Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [418,2,Mod(65,418)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(418, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("418.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 418 = 2 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 418.h (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.33774680449\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 41 x^{18} + 707 x^{16} + 6667 x^{14} + 37400 x^{12} + 126976 x^{10} + 253280 x^{8} + \cdots + 2304 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 65.10 | ||
Root | \(-2.97905i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 418.65 |
Dual form | 418.2.h.b.373.10 |
$q$-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 \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(343\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 2.57993 | + | 1.48952i | 1.48952 | + | 0.859977i | 0.999928 | − | 0.0119719i | \(-0.00381086\pi\) |
0.489596 | + | 0.871949i | \(0.337144\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.71710 | − | 2.97410i | 0.767910 | − | 1.33006i | −0.170784 | − | 0.985309i | \(-0.554630\pi\) |
0.938694 | − | 0.344751i | \(-0.112037\pi\) | |||||||
\(6\) | 2.57993 | − | 1.48952i | 1.05325 | − | 0.608096i | ||||
\(7\) | 4.12917i | 1.56068i | 0.625356 | + | 0.780340i | \(0.284954\pi\) | ||||
−0.625356 | + | 0.780340i | \(0.715046\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.93737 | + | 5.08767i | 0.979122 | + | 1.69589i | ||||
\(10\) | −1.71710 | − | 2.97410i | −0.542995 | − | 0.940494i | ||||
\(11\) | −3.12139 | − | 1.12112i | −0.941135 | − | 0.338030i | ||||
\(12\) | − | 2.97905i | − | 0.859977i | ||||||
\(13\) | 0.367756 | + | 0.636973i | 0.101997 | + | 0.176664i | 0.912507 | − | 0.409060i | \(-0.134143\pi\) |
−0.810510 | + | 0.585725i | \(0.800810\pi\) | |||||||
\(14\) | 3.57597 | + | 2.06459i | 0.955717 | + | 0.551784i | ||||
\(15\) | 8.86000 | − | 5.11532i | 2.28764 | − | 1.32077i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0.549314 | + | 0.317147i | 0.133228 | + | 0.0769194i | 0.565133 | − | 0.825000i | \(-0.308825\pi\) |
−0.431905 | + | 0.901919i | \(0.642158\pi\) | |||||||
\(18\) | 5.87473 | 1.38469 | ||||||||
\(19\) | −3.57734 | − | 2.49051i | −0.820698 | − | 0.571363i | ||||
\(20\) | −3.43420 | −0.767910 | ||||||||
\(21\) | −6.15050 | + | 10.6530i | −1.34215 | + | 2.32467i | ||||
\(22\) | −2.53161 | + | 2.14265i | −0.539742 | + | 0.456814i | ||||
\(23\) | −2.44271 | − | 4.23090i | −0.509341 | − | 0.882204i | −0.999941 | − | 0.0108198i | \(-0.996556\pi\) |
0.490601 | − | 0.871385i | \(-0.336777\pi\) | |||||||
\(24\) | −2.57993 | − | 1.48952i | −0.526626 | − | 0.304048i | ||||
\(25\) | −3.39686 | − | 5.88354i | −0.679373 | − | 1.17671i | ||||
\(26\) | 0.735513 | 0.144246 | ||||||||
\(27\) | 8.56397i | 1.64814i | ||||||||
\(28\) | 3.57597 | − | 2.06459i | 0.675794 | − | 0.390170i | ||||
\(29\) | −5.19100 | − | 8.99108i | −0.963945 | − | 1.66960i | −0.712423 | − | 0.701750i | \(-0.752402\pi\) |
−0.251522 | − | 0.967851i | \(-0.580931\pi\) | |||||||
