\) | −109.048 | − | 109.048i | −0.161075 | − | 0.161075i | 0.621968 | − | 0.783043i | \(-0.286334\pi\) |
−0.783043 | + | 0.621968i | \(0.786334\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 453.963 | 0.668576 | ||||||||
\(680\) | −937.396 | + | 637.514i | −1.37852 | + | 0.937521i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −550.731 | + | 485.644i | −0.807523 | + | 0.712088i | ||||
\(683\) | 784.278 | − | 784.278i | 1.14828 | − | 1.14828i | 0.161394 | − | 0.986890i | \(-0.448401\pi\) |
0.986890 | − | 0.161394i | \(-0.0515990\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.14432 | − | 7.14432i | 0.0104297 | − | 0.0104297i | ||||
\(686\) | 41.3710 | − | 658.750i | 0.0603076 | − | 0.960277i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 636.250 | − | 376.662i | 0.924782 | − | 0.547474i | ||||
\(689\) | 4.09241 | 0.00593964 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −99.4915 | − | 99.4915i | −0.143982 | − | 0.143982i | 0.631442 | − | 0.775423i | \(-0.282464\pi\) |
−0.775423 | + | 0.631442i | \(0.782464\pi\) | |||||||
\(692\) | −951.628 | + | 738.500i | −1.37518 | + | 1.06720i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 358.531 | + | 406.582i | 0.516615 | + | 0.585853i | ||||
\(695\) | 726.877 | 1.04587 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1452.78i | 2.08433i | ||||||||
\(698\) | 36.4379 | + | 41.3213i | 0.0522032 | + | 0.0591996i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.79346 | − | 45.9427i | 0.00827637 | − | 0.0656324i | ||||
\(701\) | −177.909 | + | 177.909i | −0.253794 | + | 0.253794i | −0.822524 | − | 0.568730i | \(-0.807435\pi\) |
0.568730 | + | 0.822524i | \(0.307435\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1694.63i | 2.41057i | ||||||||
\(704\) | 566.723 | − | 245.695i | 0.805005 | − | 0.348999i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.3998 | − | 165.596i | 0.0147306 | − | 0.234555i | ||||
\(707\) | −6.54353 | − | 6.54353i | −0.00925535 | − | 0.00925535i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −208.080 | − | 208.080i | −0.293484 | − | 0.293484i | 0.544971 | − | 0.838455i | \(-0.316541\pi\) |
−0.838455 | + | 0.544971i | \(0.816541\pi\) | |||||||
\(710\) | 282.879 | − | 249.448i | 0.398421 | − | 0.351335i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −567.587 | − | 108.076i | −0.797173 | − | 0.151791i | ||||
\(713\) | 1074.03i | 1.50635i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 194.841 | − | 194.841i | 0.272506 | − | 0.272506i | ||||
\(716\) | 682.707 | + | 879.734i | 0.953501 | + | 1.22868i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −44.8519 | + | 714.176i | −0.0624678 | + | 0.994674i | ||||
\(719\) | − | 1013.84i | − | 1.41007i | −0.709171 | − | 0.705036i | \(-0.750931\pi\) | ||
0.709171 | − | 0.705036i | \(-0.249069\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −113.134 | −0.156913 | ||||||||
\(722\) | 837.364 | + | 52.5883i | 1.15978 | + | 0.0728370i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 95.1413 | + | 122.599i | 0.131411 | + | 0.169335i | ||||
\(725\) | −61.1957 | − | 61.1957i | −0.0844079 | − | 0.0844079i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 697.156 | 0.958949 | 0.479474 | − | 0.877556i | \(-0.340827\pi\) | ||||
0.479474 | + | 0.877556i | \(0.340827\pi\) | |||||||
\(728\) | −110.318 | − | 162.211i | −0.151536 | − | 0.222817i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −191.742 | − | 217.440i | −0.262661 | − | 0.297863i | ||||
\(731\) | −984.189 | + | 984.189i | −1.34636 | + | 1.34636i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39.9608 | + | 39.9608i | −0.0545168 | + | 0.0545168i | −0.733840 | − | 0.679323i | \(-0.762274\pi\) |
0.679323 | + | 0.733840i | \(0.262274\pi\) | |||||||
