Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,3,Mod(7,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([8, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.k (of order \(12\), degree \(4\), 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: | \(1.22616118962\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 22.2 | ||
Character | \(\chi\) | \(=\) | 45.22 |
Dual form | 45.3.k.a.43.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.644680 | + | 2.40598i | −0.322340 | + | 1.20299i | 0.594619 | + | 0.804008i | \(0.297303\pi\) |
−0.916959 | + | 0.398981i | \(0.869364\pi\) | |||||||
\(3\) | −2.98224 | + | 0.325974i | −0.994079 | + | 0.108658i | ||||
\(4\) | −1.90902 | − | 1.10217i | −0.477254 | − | 0.275543i | ||||
\(5\) | −4.49898 | + | 2.18155i | −0.899796 | + | 0.436311i | ||||
\(6\) | 1.13830 | − | 7.38535i | 0.189717 | − | 1.23089i | ||||
\(7\) | 0.0176356 | − | 0.0658171i | 0.00251938 | − | 0.00940244i | −0.964655 | − | 0.263517i | \(-0.915117\pi\) |
0.967174 | + | 0.254115i | \(0.0817841\pi\) | |||||||
\(8\) | −3.16269 | + | 3.16269i | −0.395336 | + | 0.395336i | ||||
\(9\) | 8.78748 | − | 1.94426i | 0.976387 | − | 0.216029i | ||||
\(10\) | −2.34837 | − | 12.2309i | −0.234837 | − | 1.22309i | ||||
\(11\) | 4.62292 | + | 8.00713i | 0.420265 | + | 0.727921i | 0.995965 | − | 0.0897404i | \(-0.0286037\pi\) |
−0.575700 | + | 0.817661i | \(0.695270\pi\) | |||||||
\(12\) | 6.05242 | + | 2.66465i | 0.504368 | + | 0.222054i | ||||
\(13\) | 3.38696 | + | 12.6403i | 0.260535 | + | 0.972331i | 0.964927 | + | 0.262519i | \(0.0845534\pi\) |
−0.704391 | + | 0.709812i | \(0.748780\pi\) | |||||||
\(14\) | 0.146985 | + | 0.0848619i | 0.0104989 | + | 0.00606156i | ||||
\(15\) | 12.7059 | − | 7.97246i | 0.847060 | − | 0.531498i | ||||
\(16\) | −9.97912 | − | 17.2843i | −0.623695 | − | 1.08027i | ||||
\(17\) | 13.6029 | + | 13.6029i | 0.800170 | + | 0.800170i | 0.983122 | − | 0.182952i | \(-0.0585652\pi\) |
−0.182952 | + | 0.983122i | \(0.558565\pi\) | |||||||
\(18\) | −0.987258 | + | 22.3959i | −0.0548477 | + | 1.24422i | ||||
\(19\) | 5.80704i | 0.305634i | 0.988255 | + | 0.152817i | \(0.0488345\pi\) | ||||
−0.988255 | + | 0.152817i | \(0.951166\pi\) | |||||||
\(20\) | 10.9931 | + | 0.794023i | 0.549654 | + | 0.0397011i | ||||
\(21\) | −0.0311390 | + | 0.202031i | −0.00148281 | + | 0.00962052i | ||||
\(22\) | −22.2453 | + | 5.96060i | −1.01115 | + | 0.270936i | ||||
\(23\) | −11.7365 | − | 43.8013i | −0.510283 | − | 1.90440i | −0.417390 | − | 0.908728i | \(-0.637055\pi\) |
−0.0928936 | − | 0.995676i | \(-0.529612\pi\) | |||||||
\(24\) | 8.40093 | − | 10.4628i | 0.350039 | − | 0.435952i | ||||
\(25\) | 15.4816 | − | 19.6295i | 0.619266 | − | 0.785182i | ||||
\(26\) | −32.5958 | −1.25368 | ||||||||
\(27\) | −25.5726 | + | 8.66274i | −0.947133 | + | 0.320842i | ||||
\(28\) | −0.106208 | + | 0.106208i | −0.00379316 | + | 0.00379316i | ||||
\(29\) | 6.37222 | − | 3.67900i | 0.219732 | − | 0.126862i | −0.386094 | − | 0.922459i | \(-0.626176\pi\) |
0.605826 | + | 0.795597i | \(0.292843\pi\) | |||||||
\(30\) | 10.9903 | + | 35.7098i | 0.366345 | + | 1.19033i | ||||
\(31\) | −8.35363 | + | 14.4689i | −0.269472 | + | 0.466739i | −0.968726 | − | 0.248135i | \(-0.920183\pi\) |
0.699254 | + | 0.714874i | \(0.253516\pi\) | |||||||
\(32\) | 30.7378 | − | 8.23618i | 0.960558 | − | 0.257381i | ||||
\(33\) | −16.3967 | − | 22.3722i | −0.496871 | − | 0.677946i | ||||
\(34\) | −41.4978 | + | 23.9587i | −1.22052 | + | 0.704669i | ||||
\(35\) | 0.0642412 | + | 0.334583i | 0.00183546 | + | 0.00955951i | ||||
\(36\) | −18.9184 | − | 5.97368i | −0.525510 | − | 0.165936i | ||||
\(37\) | 36.0680 | + | 36.0680i | 0.974810 | + | 0.974810i | 0.999690 | − | 0.0248806i | \(-0.00792055\pi\) |
−0.0248806 | + | 0.999690i | \(0.507921\pi\) | |||||||
\(38\) | −13.9716 | − | 3.74368i | −0.367674 | − | 0.0985180i | ||||
\(39\) | −14.2211 | − | 36.5923i | −0.364644 | − | 0.938265i | ||||
\(40\) | 7.32929 | − | 21.1284i | 0.183232 | − | 0.528211i | ||||
\(41\) | −31.1567 | + | 53.9649i | −0.759919 | + | 1.31622i | 0.182973 | + | 0.983118i | \(0.441428\pi\) |
−0.942892 | + | 0.333100i | \(0.891905\pi\) | |||||||
\(42\) | −0.466007 | − | 0.205165i | −0.0110954 | − | 0.00488488i | ||||
\(43\) | 9.70259 | + | 2.59980i | 0.225642 | + | 0.0604605i | 0.369868 | − | 0.929084i | \(-0.379403\pi\) |
−0.144227 | + | 0.989545i | \(0.546069\pi\) | |||||||
\(44\) | − | 20.3810i | − | 0.463204i | ||||||
\(45\) | −35.2932 | + | 27.9176i | −0.784293 | + | 0.620390i | ||||
\(46\) | 112.951 | 2.45546 | ||||||||
\(47\) | 11.9633 | − | 44.6476i | 0.254538 | − | 0.949948i | −0.713809 | − | 0.700340i | \(-0.753032\pi\) |
0.968347 | − | 0.249608i | \(-0.0803017\pi\) | |||||||
\(48\) | 35.3944 | + | 48.2931i | 0.737382 | + | 1.00611i | ||||
\(49\) | 42.4312 | + | 24.4977i | 0.865943 | + | 0.499953i | ||||
\(50\) | 37.2475 | + | 49.9033i | 0.744951 | + | 0.998065i | ||||
\(51\) | −45.0012 | − | 36.1329i | −0.882377 | − | 0.708488i | ||||
\(52\) | 7.46602 | − | 27.8636i | 0.143577 | − | 0.535838i | ||||
\(53\) | 28.0258 | − | 28.0258i | 0.528789 | − | 0.528789i | −0.391423 | − | 0.920211i | \(-0.628017\pi\) |
0.920211 | + | 0.391423i | \(0.128017\pi\) | |||||||
\(54\) | −4.35625 | − | 67.1118i | −0.0806712 | − | 1.24281i | ||||
\(55\) | −38.2664 | − | 25.9388i | −0.695753 | − | 0.471614i | ||||
\(56\) | 0.152383 | + | 0.263935i | 0.00272112 | + | 0.00471312i | ||||
\(57\) | −1.89294 | − | 17.3180i | −0.0332096 | − | 0.303824i | ||||
\(58\) | 4.74356 | + | 17.7032i | 0.0817855 | + | 0.305228i | ||||
\(59\) | 16.3509 | + | 9.44022i | 0.277135 | + | 0.160004i | 0.632126 | − | 0.774866i | \(-0.282183\pi\) |
−0.354991 | + | 0.934870i | \(0.615516\pi\) | |||||||
\(60\) | −33.0428 | + | 1.21549i | −0.550713 | + | 0.0202582i | ||||
\(61\) | 2.69547 | + | 4.66870i | 0.0441881 | + | 0.0765360i | 0.887274 | − | 0.461244i | \(-0.152597\pi\) |
−0.843085 | + | 0.537780i | \(0.819263\pi\) | |||||||
\(62\) | −29.4265 | − | 29.4265i | −0.474621 | − | 0.474621i | ||||
\(63\) | 0.0270071 | − | 0.612655i | 0.000428684 | − | 0.00972468i | ||||
\(64\) | − | 0.568692i | − | 0.00888582i | ||||||
\(65\) | −42.8134 | − | 49.4796i | −0.658667 | − | 0.761225i | ||||
\(66\) | 64.3977 | − | 25.0273i | 0.975722 | − | 0.379202i | ||||
\(67\) | −47.9117 | + | 12.8379i | −0.715100 | + | 0.191610i | −0.597984 | − | 0.801508i | \(-0.704031\pi\) |
−0.117116 | + | 0.993118i | \(0.537365\pi\) | |||||||
\(68\) | −10.9754 | − | 40.9609i | −0.161403 | − | 0.602366i | ||||
\(69\) | 49.2792 | + | 126.800i | 0.714191 | + | 1.83768i | ||||
\(70\) | −0.846414 | − | 0.0611359i | −0.0120916 | − | 0.000873370i | ||||
\(71\) | 56.4200 | 0.794648 | 0.397324 | − | 0.917678i | \(-0.369939\pi\) | ||||
0.397324 | + | 0.917678i | \(0.369939\pi\) | |||||||
\(72\) | −21.6430 | + | 33.9412i | −0.300597 | + | 0.471405i | ||||
\(73\) | −54.7135 | + | 54.7135i | −0.749500 | + | 0.749500i | −0.974385 | − | 0.224885i | \(-0.927799\pi\) |
0.224885 | + | 0.974385i | \(0.427799\pi\) | |||||||
\(74\) | −110.031 | + | 63.5264i | −1.48691 | + | 0.858465i | ||||
\(75\) | −39.7712 | + | 63.5866i | −0.530283 | + | 0.847821i | ||||
\(76\) | 6.40036 | − | 11.0857i | 0.0842152 | − | 0.145865i | ||||
\(77\) | 0.608534 | − | 0.163056i | 0.00790303 | − | 0.00211761i | ||||
\(78\) | 97.2084 | − | 10.6254i | 1.24626 | − | 0.136223i | ||||
\(79\) | −40.9692 | + | 23.6536i | −0.518597 | + | 0.299412i | −0.736361 | − | 0.676589i | \(-0.763457\pi\) |
0.217763 | + | 0.976002i | \(0.430124\pi\) | |||||||
\(80\) | 82.6026 | + | 55.9919i | 1.03253 | + | 0.699899i | ||||
\(81\) | 73.4397 | − | 34.1704i | 0.906663 | − | 0.421856i | ||||
\(82\) | −109.752 | − | 109.752i | −1.33844 | − | 1.33844i | ||||
\(83\) | 60.0267 | + | 16.0841i | 0.723213 | + | 0.193784i | 0.601605 | − | 0.798794i | \(-0.294528\pi\) |
0.121608 | + | 0.992578i | \(0.461195\pi\) | |||||||
\(84\) | 0.282117 | − | 0.351360i | 0.00335854 | − | 0.00418285i | ||||
\(85\) | −90.8746 | − | 31.5237i | −1.06911 | − | 0.370867i | ||||
\(86\) | −12.5101 | + | 21.6682i | −0.145467 | + | 0.251956i | ||||
\(87\) | −17.8042 | + | 13.0488i | −0.204646 | + | 0.149987i | ||||
\(88\) | −39.9449 | − | 10.7032i | −0.453919 | − | 0.121627i | ||||
\(89\) | − | 59.1599i | − | 0.664718i | −0.943153 | − | 0.332359i | \(-0.892156\pi\) | ||
0.943153 | − | 0.332359i | \(-0.107844\pi\) | |||||||
\(90\) | −44.4163 | − | 102.913i | −0.493514 | − | 1.14347i | ||||
\(91\) | 0.891679 | 0.00979867 | ||||||||
\(92\) | −25.8713 | + | 96.5530i | −0.281210 | + | 1.04949i | ||||
\(93\) | 20.1960 | − | 45.8728i | 0.217162 | − | 0.493256i | ||||
\(94\) | 99.7085 | + | 57.5668i | 1.06073 | + | 0.612412i | ||||
\(95\) | −12.6684 | − | 26.1258i | −0.133351 | − | 0.275008i | ||||
\(96\) | −88.9828 | + | 34.5820i | −0.926904 | + | 0.360229i | ||||
\(97\) | 40.2595 | − | 150.251i | 0.415047 | − | 1.54898i | −0.369695 | − | 0.929153i | \(-0.620538\pi\) |
0.784742 | − | 0.619823i | \(-0.212796\pi\) | |||||||
\(98\) | −86.2954 | + | 86.2954i | −0.880566 | + | 0.880566i | ||||
\(99\) | 56.1918 | + | 61.3743i | 0.567594 | + | 0.619943i | ||||
\(100\) | −51.1898 | + | 20.4097i | −0.511898 | + | 0.204097i | ||||
\(101\) | 27.6053 | + | 47.8137i | 0.273319 | + | 0.473403i | 0.969710 | − | 0.244260i | \(-0.0785451\pi\) |
−0.696390 | + | 0.717663i | \(0.745212\pi\) | |||||||
\(102\) | 115.946 | − | 84.9779i | 1.13673 | − | 0.833116i | ||||
\(103\) | −23.6658 | − | 88.3218i | −0.229765 | − | 0.857493i | −0.980439 | − | 0.196821i | \(-0.936938\pi\) |
0.750675 | − | 0.660672i | \(-0.229729\pi\) | |||||||
\(104\) | −50.6892 | − | 29.2654i | −0.487397 | − | 0.281399i | ||||
\(105\) | −0.300648 | − | 0.976864i | −0.00286331 | − | 0.00930347i | ||||
\(106\) | 49.3618 | + | 85.4971i | 0.465677 | + | 0.806576i | ||||
\(107\) | −14.6336 | − | 14.6336i | −0.136762 | − | 0.136762i | 0.635411 | − | 0.772174i | \(-0.280831\pi\) |
−0.772174 | + | 0.635411i | \(0.780831\pi\) | |||||||
\(108\) | 58.3663 | + | 11.6480i | 0.540429 | + | 0.107852i | ||||
\(109\) | − | 112.055i | − | 1.02803i | −0.857781 | − | 0.514015i | \(-0.828157\pi\) | ||
0.857781 | − | 0.514015i | \(-0.171843\pi\) | |||||||
\(110\) | 87.0777 | − | 75.3459i | 0.791615 | − | 0.684963i | ||||
\(111\) | −119.320 | − | 95.8060i | −1.07496 | − | 0.863117i | ||||
\(112\) | −1.31359 | + | 0.351976i | −0.0117285 | + | 0.00314264i | ||||
\(113\) | 9.59771 | + | 35.8191i | 0.0849355 | + | 0.316984i | 0.995302 | − | 0.0968194i | \(-0.0308669\pi\) |
−0.910366 | + | 0.413803i | \(0.864200\pi\) | |||||||