\(30\) | − | 10.2306i | − | 1.86785i | ||||||
\(31\) | 7.65537i | 1.37494i | 0.726211 | + | 0.687472i | \(0.241280\pi\) | ||||
−0.726211 | + | 0.687472i | \(0.758720\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −6.38305 | − | 7.54180i | −1.11115 | − | 1.31286i | ||||
\(34\) | 0.549314 | − | 0.317147i | 0.0942066 | − | 0.0543902i | ||||
\(35\) | 12.2806 | + | 7.09020i | 2.07580 | + | 1.19846i | ||||
\(36\) | 2.93737 | − | 5.08767i | 0.489561 | − | 0.847945i | ||||
\(37\) | 5.00167i | 0.822269i | 0.911575 | + | 0.411135i | \(0.134867\pi\) | ||||
−0.911575 | + | 0.411135i | \(0.865133\pi\) | |||||||
\(38\) | −3.94552 | + | 1.85281i | −0.640047 | + | 0.300565i | ||||
\(39\) | 2.19113i | 0.350861i | ||||||||
\(40\) | −1.71710 | + | 2.97410i | −0.271497 | + | 0.470247i | ||||
\(41\) | 4.69970 | − | 8.14011i | 0.733969 | − | 1.27127i | −0.221205 | − | 0.975227i | \(-0.570999\pi\) |
0.955174 | − | 0.296045i | \(-0.0956678\pi\) | |||||||
\(42\) | 6.15050 | + | 10.6530i | 0.949043 | + | 1.64379i | ||||
\(43\) | 6.93593 | + | 4.00446i | 1.05772 | + | 0.610675i | 0.924801 | − | 0.380452i | \(-0.124232\pi\) |
0.132919 | + | 0.991127i | \(0.457565\pi\) | |||||||
\(44\) | 0.589780 | + | 3.26376i | 0.0889127 | + | 0.492031i | ||||
\(45\) | 20.1750 | 3.00751 | ||||||||
\(46\) | −4.88543 | −0.720317 | ||||||||
\(47\) | 0.102063 | + | 0.176779i | 0.0148875 | + | 0.0257858i | 0.873373 | − | 0.487052i | \(-0.161928\pi\) |
−0.858486 | + | 0.512838i | \(0.828594\pi\) | |||||||
\(48\) | −2.57993 | + | 1.48952i | −0.372381 | + | 0.214994i | ||||
\(49\) | −10.0501 | −1.43572 | ||||||||
\(50\) | −6.79373 | −0.960778 | ||||||||
\(51\) | 0.944795 | + | 1.63643i | 0.132298 | + | 0.229147i | ||||
\(52\) | 0.367756 | − | 0.636973i | 0.0509986 | − | 0.0883322i | ||||
\(53\) | −5.92214 | + | 3.41915i | −0.813468 | + | 0.469656i | −0.848159 | − | 0.529742i | \(-0.822289\pi\) |
0.0346908 | + | 0.999398i | \(0.488955\pi\) | |||||||
\(54\) | 7.41662 | + | 4.28199i | 1.00927 | + | 0.582704i | ||||
\(55\) | −8.69406 | + | 7.35828i | −1.17231 | + | 0.992190i | ||||
\(56\) | − | 4.12917i | − | 0.551784i | ||||||
\(57\) | −5.51961 | − | 11.7539i | −0.731090 | − | 1.55684i | ||||
\(58\) | −10.3820 | −1.36322 | ||||||||
\(59\) | 1.83644 | + | 1.06027i | 0.239084 | + | 0.138035i | 0.614756 | − | 0.788718i | \(-0.289255\pi\) |
−0.375672 | + | 0.926753i | \(0.622588\pi\) | |||||||
\(60\) | −8.86000 | − | 5.11532i | −1.14382 | − | 0.660386i | ||||
\(61\) | 0.547594 | − | 0.316154i | 0.0701122 | − | 0.0404793i | −0.464534 | − | 0.885555i | \(-0.653778\pi\) |
0.534646 | + | 0.845076i | \(0.320445\pi\) | |||||||
\(62\) | 6.62974 | + | 3.82768i | 0.841978 | + | 0.486116i | ||||
\(63\) | −21.0079 | + | 12.1289i | −2.64674 | + | 1.52810i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.52590 | 0.313299 | ||||||||
\(66\) | −9.72291 | + | 1.75698i | −1.19681 | + | 0.216270i | ||||
\(67\) | 9.31419 | − | 5.37755i | 1.13791 | − | 0.656972i | 0.191997 | − | 0.981395i | \(-0.438503\pi\) |
0.945912 | + | 0.324423i | \(0.105170\pi\) | |||||||