\(734\) | −1300.89 | − | 81.6991i | −1.77234 | − | 0.111307i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 278.717 | − | 859.441i | 0.378692 | − | 1.16772i | ||||
\(737\) | −273.945 | −0.371703 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −236.377 | − | 236.377i | −0.319860 | − | 0.319860i | 0.528853 | − | 0.848713i | \(-0.322622\pi\) |
−0.848713 | + | 0.528853i | \(0.822622\pi\) | |||||||
\(740\) | 142.818 | − | 1132.56i | 0.192998 | − | 1.53049i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.08794 | + | 3.60481i | −0.00550935 | + | 0.00485824i | ||||
\(743\) | −804.248 | −1.08243 | −0.541217 | − | 0.840883i | \(-0.682036\pi\) | ||||
−0.541217 | + | 0.840883i | \(0.682036\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 530.258i | 0.711755i | ||||||||
\(746\) | 423.691 | − | 373.618i | 0.567950 | − | 0.500828i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −918.610 | + | 712.877i | −1.22809 | + | 0.953043i | ||||
\(749\) | −163.185 | + | 163.185i | −0.217870 | + | 0.217870i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 607.492i | 0.808911i | 0.914558 | + | 0.404456i | \(0.132539\pi\) | ||||
−0.914558 | + | 0.404456i | \(0.867461\pi\) | |||||||
\(752\) | −62.8801 | + | 245.358i | −0.0836171 | + | 0.326274i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −365.906 | − | 22.9797i | −0.485287 | − | 0.0304771i | ||||
\(755\) | −351.131 | − | 351.131i | −0.465074 | − | 0.465074i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.6797 | − | 11.6797i | −0.0154289 | − | 0.0154289i | 0.699350 | − | 0.714779i | \(-0.253473\pi\) |
−0.714779 | + | 0.699350i | \(0.753473\pi\) | |||||||
\(758\) | 617.716 | + | 700.503i | 0.814929 | + | 0.924147i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1032.96 | − | 196.689i | −1.35916 | − | 0.258801i | ||||
\(761\) | 659.125i | 0.866130i | 0.901363 | + | 0.433065i | \(0.142568\pi\) | ||||
−0.901363 | + | 0.433065i | \(0.857432\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −148.840 | + | 148.840i | −0.195073 | + | 0.195073i | ||||
\(764\) | −122.313 | + | 969.954i | −0.160096 | + | 1.26957i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 347.882 | + | 21.8478i | 0.454154 | + | 0.0285219i | ||||
\(767\) | 85.6224i | 0.111633i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −178.802 | −0.232512 | −0.116256 | − | 0.993219i | \(-0.537089\pi\) | ||||
−0.116256 | + | 0.993219i | \(0.537089\pi\) | |||||||
\(770\) | −23.0016 | + | 366.255i | −0.0298722 | + | 0.475656i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1012.15 | − | 127.633i | −1.31107 | − | 0.165328i | ||||
\(773\) | 91.8171 | + | 91.8171i | 0.118780 | + | 0.118780i | 0.763998 | − | 0.645218i | \(-0.223234\pi\) |
−0.645218 | + | 0.763998i | \(0.723234\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 108.979 | 0.140618 | ||||||||
\(776\) | 168.111 | − | 882.877i | 0.216637 | − | 1.13773i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −440.906 | + | 388.798i | −0.566717 | + | 0.499741i | ||||
\(779\) | −952.860 | + | 952.860i | −1.22318 | + | 1.22318i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 273.541 | − | 273.541i | 0.350245 | − | 0.350245i | ||||
\(782\) | −106.604 | + | 1697.46i | −0.136323 | + | 2.17066i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −506.376 | − | 129.773i | −0.645887 | − | 0.165527i | ||||
\(785\) | −1264.58 | −1.61093 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 214.856 | + | 214.856i | 0.273006 | + | 0.273006i | 0.830309 | − | 0.557303i | \(-0.188164\pi\) |
−0.557303 | + | 0.830309i | \(0.688164\pi\) | |||||||
\(788\) | −673.612 | − | 868.014i | −0.854838 | − | 1.10154i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −809.831 | − | 918.365i | −1.02510 | − | 1.16249i | ||||
\(791\) | −224.654 | −0.284012 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 325.641i | − | 0.410645i | ||||||