\(114\) | 42.8870 | + | 6.61017i | 0.376202 | + | 0.0579840i | ||||
\(115\) | 148.357 | + | 171.457i | 1.29006 | + | 1.49093i | ||||
\(116\) | −16.2196 | −0.139824 | ||||||||
\(117\) | 54.3389 | + | 104.491i | 0.464435 | + | 0.893088i | ||||
\(118\) | −33.2541 | + | 33.2541i | −0.281814 | + | 0.281814i | ||||
\(119\) | 1.13520 | − | 0.655407i | 0.00953948 | − | 0.00550762i | ||||
\(120\) | −14.9704 | + | 65.3992i | −0.124753 | + | 0.544993i | ||||
\(121\) | 17.7573 | − | 30.7565i | 0.146754 | − | 0.254186i | ||||
\(122\) | −12.9705 | + | 3.47543i | −0.106316 | + | 0.0284872i | ||||
\(123\) | 75.3254 | − | 171.092i | 0.612402 | − | 1.39100i | ||||
\(124\) | 31.8944 | − | 18.4143i | 0.257213 | − | 0.148502i | ||||
\(125\) | −26.8287 | + | 122.087i | −0.214629 | + | 0.976696i | ||||
\(126\) | 1.45662 | + | 0.459945i | 0.0115605 | + | 0.00365035i | ||||
\(127\) | 151.793 | + | 151.793i | 1.19522 | + | 1.19522i | 0.975580 | + | 0.219643i | \(0.0704892\pi\) |
0.219643 | + | 0.975580i | \(0.429511\pi\) | |||||||
\(128\) | 124.320 | + | 33.3113i | 0.971247 | + | 0.260245i | ||||
\(129\) | −29.7829 | − | 4.59044i | −0.230875 | − | 0.0355848i | ||||
\(130\) | 146.648 | − | 71.1095i | 1.12806 | − | 0.546996i | ||||
\(131\) | −0.751448 | + | 1.30155i | −0.00573624 | + | 0.00993547i | −0.868879 | − | 0.495024i | \(-0.835159\pi\) |
0.863143 | + | 0.504960i | \(0.168493\pi\) | |||||||
\(132\) | 6.64367 | + | 60.7809i | 0.0503308 | + | 0.460462i | ||||
\(133\) | 0.382203 | + | 0.102411i | 0.00287370 | + | 0.000770006i | ||||
\(134\) | − | 123.551i | − | 0.922021i | ||||||
\(135\) | 96.1523 | − | 94.7615i | 0.712239 | − | 0.701937i | ||||
\(136\) | −86.0434 | −0.632672 | ||||||||
\(137\) | −18.0785 | + | 67.4699i | −0.131960 | + | 0.492481i | −0.999992 | − | 0.00402717i | \(-0.998718\pi\) |
0.868032 | + | 0.496508i | \(0.165385\pi\) | |||||||
\(138\) | −336.847 | + | 36.8192i | −2.44092 | + | 0.266805i | ||||
\(139\) | −106.332 | − | 61.3909i | −0.764980 | − | 0.441661i | 0.0661012 | − | 0.997813i | \(-0.478944\pi\) |
−0.831081 | + | 0.556152i | \(0.812277\pi\) | |||||||
\(140\) | 0.246130 | − | 0.709529i | 0.00175807 | − | 0.00506806i | ||||
\(141\) | −21.1234 | + | 137.049i | −0.149811 | + | 0.971981i | ||||
\(142\) | −36.3728 | + | 135.745i | −0.256147 | + | 0.955953i | ||||
\(143\) | −85.5549 | + | 85.5549i | −0.598286 | + | 0.598286i | ||||
\(144\) | −121.297 | − | 132.484i | −0.842338 | − | 0.920027i | ||||
\(145\) | −20.6426 | + | 30.4531i | −0.142362 | + | 0.210021i | ||||
\(146\) | −96.3668 | − | 166.912i | −0.660047 | − | 1.14323i | ||||
\(147\) | −134.526 | − | 59.2264i | −0.915140 | − | 0.402901i | ||||
\(148\) | −29.1013 | − | 108.607i | −0.196630 | − | 0.733834i | ||||
\(149\) | −23.0090 | − | 13.2842i | −0.154423 | − | 0.0891560i | 0.420797 | − | 0.907155i | \(-0.361750\pi\) |
−0.575220 | + | 0.817999i | \(0.695084\pi\) | |||||||
\(150\) | −127.348 | − | 136.682i | −0.848988 | − | 0.911211i | ||||
\(151\) | −49.2414 | − | 85.2887i | −0.326102 | − | 0.564826i | 0.655633 | − | 0.755080i | \(-0.272402\pi\) |
−0.981735 | + | 0.190254i | \(0.939069\pi\) | |||||||
\(152\) | −18.3659 | − | 18.3659i | −0.120828 | − | 0.120828i | ||||
\(153\) | 145.983 | + | 93.0876i | 0.954136 | + | 0.608415i | ||||
\(154\) | 1.56924i | 0.0101899i | ||||||||
\(155\) | 6.01810 | − | 83.3193i | 0.0388264 | − | 0.537544i | ||||
\(156\) | −13.1826 | + | 85.5295i | −0.0845042 | + | 0.548266i | ||||
\(157\) | 166.811 | − | 44.6968i | 1.06249 | − | 0.284693i | 0.315086 | − | 0.949063i | \(-0.397967\pi\) |
0.747404 | + | 0.664370i | \(0.231300\pi\) | |||||||
\(158\) | −30.4980 | − | 113.820i | −0.193025 | − | 0.720379i | ||||
\(159\) | −74.4439 | + | 92.7152i | −0.468201 | + | 0.583115i | ||||
\(160\) | −120.321 | + | 104.111i | −0.752008 | + | 0.650692i | ||||
\(161\) | −3.08985 | −0.0191916 | ||||||||
\(162\) | 34.8680 | + | 198.723i | 0.215235 | + | 1.22669i | ||||
\(163\) | −65.0824 | + | 65.0824i | −0.399278 | + | 0.399278i | −0.877978 | − | 0.478700i | \(-0.841108\pi\) |
0.478700 | + | 0.877978i | \(0.341108\pi\) | |||||||
\(164\) | 118.957 | − | 68.6800i | 0.725349 | − | 0.418780i | ||||
\(165\) | 122.575 | + | 64.8817i | 0.742878 | + | 0.393222i | ||||
\(166\) | −77.3960 | + | 134.054i | −0.466241 | + | 0.807553i | ||||
\(167\) | 192.960 | − | 51.7034i | 1.15545 | − | 0.309601i | 0.370301 | − | 0.928912i | \(-0.379255\pi\) |
0.785146 | + | 0.619311i | \(0.212588\pi\) | |||||||
\(168\) | −0.540478 | − | 0.737444i | −0.00321713 | − | 0.00438955i | ||||
\(169\) | −1.94752 | + | 1.12440i | −0.0115238 | + | 0.00665325i | ||||
\(170\) | 134.430 | − | 198.320i | 0.790767 | − | 1.16659i | ||||
\(171\) | 11.2904 | + | 51.0293i | 0.0660258 | + | 0.298417i | ||||
\(172\) | −15.6570 | − | 15.6570i | −0.0910290 | − | 0.0910290i | ||||
\(173\) | −33.4003 | − | 8.94958i | −0.193065 | − | 0.0517317i | 0.160991 | − | 0.986956i | \(-0.448531\pi\) |
−0.354056 | + | 0.935224i | \(0.615198\pi\) | |||||||
\(174\) | −19.9172 | − | 51.2489i | −0.114467 | − | 0.294534i | ||||
\(175\) | −1.01893 | − | 1.36514i | −0.00582246 | − | 0.00780077i | ||||
\(176\) | 92.2653 | − | 159.808i | 0.524235 | − | 0.908001i | ||||
\(177\) | −51.8397 | − | 22.8230i | −0.292879 | − | 0.128944i | ||||
\(178\) | 142.337 | + | 38.1392i | 0.799648 | + | 0.214265i | ||||
\(179\) | 185.962i | 1.03890i | 0.854502 | + | 0.519448i | \(0.173862\pi\) | ||||
−0.854502 | + | 0.519448i | \(0.826138\pi\) | |||||||
\(180\) | 98.1452 | − | 14.3960i | 0.545251 | − | 0.0799776i | ||||
\(181\) | −97.7851 | −0.540249 | −0.270125 | − | 0.962825i | \(-0.587065\pi\) | ||||
−0.270125 | + | 0.962825i | \(0.587065\pi\) | |||||||
\(182\) | −0.574847 | + | 2.14536i | −0.00315850 | + | 0.0117877i | ||||
\(183\) | −9.56041 | − | 13.0445i | −0.0522427 | − | 0.0712814i | ||||
\(184\) | 175.649 | + | 101.411i | 0.954613 | + | 0.551146i | ||||
\(185\) | −240.953 | − | 83.5848i | −1.30245 | − | 0.451810i | ||||
\(186\) | 97.3490 | + | 78.1645i | 0.523382 | + | 0.420239i | ||||
\(187\) | −46.0350 | + | 171.805i | −0.246177 | + | 0.918744i | ||||
\(188\) | −72.0473 | + | 72.0473i | −0.383231 | + | 0.383231i | ||||
\(189\) | 0.119168 | + | 1.83589i | 0.000630518 | + | 0.00971368i | ||||
\(190\) | 71.0251 | − | 13.6371i | 0.373816 | − | 0.0717741i | ||||
\(191\) | −68.2090 | − | 118.141i | −0.357115 | − | 0.618542i | 0.630362 | − | 0.776301i | \(-0.282906\pi\) |
−0.987478 | + | 0.157759i | \(0.949573\pi\) | |||||||
\(192\) | 0.185379 | + | 1.69598i | 0.000965515 | + | 0.00883321i | ||||
\(193\) | 23.9050 | + | 89.2148i | 0.123860 | + | 0.462253i | 0.999796 | − | 0.0201740i | \(-0.00642202\pi\) |
−0.875936 | + | 0.482427i | \(0.839755\pi\) | |||||||
\(194\) | 335.545 | + | 193.727i | 1.72961 | + | 0.998594i | ||||
\(195\) | 143.809 | + | 133.604i | 0.737481 | + | 0.685149i | ||||
\(196\) | −54.0013 | − | 93.5329i | −0.275517 | − | 0.477209i | ||||
\(197\) | −170.623 | − | 170.623i | −0.866107 | − | 0.866107i | 0.125932 | − | 0.992039i | \(-0.459808\pi\) |
−0.992039 | + | 0.125932i | \(0.959808\pi\) | |||||||
\(198\) | −183.891 | + | 95.6294i | −0.928742 | + | 0.482977i | ||||
\(199\) | − | 36.4196i | − | 0.183013i | −0.995804 | − | 0.0915066i | \(-0.970832\pi\) | ||
0.995804 | − | 0.0915066i | \(-0.0291683\pi\) | |||||||
\(200\) | 13.1185 | + | 111.046i | 0.0655925 | + | 0.555229i | ||||
\(201\) | 138.699 | − | 53.9036i | 0.690046 | − | 0.268177i | ||||
\(202\) | −132.835 | + | 35.5931i | −0.657601 | + | 0.176204i | ||||
\(203\) | −0.129763 | − | 0.484283i | −0.000639227 | − | 0.00238563i | ||||
\(204\) | 46.0835 | + | 118.577i | 0.225900 | + | 0.581261i | ||||
\(205\) | 22.4458 | − | 310.757i | 0.109492 | − | 1.51589i | ||||
\(206\) | 227.757 | 1.10562 | ||||||||
\(207\) | −188.296 | − | 362.084i | −0.909641 | − | 1.74920i | ||||
\(208\) | 184.681 | − | 184.681i | 0.887887 | − | 0.887887i | ||||
\(209\) | −46.4977 | + | 26.8455i | −0.222477 | + | 0.128447i | ||||
\(210\) | 2.54414 | − | 0.0935869i | 0.0121149 | − | 0.000445652i | ||||
\(211\) | 96.8033 | − | 167.668i | 0.458784 | − | 0.794636i | −0.540113 | − | 0.841592i | \(-0.681619\pi\) |
0.998897 | + | 0.0469559i | \(0.0149520\pi\) | |||||||
\(212\) | −84.3909 | + | 22.6125i | −0.398070 | + | 0.106663i | ||||
\(213\) | −168.258 | + | 18.3914i | −0.789943 | + | 0.0863448i | ||||
\(214\) | 44.6420 | − | 25.7741i | 0.208607 | − | 0.120440i | ||||
\(215\) | −49.3234 | + | 9.47028i | −0.229411 | + | 0.0440478i | ||||
\(216\) | 53.4805 | − | 108.276i | 0.247595 | − | 0.501276i | ||||
\(217\) | 0.804980 | + | 0.804980i | 0.00370959 | + | 0.00370959i | ||||
\(218\) | 269.603 | + | 72.2398i | 1.23671 | + | 0.331375i | ||||
\(219\) | 145.334 | − | 181.004i | 0.663623 | − | 0.826502i | ||||
\(220\) | 44.4622 | + | 91.6936i | 0.202101 | + | 0.416789i | ||||
\(221\) | −125.872 | + | 218.017i | −0.569558 | + | 0.986503i | ||||
\(222\) | 307.431 | − | 225.318i | 1.38482 | − | 1.01495i | ||||
\(223\) | 92.4808 | + | 24.7802i | 0.414712 | + | 0.111122i | 0.460141 | − | 0.887846i | \(-0.347799\pi\) |
−0.0454290 | + | 0.998968i | \(0.514465\pi\) | |||||||
\(224\) | − | 2.16833i | − | 0.00968002i | ||||||
\(225\) | 97.8797 | − | 202.595i | 0.435021 | − | 0.900420i | ||||
\(226\) | −92.3675 | −0.408706 | ||||||||
\(227\) | −85.2664 | + | 318.219i | −0.375623 | + | 1.40184i | 0.476810 | + | 0.879007i | \(0.341793\pi\) |
−0.852433 | + | 0.522837i | \(0.824874\pi\) | |||||||
\(228\) | −15.4737 | + | 35.1467i | −0.0678672 | + | 0.154152i | ||||
\(229\) | −360.256 | − | 207.994i | −1.57317 | − | 0.908269i | −0.995777 | − | 0.0918017i | \(-0.970737\pi\) |
−0.577391 | − | 0.816468i | \(-0.695929\pi\) | |||||||
\(230\) | −508.165 | + | 246.409i | −2.20941 | + | 1.07134i | ||||
\(231\) | −1.76164 | + | 0.684638i | −0.00762615 | + | 0.00296380i | ||||
\(232\) | −8.51781 | + | 31.7889i | −0.0367147 | + | 0.137021i | ||||
\(233\) | −22.0213 | + | 22.0213i | −0.0945121 | + | 0.0945121i | −0.752782 | − | 0.658270i | \(-0.771289\pi\) |
0.658270 | + | 0.752782i | \(0.271289\pi\) | |||||||
\(234\) | −286.435 | + | 63.3748i | −1.22408 | + | 0.270833i | ||||
\(235\) | 43.5785 | + | 226.967i | 0.185441 | + | 0.965817i | ||||
\(236\) | −20.8095 | − | 36.0431i | −0.0881758 | − | 0.152725i | ||||
\(237\) | 114.469 | − | 83.8955i | 0.482993 | − | 0.353989i | ||||
\(238\) | 0.845055 | + | 3.15379i | 0.00355065 | + | 0.0132512i | ||||
\(239\) | 267.552 | + | 154.471i | 1.11946 | + | 0.646323i | 0.941264 | − | 0.337672i | \(-0.109639\pi\) |
0.178200 | + | 0.983994i | \(0.442973\pi\) | |||||||