\(68\) | − | 0.634293i | − | 0.0769194i | ||||||
\(69\) | − | 14.5539i | − | 1.75209i | ||||||
\(70\) | 12.2806 | − | 7.09020i | 1.46781 | − | 0.847441i | ||||
\(71\) | 1.78588 | + | 1.03108i | 0.211944 | + | 0.122366i | 0.602215 | − | 0.798334i | \(-0.294285\pi\) |
−0.390270 | + | 0.920700i | \(0.627618\pi\) | |||||||
\(72\) | −2.93737 | − | 5.08767i | −0.346172 | − | 0.599587i | ||||
\(73\) | −1.12051 | − | 0.646925i | −0.131145 | − | 0.0757168i | 0.432992 | − | 0.901398i | \(-0.357458\pi\) |
−0.564137 | + | 0.825681i | \(0.690791\pi\) | |||||||
\(74\) | 4.33157 | + | 2.50083i | 0.503535 | + | 0.290716i | ||||
\(75\) | − | 20.2389i | − | 2.33698i | ||||||
\(76\) | −0.368179 | + | 4.34332i | −0.0422330 | + | 0.498213i | ||||
\(77\) | 4.62929 | − | 12.8888i | 0.527556 | − | 1.46881i | ||||
\(78\) | 1.89757 | + | 1.09556i | 0.214858 | + | 0.124048i | ||||
\(79\) | −8.45613 | + | 14.6465i | −0.951389 | + | 1.64785i | −0.208966 | + | 0.977923i | \(0.567010\pi\) |
−0.742423 | + | 0.669932i | \(0.766323\pi\) | |||||||
\(80\) | 1.71710 | + | 2.97410i | 0.191978 | + | 0.332515i | ||||
\(81\) | −3.94415 | + | 6.83146i | −0.438238 | + | 0.759051i | ||||
\(82\) | −4.69970 | − | 8.14011i | −0.518995 | − | 0.898925i | ||||
\(83\) | 3.25643i | 0.357439i | 0.983900 | + | 0.178720i | \(0.0571955\pi\) | ||||
−0.983900 | + | 0.178720i | \(0.942804\pi\) | |||||||
\(84\) | 12.3010 | 1.34215 | ||||||||
\(85\) | 1.88645 | − | 1.08915i | 0.204615 | − | 0.118134i | ||||
\(86\) | 6.93593 | − | 4.00446i | 0.747921 | − | 0.431812i | ||||
\(87\) | − | 30.9285i | − | 3.31588i | ||||||
\(88\) | 3.12139 | + | 1.12112i | 0.332742 | + | 0.119512i | ||||
\(89\) | −9.59246 | + | 5.53821i | −1.01680 | + | 0.587049i | −0.913175 | − | 0.407568i | \(-0.866377\pi\) |
−0.103624 | + | 0.994617i | \(0.533044\pi\) | |||||||
\(90\) | 10.0875 | − | 17.4721i | 1.06332 | − | 1.84172i | ||||
\(91\) | −2.63017 | + | 1.51853i | −0.275717 | + | 0.159185i | ||||
\(92\) | −2.44271 | + | 4.23090i | −0.254670 | + | 0.441102i | ||||
\(93\) | −11.4029 | + | 19.7503i | −1.18242 | + | 2.04801i | ||||
\(94\) | 0.204127 | 0.0210541 | ||||||||
\(95\) | −13.5497 | + | 6.36291i | −1.39017 | + | 0.652821i | ||||
\(96\) | 2.97905i | 0.304048i | ||||||||
\(97\) | 0.135282 | + | 0.0781049i | 0.0137358 | + | 0.00793035i | 0.506852 | − | 0.862033i | \(-0.330809\pi\) |
−0.493116 | + | 0.869963i | \(0.664142\pi\) | |||||||
\(98\) | −5.02503 | + | 8.70360i | −0.507604 | + | 0.879196i | ||||
\(99\) | −3.46480 | − | 19.1737i | −0.348226 | − | 1.92703i | ||||
\(100\) | −3.39686 | + | 5.88354i | −0.339686 | + | 0.588354i | ||||
\(101\) | −6.12946 | + | 3.53884i | −0.609904 | + | 0.352128i | −0.772928 | − | 0.634494i | \(-0.781209\pi\) |
0.163024 | + | 0.986622i | \(0.447875\pi\) | |||||||
\(102\) | 1.88959 | 0.187097 | ||||||||
\(103\) | − | 11.9269i | − | 1.17520i | −0.809153 | − | 0.587598i | \(-0.800074\pi\) | ||
0.809153 | − | 0.587598i | \(-0.199926\pi\) | |||||||
\(104\) | −0.367756 | − | 0.636973i | −0.0360615 | − | 0.0624603i | ||||
\(105\) | 21.1221 | + | 36.5845i | 2.06130 | + | 3.57028i | ||||
