Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,2,Mod(38,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.38");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.c (of order \(4\), degree \(2\), not 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: | \(2.30767661842\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.722204136308736.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 18x^{8} + 69x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 251.5 | ||
Root | \(1.08335 - 1.08335i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 289.251 |
Dual form | 289.2.c.d.38.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/289\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.87939i | 1.32893i | 0.747321 | + | 0.664463i | \(0.231340\pi\) | ||||
−0.747321 | + | 0.664463i | \(0.768660\pi\) | |||||||
\(3\) | −1.79046 | − | 1.79046i | −1.03372 | − | 1.03372i | −0.999411 | − | 0.0343097i | \(-0.989077\pi\) |
−0.0343097 | − | 0.999411i | \(-0.510923\pi\) | |||||||
\(4\) | −1.53209 | −0.766044 | ||||||||
\(5\) | 0.0852875 | + | 0.0852875i | 0.0381417 | + | 0.0381417i | 0.725920 | − | 0.687779i | \(-0.241414\pi\) |
−0.687779 | + | 0.725920i | \(0.741414\pi\) | |||||||
\(6\) | 3.36496 | − | 3.36496i | 1.37374 | − | 1.37374i | ||||
\(7\) | −1.08335 | + | 1.08335i | −0.409468 | + | 0.409468i | −0.881553 | − | 0.472085i | \(-0.843502\pi\) |
0.472085 | + | 0.881553i | \(0.343502\pi\) | |||||||
\(8\) | 0.879385i | 0.310910i | ||||||||
\(9\) | 3.41147i | 1.13716i | ||||||||
\(10\) | −0.160288 | + | 0.160288i | −0.0506875 | + | 0.0506875i | ||||
\(11\) | −1.90536 | + | 1.90536i | −0.574489 | + | 0.574489i | −0.933380 | − | 0.358891i | \(-0.883155\pi\) |
0.358891 | + | 0.933380i | \(0.383155\pi\) | |||||||
\(12\) | 2.74314 | + | 2.74314i | 0.791876 | + | 0.791876i | ||||
\(13\) | −4.57398 | −1.26859 | −0.634297 | − | 0.773090i | \(-0.718710\pi\) | ||||
−0.634297 | + | 0.773090i | \(0.718710\pi\) | |||||||
\(14\) | −2.03603 | − | 2.03603i | −0.544153 | − | 0.544153i | ||||
\(15\) | − | 0.305407i | − | 0.0788558i | ||||||
\(16\) | −4.71688 | −1.17922 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −6.41147 | −1.51120 | ||||||||
\(19\) | 1.87939i | 0.431161i | 0.976486 | + | 0.215580i | \(0.0691643\pi\) | ||||
−0.976486 | + | 0.215580i | \(0.930836\pi\) | |||||||
\(20\) | −0.130668 | − | 0.130668i | −0.0292183 | − | 0.0292183i | ||||
\(21\) | 3.87939 | 0.846551 | ||||||||
\(22\) | −3.58091 | − | 3.58091i | −0.763454 | − | 0.763454i | ||||
\(23\) | −5.24070 | + | 5.24070i | −1.09276 | + | 1.09276i | −0.0975296 | + | 0.995233i | \(0.531094\pi\) |
−0.995233 | + | 0.0975296i | \(0.968906\pi\) | |||||||
\(24\) | 1.57450 | − | 1.57450i | 0.321394 | − | 0.321394i | ||||
\(25\) | − | 4.98545i | − | 0.997090i | ||||||
\(26\) | − | 8.59627i | − | 1.68587i | ||||||
\(27\) | 0.736727 | − | 0.736727i | 0.141783 | − | 0.141783i | ||||
\(28\) | 1.65979 | − | 1.65979i | 0.313671 | − | 0.313671i | ||||
\(29\) | 2.41228 | + | 2.41228i | 0.447948 | + | 0.447948i | 0.894672 | − | 0.446724i | \(-0.147409\pi\) |
−0.446724 | + | 0.894672i | \(0.647409\pi\) | |||||||
\(30\) | 0.573978 | 0.104794 | ||||||||
\(31\) | −2.71352 | − | 2.71352i | −0.487363 | − | 0.487363i | 0.420110 | − | 0.907473i | \(-0.361991\pi\) |
−0.907473 | + | 0.420110i | \(0.861991\pi\) | |||||||
\(32\) | − | 7.10607i | − | 1.25619i | ||||||
\(33\) | 6.82295 | 1.18772 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.184793 | −0.0312356 | ||||||||
\(36\) | − | 5.22668i | − | 0.871114i | ||||||
\(37\) | 3.71158 | + | 3.71158i | 0.610180 | + | 0.610180i | 0.942993 | − | 0.332813i | \(-0.107998\pi\) |
−0.332813 | + | 0.942993i | \(0.607998\pi\) | |||||||
\(38\) | −3.53209 | −0.572980 | ||||||||
\(39\) | 8.18951 | + | 8.18951i | 1.31137 | + | 1.31137i | ||||
\(40\) | −0.0750006 | + | 0.0750006i | −0.0118586 | + | 0.0118586i | ||||
\(41\) | 4.41869 | − | 4.41869i | 0.690083 | − | 0.690083i | −0.272167 | − | 0.962250i | \(-0.587740\pi\) |
0.962250 | + | 0.272167i | \(0.0877402\pi\) | |||||||
\(42\) | 7.29086i | 1.12500i | ||||||||
\(43\) | 5.49020i | 0.837248i | 0.908160 | + | 0.418624i | \(0.137487\pi\) | ||||
−0.908160 | + | 0.418624i | \(0.862513\pi\) | |||||||
\(44\) | 2.91919 | − | 2.91919i | 0.440084 | − | 0.440084i | ||||
\(45\) | −0.290956 | + | 0.290956i | −0.0433732 | + | 0.0433732i | ||||
\(46\) | −9.84930 | − | 9.84930i | −1.45220 | − | 1.45220i | ||||
\(47\) | 7.34730 | 1.07171 | 0.535857 | − | 0.844309i | \(-0.319989\pi\) | ||||
0.535857 | + | 0.844309i | \(0.319989\pi\) | |||||||
\(48\) | 8.44537 | + | 8.44537i | 1.21898 | + | 1.21898i | ||||
\(49\) | 4.65270i | 0.664672i | ||||||||
\(50\) | 9.36959 | 1.32506 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.00774 | 0.971799 | ||||||||
\(53\) | − | 0.822948i | − | 0.113041i | −0.998401 | − | 0.0565203i | \(-0.981999\pi\) | ||
0.998401 | − | 0.0565203i | \(-0.0180006\pi\) | |||||||
\(54\) | 1.38459 | + | 1.38459i | 0.188419 | + | 0.188419i | ||||
\(55\) | −0.325008 | −0.0438240 | ||||||||
\(56\) | −0.952682 | − | 0.952682i | −0.127308 | − | 0.127308i | ||||
\(57\) | 3.36496 | − | 3.36496i | 0.445700 | − | 0.445700i | ||||
\(58\) | −4.53360 | + | 4.53360i | −0.595290 | + | 0.595290i | ||||
\(59\) | − | 3.14290i | − | 0.409171i | −0.978849 | − | 0.204586i | \(-0.934415\pi\) | ||
0.978849 | − | 0.204586i | \(-0.0655847\pi\) | |||||||
\(60\) | 0.467911i | 0.0604071i | ||||||||
\(61\) | 0.867395 | − | 0.867395i | 0.111059 | − | 0.111059i | −0.649394 | − | 0.760452i | \(-0.724977\pi\) |
0.760452 | + | 0.649394i | \(0.224977\pi\) | |||||||
\(62\) | 5.09975 | − | 5.09975i | 0.647669 | − | 0.647669i | ||||
\(63\) | −3.69582 | − | 3.69582i | −0.465630 | − | 0.465630i | ||||
\(64\) | 3.92127 | 0.490159 | ||||||||
\(65\) | −0.390103 | − | 0.390103i | −0.0483863 | − | 0.0483863i | ||||
\(66\) | 12.8229i | 1.57840i | ||||||||
\(67\) | −14.6236 | −1.78656 | −0.893279 | − | 0.449503i | \(-0.851601\pi\) | ||||
−0.893279 | + | 0.449503i | \(0.851601\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 18.7665 | 2.25922 | ||||||||
\(70\) | − | 0.347296i | − | 0.0415099i | ||||||
\(71\) | 0.120381 | + | 0.120381i | 0.0142866 | + | 0.0142866i | 0.714214 | − | 0.699927i | \(-0.246784\pi\) |
−0.699927 | + | 0.714214i | \(0.746784\pi\) | |||||||
\(72\) | −3.00000 | −0.353553 | ||||||||
\(73\) | −8.34433 | − | 8.34433i | −0.976630 | − | 0.976630i | 0.0231035 | − | 0.999733i | \(-0.492645\pi\) |
−0.999733 | + | 0.0231035i | \(0.992645\pi\) | |||||||
\(74\) | −6.97549 | + | 6.97549i | −0.810885 | + | 0.810885i | ||||
\(75\) | −8.92624 | + | 8.92624i | −1.03071 | + | 1.03071i | ||||
\(76\) | − | 2.87939i | − | 0.330288i | ||||||
\(77\) | − | 4.12836i | − | 0.470470i | ||||||
\(78\) | −15.3912 | + | 15.3912i | −1.74272 | + | 1.74272i | ||||
\(79\) | 2.93305 | − | 2.93305i | 0.329994 | − | 0.329994i | −0.522590 | − | 0.852584i | \(-0.675034\pi\) |
0.852584 | + | 0.522590i | \(0.175034\pi\) | |||||||
\(80\) | −0.402291 | − | 0.402291i | −0.0449775 | − | 0.0449775i | ||||
\(81\) | 7.59627 | 0.844030 | ||||||||
\(82\) | 8.30442 | + | 8.30442i | 0.917070 | + | 0.917070i | ||||
\(83\) | 2.43376i | 0.267140i | 0.991039 | + | 0.133570i | \(0.0426441\pi\) | ||||
−0.991039 | + | 0.133570i | \(0.957356\pi\) | |||||||
\(84\) | −5.94356 | −0.648496 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.3182 | −1.11264 | ||||||||
\(87\) | − | 8.63816i | − | 0.926108i | ||||||
\(88\) | −1.67555 | − | 1.67555i | −0.178614 | − | 0.178614i | ||||
\(89\) | 15.0915 | 1.59970 | 0.799849 | − | 0.600201i | \(-0.204913\pi\) | ||||
0.799849 | + | 0.600201i | \(0.204913\pi\) | |||||||
\(90\) | −0.546819 | − | 0.546819i | −0.0576398 | − | 0.0576398i | ||||
\(91\) | 4.95522 | − | 4.95522i | 0.519448 | − | 0.519448i | ||||
\(92\) | 8.02922 | − | 8.02922i | 0.837104 | − | 0.837104i | ||||
\(93\) | 9.71688i | 1.00759i | ||||||||
\(94\) | 13.8084i | 1.42423i | ||||||||
\(95\) | −0.160288 | + | 0.160288i | −0.0164452 | + | 0.0164452i | ||||
\(96\) | −12.7231 | + | 12.7231i | −1.29855 | + | 1.29855i | ||||
\(97\) | 7.91432 | + | 7.91432i | 0.803577 | + | 0.803577i | 0.983653 | − | 0.180076i | \(-0.0576343\pi\) |
−0.180076 | + | 0.983653i | \(0.557634\pi\) | |||||||
\(98\) | −8.74422 | −0.883300 | ||||||||
\(99\) | −6.50010 | − | 6.50010i | −0.653285 | − | 0.653285i | ||||
\(100\) | 7.63816i | 0.763816i | ||||||||
\(101\) | 7.78106 | 0.774244 | 0.387122 | − | 0.922028i | \(-0.373469\pi\) | ||||
0.387122 | + | 0.922028i | \(0.373469\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.8598 | −1.07005 | −0.535023 | − | 0.844837i | \(-0.679697\pi\) | ||||
−0.535023 | + | 0.844837i | \(0.679697\pi\) | |||||||
\(104\) | − | 4.02229i | − | 0.394418i | ||||||
\(105\) | 0.330863 | + | 0.330863i | 0.0322889 | + | 0.0322889i | ||||
\(106\) | 1.54664 | 0.150223 | ||||||||
\(107\) | 8.51490 | + | 8.51490i | 0.823167 | + | 0.823167i | 0.986561 | − | 0.163394i | \(-0.0522443\pi\) |
−0.163394 | + | 0.986561i | \(0.552244\pi\) | |||||||
\(108\) | −1.12873 | + | 1.12873i | −0.108612 | + | 0.108612i | ||||
\(109\) | −4.67455 | + | 4.67455i | −0.447741 | + | 0.447741i | −0.894603 | − | 0.446862i | \(-0.852541\pi\) |