\(794\) | 69.7764 | + | 79.1280i | 0.0878796 | + | 0.0996574i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 673.852 | + | 84.9740i | 0.846548 | + | 0.106751i | ||||
\(797\) | 332.028 | − | 332.028i | 0.416598 | − | 0.416598i | −0.467432 | − | 0.884029i | \(-0.654821\pi\) |
0.884029 | + | 0.467432i | \(0.154821\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 476.801i | − | 0.596747i | ||||||
\(800\) | −87.2050 | − | 28.2807i | −0.109006 | − | 0.0353508i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 65.7756 | − | 1047.34i | 0.0820144 | − | 1.30592i | ||||
\(803\) | −210.262 | − | 210.262i | −0.261846 | − | 0.261846i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 379.562 | + | 379.562i | 0.471506 | + | 0.471506i | ||||
\(806\) | 346.268 | − | 305.346i | 0.429613 | − | 0.378841i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15.1492 | + | 10.3028i | −0.0187490 | + | 0.0127510i | ||||
\(809\) | 421.989i | 0.521618i | 0.965390 | + | 0.260809i | \(0.0839893\pi\) | ||||
−0.965390 | + | 0.260809i | \(0.916011\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 532.822 | − | 532.822i | 0.656994 | − | 0.656994i | −0.297674 | − | 0.954668i | \(-0.596211\pi\) |
0.954668 | + | 0.297674i | \(0.0962107\pi\) | |||||||
\(812\) | 385.748 | − | 299.355i | 0.475059 | − | 0.368664i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 73.3885 | − | 1168.56i | 0.0901579 | − | 1.43558i | ||||
\(815\) | 395.310i | 0.485042i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1291.04 | −1.58022 | ||||||||
\(818\) | −1571.62 | − | 98.7012i | −1.92129 | − | 0.120662i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 717.123 | − | 556.515i | 0.874540 | − | 0.678677i | ||||
\(821\) | 797.754 | + | 797.754i | 0.971686 | + | 0.971686i | 0.999610 | − | 0.0279241i | \(-0.00888968\pi\) |
−0.0279241 | + | 0.999610i | \(0.508890\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 863.777 | 1.04955 | 0.524773 | − | 0.851242i | \(-0.324150\pi\) | ||||
0.524773 | + | 0.851242i | \(0.324150\pi\) | |||||||
\(824\) | −41.8956 | + | 220.026i | −0.0508442 | + | 0.267022i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −75.4207 | − | 85.5287i | −0.0913084 | − | 0.103546i | ||||
\(827\) | 1154.08 | − | 1154.08i | 1.39550 | − | 1.39550i | 0.583098 | − | 0.812402i | \(-0.301840\pi\) |
0.812402 | − | 0.583098i | \(-0.198160\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 473.183 | − | 473.183i | 0.570788 | − | 0.570788i | −0.361561 | − | 0.932349i | \(-0.617756\pi\) |
0.932349 | + | 0.361561i | \(0.117756\pi\) | |||||||
\(830\) | −30.0357 | − | 1.88631i | −0.0361876 | − | 0.00227266i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −356.324 | + | 154.479i | −0.428274 | + | 0.185672i | ||||
\(833\) | 984.033 | 1.18131 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 217.537 | + | 217.537i | 0.260523 | + | 0.260523i | ||||
\(836\) | −1070.07 | − | 134.938i | −1.27999 | − | 0.161409i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −64.0177 | + | 56.4519i | −0.0763934 | + | 0.0673651i | ||||
\(839\) | −561.776 | −0.669578 | −0.334789 | − | 0.942293i | \(-0.608665\pi\) | ||||
−0.334789 | + | 0.942293i | \(0.608665\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 71.5574i | − | 0.0850861i | ||||||
\(842\) | −553.737 | + | 488.295i | −0.657645 | + | 0.579923i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 460.189 | + | 592.998i | 0.545248 | + | 0.702605i | ||||
\(845\) | 439.723 | − | 439.723i | 0.520382 | − | 0.520382i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 112.540i | − | 0.132869i | ||||||
\(848\) | 5.49689 | + | 9.28524i | 0.00648218 | + | 0.0109496i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 172.236 | + | 10.8168i | 0.202631 | + | 0.0127257i | ||||