\(240\) | −264.593 | − | 140.055i | −1.10247 | − | 0.583562i | ||||
\(241\) | −12.8569 | − | 22.2688i | −0.0533481 | − | 0.0924016i | 0.838118 | − | 0.545489i | \(-0.183656\pi\) |
−0.891466 | + | 0.453087i | \(0.850323\pi\) | |||||||
\(242\) | 62.5517 | + | 62.5517i | 0.258478 | + | 0.258478i | ||||
\(243\) | −207.876 | + | 125.844i | −0.855457 | + | 0.517875i | ||||
\(244\) | − | 11.8835i | − | 0.0487028i | ||||||
\(245\) | −244.340 | − | 17.6485i | −0.997307 | − | 0.0720349i | ||||
\(246\) | 363.084 | + | 291.531i | 1.47595 | + | 1.18509i | ||||
\(247\) | −73.4028 | + | 19.6682i | −0.297177 | + | 0.0796284i | ||||
\(248\) | −19.3407 | − | 72.1806i | −0.0779868 | − | 0.291051i | ||||
\(249\) | −184.257 | − | 28.3995i | −0.739987 | − | 0.114054i | ||||
\(250\) | −276.443 | − | 143.256i | −1.10577 | − | 0.573025i | ||||
\(251\) | 275.877 | 1.09911 | 0.549556 | − | 0.835457i | \(-0.314797\pi\) | ||||
0.549556 | + | 0.835457i | \(0.314797\pi\) | |||||||
\(252\) | −0.726807 | + | 1.13980i | −0.00288416 | + | 0.00452302i | ||||
\(253\) | 296.465 | − | 296.465i | 1.17180 | − | 1.17180i | ||||
\(254\) | −463.070 | + | 267.353i | −1.82311 | + | 1.05257i | ||||
\(255\) | 281.286 | + | 64.3884i | 1.10308 | + | 0.252503i | ||||
\(256\) | −159.155 | + | 275.665i | −0.621701 | + | 1.07682i | ||||
\(257\) | −6.18001 | + | 1.65593i | −0.0240467 | + | 0.00644330i | −0.270822 | − | 0.962629i | \(-0.587296\pi\) |
0.246776 | + | 0.969073i | \(0.420629\pi\) | |||||||
\(258\) | 30.2449 | − | 68.6977i | 0.117228 | − | 0.266270i | ||||
\(259\) | 3.00997 | − | 1.73781i | 0.0116215 | − | 0.00670968i | ||||
\(260\) | 27.1964 | + | 141.645i | 0.104602 | + | 0.544789i | ||||
\(261\) | 48.8428 | − | 44.7185i | 0.187137 | − | 0.171335i | ||||
\(262\) | −2.64705 | − | 2.64705i | −0.0101032 | − | 0.0101032i | ||||
\(263\) | −205.249 | − | 54.9964i | −0.780416 | − | 0.209112i | −0.153448 | − | 0.988157i | \(-0.549038\pi\) |
−0.626968 | + | 0.779045i | \(0.715704\pi\) | |||||||
\(264\) | 122.614 | + | 18.8985i | 0.464447 | + | 0.0715852i | ||||
\(265\) | −64.9477 | + | 187.227i | −0.245086 | + | 0.706518i | ||||
\(266\) | −0.492797 | + | 0.853549i | −0.00185262 | + | 0.00320883i | ||||
\(267\) | 19.2846 | + | 176.429i | 0.0722269 | + | 0.660782i | ||||
\(268\) | 105.614 | + | 28.2991i | 0.394081 | + | 0.105594i | ||||
\(269\) | − | 349.046i | − | 1.29757i | −0.760973 | − | 0.648784i | \(-0.775278\pi\) | ||
0.760973 | − | 0.648784i | \(-0.224722\pi\) | |||||||
\(270\) | 166.007 | + | 292.431i | 0.614839 | + | 1.08308i | ||||
\(271\) | −202.277 | −0.746409 | −0.373205 | − | 0.927749i | \(-0.621741\pi\) | ||||
−0.373205 | + | 0.927749i | \(0.621741\pi\) | |||||||
\(272\) | 99.3722 | − | 370.862i | 0.365339 | − | 1.36346i | ||||
\(273\) | −2.65920 | + | 0.290664i | −0.00974065 | + | 0.00106470i | ||||
\(274\) | −150.676 | − | 86.9930i | −0.549913 | − | 0.317493i | ||||
\(275\) | 228.747 | + | 33.2177i | 0.831806 | + | 0.120792i | ||||
\(276\) | 45.6806 | − | 296.377i | 0.165509 | − | 1.07383i | ||||
\(277\) | 62.8000 | − | 234.373i | 0.226715 | − | 0.846112i | −0.754995 | − | 0.655730i | \(-0.772361\pi\) |
0.981710 | − | 0.190381i | \(-0.0609725\pi\) | |||||||
\(278\) | 216.255 | − | 216.255i | 0.777897 | − | 0.777897i | ||||
\(279\) | −45.2760 | + | 143.387i | −0.162280 | + | 0.513932i | ||||
\(280\) | −1.26136 | − | 0.855006i | −0.00450484 | − | 0.00305359i | ||||
\(281\) | 140.160 | + | 242.764i | 0.498789 | + | 0.863929i | 0.999999 | − | 0.00139729i | \(-0.000444772\pi\) |
−0.501210 | + | 0.865326i | \(0.667111\pi\) | |||||||
\(282\) | −316.120 | − | 139.175i | −1.12099 | − | 0.493530i | ||||
\(283\) | 99.8610 | + | 372.686i | 0.352866 | + | 1.31691i | 0.883149 | + | 0.469092i | \(0.155419\pi\) |
−0.530283 | + | 0.847820i | \(0.677914\pi\) | |||||||
\(284\) | −107.707 | − | 62.1845i | −0.379249 | − | 0.218959i | ||||
\(285\) | 46.2964 | + | 73.7837i | 0.162444 | + | 0.258890i | ||||
\(286\) | −150.688 | − | 260.999i | −0.526880 | − | 0.912583i | ||||
\(287\) | 3.00235 | + | 3.00235i | 0.0104611 | + | 0.0104611i | ||||
\(288\) | 254.095 | − | 132.138i | 0.882274 | − | 0.458812i | ||||
\(289\) | 81.0774i | 0.280545i | ||||||||
\(290\) | −59.9617 | − | 69.2980i | −0.206764 | − | 0.238959i | ||||
\(291\) | −71.0857 | + | 461.207i | −0.244281 | + | 1.58490i | ||||
\(292\) | 164.753 | − | 44.1453i | 0.564222 | − | 0.151183i | ||||
\(293\) | −10.9337 | − | 40.8052i | −0.0373164 | − | 0.139267i | 0.944754 | − | 0.327779i | \(-0.106300\pi\) |
−0.982071 | + | 0.188512i | \(0.939633\pi\) | |||||||
\(294\) | 229.223 | − | 285.484i | 0.779672 | − | 0.971032i | ||||
\(295\) | −94.1569 | − | 6.80090i | −0.319176 | − | 0.0230539i | ||||
\(296\) | −228.143 | −0.770755 | ||||||||
\(297\) | −187.584 | − | 164.716i | −0.631595 | − | 0.554598i | ||||
\(298\) | 46.7950 | − | 46.7950i | 0.157030 | − | 0.157030i | ||||
\(299\) | 513.910 | − | 296.706i | 1.71876 | − | 0.992329i | ||||
\(300\) | 146.007 | − | 77.5531i | 0.486691 | − | 0.258510i | ||||
\(301\) | 0.342223 | − | 0.592747i | 0.00113695 | − | 0.00196926i | ||||
\(302\) | 236.948 | − | 63.4899i | 0.784595 | − | 0.210232i | ||||
\(303\) | −97.9115 | − | 133.593i | −0.323140 | − | 0.440902i | ||||
\(304\) | 100.371 | − | 57.9492i | 0.330168 | − | 0.190622i | ||||
\(305\) | −22.3119 | − | 15.1240i | −0.0731537 | − | 0.0495870i | ||||
\(306\) | −318.079 | + | 291.220i | −1.03947 | + | 0.951698i | ||||
\(307\) | −85.1111 | − | 85.1111i | −0.277235 | − | 0.277235i | 0.554769 | − | 0.832004i | \(-0.312806\pi\) |
−0.832004 | + | 0.554769i | \(0.812806\pi\) | |||||||
\(308\) | −1.34142 | − | 0.359431i | −0.00435525 | − | 0.00116699i | ||||
\(309\) | 99.3675 | + | 255.682i | 0.321578 | + | 0.827450i | ||||
\(310\) | 196.585 | + | 68.1937i | 0.634144 | + | 0.219980i | ||||
\(311\) | 227.093 | − | 393.336i | 0.730202 | − | 1.26475i | −0.226595 | − | 0.973989i | \(-0.572759\pi\) |
0.956797 | − | 0.290758i | \(-0.0939074\pi\) | |||||||
\(312\) | 160.707 | + | 70.7531i | 0.515087 | + | 0.226773i | ||||
\(313\) | −287.001 | − | 76.9018i | −0.916937 | − | 0.245693i | −0.230661 | − | 0.973034i | \(-0.574089\pi\) |
−0.686276 | + | 0.727342i | \(0.740756\pi\) | |||||||
\(314\) | 430.158i | 1.36993i | ||||||||
\(315\) | 1.21503 | + | 2.81524i | 0.00385725 | + | 0.00893726i | ||||
\(316\) | 104.281 | 0.330004 | ||||||||
\(317\) | −22.8819 | + | 85.3965i | −0.0721827 | + | 0.269389i | −0.992580 | − | 0.121596i | \(-0.961199\pi\) |
0.920397 | + | 0.390985i | \(0.127866\pi\) | |||||||
\(318\) | −175.078 | − | 238.882i | −0.550561 | − | 0.751201i | ||||
\(319\) | 58.9165 | + | 34.0155i | 0.184691 | + | 0.106632i | ||||
\(320\) | 1.24063 | + | 2.55854i | 0.00387698 | + | 0.00799542i | ||||
\(321\) | 48.4109 | + | 38.8706i | 0.150813 | + | 0.121092i | ||||
\(322\) | 1.99197 | − | 7.43412i | 0.00618623 | − | 0.0230873i | ||||
\(323\) | −78.9926 | + | 78.9926i | −0.244559 | + | 0.244559i | ||||
\(324\) | −177.859 | − | 15.7113i | −0.548948 | − | 0.0484917i | ||||
\(325\) | 300.559 | + | 129.208i | 0.924797 | + | 0.397564i | ||||
\(326\) | −114.629 | − | 198.544i | −0.351624 | − | 0.609031i | ||||
\(327\) | 36.5271 | + | 334.176i | 0.111704 | + | 1.02194i | ||||
\(328\) | −72.1354 | − | 269.213i | −0.219925 | − | 0.820771i | ||||
\(329\) | −2.72759 | − | 1.57478i | −0.00829055 | − | 0.00478655i | ||||
\(330\) | −235.125 | + | 253.084i | −0.712501 | + | 0.766922i | ||||
\(331\) | 223.152 | + | 386.510i | 0.674175 | + | 1.16770i | 0.976709 | + | 0.214566i | \(0.0688338\pi\) |
−0.302535 | + | 0.953138i | \(0.597833\pi\) | |||||||
\(332\) | −96.8645 | − | 96.8645i | −0.291761 | − | 0.291761i | ||||
\(333\) | 387.072 | + | 246.821i | 1.16238 | + | 0.741204i | ||||
\(334\) | 497.589i | 1.48979i | ||||||||
\(335\) | 187.547 | − | 162.279i | 0.559842 | − | 0.484416i | ||||
\(336\) | 3.80271 | − | 1.47787i | 0.0113176 | − | 0.00439843i | ||||
\(337\) | −28.2958 | + | 7.58184i | −0.0839638 | + | 0.0224980i | −0.300556 | − | 0.953764i | \(-0.597172\pi\) |
0.216593 | + | 0.976262i | \(0.430506\pi\) | |||||||
\(338\) | −1.44975 | − | 5.41056i | −0.00428921 | − | 0.0160076i | ||||
\(339\) | −40.2988 | − | 103.693i | −0.118875 | − | 0.305878i | ||||
\(340\) | 138.737 | + | 160.339i | 0.408049 | + | 0.471584i | ||||
\(341\) | −154.473 | −0.452999 | ||||||||
\(342\) | −130.054 | − | 5.73305i | −0.380275 | − | 0.0167633i | ||||
\(343\) | 4.72156 | − | 4.72156i | 0.0137655 | − | 0.0137655i | ||||
\(344\) | −38.9086 | + | 22.4639i | −0.113107 | + | 0.0653021i | ||||
\(345\) | −498.327 | − | 462.966i | −1.44443 | − | 1.34193i | ||||
\(346\) | 43.0650 | − | 74.5907i | 0.124465 | − | 0.215580i | ||||
\(347\) | −326.160 | + | 87.3943i | −0.939942 | + | 0.251857i | −0.696089 | − | 0.717956i | \(-0.745078\pi\) |
−0.243853 | + | 0.969812i | \(0.578411\pi\) | |||||||
\(348\) | 48.3706 | − | 5.28716i | 0.138996 | − | 0.0151930i | ||||
\(349\) | −51.4915 | + | 29.7286i | −0.147540 | + | 0.0851823i | −0.571953 | − | 0.820287i | \(-0.693814\pi\) |
0.424413 | + | 0.905469i | \(0.360481\pi\) | |||||||
\(350\) | 3.94137 | − | 1.57145i | 0.0112611 | − | 0.00448985i | ||||
\(351\) | −196.113 | − | 293.905i | −0.558727 | − | 0.837336i | ||||
\(352\) | 208.047 | + | 208.047i | 0.591042 | + | 0.591042i | ||||
\(353\) | 514.426 | + | 137.840i | 1.45730 | + | 0.390482i | 0.898555 | − | 0.438860i | \(-0.144618\pi\) |
0.558742 | + | 0.829342i | \(0.311284\pi\) | |||||||
\(354\) | 88.3316 | − | 110.012i | 0.249524 | − | 0.310767i | ||||
\(355\) | −253.832 | + | 123.083i | −0.715021 | + | 0.346713i | ||||
\(356\) | −65.2043 | + | 112.937i | −0.183158 | + | 0.317239i | ||||
\(357\) | −3.17178 | + | 2.32462i | −0.00888455 | + | 0.00651155i | ||||
\(358\) | −447.421 | − | 119.886i | −1.24978 | − | 0.334878i | ||||
\(359\) | − | 342.196i | − | 0.953192i | −0.879122 | − | 0.476596i | \(-0.841870\pi\) | ||
0.879122 | − | 0.476596i | \(-0.158130\pi\) | |||||||
\(360\) | 23.3268 | − | 199.916i | 0.0647966 | − | 0.555322i | ||||
\(361\) | 327.278 | 0.906588 | ||||||||
\(362\) | 63.0401 | − | 235.269i | 0.174144 | − | 0.649914i | ||||
\(363\) | −42.9306 | + | 97.5117i | −0.118266 | + | 0.268627i | ||||
\(364\) | −1.70223 | − | 0.982783i | −0.00467646 | − | 0.00269995i | ||||
\(365\) | 126.795 | − | 365.516i | 0.347382 | − | 1.00141i | ||||
\(366\) | 37.5482 | − | 14.5926i | 0.102591 | − | 0.0398705i | ||||
\(367\) | −95.2584 | + | 355.509i | −0.259560 | + | 0.968690i | 0.705937 | + | 0.708275i | \(0.250526\pi\) |
−0.965497 | + | 0.260416i | \(0.916140\pi\) | |||||||