0.446862 | + | 0.894603i | \(0.352541\pi\) | |||||||
\(110\) | − | 0.610815i | − | 0.0582389i | ||||||
\(111\) | − | 13.2909i | − | 1.26151i | ||||||
\(112\) | 5.11004 | − | 5.11004i | 0.482853 | − | 0.482853i | ||||
\(113\) | 3.59667 | − | 3.59667i | 0.338347 | − | 0.338347i | −0.517398 | − | 0.855745i | \(-0.673099\pi\) |
0.855745 | + | 0.517398i | \(0.173099\pi\) | |||||||
\(114\) | 6.32405 | + | 6.32405i | 0.592302 | + | 0.592302i | ||||
\(115\) | −0.893933 | −0.0833597 | ||||||||
\(116\) | −3.69582 | − | 3.69582i | −0.343148 | − | 0.343148i | ||||
\(117\) | − | 15.6040i | − | 1.44259i | ||||||
\(118\) | 5.90673 | 0.543758 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.268571 | 0.0245170 | ||||||||
\(121\) | 3.73917i | 0.339925i | ||||||||
\(122\) | 1.63017 | + | 1.63017i | 0.147589 | + | 0.147589i | ||||
\(123\) | −15.8229 | −1.42671 | ||||||||
\(124\) | 4.15735 | + | 4.15735i | 0.373341 | + | 0.373341i | ||||
\(125\) | 0.851634 | − | 0.851634i | 0.0761725 | − | 0.0761725i | ||||
\(126\) | 6.94587 | − | 6.94587i | 0.618788 | − | 0.618788i | ||||
\(127\) | − | 2.20439i | − | 0.195608i | −0.995206 | − | 0.0978041i | \(-0.968818\pi\) | ||
0.995206 | − | 0.0978041i | \(-0.0311819\pi\) | |||||||
\(128\) | − | 6.84255i | − | 0.604802i | ||||||
\(129\) | 9.82997 | − | 9.82997i | 0.865480 | − | 0.865480i | ||||
\(130\) | 0.733154 | − | 0.733154i | 0.0643019 | − | 0.0643019i | ||||
\(131\) | −1.40940 | − | 1.40940i | −0.123140 | − | 0.123140i | 0.642851 | − | 0.765991i | \(-0.277751\pi\) |
−0.765991 | + | 0.642851i | \(0.777751\pi\) | |||||||
\(132\) | −10.4534 | −0.909848 | ||||||||
\(133\) | −2.03603 | − | 2.03603i | −0.176546 | − | 0.176546i | ||||
\(134\) | − | 27.4834i | − | 2.37420i | ||||||
\(135\) | 0.125667 | 0.0108157 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.6236 | −1.07851 | −0.539254 | − | 0.842143i | \(-0.681294\pi\) | ||||
−0.539254 | + | 0.842143i | \(0.681294\pi\) | |||||||
\(138\) | 35.2695i | 3.00234i | ||||||||
\(139\) | −3.70130 | − | 3.70130i | −0.313940 | − | 0.313940i | 0.532494 | − | 0.846434i | \(-0.321255\pi\) |
−0.846434 | + | 0.532494i | \(0.821255\pi\) | |||||||
\(140\) | 0.283119 | 0.0239279 | ||||||||
\(141\) | −13.1550 | − | 13.1550i | −1.10785 | − | 1.10785i | ||||
\(142\) | −0.226242 | + | 0.226242i | −0.0189858 | + | 0.0189858i | ||||
\(143\) | 8.71510 | − | 8.71510i | 0.728793 | − | 0.728793i | ||||
\(144\) | − | 16.0915i | − | 1.34096i | ||||||
\(145\) | 0.411474i | 0.0341711i | ||||||||
\(146\) | 15.6822 | − | 15.6822i | 1.29787 | − | 1.29787i | ||||
\(147\) | 8.33047 | − | 8.33047i | 0.687085 | − | 0.687085i | ||||
\(148\) | −5.68647 | − | 5.68647i | −0.467425 | − | 0.467425i | ||||
\(149\) | −9.65270 | −0.790780 | −0.395390 | − | 0.918513i | \(-0.629391\pi\) | ||||
−0.395390 | + | 0.918513i | \(0.629391\pi\) | |||||||
\(150\) | −16.7758 | − | 16.7758i | −1.36974 | − | 1.36974i | ||||
\(151\) | − | 1.20708i | − | 0.0982309i | −0.998793 | − | 0.0491154i | \(-0.984360\pi\) | ||
0.998793 | − | 0.0491154i | \(-0.0156402\pi\) | |||||||
\(152\) | −1.65270 | −0.134052 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.75877 | 0.625220 | ||||||||
\(155\) | − | 0.462859i | − | 0.0371777i | ||||||
\(156\) | −12.5471 | − | 12.5471i | −1.00457 | − | 1.00457i | ||||
\(157\) | −15.0942 | −1.20465 | −0.602324 | − | 0.798251i | \(-0.705759\pi\) | ||||
−0.602324 | + | 0.798251i | \(0.705759\pi\) | |||||||
\(158\) | 5.51233 | + | 5.51233i | 0.438537 | + | 0.438537i | ||||
\(159\) | −1.47345 | + | 1.47345i | −0.116852 | + | 0.116852i | ||||
\(160\) | 0.606059 | − | 0.606059i | 0.0479132 | − | 0.0479132i | ||||
\(161\) | − | 11.3550i | − | 0.894902i | ||||||
\(162\) | 14.2763i | 1.12165i | ||||||||
\(163\) | −4.63464 | + | 4.63464i | −0.363013 | + | 0.363013i | −0.864921 | − | 0.501908i | \(-0.832632\pi\) |
0.501908 | + | 0.864921i | \(0.332632\pi\) | |||||||
\(164\) | −6.76982 | + | 6.76982i | −0.528634 | + | 0.528634i | ||||
\(165\) | 0.581912 | + | 0.581912i | 0.0453018 | + | 0.0453018i | ||||
\(166\) | −4.57398 | −0.355010 | ||||||||
\(167\) | 2.78852 | + | 2.78852i | 0.215782 | + | 0.215782i | 0.806718 | − | 0.590936i | \(-0.201241\pi\) |
−0.590936 | + | 0.806718i | \(0.701241\pi\) | |||||||
\(168\) | 3.41147i | 0.263201i | ||||||||
\(169\) | 7.92127 | 0.609329 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.41147 | −0.490298 | ||||||||
\(172\) | − | 8.41147i | − | 0.641369i | ||||||
\(173\) | 13.3884 | + | 13.3884i | 1.01790 | + | 1.01790i | 0.999837 | + | 0.0180650i | \(0.00575057\pi\) |
0.0180650 | + | 0.999837i | \(0.494249\pi\) | |||||||
\(174\) | 16.2344 | 1.23073 | ||||||||
\(175\) | 5.40099 | + | 5.40099i | 0.408277 | + | 0.408277i | ||||
\(176\) | 8.98738 | − | 8.98738i | 0.677449 | − | 0.677449i | ||||
\(177\) | −5.62723 | + | 5.62723i | −0.422969 | + | 0.422969i | ||||
\(178\) | 28.3628i | 2.12588i | ||||||||
\(179\) | 7.25402i | 0.542191i | 0.962552 | + | 0.271096i | \(0.0873859\pi\) | ||||
−0.962552 | + | 0.271096i | \(0.912614\pi\) | |||||||
\(180\) | 0.445771 | − | 0.445771i | 0.0332258 | − | 0.0332258i | ||||
\(181\) | −17.7479 | + | 17.7479i | −1.31919 | + | 1.31919i | −0.404769 | + | 0.914419i | \(0.632648\pi\) |
−0.914419 | + | 0.404769i | \(0.867352\pi\) | |||||||
\(182\) | 9.31277 | + | 9.31277i | 0.690308 | + | 0.690308i | ||||
\(183\) | −3.10607 | −0.229607 | ||||||||
\(184\) | −4.60860 | − | 4.60860i | −0.339750 | − | 0.339750i | ||||
\(185\) | 0.633103i | 0.0465467i | ||||||||
\(186\) | −18.2618 | −1.33902 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −11.2567 | −0.820980 | ||||||||
\(189\) | 1.59627i | 0.116111i | ||||||||
\(190\) | −0.301243 | − | 0.301243i | −0.0218545 | − | 0.0218545i | ||||
\(191\) | −14.1557 | −1.02427 | −0.512135 | − | 0.858905i | \(-0.671145\pi\) | ||||
−0.512135 | + | 0.858905i | \(0.671145\pi\) | |||||||
\(192\) | −7.02087 | − | 7.02087i | −0.506688 | − | 0.506688i | ||||
\(193\) | 11.6185 | − | 11.6185i | 0.836320 | − | 0.836320i | −0.152053 | − | 0.988372i | \(-0.548588\pi\) |
0.988372 | + | 0.152053i | \(0.0485884\pi\) | |||||||
\(194\) | −14.8740 | + | 14.8740i | −1.06789 | + | 1.06789i | ||||
\(195\) | 1.39693i | 0.100036i | ||||||||
\(196\) | − | 7.12836i | − | 0.509168i | ||||||
\(197\) | −14.3115 | + | 14.3115i | −1.01965 | + | 1.01965i | −0.0198470 | + | 0.999803i | \(0.506318\pi\) |
−0.999803 | + | 0.0198470i | \(0.993682\pi\) | |||||||
\(198\) | 12.2162 | − | 12.2162i | 0.868167 | − | 0.868167i | ||||
\(199\) | 15.6803 | + | 15.6803i | 1.11155 | + | 1.11155i | 0.992941 | + | 0.118606i | \(0.0378425\pi\) |
0.118606 | + | 0.992941i | \(0.462158\pi\) | |||||||
\(200\) | 4.38413 | 0.310005 | ||||||||
\(201\) | 26.1829 | + | 26.1829i | 1.84680 | + | 1.84680i | ||||
\(202\) | 14.6236i | 1.02891i | ||||||||
\(203\) | −5.22668 | −0.366841 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.753718 | 0.0526420 | ||||||||
\(206\) | − | 20.4097i | − | 1.42201i | ||||||
\(207\) | −17.8785 | − | 17.8785i | −1.24264 | − | 1.24264i | ||||
\(208\) | 21.5749 | 1.49595 | ||||||||
\(209\) | −3.58091 | − | 3.58091i | −0.247697 | − | 0.247697i | ||||
\(210\) | −0.621819 | + | 0.621819i | −0.0429096 | + | 0.0429096i | ||||
\(211\) | 5.08232 | − | 5.08232i | 0.349881 | − | 0.349881i | −0.510184 | − | 0.860065i | \(-0.670423\pi\) |
0.860065 | + | 0.510184i | \(0.170423\pi\) | |||||||
\(212\) | 1.26083i | 0.0865942i | ||||||||
\(213\) | − | 0.431074i | − | 0.0295367i | ||||||
\(214\) | −16.0028 | + | 16.0028i | −1.09393 | + | 1.09393i | ||||
\(215\) | −0.468245 | + | 0.468245i | −0.0319341 | + | 0.0319341i | ||||
\(216\) | 0.647867 | + | 0.647867i | 0.0440817 | + | 0.0440817i | ||||
\(217\) | 5.87939 | 0.399119 | ||||||||
\(218\) | −8.78528 | − | 8.78528i | −0.595014 | − | 0.595014i | ||||
\(219\) | 29.8803i | 2.01912i | ||||||||
\(220\) | 0.497941 | 0.0335711 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 24.9786 | 1.67646 | ||||||||
\(223\) | 6.01960i | 0.403102i | 0.979478 | + | 0.201551i | \(0.0645982\pi\) | ||||
−0.979478 | + | 0.201551i | \(0.935402\pi\) | |||||||
\(224\) | 7.69836 | + | 7.69836i | 0.514368 | + | 0.514368i | ||||
\(225\) | 17.0077 | 1.13385 | ||||||||
\(226\) | 6.75954 | + | 6.75954i | 0.449638 | + | 0.449638i | ||||
\(227\) | −15.5812 | + | 15.5812i | −1.03416 | + | 1.03416i | −0.0347620 | + | 0.999396i | \(0.511067\pi\) |
−0.999396 | + | 0.0347620i | \(0.988933\pi\) | |||||||
\(228\) | −5.15542 | + | 5.15542i | −0.341426 | + | 0.341426i | ||||
\(229\) | 3.69965i | 0.244479i | 0.992501 | + | 0.122240i | \(0.0390077\pi\) | ||||
−0.992501 | + | 0.122240i | \(0.960992\pi\) | |||||||
\(230\) | − | 1.68004i | − | 0.110779i | ||||||
\(231\) | −7.39164 | + | 7.39164i | −0.486334 | + | 0.486334i | ||||
\(232\) | −2.12132 | + | 2.12132i | −0.139272 | + | 0.139272i | ||||
\(233\) | −20.6126 | − | 20.6126i | −1.35038 | − | 1.35038i | −0.885237 | − | 0.465141i | \(-0.846004\pi\) |
−0.465141 | − | 0.885237i | \(-0.653996\pi\) | |||||||
\(234\) | 29.3259 | 1.91710 | ||||||||
\(235\) | 0.626633 | + | 0.626633i | 0.0408770 | + | 0.0408770i | ||||
\(236\) | 4.81521i | 0.313443i | ||||||||