\(851\) | −1211.02 | − | 1211.02i | −1.42306 | − | 1.42306i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −431.517 | − | 431.517i | −0.505881 | − | 0.505881i | 0.407378 | − | 0.913259i | \(-0.366443\pi\) |
−0.913259 | + | 0.407378i | \(0.866443\pi\) | |||||||
\(854\) | 286.842 | + | 325.285i | 0.335881 | + | 0.380896i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 256.935 | + | 377.796i | 0.300158 | + | 0.441350i | ||||
\(857\) | − | 448.237i | − | 0.523030i | −0.965199 | − | 0.261515i | \(-0.915778\pi\) | ||
0.965199 | − | 0.261515i | \(-0.0842221\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −617.299 | + | 617.299i | −0.718625 | + | 0.718625i | −0.968324 | − | 0.249699i | \(-0.919668\pi\) |
0.249699 | + | 0.968324i | \(0.419668\pi\) | |||||||
\(860\) | 862.830 | + | 108.804i | 1.00329 | + | 0.126517i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 918.169 | + | 57.6631i | 1.06516 | + | 0.0668946i | ||||
\(863\) | 1588.33i | 1.84047i | 0.391363 | + | 0.920236i | \(0.372004\pi\) | ||||
−0.391363 | + | 0.920236i | \(0.627996\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1416.81 | −1.63793 | ||||||||
\(866\) | −55.8149 | + | 888.740i | −0.0644514 | + | 1.02626i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −76.9250 | + | 610.023i | −0.0886233 | + | 0.702791i | ||||
\(869\) | −888.050 | − | 888.050i | −1.02192 | − | 1.02192i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 172.241 | 0.197751 | ||||||||
\(872\) | 234.350 | + | 344.586i | 0.268750 | + | 0.395168i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1183.26 | + | 1043.42i | −1.35385 | + | 1.19385i | ||||
\(875\) | 374.593 | − | 374.593i | 0.428106 | − | 0.428106i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 535.285 | − | 535.285i | 0.610359 | − | 0.610359i | −0.332680 | − | 0.943040i | \(-0.607953\pi\) |
0.943040 | + | 0.332680i | \(0.107953\pi\) | |||||||
\(878\) | 44.6858 | − | 711.532i | 0.0508950 | − | 0.810401i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 703.783 | + | 180.365i | 0.799753 | + | 0.204960i | ||||
\(881\) | −517.437 | −0.587330 | −0.293665 | − | 0.955908i | \(-0.594875\pi\) | ||||
−0.293665 | + | 0.955908i | \(0.594875\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1192.91 | − | 1192.91i | −1.35097 | − | 1.35097i | −0.884574 | − | 0.466399i | \(-0.845551\pi\) |
−0.466399 | − | 0.884574i | \(-0.654449\pi\) | |||||||
\(884\) | 577.570 | − | 448.217i | 0.653360 | − | 0.507032i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 671.121 | + | 761.066i | 0.757473 | + | 0.858991i | ||||
\(887\) | 1750.36 | 1.97335 | 0.986675 | − | 0.162704i | \(-0.0520217\pi\) | ||||
0.986675 | + | 0.162704i | \(0.0520217\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 444.203i | 0.499666i | ||||||||
\(890\) | −449.479 | − | 509.718i | −0.505032 | − | 0.572717i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.1835 | + | 104.547i | −0.0147797 | + | 0.117205i | ||||
\(893\) | 312.728 | − | 312.728i | 0.350199 | − | 0.350199i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1309.77i | 1.46343i | ||||||||
\(896\) | 219.860 | − | 468.179i | 0.245380 | − | 0.522521i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.59802 | − | 89.1373i | 0.00623388 | − | 0.0992620i | ||||
\(899\) | 812.551 | + | 812.551i | 0.903839 | + | 0.903839i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.3630 | − | 14.3630i | −0.0159411 | − | 0.0159411i | ||||
\(902\) | 698.328 | − | 615.798i | 0.774199 | − | 0.682703i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −83.1933 | + | 436.912i | −0.0920280 | + | 0.483310i | ||||
\(905\) | 182.528i | 0.201689i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 86.0833 | − | 86.0833i | 0.0949099 | − | 0.0949099i | −0.658058 | − | 0.752968i | \(-0.728622\pi\) |