\(368\) | −639.956 | + | 639.956i | −1.73901 | + | 1.73901i | ||||
\(369\) | −168.867 | + | 534.793i | −0.457633 | + | 1.44930i | ||||
\(370\) | 356.441 | − | 525.843i | 0.963354 | − | 1.42120i | ||||
\(371\) | −1.35032 | − | 2.33883i | −0.00363968 | − | 0.00630412i | ||||
\(372\) | −89.1142 | + | 65.3125i | −0.239554 | + | 0.175571i | ||||
\(373\) | 86.1459 | + | 321.501i | 0.230954 | + | 0.861933i | 0.979931 | + | 0.199337i | \(0.0638787\pi\) |
−0.748977 | + | 0.662596i | \(0.769455\pi\) | |||||||
\(374\) | −383.681 | − | 221.519i | −1.02589 | − | 0.592296i | ||||
\(375\) | 40.2124 | − | 372.838i | 0.107233 | − | 0.994234i | ||||
\(376\) | 103.370 | + | 179.042i | 0.274921 | + | 0.476177i | ||||
\(377\) | 68.0862 | + | 68.0862i | 0.180600 | + | 0.180600i | ||||
\(378\) | −4.49392 | − | 0.896843i | −0.0118887 | − | 0.00237260i | ||||
\(379\) | − | 203.700i | − | 0.537466i | −0.963215 | − | 0.268733i | \(-0.913395\pi\) | ||
0.963215 | − | 0.268733i | \(-0.0866049\pi\) | |||||||
\(380\) | −4.61092 | + | 63.8373i | −0.0121340 | + | 0.167993i | ||||
\(381\) | −502.164 | − | 403.203i | −1.31802 | − | 1.05828i | ||||
\(382\) | 328.219 | − | 87.9460i | 0.859212 | − | 0.230225i | ||||
\(383\) | −5.35538 | − | 19.9865i | −0.0139827 | − | 0.0521842i | 0.958582 | − | 0.284817i | \(-0.0919327\pi\) |
−0.972565 | + | 0.232633i | \(0.925266\pi\) | |||||||
\(384\) | −381.609 | − | 58.8174i | −0.993774 | − | 0.153170i | ||||
\(385\) | −2.38206 | + | 2.06114i | −0.00618718 | + | 0.00535360i | ||||
\(386\) | −230.060 | −0.596010 | ||||||||
\(387\) | 90.3161 | + | 3.98132i | 0.233375 | + | 0.0102876i | ||||
\(388\) | −242.458 | + | 242.458i | −0.624892 | + | 0.624892i | ||||
\(389\) | −160.439 | + | 92.6297i | −0.412440 | + | 0.238123i | −0.691838 | − | 0.722053i | \(-0.743199\pi\) |
0.279397 | + | 0.960176i | \(0.409865\pi\) | |||||||
\(390\) | −414.159 | + | 259.869i | −1.06195 | + | 0.666330i | ||||
\(391\) | 436.174 | − | 755.475i | 1.11553 | − | 1.93216i | ||||
\(392\) | −211.675 | + | 56.7182i | −0.539988 | + | 0.144689i | ||||
\(393\) | 1.81673 | − | 4.12647i | 0.00462271 | − | 0.0104999i | ||||
\(394\) | 520.513 | − | 300.518i | 1.32110 | − | 0.762737i | ||||
\(395\) | 132.718 | − | 195.793i | 0.335995 | − | 0.495680i | ||||
\(396\) | −39.6260 | − | 179.098i | −0.100066 | − | 0.452266i | ||||
\(397\) | −236.474 | − | 236.474i | −0.595652 | − | 0.595652i | 0.343501 | − | 0.939152i | \(-0.388387\pi\) |
−0.939152 | + | 0.343501i | \(0.888387\pi\) | |||||||
\(398\) | 87.6248 | + | 23.4790i | 0.220163 | + | 0.0589925i | ||||
\(399\) | −1.17320 | − | 0.180825i | −0.00294036 | − | 0.000453197i | ||||
\(400\) | −493.777 | − | 71.7045i | −1.23444 | − | 0.179261i | ||||
\(401\) | −34.0375 | + | 58.9547i | −0.0848816 | + | 0.147019i | −0.905341 | − | 0.424686i | \(-0.860385\pi\) |
0.820459 | + | 0.571705i | \(0.193718\pi\) | |||||||
\(402\) | 40.2743 | + | 368.458i | 0.100185 | + | 0.916562i | ||||
\(403\) | −211.185 | − | 56.5868i | −0.524032 | − | 0.140414i | ||||
\(404\) | − | 121.703i | − | 0.301245i | ||||||
\(405\) | −255.859 | + | 313.944i | −0.631751 | + | 0.775171i | ||||
\(406\) | 1.24883 | 0.00307593 | ||||||||
\(407\) | −122.062 | + | 455.540i | −0.299906 | + | 1.11926i | ||||
\(408\) | 256.602 | − | 28.0479i | 0.628926 | − | 0.0687449i | ||||
\(409\) | 326.511 | + | 188.511i | 0.798315 | + | 0.460907i | 0.842882 | − | 0.538099i | \(-0.180857\pi\) |
−0.0445668 | + | 0.999006i | \(0.514191\pi\) | |||||||
\(410\) | 733.204 | + | 254.343i | 1.78830 | + | 0.620348i | ||||
\(411\) | 31.9210 | − | 207.104i | 0.0776666 | − | 0.503904i | ||||
\(412\) | −52.1674 | + | 194.691i | −0.126620 | + | 0.472552i | ||||
\(413\) | 0.909687 | − | 0.909687i | 0.00220263 | − | 0.00220263i | ||||
\(414\) | 992.557 | − | 219.607i | 2.39748 | − | 0.530451i | ||||
\(415\) | −305.147 | + | 58.5894i | −0.735295 | + | 0.141179i | ||||
\(416\) | 208.216 | + | 360.640i | 0.500518 | + | 0.866923i | ||||
\(417\) | 337.120 | + | 148.421i | 0.808440 | + | 0.355925i | ||||
\(418\) | −34.6135 | − | 129.179i | −0.0828074 | − | 0.309041i | ||||
\(419\) | −198.025 | − | 114.330i | −0.472613 | − | 0.272863i | 0.244720 | − | 0.969594i | \(-0.421304\pi\) |
−0.717333 | + | 0.696731i | \(0.754637\pi\) | |||||||
\(420\) | −0.502730 | + | 2.19622i | −0.00119698 | + | 0.00522908i | ||||
\(421\) | 204.894 | + | 354.887i | 0.486684 | + | 0.842961i | 0.999883 | − | 0.0153086i | \(-0.00487306\pi\) |
−0.513199 | + | 0.858270i | \(0.671540\pi\) | |||||||
\(422\) | 340.999 | + | 340.999i | 0.808055 | + | 0.808055i | ||||
\(423\) | 18.3205 | − | 415.599i | 0.0433108 | − | 0.982504i | ||||
\(424\) | 177.274i | 0.418098i | ||||||||
\(425\) | 477.614 | − | 56.4234i | 1.12380 | − | 0.132761i | ||||
\(426\) | 64.2230 | − | 416.681i | 0.150758 | − | 0.978125i | ||||
\(427\) | 0.354816 | − | 0.0950727i | 0.000830951 | − | 0.000222653i | ||||
\(428\) | 11.8070 | + | 44.0644i | 0.0275865 | + | 0.102954i | ||||
\(429\) | 227.256 | − | 283.034i | 0.529735 | − | 0.659752i | ||||
\(430\) | 9.01251 | − | 124.776i | 0.0209593 | − | 0.290177i | ||||
\(431\) | 46.4787 | 0.107839 | 0.0539196 | − | 0.998545i | \(-0.482829\pi\) | ||||
0.0539196 | + | 0.998545i | \(0.482829\pi\) | |||||||
\(432\) | 404.922 | + | 355.559i | 0.937319 | + | 0.823053i | ||||
\(433\) | −430.638 | + | 430.638i | −0.994544 | + | 0.994544i | −0.999985 | − | 0.00544093i | \(-0.998268\pi\) |
0.00544093 | + | 0.999985i | \(0.498268\pi\) | |||||||
\(434\) | −2.45572 | + | 1.41781i | −0.00565834 | + | 0.00326684i | ||||
\(435\) | 51.6341 | − | 97.5474i | 0.118699 | − | 0.224247i | ||||
\(436\) | −123.504 | + | 213.916i | −0.283266 | + | 0.490632i | ||||
\(437\) | 254.356 | − | 68.1545i | 0.582050 | − | 0.155960i | ||||
\(438\) | 341.798 | + | 466.359i | 0.780360 | + | 1.06475i | ||||
\(439\) | 335.332 | − | 193.604i | 0.763855 | − | 0.441012i | −0.0668232 | − | 0.997765i | \(-0.521286\pi\) |
0.830678 | + | 0.556753i | \(0.187953\pi\) | |||||||
\(440\) | 203.061 | − | 38.9885i | 0.461502 | − | 0.0886101i | ||||
\(441\) | 420.494 | + | 132.775i | 0.953500 | + | 0.301078i | ||||
\(442\) | −443.397 | − | 443.397i | −1.00316 | − | 1.00316i | ||||
\(443\) | −708.648 | − | 189.882i | −1.59966 | − | 0.428627i | −0.654717 | − | 0.755874i | \(-0.727212\pi\) |
−0.944939 | + | 0.327247i | \(0.893879\pi\) | |||||||
\(444\) | 122.190 | + | 314.407i | 0.275203 | + | 0.708124i | ||||
\(445\) | 129.060 | + | 266.159i | 0.290024 | + | 0.598110i | ||||
\(446\) | −119.241 | + | 206.531i | −0.267357 | + | 0.463075i | ||||
\(447\) | 72.9486 | + | 32.1164i | 0.163196 | + | 0.0718489i | ||||
\(448\) | −0.0374297 | − | 0.0100292i | −8.35483e−5 | − | 2.23867e-5i | ||||
\(449\) | 141.098i | 0.314250i | 0.987579 | + | 0.157125i | \(0.0502226\pi\) | ||||
−0.987579 | + | 0.157125i | \(0.949777\pi\) | |||||||
\(450\) | 424.337 | + | 366.105i | 0.942971 | + | 0.813567i | ||||
\(451\) | −576.139 | −1.27747 | ||||||||
\(452\) | 21.1566 | − | 78.9577i | 0.0468067 | − | 0.174685i | ||||
\(453\) | 174.652 | + | 238.300i | 0.385544 | + | 0.526048i | ||||
\(454\) | −710.657 | − | 410.298i | −1.56532 | − | 0.903740i | ||||
\(455\) | −4.01165 | + | 1.94525i | −0.00881680 | + | 0.00427527i | ||||
\(456\) | 60.7582 | + | 48.7846i | 0.133242 | + | 0.106984i | ||||
\(457\) | 190.044 | − | 709.254i | 0.415851 | − | 1.55198i | −0.367273 | − | 0.930113i | \(-0.619709\pi\) |
0.783124 | − | 0.621865i | \(-0.213625\pi\) | |||||||
\(458\) | 732.678 | − | 732.678i | 1.59973 | − | 1.59973i | ||||
\(459\) | −465.699 | − | 230.023i | −1.01460 | − | 0.501139i | ||||
\(460\) | −94.2412 | − | 490.830i | −0.204872 | − | 1.06702i | ||||
\(461\) | −321.041 | − | 556.060i | −0.696402 | − | 1.20620i | −0.969706 | − | 0.244275i | \(-0.921450\pi\) |
0.273304 | − | 0.961928i | \(-0.411883\pi\) | |||||||
\(462\) | −0.511530 | − | 4.67984i | −0.00110721 | − | 0.0101295i | ||||
\(463\) | −71.8346 | − | 268.091i | −0.155150 | − | 0.579029i | −0.999092 | − | 0.0425948i | \(-0.986438\pi\) |
0.843942 | − | 0.536434i | \(-0.180229\pi\) | |||||||
\(464\) | −127.178 | − | 73.4265i | −0.274091 | − | 0.158247i | ||||
\(465\) | 9.21251 | + | 250.440i | 0.0198118 | + | 0.538580i | ||||
\(466\) | −38.7861 | − | 67.1795i | −0.0832320 | − | 0.144162i | ||||
\(467\) | −57.4439 | − | 57.4439i | −0.123006 | − | 0.123006i | 0.642924 | − | 0.765930i | \(-0.277721\pi\) |
−0.765930 | + | 0.642924i | \(0.777721\pi\) | |||||||
\(468\) | 11.4334 | − | 259.366i | 0.0244304 | − | 0.554202i | ||||
\(469\) | 3.37981i | 0.00720642i | ||||||||
\(470\) | −574.172 | − | 41.4721i | −1.22164 | − | 0.0882384i | ||||
\(471\) | −482.900 | + | 187.673i | −1.02526 | + | 0.398456i | ||||
\(472\) | −81.5694 | + | 21.8565i | −0.172817 | + | 0.0463061i | ||||
\(473\) | 24.0373 | + | 89.7086i | 0.0508189 | + | 0.189659i | ||||
\(474\) | 128.055 | + | 329.497i | 0.270157 | + | 0.695140i | ||||
\(475\) | 113.990 | + | 89.9026i | 0.239978 | + | 0.189269i | ||||
\(476\) | −2.88948 | −0.00607034 | ||||||||
\(477\) | 191.787 | − | 300.766i | 0.402068 | − | 0.630536i | ||||
\(478\) | −544.139 | + | 544.139i | −1.13837 | + | 1.13837i | ||||
\(479\) | −419.328 | + | 242.099i | −0.875423 | + | 0.505426i | −0.869147 | − | 0.494554i | \(-0.835331\pi\) |
−0.00627671 | + | 0.999980i | \(0.501998\pi\) | |||||||
\(480\) | 324.889 | − | 349.704i | 0.676853 | − | 0.728551i | ||||
\(481\) | −333.749 | + | 578.071i | −0.693866 | + | 1.20181i | ||||
\(482\) | 61.8668 | − | 16.5771i | 0.128354 | − | 0.0343924i | ||||
\(483\) | 9.21467 | − | 1.00721i | 0.0190780 | − | 0.00208532i | ||||
\(484\) | −67.7979 | + | 39.1431i | −0.140078 | + | 0.0808742i | ||||
\(485\) | 146.653 | + | 763.803i | 0.302378 | + | 1.57485i | ||||
\(486\) | −168.763 | − | 581.274i | −0.347250 | − | 1.19604i | ||||
\(487\) | −162.179 | − | 162.179i | −0.333017 | − | 0.333017i | 0.520714 | − | 0.853731i | \(-0.325666\pi\) |
−0.853731 | + | 0.520714i | \(0.825666\pi\) | |||||||
\(488\) | −23.2906 | − | 6.24069i | −0.0477266 | − | 0.0127883i | ||||
\(489\) | 172.876 | − | 215.306i | 0.353530 | − | 0.440299i | ||||
\(490\) | 199.983 | − | 576.500i | 0.408129 | − | 1.17653i | ||||
\(491\) | −395.023 | + | 684.199i | −0.804527 | + | 1.39348i | 0.112083 | + | 0.993699i | \(0.464248\pi\) |
−0.916610 | + | 0.399783i | \(0.869086\pi\) | |||||||
\(492\) | −332.371 | + | 243.597i | −0.675550 | + | 0.495116i | ||||
\(493\) | 136.726 | + | 36.6356i | 0.277334 | + | 0.0743115i | ||||
\(494\) | − | 189.285i | − | 0.383168i | ||||||
\(495\) | −386.697 | − | 153.536i | −0.781206 | − | 0.310175i | ||||