\(237\) | −10.5030 | −0.682243 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.4834 | 0.807484 | 0.403742 | − | 0.914873i | \(-0.367709\pi\) | ||||
0.403742 | + | 0.914873i | \(0.367709\pi\) | |||||||
\(240\) | 1.44057i | 0.0929884i | ||||||||
\(241\) | −11.4673 | − | 11.4673i | −0.738673 | − | 0.738673i | 0.233649 | − | 0.972321i | \(-0.424933\pi\) |
−0.972321 | + | 0.233649i | \(0.924933\pi\) | |||||||
\(242\) | −7.02734 | −0.451735 | ||||||||
\(243\) | −15.8110 | − | 15.8110i | −1.01427 | − | 1.01427i | ||||
\(244\) | −1.32893 | + | 1.32893i | −0.0850758 | + | 0.0850758i | ||||
\(245\) | −0.396818 | + | 0.396818i | −0.0253517 | + | 0.0253517i | ||||
\(246\) | − | 29.7374i | − | 1.89599i | ||||||
\(247\) | − | 8.59627i | − | 0.546967i | ||||||
\(248\) | 2.38623 | − | 2.38623i | 0.151526 | − | 0.151526i | ||||
\(249\) | 4.35755 | − | 4.35755i | 0.276148 | − | 0.276148i | ||||
\(250\) | 1.60055 | + | 1.60055i | 0.101228 | + | 0.101228i | ||||
\(251\) | −15.9959 | −1.00965 | −0.504826 | − | 0.863221i | \(-0.668443\pi\) | ||||
−0.504826 | + | 0.863221i | \(0.668443\pi\) | |||||||
\(252\) | 5.66233 | + | 5.66233i | 0.356693 | + | 0.356693i | ||||
\(253\) | − | 19.9709i | − | 1.25556i | ||||||
\(254\) | 4.14290 | 0.259949 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.7023 | 1.29390 | ||||||||
\(257\) | 9.66044i | 0.602602i | 0.953529 | + | 0.301301i | \(0.0974209\pi\) | ||||
−0.953529 | + | 0.301301i | \(0.902579\pi\) | |||||||
\(258\) | 18.4743 | + | 18.4743i | 1.15016 | + | 1.15016i | ||||
\(259\) | −8.04189 | −0.499699 | ||||||||
\(260\) | 0.597673 | + | 0.597673i | 0.0370661 | + | 0.0370661i | ||||
\(261\) | −8.22942 | + | 8.22942i | −0.509388 | + | 0.509388i | ||||
\(262\) | 2.64881 | − | 2.64881i | 0.163644 | − | 0.163644i | ||||
\(263\) | 27.9813i | 1.72540i | 0.505714 | + | 0.862701i | \(0.331229\pi\) | ||||
−0.505714 | + | 0.862701i | \(0.668771\pi\) | |||||||
\(264\) | 6.00000i | 0.369274i | ||||||||
\(265\) | 0.0701872 | − | 0.0701872i | 0.00431157 | − | 0.00431157i | ||||
\(266\) | 3.82649 | − | 3.82649i | 0.234617 | − | 0.234617i | ||||
\(267\) | −27.0207 | − | 27.0207i | −1.65364 | − | 1.65364i | ||||
\(268\) | 22.4047 | 1.36858 | ||||||||
\(269\) | 4.69936 | + | 4.69936i | 0.286525 | + | 0.286525i | 0.835704 | − | 0.549179i | \(-0.185060\pi\) |
−0.549179 | + | 0.835704i | \(0.685060\pi\) | |||||||
\(270\) | 0.236177i | 0.0143733i | ||||||||
\(271\) | 17.0000 | 1.03268 | 0.516338 | − | 0.856385i | \(-0.327295\pi\) | ||||
0.516338 | + | 0.856385i | \(0.327295\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −17.7442 | −1.07393 | ||||||||
\(274\) | − | 23.7246i | − | 1.43326i | ||||||
\(275\) | 9.49910 | + | 9.49910i | 0.572818 | + | 0.572818i | ||||
\(276\) | −28.7520 | −1.73066 | ||||||||
\(277\) | 14.2474 | + | 14.2474i | 0.856044 | + | 0.856044i | 0.990869 | − | 0.134825i | \(-0.0430473\pi\) |
−0.134825 | + | 0.990869i | \(0.543047\pi\) | |||||||
\(278\) | 6.95616 | − | 6.95616i | 0.417203 | − | 0.417203i | ||||
\(279\) | 9.25710 | − | 9.25710i | 0.554208 | − | 0.554208i | ||||
\(280\) | − | 0.162504i | − | 0.00971146i | ||||||
\(281\) | 16.4730i | 0.982695i | 0.870964 | + | 0.491347i | \(0.163495\pi\) | ||||
−0.870964 | + | 0.491347i | \(0.836505\pi\) | |||||||
\(282\) | 24.7234 | − | 24.7234i | 1.47225 | − | 1.47225i | ||||
\(283\) | 13.0430 | − | 13.0430i | 0.775327 | − | 0.775327i | −0.203705 | − | 0.979032i | \(-0.565298\pi\) |
0.979032 | + | 0.203705i | \(0.0652983\pi\) | |||||||
\(284\) | −0.184435 | − | 0.184435i | −0.0109442 | − | 0.0109442i | ||||
\(285\) | 0.573978 | 0.0339995 | ||||||||
\(286\) | 16.3790 | + | 16.3790i | 0.968512 | + | 0.968512i | ||||
\(287\) | 9.57398i | 0.565134i | ||||||||
\(288\) | 24.2422 | 1.42848 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −0.773318 | −0.0454108 | ||||||||
\(291\) | − | 28.3405i | − | 1.66135i | ||||||
\(292\) | 12.7842 | + | 12.7842i | 0.748142 | + | 0.748142i | ||||
\(293\) | 10.9513 | 0.639782 | 0.319891 | − | 0.947454i | \(-0.396354\pi\) | ||||
0.319891 | + | 0.947454i | \(0.396354\pi\) | |||||||
\(294\) | 15.6562 | + | 15.6562i | 0.913086 | + | 0.913086i | ||||
\(295\) | 0.268050 | − | 0.268050i | 0.0156065 | − | 0.0156065i | ||||
\(296\) | −3.26391 | + | 3.26391i | −0.189711 | + | 0.189711i | ||||
\(297\) | 2.80747i | 0.162906i | ||||||||
\(298\) | − | 18.1411i | − | 1.05089i | ||||||
\(299\) | 23.9709 | − | 23.9709i | 1.38627 | − | 1.38627i | ||||
\(300\) | 13.6758 | − | 13.6758i | 0.789572 | − | 0.789572i | ||||
\(301\) | −5.94781 | − | 5.94781i | −0.342826 | − | 0.342826i | ||||
\(302\) | 2.26857 | 0.130542 | ||||||||
\(303\) | −13.9317 | − | 13.9317i | −0.800353 | − | 0.800353i | ||||
\(304\) | − | 8.86484i | − | 0.508433i | ||||||
\(305\) | 0.147956 | 0.00847193 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.78106 | −0.329942 | −0.164971 | − | 0.986298i | \(-0.552753\pi\) | ||||
−0.164971 | + | 0.986298i | \(0.552753\pi\) | |||||||
\(308\) | 6.32501i | 0.360401i | ||||||||
\(309\) | 19.4440 | + | 19.4440i | 1.10613 | + | 1.10613i | ||||
\(310\) | 0.869890 | 0.0494064 | ||||||||
\(311\) | 0.0852875 | + | 0.0852875i | 0.00483621 | + | 0.00483621i | 0.709521 | − | 0.704685i | \(-0.248911\pi\) |
−0.704685 | + | 0.709521i | \(0.748911\pi\) | |||||||
\(312\) | −7.20174 | + | 7.20174i | −0.407718 | + | 0.407718i | ||||
\(313\) | 7.34626 | − | 7.34626i | 0.415235 | − | 0.415235i | −0.468322 | − | 0.883558i | \(-0.655141\pi\) |
0.883558 | + | 0.468322i | \(0.155141\pi\) | |||||||
\(314\) | − | 28.3678i | − | 1.60089i | ||||||
\(315\) | − | 0.630415i | − | 0.0355199i | ||||||
\(316\) | −4.49369 | + | 4.49369i | −0.252790 | + | 0.252790i | ||||
\(317\) | −19.6587 | + | 19.6587i | −1.10414 | + | 1.10414i | −0.110237 | + | 0.993905i | \(0.535161\pi\) |
−0.993905 | + | 0.110237i | \(0.964839\pi\) | |||||||
\(318\) | −2.76919 | − | 2.76919i | −0.155288 | − | 0.155288i | ||||
\(319\) | −9.19253 | −0.514683 | ||||||||
\(320\) | 0.334436 | + | 0.334436i | 0.0186955 | + | 0.0186955i | ||||
\(321\) | − | 30.4911i | − | 1.70185i | ||||||
\(322\) | 21.3405 | 1.18926 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −11.6382 | −0.646564 | ||||||||
\(325\) | 22.8033i | 1.26490i | ||||||||
\(326\) | −8.71028 | − | 8.71028i | −0.482418 | − | 0.482418i | ||||
\(327\) | 16.7392 | 0.925678 | ||||||||
\(328\) | 3.88573 | + | 3.88573i | 0.214554 | + | 0.214554i | ||||
\(329\) | −7.95970 | + | 7.95970i | −0.438832 | + | 0.438832i | ||||
\(330\) | −1.09364 | + | 1.09364i | −0.0602028 | + | 0.0602028i | ||||
\(331\) | 8.77837i | 0.482503i | 0.970463 | + | 0.241251i | \(0.0775579\pi\) | ||||
−0.970463 | + | 0.241251i | \(0.922442\pi\) | |||||||
\(332\) | − | 3.72874i | − | 0.204641i | ||||||
\(333\) | −12.6620 | + | 12.6620i | −0.693872 | + | 0.693872i | ||||
\(334\) | −5.24070 | + | 5.24070i | −0.286759 | + | 0.286759i | ||||
\(335\) | −1.24721 | − | 1.24721i | −0.0681424 | − | 0.0681424i | ||||
\(336\) | −18.2986 | −0.998270 | ||||||||
\(337\) | −1.03316 | − | 1.03316i | −0.0562796 | − | 0.0562796i | 0.678407 | − | 0.734686i | \(-0.262671\pi\) |
−0.734686 | + | 0.678407i | \(0.762671\pi\) | |||||||
\(338\) | 14.8871i | 0.809753i | ||||||||
\(339\) | −12.8794 | −0.699512 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.3405 | 0.559969 | ||||||||
\(342\) | − | 12.0496i | − | 0.651569i | ||||||
\(343\) | −12.6240 | − | 12.6240i | −0.681630 | − | 0.681630i | ||||
\(344\) | −4.82800 | −0.260308 | ||||||||
\(345\) | 1.60055 | + | 1.60055i | 0.0861707 | + | 0.0861707i | ||||
\(346\) | −25.1620 | + | 25.1620i | −1.35272 | + | 1.35272i | ||||
\(347\) | 22.1720 | − | 22.1720i | 1.19026 | − | 1.19026i | 0.213261 | − | 0.976995i | \(-0.431591\pi\) |
0.976995 | − | 0.213261i | \(-0.0684085\pi\) | |||||||
\(348\) | 13.2344i | 0.709440i | ||||||||
\(349\) | − | 29.7743i | − | 1.59378i | −0.604125 | − | 0.796890i | \(-0.706477\pi\) | ||
0.604125 | − | 0.796890i | \(-0.293523\pi\) | |||||||
\(350\) | −10.1505 | + | 10.1505i | −0.542569 | + | 0.542569i | ||||
\(351\) | −3.36977 | + | 3.36977i | −0.179865 | + | 0.179865i | ||||
\(352\) | 13.5396 | + | 13.5396i | 0.721666 | + | 0.721666i | ||||
\(353\) | 28.3141 | 1.50701 | 0.753503 | − | 0.657444i | \(-0.228362\pi\) | ||||
0.753503 | + | 0.657444i | \(0.228362\pi\) | |||||||
\(354\) | −10.5757 | − | 10.5757i | −0.562094 | − | 0.562094i | ||||
\(355\) | 0.0205340i | 0.00108983i | ||||||||
\(356\) | −23.1215 | −1.22544 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.6331 | −0.720532 | ||||||||
\(359\) | 2.81790i | 0.148723i | 0.997231 | + | 0.0743614i | \(0.0236918\pi\) | ||||
−0.997231 | + | 0.0743614i | \(0.976308\pi\) | |||||||
\(360\) | −0.255863 | − | 0.255863i | −0.0134851 | − | 0.0134851i | ||||
\(361\) | 15.4679 | 0.814101 | ||||||||
\(362\) | −33.3551 | − | 33.3551i | −1.75310 | − | 1.75310i | ||||
\(363\) | 6.69482 | − | 6.69482i | 0.351387 | − | 0.351387i | ||||
\(364\) | −7.59184 | + | 7.59184i | −0.397920 | + | 0.397920i | ||||
\(365\) | − | 1.42333i | − | 0.0745007i | ||||||
\(366\) | − | 5.83750i | − | 0.305131i | ||||||
\(367\) | −5.88186 | + | 5.88186i | −0.307030 | + | 0.307030i | −0.843757 | − | 0.536726i | \(-0.819661\pi\) |