\(106\) | 6.83829i | 0.664194i | ||||||||
\(107\) | 7.06672 | 0.683166 | 0.341583 | − | 0.939852i | \(-0.389037\pi\) | ||||
0.341583 | + | 0.939852i | \(0.389037\pi\) | |||||||
\(108\) | 7.41662 | − | 4.28199i | 0.713664 | − | 0.412034i | ||||
\(109\) | 2.35983 | − | 4.08734i | 0.226030 | − | 0.391496i | −0.730598 | − | 0.682808i | \(-0.760758\pi\) |
0.956628 | + | 0.291312i | \(0.0940918\pi\) | |||||||
\(110\) | 2.02542 | + | 11.2084i | 0.193117 | + | 1.06868i | ||||
\(111\) | −7.45011 | + | 12.9040i | −0.707133 | + | 1.22479i | ||||
\(112\) | −3.57597 | − | 2.06459i | −0.337897 | − | 0.195085i | ||||
\(113\) | 4.61349i | 0.434000i | 0.976172 | + | 0.217000i | \(0.0696272\pi\) | ||||
−0.976172 | + | 0.217000i | \(0.930373\pi\) | |||||||
\(114\) | −12.9390 | − | 1.09682i | −1.21185 | − | 0.102727i | ||||
\(115\) | −16.7775 | −1.56451 | ||||||||
\(116\) | −5.19100 | + | 8.99108i | −0.481973 | + | 0.834801i | ||||
\(117\) | −2.16047 | + | 3.74204i | −0.199736 | + | 0.345952i | ||||
\(118\) | 1.83644 | − | 1.06027i | 0.169058 | − | 0.0976055i | ||||
\(119\) | −1.30955 | + | 2.26821i | −0.120047 | + | 0.207927i | ||||
\(120\) | −8.86000 | + | 5.11532i | −0.808804 | + | 0.466963i | ||||
\(121\) | 8.48619 | + | 6.99890i | 0.771472 | + | 0.636263i | ||||
\(122\) | − | 0.632307i | − | 0.0572464i | ||||||
\(123\) | 24.2498 | − | 14.0006i | 2.18653 | − | 1.26239i | ||||
\(124\) | 6.62974 | − | 3.82768i | 0.595368 | − | 0.343736i | ||||
\(125\) | −6.16002 | −0.550969 | ||||||||
\(126\) | 24.2578i | 2.16105i | ||||||||
\(127\) | 5.66328 | + | 9.80908i | 0.502535 | + | 0.870415i | 0.999996 | + | 0.00292914i | \(0.000932375\pi\) |
−0.497461 | + | 0.867486i | \(0.665734\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 11.9295 | + | 20.6625i | 1.05033 | + | 1.81923i | ||||
\(130\) | 1.26295 | − | 2.18749i | 0.110768 | − | 0.191856i | ||||
\(131\) | 0.135724 | + | 0.0783602i | 0.0118583 | + | 0.00684637i | 0.505917 | − | 0.862582i | \(-0.331154\pi\) |
−0.494059 | + | 0.869428i | \(0.664487\pi\) | |||||||
\(132\) | −3.33986 | + | 9.29878i | −0.290698 | + | 0.809355i | ||||
\(133\) | 10.2838 | − | 14.7714i | 0.891715 | − | 1.28085i | ||||
\(134\) | − | 10.7551i | − | 0.929099i | ||||||
\(135\) | 25.4701 | + | 14.7052i | 2.19212 | + | 1.26562i | ||||
\(136\) | −0.549314 | − | 0.317147i | −0.0471033 | − | 0.0271951i | ||||
\(137\) | 2.40597 | + | 4.16727i | 0.205556 | + | 0.356034i | 0.950310 | − | 0.311306i | \(-0.100766\pi\) |
−0.744754 | + | 0.667339i | \(0.767433\pi\) | |||||||
\(138\) | −12.6041 | − | 7.27696i | −1.07293 | − | 0.619456i | ||||
\(139\) | −7.55586 | + | 4.36238i | −0.640880 | + | 0.370012i | −0.784953 | − | 0.619555i | \(-0.787313\pi\) |
0.144074 | + | 0.989567i | \(0.453980\pi\) | |||||||
\(140\) | − | 14.1804i | − | 1.19846i | ||||||
\(141\) | 0.608103i | 0.0512115i | ||||||||
\(142\) | 1.78588 | − | 1.03108i | 0.149867 | − | 0.0865260i | ||||
\(143\) | −0.433791 | − | 2.40054i | −0.0362754 | − | 0.200743i | ||||
\(144\) | −5.87473 | −0.489561 | ||||||||