\(496\) | 333.448 | 0.672274 | ||||||||
\(497\) | 0.995002 | − | 3.71340i | 0.00200202 | − | 0.00747163i | ||||
\(498\) | 187.115 | − | 425.009i | 0.375733 | − | 0.853433i | ||||
\(499\) | 422.362 | + | 243.851i | 0.846418 | + | 0.488680i | 0.859441 | − | 0.511236i | \(-0.170812\pi\) |
−0.0130228 | + | 0.999915i | \(0.504145\pi\) | |||||||
\(500\) | 185.777 | − | 203.496i | 0.371554 | − | 0.406992i | ||||
\(501\) | −558.597 | + | 217.091i | −1.11496 | + | 0.433316i | ||||
\(502\) | −177.852 | + | 663.754i | −0.354288 | + | 1.32222i | ||||
\(503\) | 346.274 | − | 346.274i | 0.688418 | − | 0.688418i | −0.273465 | − | 0.961882i | \(-0.588170\pi\) |
0.961882 | + | 0.273465i | \(0.0881696\pi\) | |||||||
\(504\) | 1.85222 | + | 2.02305i | 0.00367504 | + | 0.00401399i | ||||
\(505\) | −228.504 | − | 154.891i | −0.452483 | − | 0.306714i | ||||
\(506\) | 522.164 | + | 904.415i | 1.03194 | + | 1.78738i | ||||
\(507\) | 5.44143 | − | 3.98806i | 0.0107326 | − | 0.00786600i | ||||
\(508\) | −122.474 | − | 457.078i | −0.241090 | − | 0.899760i | ||||
\(509\) | −362.182 | − | 209.106i | −0.711557 | − | 0.410818i | 0.100080 | − | 0.994979i | \(-0.468090\pi\) |
−0.811637 | + | 0.584162i | \(0.801423\pi\) | |||||||
\(510\) | −336.256 | + | 635.257i | −0.659326 | + | 1.24560i | ||||
\(511\) | 2.63618 | + | 4.56599i | 0.00515886 | + | 0.00893540i | ||||
\(512\) | −196.607 | − | 196.607i | −0.383998 | − | 0.383998i | ||||
\(513\) | −50.3049 | − | 148.501i | −0.0980603 | − | 0.289476i | ||||
\(514\) | − | 15.9365i | − | 0.0310049i | ||||||
\(515\) | 299.151 | + | 345.730i | 0.580875 | + | 0.671320i | ||||
\(516\) | 51.7966 | + | 41.5891i | 0.100381 | + | 0.0805990i | ||||
\(517\) | 412.804 | − | 110.610i | 0.798460 | − | 0.213947i | ||||
\(518\) | 2.24066 | + | 8.36225i | 0.00432559 | + | 0.0161433i | ||||
\(519\) | 102.525 | + | 15.8022i | 0.197543 | + | 0.0304473i | ||||
\(520\) | 291.894 | + | 21.0833i | 0.561335 | + | 0.0405449i | ||||
\(521\) | −17.3149 | −0.0332341 | −0.0166170 | − | 0.999862i | \(-0.505290\pi\) | ||||
−0.0166170 | + | 0.999862i | \(0.505290\pi\) | |||||||
\(522\) | 76.1036 | + | 146.344i | 0.145792 | + | 0.280352i | ||||
\(523\) | 577.571 | − | 577.571i | 1.10434 | − | 1.10434i | 0.110462 | − | 0.993880i | \(-0.464767\pi\) |
0.993880 | − | 0.110462i | \(-0.0352329\pi\) | |||||||
\(524\) | 2.86905 | − | 1.65645i | 0.00547529 | − | 0.00316116i | ||||
\(525\) | 3.48369 | + | 3.73901i | 0.00663560 | + | 0.00712193i | ||||
\(526\) | 264.640 | − | 458.370i | 0.503118 | − | 0.871427i | ||||
\(527\) | −310.453 | + | 83.1855i | −0.589094 | + | 0.157847i | ||||
\(528\) | −223.064 | + | 506.662i | −0.422469 | + | 0.959587i | ||||
\(529\) | −1322.68 | + | 763.649i | −2.50034 | + | 1.44357i | ||||
\(530\) | −408.594 | − | 276.964i | −0.770932 | − | 0.522574i | ||||
\(531\) | 162.038 | + | 51.1652i | 0.305156 | + | 0.0963564i | ||||
\(532\) | −0.616757 | − | 0.616757i | −0.00115932 | − | 0.00115932i | ||||
\(533\) | −787.659 | − | 211.053i | −1.47778 | − | 0.395971i | ||||
\(534\) | −436.916 | − | 67.3418i | −0.818195 | − | 0.126108i | ||||
\(535\) | 97.7600 | + | 33.9122i | 0.182729 | + | 0.0633873i | ||||
\(536\) | 110.927 | − | 192.132i | 0.206954 | − | 0.358455i | ||||
\(537\) | −60.6189 | − | 554.584i | −0.112884 | − | 1.03274i | ||||
\(538\) | 839.797 | + | 225.023i | 1.56096 | + | 0.418258i | ||||
\(539\) | 453.003i | 0.840451i | ||||||||
\(540\) | −288.000 | + | 74.9250i | −0.533333 | + | 0.138750i | ||||
\(541\) | 846.162 | 1.56407 | 0.782035 | − | 0.623234i | \(-0.214182\pi\) | ||||
0.782035 | + | 0.623234i | \(0.214182\pi\) | |||||||
\(542\) | 130.404 | − | 486.674i | 0.240598 | − | 0.897922i | ||||
\(543\) | 291.618 | − | 31.8754i | 0.537050 | − | 0.0587024i | ||||
\(544\) | 530.160 | + | 306.088i | 0.974558 | + | 0.562661i | ||||
\(545\) | 244.455 | + | 504.135i | 0.448541 | + | 0.925018i | ||||
\(546\) | 1.01500 | − | 6.58536i | 0.00185897 | − | 0.0120611i | ||||
\(547\) | −17.6950 | + | 66.0385i | −0.0323491 | + | 0.120728i | −0.980212 | − | 0.197949i | \(-0.936572\pi\) |
0.947863 | + | 0.318677i | \(0.103239\pi\) | |||||||
\(548\) | 108.876 | − | 108.876i | 0.198678 | − | 0.198678i | ||||
\(549\) | 32.7636 | + | 35.7854i | 0.0596787 | + | 0.0651828i | ||||
\(550\) | −227.389 | + | 528.944i | −0.413435 | + | 0.961717i | ||||
\(551\) | 21.3641 | + | 37.0038i | 0.0387734 | + | 0.0671575i | ||||
\(552\) | −556.884 | − | 245.174i | −1.00885 | − | 0.444156i | ||||
\(553\) | 0.834291 | + | 3.11362i | 0.00150866 | + | 0.00563041i | ||||
\(554\) | 523.410 | + | 302.191i | 0.944784 | + | 0.545471i | ||||
\(555\) | 745.826 | + | 170.725i | 1.34383 | + | 0.307613i | ||||
\(556\) | 135.327 | + | 234.392i | 0.243393 | + | 0.421569i | ||||
\(557\) | 367.003 | + | 367.003i | 0.658893 | + | 0.658893i | 0.955118 | − | 0.296225i | \(-0.0957279\pi\) |
−0.296225 | + | 0.955118i | \(0.595728\pi\) | |||||||
\(558\) | −315.797 | − | 201.372i | −0.565945 | − | 0.360881i | ||||
\(559\) | 131.449i | 0.235151i | ||||||||
\(560\) | 5.14197 | − | 4.44921i | 0.00918210 | − | 0.00794502i | ||||
\(561\) | 81.2835 | − | 527.370i | 0.144890 | − | 0.940053i | ||||
\(562\) | −674.443 | + | 180.716i | −1.20008 | + | 0.321560i | ||||
\(563\) | 81.4441 | + | 303.953i | 0.144661 | + | 0.539882i | 0.999770 | + | 0.0214341i | \(0.00682321\pi\) |
−0.855109 | + | 0.518448i | \(0.826510\pi\) | |||||||
\(564\) | 191.377 | − | 238.348i | 0.339320 | − | 0.422603i | ||||
\(565\) | −121.321 | − | 140.212i | −0.214728 | − | 0.248162i | ||||
\(566\) | −961.053 | −1.69797 | ||||||||
\(567\) | −0.953838 | − | 5.43620i | −0.00168225 | − | 0.00958765i | ||||
\(568\) | −178.439 | + | 178.439i | −0.314153 | + | 0.314153i | ||||
\(569\) | 882.789 | − | 509.679i | 1.55148 | − | 0.895745i | 0.553453 | − | 0.832880i | \(-0.313310\pi\) |
0.998022 | − | 0.0628645i | \(-0.0200236\pi\) | |||||||
\(570\) | −207.368 | + | 63.8214i | −0.363804 | + | 0.111967i | ||||
\(571\) | 443.096 | − | 767.465i | 0.776000 | − | 1.34407i | −0.158231 | − | 0.987402i | \(-0.550579\pi\) |
0.934231 | − | 0.356669i | \(-0.116088\pi\) | |||||||
\(572\) | 257.622 | − | 69.0296i | 0.450388 | − | 0.120681i | ||||
\(573\) | 241.927 | + | 330.092i | 0.422210 | + | 0.576076i | ||||
\(574\) | −9.15913 | + | 5.28803i | −0.0159567 | + | 0.00921259i | ||||
\(575\) | −1041.50 | − | 447.733i | −1.81130 | − | 0.778667i | ||||
\(576\) | −1.10569 | − | 4.99737i | −0.00191960 | − | 0.00867600i | ||||
\(577\) | 194.509 | + | 194.509i | 0.337105 | + | 0.337105i | 0.855277 | − | 0.518172i | \(-0.173387\pi\) |
−0.518172 | + | 0.855277i | \(0.673387\pi\) | |||||||
\(578\) | −195.070 | − | 52.2689i | −0.337492 | − | 0.0904307i | ||||
\(579\) | −100.372 | − | 258.267i | −0.173354 | − | 0.446058i | ||||
\(580\) | 72.9715 | − | 35.3839i | 0.125813 | − | 0.0610067i | ||||
\(581\) | 2.11722 | − | 3.66713i | 0.00364409 | − | 0.00631175i | ||||
\(582\) | −1063.83 | − | 468.361i | −1.82788 | − | 0.804745i | ||||
\(583\) | 353.967 | + | 94.8452i | 0.607147 | + | 0.162685i | ||||
\(584\) | − | 346.084i | − | 0.592609i | ||||||
\(585\) | −472.423 | − | 351.561i | −0.807561 | − | 0.600959i | ||||
\(586\) | 105.225 | 0.179565 | ||||||||
\(587\) | 207.853 | − | 775.720i | 0.354095 | − | 1.32150i | −0.527526 | − | 0.849539i | \(-0.676880\pi\) |
0.881620 | − | 0.471960i | \(-0.156453\pi\) | |||||||
\(588\) | 191.534 | + | 261.334i | 0.325738 | + | 0.444446i | ||||
\(589\) | −84.0216 | − | 48.5099i | −0.142651 | − | 0.0823598i | ||||
\(590\) | 77.0639 | − | 222.155i | 0.130617 | − | 0.376534i | ||||
\(591\) | 564.457 | + | 453.220i | 0.955089 | + | 0.766870i | ||||
\(592\) | 263.485 | − | 983.338i | 0.445075 | − | 1.66104i | ||||
\(593\) | 572.308 | − | 572.308i | 0.965106 | − | 0.965106i | −0.0343049 | − | 0.999411i | \(-0.510922\pi\) |
0.999411 | + | 0.0343049i | \(0.0109217\pi\) | |||||||
\(594\) | 517.234 | − | 345.133i | 0.870764 | − | 0.581032i | ||||
\(595\) | −3.67743 | + | 5.42516i | −0.00618055 | + | 0.00911791i | ||||
\(596\) | 29.2830 | + | 50.7197i | 0.0491326 | + | 0.0851001i | ||||
\(597\) | 11.8718 | + | 108.612i | 0.0198858 | + | 0.181930i | ||||
\(598\) | 382.561 | + | 1427.74i | 0.639734 | + | 2.38752i | ||||
\(599\) | −263.198 | − | 151.957i | −0.439396 | − | 0.253685i | 0.263945 | − | 0.964538i | \(-0.414976\pi\) |
−0.703341 | + | 0.710852i | \(0.748309\pi\) | |||||||
\(600\) | −75.3205 | − | 326.888i | −0.125534 | − | 0.544814i | ||||
\(601\) | −52.0948 | − | 90.2308i | −0.0866801 | − | 0.150134i | 0.819426 | − | 0.573185i | \(-0.194292\pi\) |
−0.906106 | + | 0.423051i | \(0.860959\pi\) | |||||||
\(602\) | 1.20551 | + | 1.20551i | 0.00200251 | + | 0.00200251i | ||||
\(603\) | −396.063 | + | 205.966i | −0.656821 | + | 0.341568i | ||||
\(604\) | 217.090i | 0.359420i | ||||||||
\(605\) | −12.7926 | + | 177.111i | −0.0211449 | + | 0.292746i | ||||
\(606\) | 384.544 | − | 149.448i | 0.634561 | − | 0.246614i | ||||
\(607\) | −283.439 | + | 75.9472i | −0.466950 | + | 0.125119i | −0.484620 | − | 0.874725i | \(-0.661042\pi\) |
0.0176696 | + | 0.999844i | \(0.494375\pi\) | |||||||
\(608\) | 47.8279 | + | 178.496i | 0.0786642 | + | 0.293579i | ||||
\(609\) | 0.544848 | + | 1.40195i | 0.000894660 | + | 0.00230205i | ||||
\(610\) | 50.7721 | − | 43.9317i | 0.0832330 | − | 0.0720193i | ||||
\(611\) | 604.878 | 0.989980 | ||||||||
\(612\) | −176.085 | − | 338.604i | −0.287721 | − | 0.553274i | ||||
\(613\) | 610.767 | − | 610.767i | 0.996357 | − | 0.996357i | −0.00363596 | − | 0.999993i | \(-0.501157\pi\) |
0.999993 | + | 0.00363596i | \(0.00115736\pi\) | |||||||
\(614\) | 259.645 | − | 149.906i | 0.422874 | − | 0.244147i | ||||
\(615\) | 34.3600 | + | 934.068i | 0.0558699 | + | 1.51881i | ||||
\(616\) | −1.40891 | + | 2.44030i | −0.00228719 | + | 0.00396152i | ||||
\(617\) | 972.818 | − | 260.666i | 1.57669 | − | 0.422473i | 0.638791 | − | 0.769381i | \(-0.279435\pi\) |
0.937899 | + | 0.346908i | \(0.112768\pi\) | |||||||
\(618\) | −679.226 | + | 74.2429i | −1.09907 | + | 0.120134i | ||||
\(619\) | −189.444 | + | 109.376i | −0.306049 | + | 0.176697i | −0.645157 | − | 0.764050i | \(-0.723208\pi\) |
0.339108 | + | 0.940747i | \(0.389875\pi\) | |||||||
\(620\) | −103.321 | + | 152.425i | −0.166646 | + | 0.245847i | ||||
\(621\) | 679.572 | + | 1018.44i | 1.09432 | + | 1.64000i | ||||
\(622\) | 799.956 | + | 799.956i | 1.28610 | + | 1.28610i | ||||
\(623\) | −3.89373 | − | 1.04332i | −0.00624997 | − | 0.00167467i | ||||
\(624\) | −490.560 | + | 610.962i | −0.786154 | + | 0.979106i | ||||
\(625\) | −145.638 | − | 607.795i | −0.233020 | − | 0.972472i | ||||