0.536726 | + | 0.843757i | \(0.319661\pi\) | |||||||
\(368\) | 24.7198 | − | 24.7198i | 1.28861 | − | 1.28861i | ||||
\(369\) | 15.0742 | + | 15.0742i | 0.784734 | + | 0.784734i | ||||
\(370\) | −1.18984 | −0.0618571 | ||||||||
\(371\) | 0.891541 | + | 0.891541i | 0.0462865 | + | 0.0462865i | ||||
\(372\) | − | 14.8871i | − | 0.771862i | ||||||
\(373\) | −9.21894 | −0.477339 | −0.238669 | − | 0.971101i | \(-0.576711\pi\) | ||||
−0.238669 | + | 0.971101i | \(0.576711\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.04963 | −0.157482 | ||||||||
\(376\) | 6.46110i | 0.333206i | ||||||||
\(377\) | −11.0337 | − | 11.0337i | −0.568264 | − | 0.568264i | ||||
\(378\) | −3.00000 | −0.154303 | ||||||||
\(379\) | −7.32759 | − | 7.32759i | −0.376393 | − | 0.376393i | 0.493406 | − | 0.869799i | \(-0.335752\pi\) |
−0.869799 | + | 0.493406i | \(0.835752\pi\) | |||||||
\(380\) | 0.245576 | − | 0.245576i | 0.0125978 | − | 0.0125978i | ||||
\(381\) | −3.94687 | + | 3.94687i | −0.202204 | + | 0.202204i | ||||
\(382\) | − | 26.6040i | − | 1.36118i | ||||||
\(383\) | 13.2713i | 0.678130i | 0.940763 | + | 0.339065i | \(0.110111\pi\) | ||||
−0.940763 | + | 0.339065i | \(0.889889\pi\) | |||||||
\(384\) | −12.2513 | + | 12.2513i | −0.625196 | + | 0.625196i | ||||
\(385\) | 0.352097 | − | 0.352097i | 0.0179445 | − | 0.0179445i | ||||
\(386\) | 21.8357 | + | 21.8357i | 1.11141 | + | 1.11141i | ||||
\(387\) | −18.7297 | −0.952083 | ||||||||
\(388\) | −12.1254 | − | 12.1254i | −0.615576 | − | 0.615576i | ||||
\(389\) | 26.2763i | 1.33226i | 0.745835 | + | 0.666131i | \(0.232051\pi\) | ||||
−0.745835 | + | 0.666131i | \(0.767949\pi\) | |||||||
\(390\) | −2.62536 | −0.132940 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −4.09152 | −0.206653 | ||||||||
\(393\) | 5.04694i | 0.254585i | ||||||||
\(394\) | −26.8968 | − | 26.8968i | −1.35504 | − | 1.35504i | ||||
\(395\) | 0.500305 | 0.0251731 | ||||||||
\(396\) | 9.95874 | + | 9.95874i | 0.500445 | + | 0.500445i | ||||
\(397\) | 18.0147 | − | 18.0147i | 0.904130 | − | 0.904130i | −0.0916602 | − | 0.995790i | \(-0.529217\pi\) |
0.995790 | + | 0.0916602i | \(0.0292173\pi\) | |||||||
\(398\) | −29.4693 | + | 29.4693i | −1.47716 | + | 1.47716i | ||||
\(399\) | 7.29086i | 0.365000i | ||||||||
\(400\) | 23.5158i | 1.17579i | ||||||||
\(401\) | 0.636920 | − | 0.636920i | 0.0318062 | − | 0.0318062i | −0.691025 | − | 0.722831i | \(-0.742840\pi\) |
0.722831 | + | 0.691025i | \(0.242840\pi\) | |||||||
\(402\) | −49.2078 | + | 49.2078i | −2.45426 | + | 2.45426i | ||||
\(403\) | 12.4116 | + | 12.4116i | 0.618265 | + | 0.618265i | ||||
\(404\) | −11.9213 | −0.593106 | ||||||||
\(405\) | 0.647867 | + | 0.647867i | 0.0321928 | + | 0.0321928i | ||||
\(406\) | − | 9.82295i | − | 0.487505i | ||||||
\(407\) | −14.1438 | −0.701084 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.3259 | −0.757819 | −0.378910 | − | 0.925434i | \(-0.623701\pi\) | ||||
−0.378910 | + | 0.925434i | \(0.623701\pi\) | |||||||
\(410\) | 1.41653i | 0.0699573i | ||||||||
\(411\) | 22.6020 | + | 22.6020i | 1.11488 | + | 1.11488i | ||||
\(412\) | 16.6382 | 0.819703 | ||||||||
\(413\) | 3.40487 | + | 3.40487i | 0.167542 | + | 0.167542i | ||||
\(414\) | 33.6006 | − | 33.6006i | 1.65138 | − | 1.65138i | ||||
\(415\) | −0.207570 | + | 0.207570i | −0.0101892 | + | 0.0101892i | ||||
\(416\) | 32.5030i | 1.59359i | ||||||||
\(417\) | 13.2540i | 0.649052i | ||||||||
\(418\) | 6.72992 | − | 6.72992i | 0.329171 | − | 0.329171i | ||||
\(419\) | 1.68584 | − | 1.68584i | 0.0823585 | − | 0.0823585i | −0.664727 | − | 0.747086i | \(-0.731452\pi\) |
0.747086 | + | 0.664727i | \(0.231452\pi\) | |||||||
\(420\) | −0.506912 | − | 0.506912i | −0.0247348 | − | 0.0247348i | ||||
\(421\) | 8.28581 | 0.403826 | 0.201913 | − | 0.979404i | \(-0.435284\pi\) | ||||
0.201913 | + | 0.979404i | \(0.435284\pi\) | |||||||
\(422\) | 9.55163 | + | 9.55163i | 0.464966 | + | 0.464966i | ||||
\(423\) | 25.0651i | 1.21871i | ||||||||
\(424\) | 0.723689 | 0.0351454 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.810155 | 0.0392521 | ||||||||
\(427\) | 1.87939i | 0.0909498i | ||||||||
\(428\) | −13.0456 | − | 13.0456i | −0.630582 | − | 0.630582i | ||||
\(429\) | −31.2080 | −1.50674 | ||||||||
\(430\) | −0.880014 | − | 0.880014i | −0.0424380 | − | 0.0424380i | ||||
\(431\) | 22.8531 | − | 22.8531i | 1.10079 | − | 1.10079i | 0.106479 | − | 0.994315i | \(-0.466042\pi\) |
0.994315 | − | 0.106479i | \(-0.0339577\pi\) | |||||||
\(432\) | −3.47505 | + | 3.47505i | −0.167194 | + | 0.167194i | ||||
\(433\) | − | 15.0642i | − | 0.723938i | −0.932190 | − | 0.361969i | \(-0.882105\pi\) | ||
0.932190 | − | 0.361969i | \(-0.117895\pi\) | |||||||
\(434\) | 11.0496i | 0.530399i | ||||||||
\(435\) | 0.736727 | − | 0.736727i | 0.0353233 | − | 0.0353233i | ||||
\(436\) | 7.16183 | − | 7.16183i | 0.342989 | − | 0.342989i | ||||
\(437\) | −9.84930 | − | 9.84930i | −0.471156 | − | 0.471156i | ||||
\(438\) | −56.1566 | −2.68327 | ||||||||
\(439\) | −1.81942 | − | 1.81942i | −0.0868360 | − | 0.0868360i | 0.662355 | − | 0.749191i | \(-0.269557\pi\) |
−0.749191 | + | 0.662355i | \(0.769557\pi\) | |||||||
\(440\) | − | 0.285807i | − | 0.0136253i | ||||||
\(441\) | −15.8726 | −0.755837 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.4662 | 1.11491 | 0.557455 | − | 0.830207i | \(-0.311778\pi\) | ||||
0.557455 | + | 0.830207i | \(0.311778\pi\) | |||||||
\(444\) | 20.3628i | 0.966375i | ||||||||
\(445\) | 1.28712 | + | 1.28712i | 0.0610153 | + | 0.0610153i | ||||
\(446\) | −11.3131 | −0.535693 | ||||||||
\(447\) | 17.2828 | + | 17.2828i | 0.817446 | + | 0.817446i | ||||
\(448\) | −4.24811 | + | 4.24811i | −0.200705 | + | 0.200705i | ||||
\(449\) | −13.3346 | + | 13.3346i | −0.629301 | + | 0.629301i | −0.947892 | − | 0.318591i | \(-0.896790\pi\) |
0.318591 | + | 0.947892i | \(0.396790\pi\) | |||||||
\(450\) | 31.9641i | 1.50680i | ||||||||
\(451\) | 16.8384i | 0.792891i | ||||||||
\(452\) | −5.51043 | + | 5.51043i | −0.259189 | + | 0.259189i | ||||
\(453\) | −2.16123 | + | 2.16123i | −0.101543 | + | 0.101543i | ||||
\(454\) | −29.2830 | − | 29.2830i | −1.37432 | − | 1.37432i | ||||
\(455\) | 0.845237 | 0.0396253 | ||||||||
\(456\) | 2.95910 | + | 2.95910i | 0.138572 | + | 0.138572i | ||||
\(457\) | 2.10782i | 0.0985997i | 0.998784 | + | 0.0492999i | \(0.0156990\pi\) | ||||
−0.998784 | + | 0.0492999i | \(0.984301\pi\) | |||||||
\(458\) | −6.95306 | −0.324895 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.36959 | 0.0638572 | ||||||||
\(461\) | 21.9077i | 1.02034i | 0.860073 | + | 0.510171i | \(0.170418\pi\) | ||||
−0.860073 | + | 0.510171i | \(0.829582\pi\) | |||||||
\(462\) | −13.8917 | − | 13.8917i | −0.646303 | − | 0.646303i | ||||
\(463\) | −14.1557 | −0.657871 | −0.328936 | − | 0.944352i | \(-0.606690\pi\) | ||||
−0.328936 | + | 0.944352i | \(0.606690\pi\) | |||||||
\(464\) | −11.3784 | − | 11.3784i | −0.528230 | − | 0.528230i | ||||
\(465\) | −0.828729 | + | 0.828729i | −0.0384314 | + | 0.0384314i | ||||
\(466\) | 38.7391 | − | 38.7391i | 1.79455 | − | 1.79455i | ||||
\(467\) | − | 29.6878i | − | 1.37379i | −0.726758 | − | 0.686893i | \(-0.758974\pi\) | ||
0.726758 | − | 0.686893i | \(-0.241026\pi\) | |||||||
\(468\) | 23.9067i | 1.10509i | ||||||||
\(469\) | 15.8425 | − | 15.8425i | 0.731538 | − | 0.731538i | ||||
\(470\) | −1.17768 | + | 1.17768i | −0.0543225 | + | 0.0543225i | ||||
\(471\) | 27.0255 | + | 27.0255i | 1.24527 | + | 1.24527i | ||||
\(472\) | 2.76382 | 0.127215 | ||||||||
\(473\) | −10.4608 | − | 10.4608i | −0.480990 | − | 0.480990i | ||||
\(474\) | − | 19.7392i | − | 0.906650i | ||||||
\(475\) | 9.36959 | 0.429906 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.80747 | 0.128545 | ||||||||
\(478\) | 23.4611i | 1.07309i | ||||||||
\(479\) | −27.0793 | − | 27.0793i | −1.23728 | − | 1.23728i | −0.961106 | − | 0.276178i | \(-0.910932\pi\) |
−0.276178 | − | 0.961106i | \(-0.589068\pi\) | |||||||
\(480\) | −2.17024 | −0.0990577 | ||||||||
\(481\) | −16.9767 | − | 16.9767i | −0.774071 | − | 0.774071i | ||||
\(482\) | 21.5514 | − | 21.5514i | 0.981641 | − | 0.981641i | ||||
\(483\) | −20.3307 | + | 20.3307i | −0.925079 | + | 0.925079i | ||||
\(484\) | − | 5.72874i | − | 0.260397i | ||||||
\(485\) | 1.34998i | 0.0612996i | ||||||||
\(486\) | 29.7149 | − | 29.7149i | 1.34790 | − | 1.34790i | ||||
\(487\) | 16.5116 | − | 16.5116i | 0.748212 | − | 0.748212i | −0.225932 | − | 0.974143i | \(-0.572543\pi\) |
0.974143 | + | 0.225932i | \(0.0725426\pi\) | |||||||
\(488\) | 0.762774 | + | 0.762774i | 0.0345292 | + | 0.0345292i | ||||
\(489\) | 16.5963 | 0.750509 | ||||||||
\(490\) | −0.745773 | − | 0.745773i | −0.0336906 | − | 0.0336906i | ||||
\(491\) | − | 31.3928i | − | 1.41674i | −0.705843 | − | 0.708369i | \(-0.749431\pi\) | ||
0.705843 | − | 0.708369i | \(-0.250569\pi\) | |||||||
\(492\) | 24.2422 | 1.09292 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 16.1557 | 0.726879 | ||||||||
\(495\) | − | 1.10876i | − | 0.0498348i | ||||||
\(496\) | 12.7994 | + | 12.7994i | 0.574708 | + | 0.574708i | ||||
\(497\) | −0.260830 | −0.0116998 | ||||||||
\(498\) | 8.18951 | + | 8.18951i | 0.366981 | + | 0.366981i | ||||