0.752968 | + | 0.658058i | \(0.228622\pi\) | |||||||
\(908\) | −243.935 | − | 314.333i | −0.268651 | − | 0.346182i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 14.4621 | − | 230.280i | 0.0158925 | − | 0.253055i | ||||
\(911\) | 44.7701i | 0.0491439i | 0.999698 | + | 0.0245719i | \(0.00782228\pi\) | ||||
−0.999698 | + | 0.0245719i | \(0.992178\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.8683 | −0.0338098 | ||||||||
\(914\) | −168.135 | − | 10.5593i | −0.183955 | − | 0.0115528i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 747.753 | + | 963.552i | 0.816324 | + | 1.05191i | ||||
\(917\) | 305.812 | + | 305.812i | 0.333492 | + | 0.333492i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 498.982 | 0.542962 | 0.271481 | − | 0.962444i | \(-0.412487\pi\) | ||||
0.271481 | + | 0.962444i | \(0.412487\pi\) | |||||||
\(920\) | 878.740 | − | 597.622i | 0.955152 | − | 0.649590i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 384.144 | + | 435.628i | 0.416642 | + | 0.472481i | ||||
\(923\) | −171.987 | + | 171.987i | −0.186335 | + | 0.186335i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −122.879 | + | 122.879i | −0.132842 | + | 0.132842i | ||||
\(926\) | −540.229 | − | 33.9276i | −0.583401 | − | 0.0366389i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −439.343 | − | 861.067i | −0.473430 | − | 0.927874i | ||||
\(929\) | 1460.97 | 1.57262 | 0.786311 | − | 0.617831i | \(-0.211988\pi\) | ||||
0.786311 | + | 0.617831i | \(0.211988\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 645.415 | + | 645.415i | 0.693250 | + | 0.693250i | ||||
\(932\) | −92.0082 | + | 729.634i | −0.0987213 | + | 0.782869i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −488.753 | + | 430.991i | −0.523290 | + | 0.461446i | ||||
\(935\) | −1367.65 | −1.46273 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 594.005i | − | 0.633943i | −0.948435 | − | 0.316972i | \(-0.897334\pi\) | ||
0.948435 | − | 0.316972i | \(-0.102666\pi\) | |||||||
\(938\) | −172.053 | + | 151.719i | −0.183425 | + | 0.161747i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −235.359 | + | 182.648i | −0.250382 | + | 0.194306i | ||||
\(941\) | −767.764 | + | 767.764i | −0.815902 | + | 0.815902i | −0.985511 | − | 0.169610i | \(-0.945749\pi\) |
0.169610 | + | 0.985511i | \(0.445749\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1361.87i | − | 1.44419i | ||||||
\(944\) | −194.268 | + | 115.007i | −0.205792 | + | 0.121830i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 890.259 | + | 55.9102i | 0.941077 | + | 0.0591017i | ||||
\(947\) | 205.644 | + | 205.644i | 0.217153 | + | 0.217153i | 0.807297 | − | 0.590145i | \(-0.200929\pi\) |
−0.590145 | + | 0.807297i | \(0.700929\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 132.201 | + | 132.201i | 0.139306 | + | 0.139306i | ||||
\(950\) | 105.873 | + | 120.062i | 0.111445 | + | 0.126381i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −182.125 | + | 956.480i | −0.191308 | + | 1.00471i | ||||
\(953\) | − | 1714.17i | − | 1.79871i | −0.437215 | − | 0.899357i | \(-0.644035\pi\) | ||
0.437215 | − | 0.899357i | \(-0.355965\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −813.098 | + | 813.098i | −0.851412 | + | 0.851412i | ||||
\(956\) | −157.732 | + | 1250.83i | −0.164991 | + | 1.30840i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1149.56 | + | 72.1948i | 1.19995 | + | 0.0753599i | ||||
\(959\) | − | 8.67783i | − | 0.00904883i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −486.009 | −0.505733 | ||||||||
\(962\) | −46.1426 | + | 734.728i | −0.0479653 | + | 0.763750i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1300.91 | + | 164.047i | 1.34949 | + | 0.170174i | ||||
\(965\) | −848.466 | − | 848.466i | −0.879240 | − | 0.879240i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1375.76 | −1.42271 | −0.711356 | − | 0.702832i | \(-0.751919\pi\) | ||||