\(626\) | 370.048 | − | 640.942i | 0.591131 | − | 1.02387i | ||||
\(627\) | 129.916 | − | 95.2166i | 0.207203 | − | 0.151861i | ||||
\(628\) | −367.708 | − | 98.5271i | −0.585523 | − | 0.156890i | ||||
\(629\) | 981.257i | 1.56003i | ||||||||
\(630\) | −7.55671 | + | 1.10842i | −0.0119948 | + | 0.00175940i | ||||
\(631\) | −427.714 | −0.677835 | −0.338917 | − | 0.940816i | \(-0.610061\pi\) | ||||
−0.338917 | + | 0.940816i | \(0.610061\pi\) | |||||||
\(632\) | 54.7639 | − | 204.382i | 0.0866517 | − | 0.323389i | ||||
\(633\) | −234.035 | + | 531.582i | −0.369724 | + | 0.839782i | ||||
\(634\) | −190.711 | − | 110.107i | −0.300805 | − | 0.173670i | ||||
\(635\) | −1014.06 | − | 351.770i | −1.59695 | − | 0.553968i | ||||
\(636\) | 244.303 | − | 94.9450i | 0.384124 | − | 0.149285i | ||||
\(637\) | −165.945 | + | 619.316i | −0.260511 | + | 0.972239i | ||||
\(638\) | −119.823 | + | 119.823i | −0.187810 | + | 0.187810i | ||||
\(639\) | 495.790 | − | 109.695i | 0.775884 | − | 0.171667i | ||||
\(640\) | −631.982 | + | 121.343i | −0.987472 | + | 0.189598i | ||||
\(641\) | −256.912 | − | 444.984i | −0.400798 | − | 0.694203i | 0.593024 | − | 0.805185i | \(-0.297934\pi\) |
−0.993822 | + | 0.110982i | \(0.964600\pi\) | |||||||
\(642\) | −124.731 | + | 91.4165i | −0.194286 | + | 0.142393i | ||||
\(643\) | −50.3713 | − | 187.988i | −0.0783379 | − | 0.292361i | 0.915632 | − | 0.402019i | \(-0.131691\pi\) |
−0.993969 | + | 0.109657i | \(0.965025\pi\) | |||||||
\(644\) | 5.89858 | + | 3.40555i | 0.00915929 | + | 0.00528812i | ||||
\(645\) | 144.007 | − | 44.3208i | 0.223267 | − | 0.0687143i | ||||
\(646\) | −139.129 | − | 240.979i | −0.215371 | − | 0.373033i | ||||
\(647\) | −139.726 | − | 139.726i | −0.215960 | − | 0.215960i | 0.590833 | − | 0.806794i | \(-0.298799\pi\) |
−0.806794 | + | 0.590833i | \(0.798799\pi\) | |||||||
\(648\) | −124.197 | + | 340.337i | −0.191661 | + | 0.525211i | ||||
\(649\) | 174.565i | 0.268976i | ||||||||
\(650\) | −504.636 | + | 639.841i | −0.776364 | + | 0.984370i | ||||
\(651\) | −2.66304 | − | 2.13824i | −0.00409070 | − | 0.00328455i | ||||
\(652\) | 195.975 | − | 52.5114i | 0.300576 | − | 0.0805390i | ||||
\(653\) | −166.789 | − | 622.466i | −0.255420 | − | 0.953240i | −0.967856 | − | 0.251503i | \(-0.919075\pi\) |
0.712437 | − | 0.701737i | \(-0.247592\pi\) | |||||||
\(654\) | −827.568 | − | 127.553i | −1.26539 | − | 0.195035i | ||||
\(655\) | 0.541356 | − | 7.49495i | 0.000826498 | − | 0.0114427i | ||||
\(656\) | 1243.66 | 1.89583 | ||||||||
\(657\) | −374.417 | + | 587.172i | −0.569888 | + | 0.893716i | ||||
\(658\) | 5.54730 | − | 5.54730i | 0.00843054 | − | 0.00843054i | ||||
\(659\) | 210.200 | − | 121.359i | 0.318968 | − | 0.184156i | −0.331965 | − | 0.943292i | \(-0.607711\pi\) |
0.650932 | + | 0.759136i | \(0.274378\pi\) | |||||||
\(660\) | −162.487 | − | 258.959i | −0.246192 | − | 0.392362i | ||||
\(661\) | −331.364 | + | 573.939i | −0.501307 | + | 0.868288i | 0.498692 | + | 0.866779i | \(0.333814\pi\) |
−0.999999 | + | 0.00150927i | \(0.999520\pi\) | |||||||
\(662\) | −1073.80 | + | 287.723i | −1.62205 | + | 0.434627i | ||||
\(663\) | 304.313 | − | 691.210i | 0.458994 | − | 1.04255i | ||||
\(664\) | −240.715 | + | 138.977i | −0.362522 | + | 0.209302i | ||||
\(665\) | −1.94294 | + | 0.373051i | −0.00292171 | + | 0.000560979i | ||||
\(666\) | −843.384 | + | 772.167i | −1.26634 | + | 1.15941i | ||||
\(667\) | −235.933 | − | 235.933i | −0.353722 | − | 0.353722i | ||||
\(668\) | −425.349 | − | 113.972i | −0.636750 | − | 0.170617i | ||||
\(669\) | −283.877 | − | 43.7540i | −0.424331 | − | 0.0654021i | ||||
\(670\) | 269.533 | + | 555.853i | 0.402288 | + | 0.829631i | ||||
\(671\) | −24.9219 | + | 43.1660i | −0.0371414 | + | 0.0643308i | ||||
\(672\) | 0.706817 | + | 6.46646i | 0.00105181 | + | 0.00962271i | ||||
\(673\) | −467.643 | − | 125.305i | −0.694864 | − | 0.186188i | −0.105935 | − | 0.994373i | \(-0.533784\pi\) |
−0.588929 | + | 0.808185i | \(0.700450\pi\) | |||||||
\(674\) | − | 72.9670i | − | 0.108260i | ||||||
\(675\) | −225.860 | + | 636.091i | −0.334607 | + | 0.942358i | ||||
\(676\) | 4.95712 | 0.00733302 | ||||||||
\(677\) | −113.880 | + | 425.004i | −0.168212 | + | 0.627776i | 0.829397 | + | 0.558660i | \(0.188684\pi\) |
−0.997609 | + | 0.0691156i | \(0.977982\pi\) | |||||||
\(678\) | 275.462 | − | 30.1094i | 0.406286 | − | 0.0444091i | ||||
\(679\) | −9.17906 | − | 5.29953i | −0.0135185 | − | 0.00780490i | ||||
\(680\) | 387.108 | − | 187.708i | 0.569276 | − | 0.276042i | ||||
\(681\) | 150.554 | − | 976.798i | 0.221077 | − | 1.43436i | ||||
\(682\) | 99.5854 | − | 371.658i | 0.146020 | − | 0.544953i | ||||
\(683\) | −336.034 | + | 336.034i | −0.491998 | + | 0.491998i | −0.908935 | − | 0.416938i | \(-0.863103\pi\) |
0.416938 | + | 0.908935i | \(0.363103\pi\) | |||||||
\(684\) | 34.6894 | − | 109.860i | 0.0507155 | − | 0.160614i | ||||
\(685\) | −65.8544 | − | 342.985i | −0.0961379 | − | 0.500708i | ||||
\(686\) | 8.31607 | + | 14.4039i | 0.0121226 | + | 0.0209969i | ||||
\(687\) | 1142.17 | + | 502.853i | 1.66254 | + | 0.731954i | ||||
\(688\) | −51.8875 | − | 193.647i | −0.0754179 | − | 0.281463i | ||||
\(689\) | 449.177 | + | 259.332i | 0.651926 | + | 0.376389i | ||||
\(690\) | 1435.15 | − | 900.499i | 2.07992 | − | 1.30507i | ||||
\(691\) | −465.054 | − | 805.496i | −0.673015 | − | 1.16570i | −0.977045 | − | 0.213034i | \(-0.931665\pi\) |
0.304029 | − | 0.952663i | \(-0.401668\pi\) | |||||||
\(692\) | 53.8977 | + | 53.8977i | 0.0778869 | + | 0.0778869i | ||||
\(693\) | 5.03045 | − | 2.61600i | 0.00725895 | − | 0.00377489i | ||||
\(694\) | − | 841.075i | − | 1.21192i | ||||||
\(695\) | 612.314 | + | 44.2270i | 0.881027 | + | 0.0636360i | ||||
\(696\) | 15.0398 | − | 97.5786i | 0.0216089 | − | 0.140199i | ||||
\(697\) | −1157.90 | + | 310.258i | −1.66126 | + | 0.445134i | ||||
\(698\) | −38.3309 | − | 143.053i | −0.0549153 | − | 0.204947i | ||||
\(699\) | 58.4944 | − | 72.8512i | 0.0836830 | − | 0.104222i | ||||
\(700\) | 0.440541 | + | 3.72910i | 0.000629345 | + | 0.00532729i | ||||
\(701\) | −1057.58 | −1.50868 | −0.754338 | − | 0.656486i | \(-0.772042\pi\) | ||||
−0.754338 | + | 0.656486i | \(0.772042\pi\) | |||||||
\(702\) | 833.559 | − | 282.369i | 1.18741 | − | 0.402235i | ||||
\(703\) | −209.448 | + | 209.448i | −0.297935 | + | 0.297935i | ||||
\(704\) | 4.55359 | − | 2.62902i | 0.00646817 | − | 0.00373440i | ||||
\(705\) | −203.947 | − | 662.664i | −0.289286 | − | 0.939949i | ||||
\(706\) | −663.280 | + | 1148.83i | −0.939490 | + | 1.62724i | ||||
\(707\) | 3.63379 | − | 0.973672i | 0.00513974 | − | 0.00137719i | ||||
\(708\) | 73.8079 | + | 100.706i | 0.104248 | + | 0.142240i | ||||
\(709\) | 450.749 | − | 260.240i | 0.635754 | − | 0.367053i | −0.147223 | − | 0.989103i | \(-0.547034\pi\) |
0.782977 | + | 0.622051i | \(0.213700\pi\) | |||||||
\(710\) | −132.495 | − | 690.065i | −0.186613 | − | 0.971922i | ||||
\(711\) | −314.027 | + | 287.510i | −0.441670 | + | 0.404374i | ||||
\(712\) | 187.104 | + | 187.104i | 0.262787 | + | 0.262787i | ||||
\(713\) | 731.800 | + | 196.085i | 1.02637 | + | 0.275014i | ||||
\(714\) | −3.54821 | − | 9.12988i | −0.00496948 | − | 0.0127870i | ||||
\(715\) | 198.267 | − | 571.552i | 0.277297 | − | 0.799374i | ||||
\(716\) | 204.962 | − | 355.005i | 0.286260 | − | 0.495817i | ||||
\(717\) | −848.257 | − | 373.455i | −1.18306 | − | 0.520857i | ||||
\(718\) | 823.316 | + | 220.607i | 1.14668 | + | 0.307252i | ||||
\(719\) | 1211.89i | 1.68553i | 0.538285 | + | 0.842763i | \(0.319072\pi\) | ||||
−0.538285 | + | 0.842763i | \(0.680928\pi\) | |||||||
\(720\) | 834.732 | + | 331.427i | 1.15935 | + | 0.460315i | ||||
\(721\) | −6.23044 | −0.00864139 | ||||||||
\(722\) | −210.990 | + | 787.424i | −0.292230 | + | 1.09062i | ||||
\(723\) | 45.6013 | + | 62.2198i | 0.0630724 | + | 0.0860578i | ||||
\(724\) | 186.673 | + | 107.776i | 0.257836 | + | 0.148862i | ||||
\(725\) | 26.4353 | − | 182.041i | 0.0364625 | − | 0.251091i | ||||
\(726\) | −206.934 | − | 166.154i | −0.285034 | − | 0.228862i | ||||
\(727\) | 53.9360 | − | 201.292i | 0.0741899 | − | 0.276880i | −0.918859 | − | 0.394587i | \(-0.870888\pi\) |
0.993048 | + | 0.117707i | \(0.0375543\pi\) | |||||||
\(728\) | −2.82010 | + | 2.82010i | −0.00387377 | + | 0.00387377i | ||||
\(729\) | 578.914 | − | 443.057i | 0.794120 | − | 0.607761i | ||||
\(730\) | 797.680 | + | 540.705i | 1.09271 | + | 0.740692i | ||||
\(731\) | 96.6185 | + | 167.348i | 0.132173 | + | 0.228930i | ||||
\(732\) | 3.87371 | + | 35.4394i | 0.00529195 | + | 0.0484145i | ||||
\(733\) | −189.606 | − | 707.621i | −0.258672 | − | 0.965376i | −0.966011 | − | 0.258502i | \(-0.916771\pi\) |
0.707339 | − | 0.706874i | \(-0.249895\pi\) | |||||||
\(734\) | −793.936 | − | 458.379i | −1.08166 | − | 0.624495i | ||||
\(735\) | 734.434 | − | 27.0164i | 0.999229 | − | 0.0367570i | ||||
\(736\) | −721.511 | − | 1249.69i | −0.980313 | − | 1.69795i | ||||
\(737\) | −324.286 | − | 324.286i | −0.440009 | − | 0.440009i | ||||
\(738\) | −1177.83 | − | 751.059i | −1.59598 | − | 1.01770i | ||||
\(739\) | − | 1243.93i | − | 1.68326i | −0.540056 | − | 0.841629i | \(-0.681597\pi\) | ||
0.540056 | − | 0.841629i | \(-0.318403\pi\) | |||||||
\(740\) | 367.859 | + | 425.137i | 0.497107 | + | 0.574509i | ||||
\(741\) | 212.493 | − | 82.5827i | 0.286766 | − | 0.111448i | ||||
\(742\) | 6.49769 | − | 1.74105i | 0.00875700 | − | 0.00234643i | ||||
\(743\) | 332.161 | + | 1239.64i | 0.447054 | + | 1.66843i | 0.710455 | + | 0.703743i | \(0.248489\pi\) |
−0.263400 | + | 0.964687i | \(0.584844\pi\) | |||||||
\(744\) | 81.2077 | + | 208.955i | 0.109150 | + | 0.280854i | ||||
\(745\) | 132.497 | + | 9.57019i | 0.177849 | + | 0.0128459i | ||||
\(746\) | −829.060 | −1.11134 | ||||||||
\(747\) | 558.755 | + | 24.6311i | 0.747999 | + | 0.0329733i | ||||
\(748\) | 277.240 | − | 277.240i | 0.370642 | − | 0.370642i | ||||
\(749\) | −1.22121 | + | 0.705066i | −0.00163045 | + | 0.000941343i | ||||
\(750\) | 871.115 | + | 337.111i | 1.16149 | + | 0.449481i | ||||
\(751\) | −470.274 | + | 814.539i | −0.626198 | + | 1.08461i | 0.362110 | + | 0.932135i | \(0.382056\pi\) |
−0.988308 | + | 0.152471i | \(0.951277\pi\) | |||||||
\(752\) | −891.087 | + | 238.766i | −1.18496 | + | 0.317508i | ||||
\(753\) | −822.731 | + | 89.9287i | −1.09260 | + | 0.119427i | ||||
\(754\) | −207.708 | + | 119.920i | −0.275474 | + | 0.159045i | ||||
\(755\) | 407.598 | + | 276.289i | 0.539865 | + | 0.365946i | ||||
\(756\) | 1.79597 | − | 3.63608i | 0.00237562 | − | 0.00480963i | ||||