\(499\) | −11.4064 | + | 11.4064i | −0.510619 | + | 0.510619i | −0.914716 | − | 0.404097i | \(-0.867586\pi\) |
0.404097 | + | 0.914716i | \(0.367586\pi\) | |||||||
\(500\) | −1.30478 | + | 1.30478i | −0.0583515 | + | 0.0583515i | ||||
\(501\) | − | 9.98545i | − | 0.446117i | ||||||
\(502\) | − | 30.0624i | − | 1.34175i | ||||||
\(503\) | −24.2988 | + | 24.2988i | −1.08343 | + | 1.08343i | −0.0872435 | + | 0.996187i | \(0.527806\pi\) |
−0.996187 | + | 0.0872435i | \(0.972194\pi\) | |||||||
\(504\) | 3.25005 | − | 3.25005i | 0.144769 | − | 0.144769i | ||||
\(505\) | 0.663627 | + | 0.663627i | 0.0295310 | + | 0.0295310i | ||||
\(506\) | 37.5330 | 1.66855 | ||||||||
\(507\) | −14.1827 | − | 14.1827i | −0.629876 | − | 0.629876i | ||||
\(508\) | 3.37733i | 0.149845i | ||||||||
\(509\) | 20.0283 | 0.887738 | 0.443869 | − | 0.896092i | \(-0.353606\pi\) | ||||
0.443869 | + | 0.896092i | \(0.353606\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.0797 | 0.799797 | ||||||||
\(512\) | 25.2226i | 1.11469i | ||||||||
\(513\) | 1.38459 | + | 1.38459i | 0.0611313 | + | 0.0611313i | ||||
\(514\) | −18.1557 | −0.800813 | ||||||||
\(515\) | −0.926204 | − | 0.926204i | −0.0408134 | − | 0.0408134i | ||||
\(516\) | −15.0604 | + | 15.0604i | −0.662996 | + | 0.662996i | ||||
\(517\) | −13.9993 | + | 13.9993i | −0.615688 | + | 0.615688i | ||||
\(518\) | − | 15.1138i | − | 0.664063i | ||||||
\(519\) | − | 47.9427i | − | 2.10445i | ||||||
\(520\) | 0.343051 | − | 0.343051i | 0.0150438 | − | 0.0150438i | ||||
\(521\) | 3.94978 | − | 3.94978i | 0.173043 | − | 0.173043i | −0.615272 | − | 0.788315i | \(-0.710954\pi\) |
0.788315 | + | 0.615272i | \(0.210954\pi\) | |||||||
\(522\) | −15.4662 | − | 15.4662i | −0.676939 | − | 0.676939i | ||||
\(523\) | −5.51249 | −0.241044 | −0.120522 | − | 0.992711i | \(-0.538457\pi\) | ||||
−0.120522 | + | 0.992711i | \(0.538457\pi\) | |||||||
\(524\) | 2.15933 | + | 2.15933i | 0.0943306 | + | 0.0943306i | ||||
\(525\) | − | 19.3405i | − | 0.844088i | ||||||
\(526\) | −52.5877 | −2.29293 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −32.1830 | −1.40059 | ||||||||
\(529\) | − | 31.9299i | − | 1.38826i | ||||||
\(530\) | 0.131909 | + | 0.131909i | 0.00572975 | + | 0.00572975i | ||||
\(531\) | 10.7219 | 0.465292 | ||||||||
\(532\) | 3.11938 | + | 3.11938i | 0.135242 | + | 0.135242i | ||||
\(533\) | −20.2110 | + | 20.2110i | −0.875435 | + | 0.875435i | ||||
\(534\) | 50.7823 | − | 50.7823i | 2.19757 | − | 2.19757i | ||||
\(535\) | 1.45243i | 0.0627940i | ||||||||
\(536\) | − | 12.8598i | − | 0.555458i | ||||||
\(537\) | 12.9880 | − | 12.9880i | 0.560474 | − | 0.560474i | ||||
\(538\) | −8.83190 | + | 8.83190i | −0.380770 | + | 0.380770i | ||||
\(539\) | −8.86510 | − | 8.86510i | −0.381847 | − | 0.381847i | ||||
\(540\) | −0.192533 | −0.00828531 | ||||||||
\(541\) | −9.89592 | − | 9.89592i | −0.425459 | − | 0.425459i | 0.461619 | − | 0.887078i | \(-0.347269\pi\) |
−0.887078 | + | 0.461619i | \(0.847269\pi\) | |||||||
\(542\) | 31.9495i | 1.37235i | ||||||||
\(543\) | 63.5536 | 2.72734 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.797362 | −0.0341552 | ||||||||
\(546\) | − | 33.3482i | − | 1.42717i | ||||||
\(547\) | 20.8013 | + | 20.8013i | 0.889399 | + | 0.889399i | 0.994465 | − | 0.105066i | \(-0.0335055\pi\) |
−0.105066 | + | 0.994465i | \(0.533506\pi\) | |||||||
\(548\) | 19.3405 | 0.826185 | ||||||||
\(549\) | 2.95910 | + | 2.95910i | 0.126291 | + | 0.126291i | ||||
\(550\) | −17.8525 | + | 17.8525i | −0.761232 | + | 0.761232i | ||||
\(551\) | −4.53360 | + | 4.53360i | −0.193138 | + | 0.193138i | ||||
\(552\) | 16.5030i | 0.702414i | ||||||||
\(553\) | 6.35504i | 0.270244i | ||||||||
\(554\) | −26.7764 | + | 26.7764i | −1.13762 | + | 1.13762i | ||||
\(555\) | 1.13354 | − | 1.13354i | 0.0481163 | − | 0.0481163i | ||||
\(556\) | 5.67071 | + | 5.67071i | 0.240492 | + | 0.240492i | ||||
\(557\) | −32.0574 | −1.35831 | −0.679157 | − | 0.733993i | \(-0.737655\pi\) | ||||
−0.679157 | + | 0.733993i | \(0.737655\pi\) | |||||||
\(558\) | 17.3977 | + | 17.3977i | 0.736502 | + | 0.736502i | ||||
\(559\) | − | 25.1121i | − | 1.06213i | ||||||
\(560\) | 0.871644 | 0.0368337 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −30.9590 | −1.30593 | ||||||||
\(563\) | − | 18.6483i | − | 0.785930i | −0.919553 | − | 0.392965i | \(-0.871449\pi\) | ||
0.919553 | − | 0.392965i | \(-0.128551\pi\) | |||||||
\(564\) | 20.1547 | + | 20.1547i | 0.848664 | + | 0.848664i | ||||
\(565\) | 0.613503 | 0.0258103 | ||||||||
\(566\) | 24.5129 | + | 24.5129i | 1.03035 | + | 1.03035i | ||||
\(567\) | −8.22942 | + | 8.22942i | −0.345603 | + | 0.345603i | ||||
\(568\) | −0.105861 | + | 0.105861i | −0.00444184 | + | 0.00444184i | ||||
\(569\) | 27.6554i | 1.15937i | 0.814839 | + | 0.579687i | \(0.196825\pi\) | ||||
−0.814839 | + | 0.579687i | \(0.803175\pi\) | |||||||
\(570\) | 1.07873i | 0.0451828i | ||||||||
\(571\) | 23.4591 | − | 23.4591i | 0.981734 | − | 0.981734i | −0.0181018 | − | 0.999836i | \(-0.505762\pi\) |
0.999836 | + | 0.0181018i | \(0.00576229\pi\) | |||||||
\(572\) | −13.3523 | + | 13.3523i | −0.558288 | + | 0.558288i | ||||
\(573\) | 25.3452 | + | 25.3452i | 1.05881 | + | 1.05881i | ||||
\(574\) | −17.9932 | −0.751021 | ||||||||
\(575\) | 26.1273 | + | 26.1273i | 1.08958 | + | 1.08958i | ||||
\(576\) | 13.3773i | 0.557389i | ||||||||
\(577\) | 2.70233 | 0.112500 | 0.0562498 | − | 0.998417i | \(-0.482086\pi\) | ||||
0.0562498 | + | 0.998417i | \(0.482086\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −41.6049 | −1.72904 | ||||||||
\(580\) | − | 0.630415i | − | 0.0261766i | ||||||
\(581\) | −2.63662 | − | 2.63662i | −0.109385 | − | 0.109385i | ||||
\(582\) | 53.2627 | 2.20781 | ||||||||
\(583\) | 1.56802 | + | 1.56802i | 0.0649406 | + | 0.0649406i | ||||
\(584\) | 7.33788 | − | 7.33788i | 0.303644 | − | 0.303644i | ||||
\(585\) | 1.33083 | − | 1.33083i | 0.0550229 | − | 0.0550229i | ||||
\(586\) | 20.5817i | 0.850223i | ||||||||
\(587\) | 6.31551i | 0.260669i | 0.991470 | + | 0.130335i | \(0.0416051\pi\) | ||||
−0.991470 | + | 0.130335i | \(0.958395\pi\) | |||||||
\(588\) | −12.7630 | + | 12.7630i | −0.526338 | + | 0.526338i | ||||
\(589\) | 5.09975 | − | 5.09975i | 0.210131 | − | 0.210131i | ||||
\(590\) | 0.503770 | + | 0.503770i | 0.0207399 | + | 0.0207399i | ||||
\(591\) | 51.2481 | 2.10807 | ||||||||
\(592\) | −17.5071 | − | 17.5071i | −0.719537 | − | 0.719537i | ||||
\(593\) | 10.2148i | 0.419472i | 0.977758 | + | 0.209736i | \(0.0672605\pi\) | ||||
−0.977758 | + | 0.209736i | \(0.932739\pi\) | |||||||
\(594\) | −5.27631 | −0.216490 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14.7888 | 0.605773 | ||||||||
\(597\) | − | 56.1498i | − | 2.29806i | ||||||
\(598\) | 45.0505 | + | 45.0505i | 1.84225 | + | 1.84225i | ||||
\(599\) | 21.4347 | 0.875798 | 0.437899 | − | 0.899024i | \(-0.355723\pi\) | ||||
0.437899 | + | 0.899024i | \(0.355723\pi\) | |||||||
\(600\) | −7.84960 | − | 7.84960i | −0.320459 | − | 0.320459i | ||||
\(601\) | −12.3431 | + | 12.3431i | −0.503484 | + | 0.503484i | −0.912519 | − | 0.409035i | \(-0.865865\pi\) |
0.409035 | + | 0.912519i | \(0.365865\pi\) | |||||||
\(602\) | 11.1782 | − | 11.1782i | 0.455591 | − | 0.455591i | ||||
\(603\) | − | 49.8881i | − | 2.03160i | ||||||
\(604\) | 1.84936i | 0.0752492i | ||||||||
\(605\) | −0.318905 | + | 0.318905i | −0.0129653 | + | 0.0129653i | ||||
\(606\) | 26.1829 | − | 26.1829i | 1.06361 | − | 1.06361i | ||||
\(607\) | −6.01734 | − | 6.01734i | −0.244236 | − | 0.244236i | 0.574364 | − | 0.818600i | \(-0.305249\pi\) |
−0.818600 | + | 0.574364i | \(0.805249\pi\) | |||||||
\(608\) | 13.3550 | 0.541618 | ||||||||
\(609\) | 9.35815 | + | 9.35815i | 0.379211 | + | 0.379211i | ||||
\(610\) | 0.278066i | 0.0112586i | ||||||||
\(611\) | −33.6064 | −1.35957 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.78106 | 0.395053 | 0.197527 | − | 0.980298i | \(-0.436709\pi\) | ||||
0.197527 | + | 0.980298i | \(0.436709\pi\) | |||||||
\(614\) | − | 10.8648i | − | 0.438469i | ||||||
\(615\) | −1.34950 | − | 1.34950i | −0.0544171 | − | 0.0544171i | ||||
\(616\) | 3.63041 | 0.146274 | ||||||||
\(617\) | 16.1583 | + | 16.1583i | 0.650507 | + | 0.650507i | 0.953115 | − | 0.302608i | \(-0.0978574\pi\) |
−0.302608 | + | 0.953115i | \(0.597857\pi\) | |||||||
\(618\) | −36.5427 | + | 36.5427i | −1.46996 | + | 1.46996i | ||||
\(619\) | −29.1771 | + | 29.1771i | −1.17273 | + | 1.17273i | −0.191171 | + | 0.981557i | \(0.561229\pi\) |
−0.981557 | + | 0.191171i | \(0.938771\pi\) | |||||||
\(620\) | 0.709141i | 0.0284798i | ||||||||
\(621\) | 7.72193i | 0.309871i | ||||||||
\(622\) | −0.160288 | + | 0.160288i | −0.00642697 | + | 0.00642697i | ||||
\(623\) | −16.3494 | + | 16.3494i | −0.655025 | + | 0.655025i | ||||
\(624\) | −38.6290 | − | 38.6290i | −1.54640 | − | 1.54640i | ||||
\(625\) | −24.7820 | −0.991280 | ||||||||
\(626\) | 13.8065 | + | 13.8065i | 0.551817 | + | 0.551817i | ||||
\(627\) | 12.8229i | 0.512099i | ||||||||
\(628\) | 23.1257 | 0.922815 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 1.18479 | 0.0472033 | ||||||||