−0.711356 | + | 0.702832i | \(0.751919\pi\) | |||||||
\(968\) | −218.870 | − | 41.6754i | −0.226105 | − | 0.0430531i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 792.862 | − | 699.160i | 0.817384 | − | 0.720783i | ||||
\(971\) | 1081.41 | − | 1081.41i | 1.11371 | − | 1.11371i | 0.121062 | − | 0.992645i | \(-0.461370\pi\) |
0.992645 | − | 0.121062i | \(-0.0386300\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 441.449 | − | 441.449i | 0.453699 | − | 0.453699i | ||||
\(974\) | 75.2590 | − | 1198.35i | 0.0772680 | − | 1.23034i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 738.844 | − | 437.398i | 0.757013 | − | 0.448154i | ||||
\(977\) | 18.0081 | 0.0184320 | 0.00921601 | − | 0.999958i | \(-0.497066\pi\) | ||||
0.00921601 | + | 0.999958i | \(0.497066\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −492.893 | − | 492.893i | −0.503465 | − | 0.503465i | ||||
\(980\) | −376.953 | − | 485.740i | −0.384646 | − | 0.495653i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 149.130 | + | 169.116i | 0.151863 | + | 0.172216i | ||||
\(983\) | −579.164 | −0.589180 | −0.294590 | − | 0.955624i | \(-0.595183\pi\) | ||||
−0.294590 | + | 0.955624i | \(0.595183\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 1292.32i | − | 1.31200i | ||||||
\(986\) | 1203.55 | + | 1364.85i | 1.22064 | + | 1.38423i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 672.802 | + | 84.8416i | 0.680973 | + | 0.0858720i | ||||
\(989\) | 922.605 | − | 922.605i | 0.932866 | − | 0.932866i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1389.22i | − | 1.40184i | −0.713242 | − | 0.700918i | \(-0.752774\pi\) | ||
0.713242 | − | 0.700918i | \(-0.247226\pi\) | |||||||
\(992\) | 1157.90 | + | 375.508i | 1.16724 | + | 0.378536i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 20.3036 | − | 323.295i | 0.0204262 | − | 0.325246i | ||||
\(995\) | 564.880 | + | 564.880i | 0.567719 | + | 0.567719i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 867.073 | + | 867.073i | 0.869682 | + | 0.869682i | 0.992437 | − | 0.122755i | \(-0.0391730\pi\) |
−0.122755 | + | 0.992437i | \(0.539173\pi\) | |||||||
\(998\) | −28.6206 | + | 25.2381i | −0.0286779 | + | 0.0252887i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 144.3.m.c.91.5 | 16 | ||
3.2 | odd | 2 | 48.3.l.a.43.4 | yes | 16 | ||
4.3 | odd | 2 | 576.3.m.c.271.2 | 16 | |||
8.3 | odd | 2 | 1152.3.m.c.415.7 | 16 | |||
8.5 | even | 2 | 1152.3.m.f.415.7 | 16 | |||
12.11 | even | 2 | 192.3.l.a.79.4 | 16 | |||
16.3 | odd | 4 | inner | 144.3.m.c.19.5 | 16 | ||
16.5 | even | 4 | 1152.3.m.c.991.7 | 16 | |||
16.11 | odd | 4 | 1152.3.m.f.991.7 | 16 | |||
16.13 | even | 4 | 576.3.m.c.559.2 | 16 | |||
24.5 | odd | 2 | 384.3.l.a.31.1 | 16 | |||
24.11 | even | 2 | 384.3.l.b.31.5 | 16 | |||
48.5 | odd | 4 | 384.3.l.b.223.5 | 16 | |||
48.11 | even | 4 | 384.3.l.a.223.1 | 16 | |||
48.29 | odd | 4 | 192.3.l.a.175.4 | 16 | |||
48.35 | even | 4 | 48.3.l.a.19.4 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.l.a.19.4 | ✓ | 16 | 48.35 | even | 4 | ||
48.3.l.a.43.4 | yes | 16 | 3.2 | odd | 2 | ||
144.3.m.c.19.5 | 16 | 16.3 | odd | 4 | inner | ||
144.3.m.c.91.5 | 16 | 1.1 | even | 1 | trivial | ||
192.3.l.a.79.4 | 16 | 12.11 | even | 2 | |||
192.3.l.a.175.4 | 16 | 48.29 | odd | 4 | |||
384.3.l.a.31.1 | 16 | 24.5 | odd | 2 | |||
384.3.l.a.223.1 | 16 | 48.11 | even | 4 | |||
384.3.l.b.31.5 | 16 | 24.11 | even | 2 | |||
384.3.l.b.223.5 | 16 | 48.5 | odd | 4 | |||
576.3.m.c.271.2 | 16 | 4.3 | odd | 2 | |||
576.3.m.c.559.2 | 16 | 16.13 | even | 4 | |||
1152.3.m.c.415.7 | 16 | 8.3 | odd | 2 | |||
1152.3.m.c.991.7 | 16 | 16.5 | even | 4 | |||
1152.3.m.f.415.7 | 16 | 8.5 | even | 2 | |||
1152.3.m.f.991.7 | 16 | 16.11 | odd | 4 |