\(757\) | 872.169 | + | 872.169i | 1.15214 | + | 1.15214i | 0.986123 | + | 0.166015i | \(0.0530901\pi\) |
0.166015 | + | 0.986123i | \(0.446910\pi\) | |||||||
\(758\) | 490.097 | + | 131.321i | 0.646566 | + | 0.173247i | ||||
\(759\) | −787.490 | + | 980.770i | −1.03754 | + | 1.29219i | ||||
\(760\) | 122.694 | + | 42.5615i | 0.161439 | + | 0.0560020i | ||||
\(761\) | −229.806 | + | 398.036i | −0.301979 | + | 0.523043i | −0.976584 | − | 0.215136i | \(-0.930981\pi\) |
0.674605 | + | 0.738179i | \(0.264314\pi\) | |||||||
\(762\) | 1293.83 | − | 948.260i | 1.69794 | − | 1.24444i | ||||
\(763\) | −7.37515 | − | 1.97617i | −0.00966599 | − | 0.00259000i | ||||
\(764\) | 300.712i | 0.393602i | ||||||||
\(765\) | −859.849 | − | 100.330i | −1.12399 | − | 0.131150i | ||||
\(766\) | 51.5397 | 0.0672842 | ||||||||
\(767\) | −63.9473 | + | 238.655i | −0.0833733 | + | 0.311153i | ||||
\(768\) | 384.779 | − | 873.980i | 0.501015 | − | 1.13799i | ||||
\(769\) | 775.372 | + | 447.661i | 1.00829 | + | 0.582134i | 0.910689 | − | 0.413092i | \(-0.135551\pi\) |
0.0975969 | + | 0.995226i | \(0.468884\pi\) | |||||||
\(770\) | −3.42338 | − | 7.05997i | −0.00444594 | − | 0.00916879i | ||||
\(771\) | 17.8905 | − | 6.95289i | 0.0232042 | − | 0.00901802i | ||||
\(772\) | 52.6949 | − | 196.660i | 0.0682576 | − | 0.254741i | ||||
\(773\) | 94.0446 | − | 94.0446i | 0.121662 | − | 0.121662i | −0.643654 | − | 0.765316i | \(-0.722583\pi\) |
0.765316 | + | 0.643654i | \(0.222583\pi\) | |||||||
\(774\) | −67.8039 | + | 214.732i | −0.0876020 | + | 0.277431i | ||||
\(775\) | 154.690 | + | 387.981i | 0.199600 | + | 0.500620i | ||||
\(776\) | 347.868 | + | 602.524i | 0.448283 | + | 0.776449i | ||||
\(777\) | −8.40996 | + | 6.16372i | −0.0108236 | + | 0.00793272i | ||||
\(778\) | −119.433 | − | 445.730i | −0.153513 | − | 0.572918i | ||||
\(779\) | −313.377 | − | 180.928i | −0.402281 | − | 0.232257i | ||||
\(780\) | −127.279 | − | 413.554i | −0.163178 | − | 0.530198i | ||||
\(781\) | 260.825 | + | 451.762i | 0.333963 | + | 0.578441i | ||||
\(782\) | 1536.46 | + | 1536.46i | 1.96479 | + | 1.96479i | ||||
\(783\) | −131.084 | + | 149.283i | −0.167412 | + | 0.190655i | ||||
\(784\) | − | 977.861i | − | 1.24727i | ||||||
\(785\) | −652.970 | + | 564.997i | −0.831809 | + | 0.719742i | ||||
\(786\) | 8.75699 | + | 7.03126i | 0.0111412 | + | 0.00894562i | ||||
\(787\) | 899.963 | − | 241.144i | 1.14354 | − | 0.306410i | 0.363164 | − | 0.931725i | \(-0.381696\pi\) |
0.780372 | + | 0.625315i | \(0.215030\pi\) | |||||||
\(788\) | 137.666 | + | 513.778i | 0.174704 | + | 0.652003i | ||||
\(789\) | 630.030 | + | 97.1064i | 0.798517 | + | 0.123075i | ||||
\(790\) | 385.514 | + | 445.541i | 0.487993 | + | 0.563976i | ||||
\(791\) | 2.52677 | 0.00319440 | ||||||||
\(792\) | −371.825 | − | 16.3908i | −0.469476 | − | 0.0206955i | ||||
\(793\) | −49.8843 | + | 49.8843i | −0.0629058 | + | 0.0629058i | ||||
\(794\) | 721.400 | − | 416.501i | 0.908565 | − | 0.524560i | ||||
\(795\) | 132.658 | − | 579.527i | 0.166866 | − | 0.728965i | ||||
\(796\) | −40.1407 | + | 69.5257i | −0.0504280 | + | 0.0873438i | ||||
\(797\) | 163.649 | − | 43.8496i | 0.205331 | − | 0.0550183i | −0.154687 | − | 0.987963i | \(-0.549437\pi\) |
0.360019 | + | 0.932945i | \(0.382770\pi\) | |||||||
\(798\) | 1.19140 | − | 2.70612i | 0.00149298 | − | 0.00339113i | ||||
\(799\) | 770.071 | − | 444.601i | 0.963793 | − | 0.556446i | ||||
\(800\) | 314.200 | − | 730.879i | 0.392750 | − | 0.913599i | ||||
\(801\) | −115.022 | − | 519.866i | −0.143598 | − | 0.649022i | ||||
\(802\) | −119.900 | − | 119.900i | −0.149502 | − | 0.149502i | ||||
\(803\) | −691.034 | − | 185.162i | −0.860565 | − | 0.230588i | ||||
\(804\) | −324.190 | − | 49.9674i | −0.403222 | − | 0.0621485i | ||||
\(805\) | 13.9012 | − | 6.74068i | 0.0172686 | − | 0.00837352i | ||||
\(806\) | 272.293 | − | 471.626i | 0.337833 | − | 0.585144i | ||||
\(807\) | 113.780 | + | 1040.94i | 0.140991 | + | 1.28989i | ||||
\(808\) | −238.527 | − | 63.9130i | −0.295206 | − | 0.0791003i | ||||
\(809\) | − | 1540.82i | − | 1.90459i | −0.305175 | − | 0.952296i | \(-0.598715\pi\) | ||
0.305175 | − | 0.952296i | \(-0.401285\pi\) | |||||||
\(810\) | −590.396 | − | 817.985i | −0.728884 | − | 1.00986i | ||||
\(811\) | −895.419 | −1.10409 | −0.552046 | − | 0.833813i | \(-0.686153\pi\) | ||||
−0.552046 | + | 0.833813i | \(0.686153\pi\) | |||||||
\(812\) | −0.286042 | + | 1.06752i | −0.000352269 | + | 0.00131469i | ||||
\(813\) | 603.238 | − | 65.9370i | 0.741990 | − | 0.0811033i | ||||
\(814\) | −1017.33 | − | 587.355i | −1.24979 | − | 0.721566i | ||||
\(815\) | 150.824 | − | 434.785i | 0.185060 | − | 0.533479i | ||||
\(816\) | −175.460 | + | 1138.39i | −0.215025 | + | 1.39509i | ||||
\(817\) | −15.0972 | + | 56.3434i | −0.0184788 | + | 0.0689637i | ||||
\(818\) | −664.048 | + | 664.048i | −0.811795 | + | 0.811795i | ||||
\(819\) | 7.83561 | − | 1.73366i | 0.00956729 | − | 0.00211680i | ||||
\(820\) | −385.357 | + | 568.501i | −0.469947 | + | 0.693294i | ||||
\(821\) | −322.268 | − | 558.185i | −0.392531 | − | 0.679884i | 0.600251 | − | 0.799811i | \(-0.295067\pi\) |
−0.992783 | + | 0.119927i | \(0.961734\pi\) | |||||||
\(822\) | 477.710 | + | 210.317i | 0.581156 | + | 0.255860i | ||||
\(823\) | −56.6061 | − | 211.257i | −0.0687802 | − | 0.256691i | 0.922971 | − | 0.384870i | \(-0.125754\pi\) |
−0.991751 | + | 0.128179i | \(0.959087\pi\) | |||||||
\(824\) | 354.182 | + | 204.487i | 0.429832 | + | 0.248164i | ||||
\(825\) | −693.005 | − | 24.4978i | −0.840006 | − | 0.0296943i | ||||
\(826\) | 1.60223 | + | 2.77514i | 0.00193975 | + | 0.00335974i | ||||
\(827\) | −982.768 | − | 982.768i | −1.18835 | − | 1.18835i | −0.977522 | − | 0.210831i | \(-0.932383\pi\) |
−0.210831 | − | 0.977522i | \(-0.567617\pi\) | |||||||
\(828\) | −39.6191 | + | 898.759i | −0.0478492 | + | 1.08546i | ||||
\(829\) | − | 763.031i | − | 0.920424i | −0.887809 | − | 0.460212i | \(-0.847773\pi\) | ||
0.887809 | − | 0.460212i | \(-0.152227\pi\) | |||||||
\(830\) | 55.7574 | − | 771.949i | 0.0671776 | − | 0.930059i | ||||
\(831\) | −110.885 | + | 719.427i | −0.133436 | + | 0.865736i | ||||
\(832\) | 7.18844 | − | 1.92614i | 0.00863996 | − | 0.00231507i | ||||
\(833\) | 243.948 | + | 910.427i | 0.292855 | + | 1.09295i | ||||
\(834\) | −574.431 | + | 715.418i | −0.688766 | + | 0.857816i | ||||
\(835\) | −755.327 | + | 653.564i | −0.904584 | + | 0.782711i | ||||
\(836\) | 118.353 | 0.141571 | ||||||||
\(837\) | 88.2834 | − | 442.373i | 0.105476 | − | 0.528522i | ||||
\(838\) | 402.737 | − | 402.737i | 0.480593 | − | 0.480593i | ||||
\(839\) | −946.477 | + | 546.449i | −1.12810 | + | 0.651309i | −0.943457 | − | 0.331496i | \(-0.892447\pi\) |
−0.184644 | + | 0.982805i | \(0.559113\pi\) | |||||||
\(840\) | 4.04037 | + | 2.13866i | 0.00480997 | + | 0.00254603i | ||||
\(841\) | −393.430 | + | 681.440i | −0.467812 | + | 0.810274i | ||||
\(842\) | −985.940 | + | 264.182i | −1.17095 | + | 0.313755i | ||||
\(843\) | −497.125 | − | 678.291i | −0.589709 | − | 0.804616i | ||||
\(844\) | −369.598 | + | 213.388i | −0.437913 | + | 0.252829i | ||||
\(845\) | 6.30890 | − | 9.30726i | 0.00746615 | − | 0.0110145i | ||||
\(846\) | 988.112 | + | 312.007i | 1.16798 | + | 0.368803i | ||||
\(847\) | −1.71114 | − | 1.71114i | −0.00202024 | − | 0.00202024i | ||||
\(848\) | −764.080 | − | 204.735i | −0.901038 | − | 0.241432i | ||||
\(849\) | −419.295 | − | 1078.89i | −0.493870 | − | 1.27077i | ||||
\(850\) | −172.154 | + | 1185.50i | −0.202535 | + | 1.39471i | ||||
\(851\) | 1156.51 | − | 2003.14i | 1.35900 | − | 2.35386i | ||||
\(852\) | 341.478 | + | 150.339i | 0.400795 | + | 0.176455i | ||||
\(853\) | −1588.02 | − | 425.510i | −1.86169 | − | 0.498839i | −0.861729 | − | 0.507369i | \(-0.830618\pi\) |
−0.999964 | + | 0.00853057i | \(0.997285\pi\) | |||||||
\(854\) | 0.914971i | 0.00107140i | ||||||||
\(855\) | −162.119 | − | 204.949i | −0.189612 | − | 0.239707i | ||||
\(856\) | 92.5628 | 0.108134 | ||||||||
\(857\) | 85.2695 | − | 318.230i | 0.0994977 | − | 0.371330i | −0.898165 | − | 0.439658i | \(-0.855100\pi\) |
0.997663 | + | 0.0683276i | \(0.0217663\pi\) | |||||||
\(858\) | 534.465 | + | 729.240i | 0.622920 | + | 0.849930i | ||||
\(859\) | 1361.73 | + | 786.197i | 1.58525 | + | 0.915247i | 0.994074 | + | 0.108707i | \(0.0346710\pi\) |
0.591180 | + | 0.806540i | \(0.298662\pi\) | |||||||
\(860\) | 104.597 | + | 36.2839i | 0.121624 | + | 0.0421906i | ||||
\(861\) | −9.93239 | − | 7.97502i | −0.0115359 | − | 0.00926251i | ||||
\(862\) | −29.9639 | + | 111.827i | −0.0347609 | + | 0.129729i | ||||
\(863\) | 458.505 | − | 458.505i | 0.531292 | − | 0.531292i | −0.389665 | − | 0.920957i | \(-0.627409\pi\) |
0.920957 | + | 0.389665i | \(0.127409\pi\) | |||||||
\(864\) | −714.698 | + | 476.895i | −0.827197 | + | 0.551961i | ||||
\(865\) | 169.791 | − | 32.6006i | 0.196290 | − | 0.0376885i | ||||
\(866\) | −758.481 | − | 1313.73i | −0.875844 | − | 1.51701i | ||||
\(867\) | −26.4291 | − | 241.792i | −0.0304834 | − | 0.278883i | ||||
\(868\) | −0.649494 | − | 2.42395i | −0.000748265 | − | 0.00279256i | ||||
\(869\) | −378.794 | − | 218.697i | −0.435897 | − | 0.251665i | ||||
\(870\) | 201.409 | + | 187.117i | 0.231505 | + | 0.215077i | ||||
\(871\) | −324.550 | − | 562.137i | −0.372618 | − | 0.645393i | ||||
\(872\) | 354.396 | + | 354.396i | 0.406418 | + | 0.406418i | ||||
\(873\) | 61.6532 | − | 1398.60i | 0.0706222 | − | 1.60206i | ||||
\(874\) | 655.913i | 0.750472i | ||||||||
\(875\) | 7.56226 | + | 3.91887i | 0.00864259 | + | 0.00447870i | ||||
\(876\) | −476.941 | + | 185.357i | −0.544454 | + | 0.211595i | ||||
\(877\) | −1041.72 | + | 279.129i | −1.18783 | + | 0.318277i | −0.798026 | − | 0.602623i | \(-0.794122\pi\) |
−0.389800 | + | 0.920900i | \(0.627456\pi\) | |||||||
\(878\) | 249.625 | + | 931.615i | 0.284311 | + | 1.06106i | ||||
\(879\) | 45.9083 | + | 118.127i | 0.0522279 | + | 0.134387i | ||||
\(880\) | −66.4695 | + | 920.256i | −0.0755335 | + | 1.04574i | ||||
\(881\) | 1585.15 | 1.79927 | 0.899633 | − | 0.436647i | \(-0.143834\pi\) | ||||
0.899633 | + | 0.436647i | \(0.143834\pi\) | |||||||
\(882\) | −590.539 | + | 926.101i | −0.669545 | + | 1.05000i | ||||
\(883\) | −1004.45 | + | 1004.45i | −1.13755 | + | 1.13755i | −0.148657 | + | 0.988889i | \(0.547495\pi\) |
−0.988889 | + | 0.148657i | \(0.952505\pi\) | |||||||
\(884\) | 480.584 | − | 277.466i | 0.543648 | − | 0.313875i | ||||
\(885\) | 283.015 | − | 10.4108i | 0.319791 | − | 0.0117636i | ||||
\(886\) | 913.702 | − | 1582.58i | 1.03127 | − | 1.78621i | ||||