\(631\) | − | 9.54252i | − | 0.379882i | −0.981796 | − | 0.189941i | \(-0.939170\pi\) | ||
0.981796 | − | 0.189941i | \(-0.0608296\pi\) | |||||||
\(632\) | 2.57928 | + | 2.57928i | 0.102598 | + | 0.102598i | ||||
\(633\) | −18.1993 | −0.723359 | ||||||||
\(634\) | −36.9463 | − | 36.9463i | −1.46732 | − | 1.46732i | ||||
\(635\) | 0.188007 | − | 0.188007i | 0.00746084 | − | 0.00746084i | ||||
\(636\) | 2.25746 | − | 2.25746i | 0.0895142 | − | 0.0895142i | ||||
\(637\) | − | 21.2814i | − | 0.843198i | ||||||
\(638\) | − | 17.2763i | − | 0.683976i | ||||||
\(639\) | −0.410677 | + | 0.410677i | −0.0162461 | + | 0.0162461i | ||||
\(640\) | 0.583584 | − | 0.583584i | 0.0230682 | − | 0.0230682i | ||||
\(641\) | 6.66711 | + | 6.66711i | 0.263335 | + | 0.263335i | 0.826407 | − | 0.563073i | \(-0.190381\pi\) |
−0.563073 | + | 0.826407i | \(0.690381\pi\) | |||||||
\(642\) | 57.3046 | 2.26163 | ||||||||
\(643\) | −7.78241 | − | 7.78241i | −0.306908 | − | 0.306908i | 0.536801 | − | 0.843709i | \(-0.319633\pi\) |
−0.843709 | + | 0.536801i | \(0.819633\pi\) | |||||||
\(644\) | 17.3969i | 0.685535i | ||||||||
\(645\) | 1.67675 | 0.0660219 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.9840 | 1.13948 | 0.569740 | − | 0.821825i | \(-0.307044\pi\) | ||||
0.569740 | + | 0.821825i | \(0.307044\pi\) | |||||||
\(648\) | 6.68004i | 0.262417i | ||||||||
\(649\) | 5.98838 | + | 5.98838i | 0.235064 | + | 0.235064i | ||||
\(650\) | −42.8563 | −1.68096 | ||||||||
\(651\) | −10.5268 | − | 10.5268i | −0.412577 | − | 0.412577i | ||||
\(652\) | 7.10069 | − | 7.10069i | 0.278084 | − | 0.278084i | ||||
\(653\) | −10.4071 | + | 10.4071i | −0.407260 | + | 0.407260i | −0.880782 | − | 0.473522i | \(-0.842982\pi\) |
0.473522 | + | 0.880782i | \(0.342982\pi\) | |||||||
\(654\) | 31.4593i | 1.23016i | ||||||||
\(655\) | − | 0.240408i | − | 0.00939354i | ||||||
\(656\) | −20.8424 | + | 20.8424i | −0.813760 | + | 0.813760i | ||||
\(657\) | 28.4665 | − | 28.4665i | 1.11058 | − | 1.11058i | ||||
\(658\) | −14.9593 | − | 14.9593i | −0.583176 | − | 0.583176i | ||||
\(659\) | −2.19759 | −0.0856058 | −0.0428029 | − | 0.999084i | \(-0.513629\pi\) | ||||
−0.0428029 | + | 0.999084i | \(0.513629\pi\) | |||||||
\(660\) | −0.891541 | − | 0.891541i | −0.0347032 | − | 0.0347032i | ||||
\(661\) | 26.6023i | 1.03471i | 0.855772 | + | 0.517354i | \(0.173083\pi\) | ||||
−0.855772 | + | 0.517354i | \(0.826917\pi\) | |||||||
\(662\) | −16.4979 | −0.641211 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.14022 | −0.0830565 | ||||||||
\(665\) | − | 0.347296i | − | 0.0134676i | ||||||
\(666\) | −23.7967 | − | 23.7967i | −0.922104 | − | 0.922104i | ||||
\(667\) | −25.2841 | −0.979002 | ||||||||
\(668\) | −4.27226 | − | 4.27226i | −0.165299 | − | 0.165299i | ||||
\(669\) | 10.7778 | − | 10.7778i | 0.416695 | − | 0.416695i | ||||
\(670\) | 2.34399 | − | 2.34399i | 0.0905562 | − | 0.0905562i | ||||
\(671\) | 3.30541i | 0.127604i | ||||||||
\(672\) | − | 27.5672i | − | 1.06343i | ||||||
\(673\) | 5.12222 | − | 5.12222i | 0.197447 | − | 0.197447i | −0.601458 | − | 0.798905i | \(-0.705413\pi\) |
0.798905 | + | 0.601458i | \(0.205413\pi\) | |||||||
\(674\) | 1.94170 | − | 1.94170i | 0.0747915 | − | 0.0747915i | ||||
\(675\) | −3.67292 | − | 3.67292i | −0.141371 | − | 0.141371i | ||||
\(676\) | −12.1361 | −0.466773 | ||||||||
\(677\) | −16.2120 | − | 16.2120i | −0.623079 | − | 0.623079i | 0.323239 | − | 0.946317i | \(-0.395228\pi\) |
−0.946317 | + | 0.323239i | \(0.895228\pi\) | |||||||
\(678\) | − | 24.2053i | − | 0.929600i | ||||||
\(679\) | −17.1480 | −0.658078 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 55.7948 | 2.13806 | ||||||||
\(682\) | 19.4338i | 0.744157i | ||||||||
\(683\) | −3.03767 | − | 3.03767i | −0.116233 | − | 0.116233i | 0.646598 | − | 0.762831i | \(-0.276191\pi\) |
−0.762831 | + | 0.646598i | \(0.776191\pi\) | |||||||
\(684\) | 9.82295 | 0.375590 | ||||||||
\(685\) | −1.07664 | − | 1.07664i | −0.0411362 | − | 0.0411362i | ||||
\(686\) | 23.7253 | − | 23.7253i | 0.905836 | − | 0.905836i | ||||
\(687\) | 6.62406 | − | 6.62406i | 0.252724 | − | 0.252724i | ||||
\(688\) | − | 25.8966i | − | 0.987299i | ||||||
\(689\) | 3.76415i | 0.143403i | ||||||||
\(690\) | −3.00805 | + | 3.00805i | −0.114514 | + | 0.114514i | ||||
\(691\) | −14.5898 | + | 14.5898i | −0.555022 | + | 0.555022i | −0.927886 | − | 0.372864i | \(-0.878376\pi\) |
0.372864 | + | 0.927886i | \(0.378376\pi\) | |||||||
\(692\) | −20.5122 | − | 20.5122i | −0.779758 | − | 0.779758i | ||||
\(693\) | 14.0838 | 0.534998 | ||||||||
\(694\) | 41.6698 | + | 41.6698i | 1.58176 | + | 1.58176i | ||||
\(695\) | − | 0.631349i | − | 0.0239484i | ||||||
\(696\) | 7.59627 | 0.287936 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 55.9573 | 2.11801 | ||||||||
\(699\) | 73.8120i | 2.79183i | ||||||||
\(700\) | −8.27480 | − | 8.27480i | −0.312758 | − | 0.312758i | ||||
\(701\) | 28.2772 | 1.06802 | 0.534008 | − | 0.845479i | \(-0.320685\pi\) | ||||
0.534008 | + | 0.845479i | \(0.320685\pi\) | |||||||
\(702\) | −6.33310 | − | 6.33310i | −0.239027 | − | 0.239027i | ||||
\(703\) | −6.97549 | + | 6.97549i | −0.263086 | + | 0.263086i | ||||
\(704\) | −7.47146 | + | 7.47146i | −0.281591 | + | 0.281591i | ||||
\(705\) | − | 2.24392i | − | 0.0845108i | ||||||
\(706\) | 53.2131i | 2.00270i | ||||||||
\(707\) | −8.42961 | + | 8.42961i | −0.317028 | + | 0.317028i | ||||
\(708\) | 8.62142 | − | 8.62142i | 0.324013 | − | 0.324013i | ||||
\(709\) | −19.1627 | − | 19.1627i | −0.719671 | − | 0.719671i | 0.248866 | − | 0.968538i | \(-0.419942\pi\) |
−0.968538 | + | 0.248866i | \(0.919942\pi\) | |||||||
\(710\) | −0.0385913 | −0.00144831 | ||||||||
\(711\) | 10.0060 | + | 10.0060i | 0.375255 | + | 0.375255i | ||||
\(712\) | 13.2713i | 0.497361i | ||||||||
\(713\) | 28.4415 | 1.06514 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.48658 | 0.0555949 | ||||||||
\(716\) | − | 11.1138i | − | 0.415342i | ||||||
\(717\) | −22.3510 | − | 22.3510i | −0.834713 | − | 0.834713i | ||||
\(718\) | −5.29591 | −0.197642 | ||||||||
\(719\) | 18.2718 | + | 18.2718i | 0.681422 | + | 0.681422i | 0.960321 | − | 0.278899i | \(-0.0899693\pi\) |
−0.278899 | + | 0.960321i | \(0.589969\pi\) | |||||||
\(720\) | 1.37241 | − | 1.37241i | 0.0511465 | − | 0.0511465i | ||||
\(721\) | 11.7650 | − | 11.7650i | 0.438150 | − | 0.438150i | ||||
\(722\) | 29.0702i | 1.08188i | ||||||||
\(723\) | 41.0634i | 1.52716i | ||||||||
\(724\) | 27.1913 | − | 27.1913i | 1.01056 | − | 1.01056i | ||||
\(725\) | 12.0263 | − | 12.0263i | 0.446645 | − | 0.446645i | ||||
\(726\) | 12.5822 | + | 12.5822i | 0.466968 | + | 0.466968i | ||||
\(727\) | 31.6290 | 1.17305 | 0.586527 | − | 0.809930i | \(-0.300495\pi\) | ||||
0.586527 | + | 0.809930i | \(0.300495\pi\) | |||||||
\(728\) | 4.35755 | + | 4.35755i | 0.161501 | + | 0.161501i | ||||
\(729\) | 33.8289i | 1.25292i | ||||||||
\(730\) | 2.67499 | 0.0990059 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 4.75877 | 0.175889 | ||||||||
\(733\) | − | 25.6040i | − | 0.945706i | −0.881141 | − | 0.472853i | \(-0.843224\pi\) | ||
0.881141 | − | 0.472853i | \(-0.156776\pi\) | |||||||
\(734\) | −11.0543 | − | 11.0543i | −0.408021 | − | 0.408021i | ||||
\(735\) | 1.42097 | 0.0524133 | ||||||||
\(736\) | 37.2408 | + | 37.2408i | 1.37271 | + | 1.37271i | ||||
\(737\) | 27.8633 | − | 27.8633i | 1.02636 | − | 1.02636i | ||||
\(738\) | −28.3303 | + | 28.3303i | −1.04285 | + | 1.04285i | ||||
\(739\) | 21.6382i | 0.795972i | 0.917391 | + | 0.397986i | \(0.130291\pi\) | ||||
−0.917391 | + | 0.397986i | \(0.869709\pi\) | |||||||
\(740\) | − | 0.969971i | − | 0.0356568i | ||||||
\(741\) | −15.3912 | + | 15.3912i | −0.565412 | + | 0.565412i | ||||
\(742\) | −1.67555 | + | 1.67555i | −0.0615114 | + | 0.0615114i | ||||
\(743\) | 18.9184 | + | 18.9184i | 0.694049 | + | 0.694049i | 0.963120 | − | 0.269072i | \(-0.0867168\pi\) |
−0.269072 | + | 0.963120i | \(0.586717\pi\) | |||||||
\(744\) | −8.54488 | −0.313271 | ||||||||
\(745\) | −0.823255 | − | 0.823255i | −0.0301617 | − | 0.0301617i | ||||
\(746\) | − | 17.3259i | − | 0.634348i | ||||||
\(747\) | −8.30272 | −0.303781 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.4492 | −0.674121 | ||||||||
\(750\) | − | 5.73143i | − | 0.209282i | ||||||
\(751\) | 29.6641 | + | 29.6641i | 1.08246 | + | 1.08246i | 0.996280 | + | 0.0861767i | \(0.0274650\pi\) |
0.0861767 | + | 0.996280i | \(0.472535\pi\) | |||||||
\(752\) | −34.6563 | −1.26379 | ||||||||
\(753\) | 28.6399 | + | 28.6399i | 1.04370 | + | 1.04370i | ||||
\(754\) | 20.7366 | − | 20.7366i | 0.755181 | − | 0.755181i | ||||
\(755\) | 0.102949 | − | 0.102949i | 0.00374670 | − | 0.00374670i | ||||
\(756\) | − | 2.44562i | − | 0.0889464i | ||||||
\(757\) | − | 4.99319i | − | 0.181481i | −0.995875 | − | 0.0907403i | \(-0.971077\pi\) | ||
0.995875 | − | 0.0907403i | \(-0.0289233\pi\) | |||||||
\(758\) | 13.7714 | − | 13.7714i | 0.500199 | − | 0.500199i | ||||
\(759\) | −35.7570 | + | 35.7570i | −1.29790 | + | 1.29790i | ||||
\(760\) | −0.140955 | − | 0.140955i | −0.00511297 | − | 0.00511297i | ||||
\(761\) | −13.2935 | −0.481891 | −0.240945 | − | 0.970539i | \(-0.577457\pi\) | ||||
−0.240945 | + | 0.970539i | \(0.577457\pi\) | |||||||
\(762\) | −7.41769 | − | 7.41769i | −0.268715 | − | 0.268715i | ||||
\(763\) | − | 10.1284i | − | 0.366671i | ||||||
\(764\) | 21.6878 | 0.784637 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −24.9418 | −0.901184 | ||||||||
\(767\) | 14.3756i | 0.519072i | ||||||||
\(768\) | −37.0666 | − | 37.0666i | −1.33753 | − | 1.33753i | ||||
\(769\) | −8.25166 | −0.297562 | −0.148781 | − | 0.988870i | \(-0.547535\pi\) | ||||
−0.148781 | + | 0.988870i | \(0.547535\pi\) | |||||||
\(770\) | 0.661726 | + | 0.661726i | 0.0238470 | + | 0.0238470i | ||||
\(771\) | 17.2966 | − | 17.2966i | 0.622922 | − | 0.622922i | ||||
\(772\) | −17.8006 | + | 17.8006i | −0.640658 | + | 0.640658i | ||||
\(773\) | 26.1043i | 0.938907i | 0.882957 | + | 0.469453i | \(0.155549\pi\) | ||||
−0.882957 | + | 0.469453i | \(0.844451\pi\) | |||||||
\(774\) | − | 35.2003i | − | 1.26525i | ||||||
\(775\) | −13.5281 | + | 13.5281i | −0.485944 | + | 0.485944i | ||||
\(776\) | −6.95973 | + | 6.95973i | −0.249840 | + | 0.249840i | ||||
\(777\) | 14.3987 | + | 14.3987i | 0.516549 | + | 0.516549i | ||||
\(778\) | −49.3833 | −1.77048 | ||||||||
\(779\) | 8.30442 | + | 8.30442i | 0.297537 | + | 0.297537i | ||||
\(780\) | − | 2.14022i | − | 0.0766320i | ||||||
\(781\) | −0.458740 | −0.0164150 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.55438 | 0.127023 | ||||||||
\(784\) | − | 21.9463i | − | 0.783795i | ||||||
\(785\) | −1.28735 | − | 1.28735i | −0.0459474 | − | 0.0459474i | ||||
\(786\) | −9.48515 | −0.338324 | ||||||||
\(787\) | −18.9953 | − | 18.9953i | −0.677109 | − | 0.677109i | 0.282236 | − | 0.959345i | \(-0.408924\pi\) |
−0.959345 | + | 0.282236i | \(0.908924\pi\) | |||||||
\(788\) | 21.9264 | − | 21.9264i | 0.781097 | − | 0.781097i | ||||
\(789\) | 50.0994 | − | 50.0994i | 1.78359 | − | 1.78359i | ||||
\(790\) | 0.940265i | 0.0334531i | ||||||||
\(791\) | 7.79292i | 0.277084i | ||||||||
\(792\) | 5.71609 | − | 5.71609i | 0.203113 | − | 0.203113i | ||||
\(793\) | −3.96745 | + | 3.96745i | −0.140888 | + | 0.140888i | ||||
\(794\) | 33.8565 | + | 33.8565i | 1.20152 | + | 1.20152i | ||||
\(795\) | −0.251334 | −0.00891391 | ||||||||
\(796\) | −24.0236 | − | 24.0236i | −0.851495 | − | 0.851495i | ||||
\(797\) | 18.8212i | 0.666681i | 0.942807 | + | 0.333340i | \(0.108176\pi\) | ||||
−0.942807 | + | 0.333340i | \(0.891824\pi\) | |||||||
\(798\) | −13.7023 | −0.485057 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −35.4270 | −1.25253 | ||||||||
\(801\) | 51.4843i | 1.81911i | ||||||||
\(802\) | 1.19702 | + | 1.19702i | 0.0422681 | + | 0.0422681i | ||||
\(803\) | 31.7980 | 1.12213 | ||||||||
\(804\) | −40.1146 | − | 40.1146i | −1.41473 | − | 1.41473i | ||||
\(805\) | 0.968443 | − | 0.968443i | 0.0341331 | − | 0.0341331i | ||||
\(806\) | −23.3261 | + | 23.3261i | −0.821628 | + | 0.821628i | ||||
\(807\) | − | 16.8280i | − | 0.592374i | ||||||
\(808\) | 6.84255i | 0.240720i | ||||||||
\(809\) | −18.2132 | + | 18.2132i | −0.640342 | + | 0.640342i | −0.950639 | − | 0.310298i | \(-0.899571\pi\) |
0.310298 | + | 0.950639i | \(0.399571\pi\) | |||||||
\(810\) | −1.21759 | + | 1.21759i | −0.0427818 | + | 0.0427818i | ||||
\(811\) | −18.7018 | − | 18.7018i | −0.656708 | − | 0.656708i | 0.297891 | − | 0.954600i | \(-0.403717\pi\) |
−0.954600 | + | 0.297891i | \(0.903717\pi\) | |||||||
\(812\) | 8.00774 | 0.281017 | ||||||||
\(813\) | −30.4378 | − | 30.4378i | −1.06750 | − | 1.06750i | ||||
\(814\) | − | 26.5817i | − | 0.931689i | ||||||
\(815\) | −0.790555 | −0.0276919 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.3182 | −0.360988 | ||||||||
\(818\) | − | 28.8033i | − | 1.00709i | ||||||
\(819\) | 16.9046 | + | 16.9046i | 0.590695 | + | 0.590695i | ||||
\(820\) | −1.15476 | −0.0403261 | ||||||||
\(821\) | −22.2760 | − | 22.2760i | −0.777437 | − | 0.777437i | 0.201957 | − | 0.979394i | \(-0.435270\pi\) |
−0.979394 | + | 0.201957i | \(0.935270\pi\) | |||||||
\(822\) | −42.4779 | + | 42.4779i | −1.48159 | + | 1.48159i | ||||
\(823\) | −8.26575 | + | 8.26575i | −0.288126 | + | 0.288126i | −0.836339 | − | 0.548213i | \(-0.815308\pi\) |
0.548213 | + | 0.836339i | \(0.315308\pi\) | |||||||
\(824\) | − | 9.54993i | − | 0.332688i | ||||||
\(825\) | − | 34.0155i | − | 1.18427i | ||||||
\(826\) | −6.39905 | + | 6.39905i | −0.222652 | + | 0.222652i | ||||
\(827\) | 2.34946 | − | 2.34946i | 0.0816989 | − | 0.0816989i | −0.665076 | − | 0.746775i | \(-0.731601\pi\) |
0.746775 | + | 0.665076i | \(0.231601\pi\) | |||||||
\(828\) | 27.3915 | + | 27.3915i | 0.951920 | + | 0.951920i | ||||
\(829\) | −6.01186 | −0.208801 | −0.104400 | − | 0.994535i | \(-0.533292\pi\) | ||||
−0.104400 | + | 0.994535i | \(0.533292\pi\) | |||||||
\(830\) | −0.390103 | − | 0.390103i | −0.0135407 | − | 0.0135407i | ||||
\(831\) | − | 51.0188i | − | 1.76982i | ||||||
\(832\) | −17.9358 | −0.621813 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −24.9094 | −0.862542 | ||||||||
\(835\) | 0.475652i | 0.0164606i | ||||||||
\(836\) | 5.48628 | + | 5.48628i | 0.189747 | + | 0.189747i | ||||
\(837\) | −3.99825 | −0.138200 | ||||||||
\(838\) | 3.16834 | + | 3.16834i | 0.109448 | + | 0.109448i | ||||
\(839\) | −29.2823 | + | 29.2823i | −1.01094 | + | 1.01094i | −0.0109989 | + | 0.999940i | \(0.503501\pi\) |
−0.999940 | + | 0.0109989i | \(0.996499\pi\) | |||||||
\(840\) | −0.290956 | + | 0.290956i | −0.0100389 | + | 0.0100389i | ||||
\(841\) | − | 17.3618i | − | 0.598684i | ||||||
\(842\) | 15.5722i | 0.536654i | ||||||||
\(843\) | 29.4941 | − | 29.4941i | 1.01583 | − | 1.01583i | ||||
\(844\) | −7.78656 | + | 7.78656i | −0.268024 | + | 0.268024i | ||||
\(845\) | 0.675586 | + | 0.675586i | 0.0232409 | + | 0.0232409i | ||||
\(846\) | −47.1070 | −1.61957 | ||||||||
\(847\) | −4.05083 | − | 4.05083i | −0.139188 | − | 0.139188i | ||||
\(848\) | 3.88175i | 0.133300i | ||||||||
\(849\) | −46.7060 | −1.60294 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −38.9026 | −1.33356 | ||||||||
\(852\) | 0.660444i | 0.0226265i | ||||||||
\(853\) | −16.9693 | − | 16.9693i | −0.581019 | − | 0.581019i | 0.354165 | − | 0.935183i | \(-0.384765\pi\) |
−0.935183 | + | 0.354165i | \(0.884765\pi\) | |||||||
\(854\) | −3.53209 | −0.120866 | ||||||||
\(855\) | −0.546819 | − | 0.546819i | −0.0187008 | − | 0.0187008i | ||||
\(856\) | −7.48788 | + | 7.48788i | −0.255930 | + | 0.255930i | ||||
\(857\) | 22.5251 | − | 22.5251i | 0.769444 | − | 0.769444i | −0.208565 | − | 0.978009i | \(-0.566879\pi\) |
0.978009 | + | 0.208565i | \(0.0668792\pi\) | |||||||
\(858\) | − | 58.6519i | − | 2.00234i | ||||||
\(859\) | 24.0806i | 0.821619i | 0.911721 | + | 0.410810i | \(0.134754\pi\) | ||||
−0.911721 | + | 0.410810i | \(0.865246\pi\) | |||||||
\(860\) | 0.717394 | − | 0.717394i | 0.0244629 | − | 0.0244629i | ||||
\(861\) | 17.1418 | − | 17.1418i | 0.584191 | − | 0.584191i | ||||
\(862\) | 42.9497 | + | 42.9497i | 1.46287 | + | 1.46287i | ||||
\(863\) | 20.8590 | 0.710047 | 0.355024 | − | 0.934857i | \(-0.384473\pi\) | ||||
0.355024 | + | 0.934857i | \(0.384473\pi\) | |||||||
\(864\) | −5.23523 | − | 5.23523i | −0.178106 | − | 0.178106i | ||||
\(865\) | 2.28373i | 0.0776491i | ||||||||
\(866\) | 28.3114 | 0.962060 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9.00774 | −0.305743 | ||||||||
\(869\) | 11.1771i | 0.379156i | ||||||||
\(870\) | 1.38459 | + | 1.38459i | 0.0469421 | + | 0.0469421i | ||||
\(871\) | 66.8881 | 2.26642 | ||||||||
\(872\) | −4.11073 | − | 4.11073i | −0.139207 | − | 0.139207i | ||||
\(873\) | −26.9995 | + | 26.9995i | −0.913794 | + | 0.913794i | ||||
\(874\) | 18.5106 | − | 18.5106i | 0.626131 | − | 0.626131i | ||||
\(875\) | 1.84524i | 0.0623804i | ||||||||
\(876\) | − | 45.7793i | − | 1.54674i | ||||||
\(877\) | 15.8158 | − | 15.8158i | 0.534061 | − | 0.534061i | −0.387717 | − | 0.921778i | \(-0.626736\pi\) |
0.921778 | + | 0.387717i | \(0.126736\pi\) | |||||||
\(878\) | 3.41939 | − | 3.41939i | 0.115399 | − | 0.115399i | ||||
\(879\) | −19.6078 | − | 19.6078i | −0.661356 | − | 0.661356i | ||||
\(880\) | 1.53302 | 0.0516782 | ||||||||
\(881\) | −39.9005 | − | 39.9005i | −1.34428 | − | 1.34428i | −0.891745 | − | 0.452539i | \(-0.850518\pi\) |
−0.452539 | − | 0.891745i | \(-0.649482\pi\) | |||||||
\(882\) | − | 29.8307i | − | 1.00445i | ||||||
\(883\) | −45.4219 | −1.52857 | −0.764284 | − | 0.644879i | \(-0.776908\pi\) | ||||
−0.764284 | + | 0.644879i | \(0.776908\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.959866 | −0.0322655 | ||||||||
\(886\) | 44.1019i | 1.48163i | ||||||||
\(887\) | −12.3614 | − | 12.3614i | −0.415055 | − | 0.415055i | 0.468440 | − | 0.883495i | \(-0.344816\pi\) |
−0.883495 | + | 0.468440i | \(0.844816\pi\) | |||||||
\(888\) | 11.6878 | 0.392216 | ||||||||
\(889\) | 2.38813 | + | 2.38813i | 0.0800953 | + | 0.0800953i | ||||
\(890\) | −2.41899 | + | 2.41899i | −0.0810848 | + | 0.0810848i | ||||
\(891\) | −14.4737 | + | 14.4737i | −0.484886 | + | 0.484886i | ||||
\(892\) | − | 9.22256i | − | 0.308794i | ||||||
\(893\) | 13.8084i | 0.462080i | ||||||||
\(894\) | −32.4810 | + | 32.4810i | −1.08633 | + | 1.08633i | ||||
\(895\) | −0.618678 | + | 0.618678i | −0.0206801 | + | 0.0206801i | ||||