\(887\) | −302.408 | + | 81.0299i | −0.340933 | + | 0.0913528i | −0.425223 | − | 0.905088i | \(-0.639804\pi\) |
0.0842901 | + | 0.996441i | \(0.473138\pi\) | |||||||
\(888\) | 680.378 | − | 74.3688i | 0.766191 | − | 0.0837487i | ||||
\(889\) | 12.6676 | − | 7.31362i | 0.0142492 | − | 0.00822680i | ||||
\(890\) | −723.576 | + | 138.929i | −0.813006 | + | 0.156100i | ||||
\(891\) | 613.112 | + | 430.074i | 0.688117 | + | 0.482687i | ||||
\(892\) | −149.235 | − | 149.235i | −0.167304 | − | 0.167304i | ||||
\(893\) | 259.270 | + | 69.4713i | 0.290336 | + | 0.0777954i | ||||
\(894\) | −124.300 | + | 154.808i | −0.139038 | + | 0.173163i | ||||
\(895\) | −405.687 | − | 836.641i | −0.453281 | − | 0.934794i | ||||
\(896\) | 4.38491 | − | 7.59489i | 0.00489387 | − | 0.00847644i | ||||
\(897\) | −1435.88 | + | 1052.37i | −1.60076 | + | 1.17321i | ||||
\(898\) | −339.479 | − | 90.9632i | −0.378039 | − | 0.101295i | ||||
\(899\) | 122.932i | 0.136743i | ||||||||
\(900\) | −410.148 | + | 278.876i | −0.455720 | + | 0.309863i | ||||
\(901\) | 762.464 | 0.846242 | ||||||||
\(902\) | 371.425 | − | 1386.18i | 0.411779 | − | 1.53678i | ||||
\(903\) | −0.827369 | + | 1.87927i | −0.000916245 | + | 0.00208114i | ||||
\(904\) | −143.639 | − | 82.9302i | −0.158893 | − | 0.0917370i | ||||
\(905\) | 439.933 | − | 213.324i | 0.486114 | − | 0.235717i | ||||
\(906\) | −685.938 | + | 266.581i | −0.757106 | + | 0.294239i | ||||
\(907\) | 95.9237 | − | 357.992i | 0.105759 | − | 0.394699i | −0.892671 | − | 0.450709i | \(-0.851171\pi\) |
0.998430 | + | 0.0560100i | \(0.0178379\pi\) | |||||||
\(908\) | 513.506 | − | 513.506i | 0.565536 | − | 0.565536i | ||||
\(909\) | 335.543 | + | 366.490i | 0.369134 | + | 0.403180i | ||||
\(910\) | −2.09399 | − | 10.9060i | −0.00230109 | − | 0.0119846i | ||||
\(911\) | 490.084 | + | 848.851i | 0.537963 | + | 0.931779i | 0.999014 | + | 0.0444052i | \(0.0141393\pi\) |
−0.461051 | + | 0.887374i | \(0.652527\pi\) | |||||||
\(912\) | −280.440 | + | 205.537i | −0.307500 | + | 0.225369i | ||||
\(913\) | 148.711 | + | 554.997i | 0.162882 | + | 0.607883i | ||||
\(914\) | 1583.93 | + | 914.484i | 1.73297 | + | 1.00053i | ||||
\(915\) | 71.4694 | + | 37.8304i | 0.0781086 | + | 0.0413447i | ||||
\(916\) | 458.489 | + | 794.127i | 0.500534 | + | 0.866951i | ||||
\(917\) | 0.0724117 | + | 0.0724117i | 7.89659e−5 | + | 7.89659e-5i | ||||
\(918\) | 853.657 | − | 972.172i | 0.929909 | − | 1.05901i | ||||
\(919\) | 1321.17i | 1.43762i | 0.695205 | + | 0.718811i | \(0.255313\pi\) | ||||
−0.695205 | + | 0.718811i | \(0.744687\pi\) | |||||||
\(920\) | −1011.47 | − | 73.0581i | −1.09943 | − | 0.0794110i | ||||
\(921\) | 281.565 | + | 226.077i | 0.305717 | + | 0.245470i | ||||
\(922\) | 1544.84 | − | 413.938i | 1.67553 | − | 0.448956i | ||||
\(923\) | 191.092 | + | 713.166i | 0.207034 | + | 0.772661i | ||||
\(924\) | 4.11759 | + | 0.634643i | 0.00445626 | + | 0.000686843i | ||||
\(925\) | 1266.39 | − | 149.606i | 1.36907 | − | 0.161736i | ||||
\(926\) | 691.330 | 0.746577 | ||||||||
\(927\) | −379.683 | − | 730.114i | −0.409583 | − | 0.787609i | ||||
\(928\) | 165.567 | − | 165.567i | 0.178413 | − | 0.178413i | ||||
\(929\) | −672.297 | + | 388.151i | −0.723678 | + | 0.417816i | −0.816105 | − | 0.577904i | \(-0.803871\pi\) |
0.0924267 | + | 0.995719i | \(0.470538\pi\) | |||||||
\(930\) | −608.491 | − | 139.288i | −0.654292 | − | 0.149772i | ||||
\(931\) | −142.259 | + | 246.400i | −0.152802 | + | 0.264662i | ||||
\(932\) | 66.3103 | − | 17.7678i | 0.0711484 | − | 0.0190642i | ||||
\(933\) | −549.027 | + | 1247.05i | −0.588454 | + | 1.33660i | ||||
\(934\) | 175.242 | − | 101.176i | 0.187625 | − | 0.108325i | ||||
\(935\) | −167.691 | − | 873.376i | −0.179349 | − | 0.934092i | ||||
\(936\) | −502.331 | − | 158.616i | −0.536678 | − | 0.169462i | ||||
\(937\) | 295.586 | + | 295.586i | 0.315459 | + | 0.315459i | 0.847020 | − | 0.531561i | \(-0.178394\pi\) |
−0.531561 | + | 0.847020i | \(0.678394\pi\) | |||||||
\(938\) | −8.13175 | − | 2.17890i | −0.00866925 | − | 0.00232292i | ||||
\(939\) | 880.974 | + | 135.784i | 0.938205 | + | 0.144605i | ||||
\(940\) | 166.964 | − | 481.315i | 0.177622 | − | 0.512037i | ||||
\(941\) | −48.8020 | + | 84.5275i | −0.0518618 | + | 0.0898273i | −0.890791 | − | 0.454413i | \(-0.849849\pi\) |
0.838929 | + | 0.544241i | \(0.183182\pi\) | |||||||
\(942\) | −140.220 | − | 1282.83i | −0.148854 | − | 1.36182i | ||||
\(943\) | 2729.40 | + | 731.341i | 2.89438 | + | 0.775548i | ||||
\(944\) | − | 376.820i | − | 0.399174i | ||||||
\(945\) | −4.54122 | − | 7.99964i | −0.00480552 | − | 0.00846523i | ||||
\(946\) | −231.333 | −0.244538 | ||||||||
\(947\) | 47.4532 | − | 177.098i | 0.0501090 | − | 0.187009i | −0.936335 | − | 0.351108i | \(-0.885805\pi\) |
0.986444 | + | 0.164099i | \(0.0524716\pi\) | |||||||
\(948\) | −310.991 | + | 33.9929i | −0.328050 | + | 0.0358575i | ||||
\(949\) | −876.908 | − | 506.283i | −0.924034 | − | 0.533491i | ||||
\(950\) | −289.790 | + | 216.298i | −0.305042 | + | 0.227682i | ||||
\(951\) | 40.4023 | − | 262.131i | 0.0424840 | − | 0.275638i | ||||
\(952\) | −1.51743 | + | 5.66313i | −0.00159394 | + | 0.00594866i | ||||
\(953\) | −16.8810 | + | 16.8810i | −0.0177135 | + | 0.0177135i | −0.715908 | − | 0.698195i | \(-0.753987\pi\) |
0.698195 | + | 0.715908i | \(0.253987\pi\) | |||||||
\(954\) | 599.995 | + | 655.332i | 0.628925 | + | 0.686931i | ||||
\(955\) | 564.603 | + | 382.714i | 0.591207 | + | 0.400748i | ||||
\(956\) | −340.507 | − | 589.776i | −0.356179 | − | 0.616920i | ||||
\(957\) | −186.791 | − | 82.2369i | −0.195184 | − | 0.0859320i | ||||
\(958\) | −312.153 | − | 1164.97i | −0.325838 | − | 1.21604i | ||||
\(959\) | 4.12185 | + | 2.37975i | 0.00429807 | + | 0.00248149i | ||||
\(960\) | −4.53388 | − | 7.22575i | −0.00472279 | − | 0.00752682i | ||||
\(961\) | 340.934 | + | 590.514i | 0.354770 | + | 0.614479i | ||||
\(962\) | −1175.66 | − | 1175.66i | −1.22210 | − | 1.22210i | ||||
\(963\) | −157.044 | − | 100.141i | −0.163078 | − | 0.103988i | ||||
\(964\) | 56.6819i | 0.0587987i | ||||||||
\(965\) | −302.175 | − | 349.226i | −0.313135 | − | 0.361892i | ||||
\(966\) | −3.51719 | + | 22.8196i | −0.00364098 | + | 0.0236228i | ||||
\(967\) | 1161.19 | − | 311.140i | 1.20082 | − | 0.321758i | 0.397665 | − | 0.917531i | \(-0.369821\pi\) |
0.803153 | + | 0.595772i | \(0.203154\pi\) | |||||||
\(968\) | 41.1125 | + | 153.434i | 0.0424716 | + | 0.158506i | ||||
\(969\) | 209.825 | − | 261.324i | 0.216538 | − | 0.269684i | ||||
\(970\) | −1932.24 | − | 139.564i | −1.99200 | − | 0.143881i | ||||
\(971\) | −608.975 | −0.627163 | −0.313582 | − | 0.949561i | \(-0.601529\pi\) | ||||
−0.313582 | + | 0.949561i | \(0.601529\pi\) | |||||||
\(972\) | 535.540 | − | 11.1225i | 0.550967 | − | 0.0114429i | ||||
\(973\) | −5.91580 | + | 5.91580i | −0.00607996 | + | 0.00607996i | ||||
\(974\) | 494.753 | − | 285.646i | 0.507960 | − | 0.293271i | ||||
\(975\) | −938.457 | − | 287.355i | −0.962520 | − | 0.294723i | ||||
\(976\) | 53.7969 | − | 93.1790i | 0.0551198 | − | 0.0954702i | ||||
\(977\) | 85.2493 | − | 22.8425i | 0.0872562 | − | 0.0233802i | −0.214927 | − | 0.976630i | \(-0.568951\pi\) |
0.302183 | + | 0.953250i | \(0.402285\pi\) | |||||||
\(978\) | 406.572 | + | 554.739i | 0.415718 | + | 0.567218i | ||||
\(979\) | 473.701 | − | 273.491i | 0.483862 | − | 0.279358i | ||||
\(980\) | 446.998 | + | 302.996i | 0.456120 | + | 0.309180i | ||||
\(981\) | −217.865 | − | 984.684i | −0.222085 | − | 1.00376i | ||||
\(982\) | −1391.51 | − | 1391.51i | −1.41701 | − | 1.41701i | ||||
\(983\) | 1378.97 | + | 369.494i | 1.40282 | + | 0.375884i | 0.879356 | − | 0.476166i | \(-0.157974\pi\) |
0.523461 | + | 0.852049i | \(0.324640\pi\) | |||||||
\(984\) | 302.881 | + | 779.343i | 0.307806 | + | 0.792015i | ||||
\(985\) | 1139.85 | + | 395.406i | 1.15721 | + | 0.401428i | ||||
\(986\) | −176.289 | + | 305.341i | −0.178792 | + | 0.309676i | ||||
\(987\) | 8.64766 | + | 3.80723i | 0.00876156 | + | 0.00385738i | ||||
\(988\) | 161.805 | + | 43.3555i | 0.163770 | + | 0.0438821i | ||||
\(989\) | − | 455.499i | − | 0.460565i | ||||||
\(990\) | 618.701 | − | 831.403i | 0.624951 | − | 0.839801i | ||||
\(991\) | 14.7275 | 0.0148613 | 0.00743063 | − | 0.999972i | \(-0.497635\pi\) | ||||
0.00743063 | + | 0.999972i | \(0.497635\pi\) | |||||||
\(992\) | −137.604 | + | 513.545i | −0.138714 | + | 0.517687i | ||||
\(993\) | −791.484 | − | 1079.92i | −0.797063 | − | 1.08754i | ||||
\(994\) | 8.29290 | + | 4.78791i | 0.00834296 | + | 0.00481681i | ||||
\(995\) | 79.4514 | + | 163.851i | 0.0798506 | + | 0.164675i | ||||
\(996\) | 320.448 | + | 257.298i | 0.321735 | + | 0.258331i | ||||
\(997\) | −59.6878 | + | 222.758i | −0.0598674 | + | 0.223428i | −0.989378 | − | 0.145368i | \(-0.953563\pi\) |
0.929510 | + | 0.368796i | \(0.120230\pi\) | |||||||
\(998\) | −858.989 | + | 858.989i | −0.860710 | + | 0.860710i | ||||
\(999\) | −1234.80 | − | 609.903i | −1.23603 | − | 0.610514i |
(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 | 45.3.k.a.22.2 | yes | 40 | |
3.2 | odd | 2 | 135.3.l.a.37.9 | 40 | |||
5.2 | odd | 4 | 225.3.o.b.193.2 | 40 | |||
5.3 | odd | 4 | inner | 45.3.k.a.13.9 | yes | 40 | |
5.4 | even | 2 | 225.3.o.b.157.9 | 40 | |||
9.2 | odd | 6 | 135.3.l.a.127.2 | 40 | |||
9.4 | even | 3 | 405.3.g.h.82.2 | 20 | |||
9.5 | odd | 6 | 405.3.g.g.82.9 | 20 | |||
9.7 | even | 3 | inner | 45.3.k.a.7.9 | ✓ | 40 | |
15.8 | even | 4 | 135.3.l.a.118.2 | 40 | |||
45.7 | odd | 12 | 225.3.o.b.43.9 | 40 | |||
45.13 | odd | 12 | 405.3.g.h.163.2 | 20 | |||
45.23 | even | 12 | 405.3.g.g.163.9 | 20 | |||
45.34 | even | 6 | 225.3.o.b.7.2 | 40 | |||
45.38 | even | 12 | 135.3.l.a.73.9 | 40 | |||
45.43 | odd | 12 | inner | 45.3.k.a.43.2 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.3.k.a.7.9 | ✓ | 40 | 9.7 | even | 3 | inner | |
45.3.k.a.13.9 | yes | 40 | 5.3 | odd | 4 | inner | |
45.3.k.a.22.2 | yes | 40 | 1.1 | even | 1 | trivial | |
45.3.k.a.43.2 | yes | 40 | 45.43 | odd | 12 | inner | |
135.3.l.a.37.9 | 40 | 3.2 | odd | 2 | |||
135.3.l.a.73.9 | 40 | 45.38 | even | 12 | |||
135.3.l.a.118.2 | 40 | 15.8 | even | 4 | |||
135.3.l.a.127.2 | 40 | 9.2 | odd | 6 | |||
225.3.o.b.7.2 | 40 | 45.34 | even | 6 | |||
225.3.o.b.43.9 | 40 | 45.7 | odd | 12 | |||
225.3.o.b.157.9 | 40 | 5.4 | even | 2 | |||
225.3.o.b.193.2 | 40 | 5.2 | odd | 4 | |||
405.3.g.g.82.9 | 20 | 9.5 | odd | 6 | |||
405.3.g.g.163.9 | 20 | 45.23 | even | 12 | |||
405.3.g.h.82.2 | 20 | 9.4 | even | 3 | |||
405.3.g.h.163.2 | 20 | 45.13 | odd | 12 |