\(896\) | 7.41288 | + | 7.41288i | 0.247647 | + | 0.247647i | ||||
\(897\) | −85.8376 | −2.86603 | ||||||||
\(898\) | −25.0609 | − | 25.0609i | −0.836294 | − | 0.836294i | ||||
\(899\) | − | 13.0915i | − | 0.436627i | ||||||
\(900\) | −26.0574 | −0.868579 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −31.6459 | −1.05369 | ||||||||
\(903\) | 21.2986i | 0.708773i | ||||||||
\(904\) | 3.16286 | + | 3.16286i | 0.105195 | + | 0.105195i | ||||
\(905\) | −3.02734 | −0.100632 | ||||||||
\(906\) | −4.06178 | − | 4.06178i | −0.134944 | − | 0.134944i | ||||
\(907\) | 7.36370 | − | 7.36370i | 0.244508 | − | 0.244508i | −0.574204 | − | 0.818712i | \(-0.694689\pi\) |
0.818712 | + | 0.574204i | \(0.194689\pi\) | |||||||
\(908\) | 23.8717 | − | 23.8717i | 0.792211 | − | 0.792211i | ||||
\(909\) | 26.5449i | 0.880438i | ||||||||
\(910\) | 1.58853i | 0.0526591i | ||||||||
\(911\) | 31.3052 | − | 31.3052i | 1.03719 | − | 1.03719i | 0.0379051 | − | 0.999281i | \(-0.487932\pi\) |
0.999281 | − | 0.0379051i | \(-0.0120685\pi\) | |||||||
\(912\) | −15.8721 | + | 15.8721i | −0.525578 | + | 0.525578i | ||||
\(913\) | −4.63721 | − | 4.63721i | −0.153469 | − | 0.153469i | ||||
\(914\) | −3.96141 | −0.131032 | ||||||||
\(915\) | −0.264909 | − | 0.264909i | −0.00875761 | − | 0.00875761i | ||||
\(916\) | − | 5.66819i | − | 0.187282i | ||||||
\(917\) | 3.05375 | 0.100844 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −31.0615 | −1.02462 | −0.512312 | − | 0.858799i | \(-0.671211\pi\) | ||||
−0.512312 | + | 0.858799i | \(0.671211\pi\) | |||||||
\(920\) | − | 0.786112i | − | 0.0259173i | ||||||
\(921\) | 10.3507 | + | 10.3507i | 0.341068 | + | 0.341068i | ||||
\(922\) | −41.1729 | −1.35596 | ||||||||
\(923\) | −0.550621 | − | 0.550621i | −0.0181239 | − | 0.0181239i | ||||
\(924\) | 11.3247 | − | 11.3247i | 0.372554 | − | 0.372554i | ||||
\(925\) | 18.5039 | − | 18.5039i | 0.608405 | − | 0.608405i | ||||
\(926\) | − | 26.6040i | − | 0.874262i | ||||||
\(927\) | − | 37.0479i | − | 1.21681i | ||||||
\(928\) | 17.1418 | − | 17.1418i | 0.562707 | − | 0.562707i | ||||
\(929\) | −15.8370 | + | 15.8370i | −0.519596 | + | 0.519596i | −0.917449 | − | 0.397853i | \(-0.869755\pi\) |
0.397853 | + | 0.917449i | \(0.369755\pi\) | |||||||
\(930\) | −1.55750 | − | 1.55750i | −0.0510725 | − | 0.0510725i | ||||
\(931\) | −8.74422 | −0.286580 | ||||||||
\(932\) | 31.5804 | + | 31.5804i | 1.03445 | + | 1.03445i | ||||
\(933\) | − | 0.305407i | − | 0.00999859i | ||||||
\(934\) | 55.7948 | 1.82566 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 13.7219 | 0.448515 | ||||||||
\(937\) | − | 58.1661i | − | 1.90020i | −0.311939 | − | 0.950102i | \(-0.600978\pi\) | ||
0.311939 | − | 0.950102i | \(-0.399022\pi\) | |||||||
\(938\) | 29.7741 | + | 29.7741i | 0.972160 | + | 0.972160i | ||||
\(939\) | −26.3063 | −0.858475 | ||||||||
\(940\) | −0.960057 | − | 0.960057i | −0.0313136 | − | 0.0313136i | ||||
\(941\) | −7.38202 | + | 7.38202i | −0.240647 | + | 0.240647i | −0.817118 | − | 0.576471i | \(-0.804429\pi\) |
0.576471 | + | 0.817118i | \(0.304429\pi\) | |||||||
\(942\) | −50.7914 | + | 50.7914i | −1.65487 | + | 1.65487i | ||||
\(943\) | 46.3141i | 1.50819i | ||||||||
\(944\) | 14.8247i | 0.482503i | ||||||||
\(945\) | −0.136142 | + | 0.136142i | −0.00442869 | + | 0.00442869i | ||||
\(946\) | 19.6599 | − | 19.6599i | 0.639200 | − | 0.639200i | ||||
\(947\) | −2.85929 | − | 2.85929i | −0.0929144 | − | 0.0929144i | 0.659122 | − | 0.752036i | \(-0.270928\pi\) |
−0.752036 | + | 0.659122i | \(0.770928\pi\) | |||||||
\(948\) | 16.0915 | 0.522628 | ||||||||
\(949\) | 38.1668 | + | 38.1668i | 1.23895 | + | 1.23895i | ||||
\(950\) | 17.6091i | 0.571313i | ||||||||
\(951\) | 70.3961 | 2.28275 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.37639 | 0.141765 | 0.0708826 | − | 0.997485i | \(-0.477418\pi\) | ||||
0.0708826 | + | 0.997485i | \(0.477418\pi\) | |||||||
\(954\) | 5.27631i | 0.170827i | ||||||||
\(955\) | −1.20730 | − | 1.20730i | −0.0390674 | − | 0.0390674i | ||||
\(956\) | −19.1257 | −0.618568 | ||||||||
\(957\) | 16.4588 | + | 16.4588i | 0.532039 | + | 0.532039i | ||||
\(958\) | 50.8924 | − | 50.8924i | 1.64426 | − | 1.64426i | ||||
\(959\) | 13.6758 | − | 13.6758i | 0.441614 | − | 0.441614i | ||||
\(960\) | − | 1.19759i | − | 0.0386519i | ||||||
\(961\) | − | 16.2736i | − | 0.524956i | ||||||
\(962\) | 31.9058 | − | 31.9058i | 1.02868 | − | 1.02868i | ||||
\(963\) | −29.0484 | + | 29.0484i | −0.936071 | + | 0.936071i | ||||
\(964\) | 17.5689 | + | 17.5689i | 0.565856 | + | 0.565856i | ||||
\(965\) | 1.98183 | 0.0637974 | ||||||||
\(966\) | −38.2092 | − | 38.2092i | −1.22936 | − | 1.22936i | ||||
\(967\) | − | 24.4371i | − | 0.785843i | −0.919572 | − | 0.392921i | \(-0.871464\pi\) | ||
0.919572 | − | 0.392921i | \(-0.128536\pi\) | |||||||
\(968\) | −3.28817 | −0.105686 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.53714 | −0.0814627 | ||||||||
\(971\) | − | 20.5253i | − | 0.658688i | −0.944210 | − | 0.329344i | \(-0.893172\pi\) | ||
0.944210 | − | 0.329344i | \(-0.106828\pi\) | |||||||
\(972\) | 24.2238 | + | 24.2238i | 0.776979 | + | 0.776979i | ||||
\(973\) | 8.01960 | 0.257097 | ||||||||
\(974\) | 31.0316 | + | 31.0316i | 0.994318 | + | 0.994318i | ||||
\(975\) | 40.8284 | − | 40.8284i | 1.30756 | − | 1.30756i | ||||
\(976\) | −4.09140 | + | 4.09140i | −0.130962 | + | 0.130962i | ||||
\(977\) | 28.3073i | 0.905630i | 0.891605 | + | 0.452815i | \(0.149580\pi\) | ||||
−0.891605 | + | 0.452815i | \(0.850420\pi\) | |||||||
\(978\) | 31.1908i | 0.997371i | ||||||||
\(979\) | −28.7548 | + | 28.7548i | −0.919009 | + | 0.919009i | ||||
\(980\) | 0.607960 | − | 0.607960i | 0.0194206 | − | 0.0194206i | ||||
\(981\) | −15.9471 | − | 15.9471i | −0.509152 | − | 0.509152i | ||||
\(982\) | 58.9992 | 1.88274 | ||||||||
\(983\) | 18.8615 | + | 18.8615i | 0.601588 | + | 0.601588i | 0.940734 | − | 0.339146i | \(-0.110138\pi\) |
−0.339146 | + | 0.940734i | \(0.610138\pi\) | |||||||
\(984\) | − | 13.9145i | − | 0.443577i | ||||||
\(985\) | −2.44118 | −0.0777824 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 28.5030 | 0.907260 | ||||||||
\(988\) | 13.1702i | 0.419001i | ||||||||
\(989\) | −28.7725 | − | 28.7725i | −0.914913 | − | 0.914913i | ||||
\(990\) | 2.08378 | 0.0662268 | ||||||||
\(991\) | 24.6679 | + | 24.6679i | 0.783602 | + | 0.783602i | 0.980437 | − | 0.196835i | \(-0.0630662\pi\) |
−0.196835 | + | 0.980437i | \(0.563066\pi\) | |||||||
\(992\) | −19.2825 | + | 19.2825i | −0.612218 | + | 0.612218i | ||||
\(993\) | 15.7173 | − | 15.7173i | 0.498773 | − | 0.498773i | ||||
\(994\) | − | 0.490200i | − | 0.0155482i | ||||||
\(995\) | 2.67467i | 0.0847927i | ||||||||
\(996\) | −6.67615 | + | 6.67615i | −0.211542 | + | 0.211542i | ||||
\(997\) | 32.0436 | − | 32.0436i | 1.01483 | − | 1.01483i | 0.0149416 | − | 0.999888i | \(-0.495244\pi\) |
0.999888 | − | 0.0149416i | \(-0.00475622\pi\) | |||||||
\(998\) | −21.4370 | − | 21.4370i | −0.678575 | − | 0.678575i | ||||
\(999\) | 5.46884 | 0.173027 |
(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 | 289.2.c.d.251.5 | 12 | ||
17.2 | even | 8 | 289.2.a.d.1.1 | ✓ | 3 | ||
17.3 | odd | 16 | 289.2.d.f.134.5 | 24 | |||
17.4 | even | 4 | inner | 289.2.c.d.38.1 | 12 | ||
17.5 | odd | 16 | 289.2.d.f.155.2 | 24 | |||
17.6 | odd | 16 | 289.2.d.f.179.1 | 24 | |||
17.7 | odd | 16 | 289.2.d.f.110.5 | 24 | |||
17.8 | even | 8 | 289.2.b.d.288.6 | 6 | |||
17.9 | even | 8 | 289.2.b.d.288.5 | 6 | |||
17.10 | odd | 16 | 289.2.d.f.110.6 | 24 | |||
17.11 | odd | 16 | 289.2.d.f.179.2 | 24 | |||
17.12 | odd | 16 | 289.2.d.f.155.1 | 24 | |||
17.13 | even | 4 | inner | 289.2.c.d.38.2 | 12 | ||
17.14 | odd | 16 | 289.2.d.f.134.6 | 24 | |||
17.15 | even | 8 | 289.2.a.e.1.1 | yes | 3 | ||
17.16 | even | 2 | inner | 289.2.c.d.251.6 | 12 | ||
51.2 | odd | 8 | 2601.2.a.x.1.3 | 3 | |||
51.32 | odd | 8 | 2601.2.a.w.1.3 | 3 | |||
68.15 | odd | 8 | 4624.2.a.bd.1.1 | 3 | |||
68.19 | odd | 8 | 4624.2.a.bg.1.3 | 3 | |||
85.19 | even | 8 | 7225.2.a.t.1.3 | 3 | |||
85.49 | even | 8 | 7225.2.a.s.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.2.a.d.1.1 | ✓ | 3 | 17.2 | even | 8 | ||
289.2.a.e.1.1 | yes | 3 | 17.15 | even | 8 | ||
289.2.b.d.288.5 | 6 | 17.9 | even | 8 | |||
289.2.b.d.288.6 | 6 | 17.8 | even | 8 | |||
289.2.c.d.38.1 | 12 | 17.4 | even | 4 | inner | ||
289.2.c.d.38.2 | 12 | 17.13 | even | 4 | inner | ||
289.2.c.d.251.5 | 12 | 1.1 | even | 1 | trivial | ||
289.2.c.d.251.6 | 12 | 17.16 | even | 2 | inner | ||
289.2.d.f.110.5 | 24 | 17.7 | odd | 16 | |||
289.2.d.f.110.6 | 24 | 17.10 | odd | 16 | |||
289.2.d.f.134.5 | 24 | 17.3 | odd | 16 | |||
289.2.d.f.134.6 | 24 | 17.14 | odd | 16 | |||
289.2.d.f.155.1 | 24 | 17.12 | odd | 16 | |||
289.2.d.f.155.2 | 24 | 17.5 | odd | 16 | |||
289.2.d.f.179.1 | 24 | 17.6 | odd | 16 | |||
289.2.d.f.179.2 | 24 | 17.11 | odd | 16 | |||
2601.2.a.w.1.3 | 3 | 51.32 | odd | 8 | |||
2601.2.a.x.1.3 | 3 | 51.2 | odd | 8 | |||
4624.2.a.bd.1.1 | 3 | 68.15 | odd | 8 | |||
4624.2.a.bg.1.3 | 3 | 68.19 | odd | 8 | |||
7225.2.a.s.1.3 | 3 | 85.49 | even | 8 | |||
7225.2.a.t.1.3 | 3 | 85.19 | even | 8 |