\(145\) | −35.6539 | −2.96089 | ||||||||
\(146\) | −1.12051 | + | 0.646925i | −0.0927337 | + | 0.0535399i | ||||
\(147\) | −25.9285 | − | 14.9698i | −2.13854 | − | 1.23469i | ||||
\(148\) | 4.33157 | − | 2.50083i | 0.356053 | − | 0.205567i | ||||
\(149\) | −3.98778 | − | 2.30235i | −0.326692 | − | 0.188615i | 0.327680 | − | 0.944789i | \(-0.393733\pi\) |
−0.654371 | + | 0.756173i | \(0.727067\pi\) | |||||||
\(150\) | −17.5274 | − | 10.1194i | −1.43110 | − | 0.826248i | ||||
\(151\) | 12.2697 | 0.998491 | 0.499246 | − | 0.866461i | \(-0.333611\pi\) | ||||
0.499246 | + | 0.866461i | \(0.333611\pi\) | |||||||
\(152\) | 3.57734 | + | 2.49051i | 0.290160 | + | 0.202007i | ||||
\(153\) | 3.72630i | 0.301254i | ||||||||
\(154\) | −8.84736 | − | 10.4535i | −0.712940 | − | 0.842364i | ||||
\(155\) | 22.7679 | + | 13.1450i | 1.82876 | + | 1.05583i | ||||
\(156\) | 1.89757 | − | 1.09556i | 0.151927 | − | 0.0877153i | ||||
\(157\) | 7.64537 | − | 13.2422i | 0.610167 | − | 1.05684i | −0.381045 | − | 0.924557i | \(-0.624436\pi\) |
0.991212 | − | 0.132284i | \(-0.0422311\pi\) | |||||||
\(158\) | 8.45613 | + | 14.6465i | 0.672734 | + | 1.16521i | ||||
\(159\) | −20.3716 | −1.61557 | ||||||||
\(160\) | 3.43420 | 0.271497 | ||||||||
\(161\) | 17.4701 | − | 10.0864i | 1.37684 | − | 0.794918i | ||||
\(162\) | 3.94415 | + | 6.83146i | 0.309881 | + | 0.536730i | ||||
\(163\) | 7.53928 | 0.590522 | 0.295261 | − | 0.955417i | \(-0.404593\pi\) | ||||
0.295261 | + | 0.955417i | \(0.404593\pi\) | |||||||
\(164\) | −9.39939 | −0.733969 | ||||||||
\(165\) | −33.3904 | + | 6.03384i | −2.59944 | + | 0.469734i | ||||
\(166\) | 2.82015 | + | 1.62821i | 0.218886 | + | 0.126374i | ||||
\(167\) | 2.58916 | + | 4.48456i | 0.200355 | + | 0.347025i | 0.948643 | − | 0.316349i | \(-0.102457\pi\) |
−0.748288 | + | 0.663374i | \(0.769124\pi\) | |||||||
\(168\) | 6.15050 | − | 10.6530i | 0.474521 | − | 0.821895i | ||||
\(169\) | 6.22951 | − | 10.7898i | 0.479193 | − | 0.829987i | ||||
\(170\) | − | 2.17829i | − | 0.167067i | ||||||
\(171\) | 2.16295 | − | 25.5159i | 0.165405 | − | 1.95125i | ||||
\(172\) | − | 8.00892i | − | 0.610675i | ||||||
\(173\) | −3.21632 | + | 5.57082i | −0.244532 | + | 0.423542i | −0.962000 | − | 0.273050i | \(-0.911968\pi\) |
0.717468 | + | 0.696592i | \(0.245301\pi\) | |||||||
\(174\) | −26.7849 | − | 15.4643i | −2.03056 | − | 1.17234i | ||||
\(175\) | 24.2941 | − | 14.0262i | 1.83647 | − | 1.06028i | ||||
\(176\) | 2.53161 | − | 2.14265i | 0.190827 | − | 0.161508i | ||||
\(177\) | 3.15859 | + | 5.47084i | 0.237414 | + | 0.411213i | ||||
\(178\) | 11.0764i | 0.830213i | ||||||||
\(179\) | 16.6994i | 1.24817i | 0.781355 | + | 0.624087i | \(0.214529\pi\) | ||||
−0.781355 | + | 0.624087i | \(0.785471\pi\) | |||||||
\(180\) | −10.0875 | − | 17.4721i | −0.751878 | − | 1.30229i | ||||
\(181\) | −1.02910 | + | 0.594151i | −0.0764924 | + | 0.0441629i | −0.537758 | − | 0.843099i | \(-0.680729\pi\) |
0.461266 | + | 0.887262i | \(0.347395\pi\) | |||||||
\(182\) | 3.03706i | 0.225122i | ||||||||
\(183\) | 1.88367 | 0.139245 | ||||||||
\(184\) | 2.44271 | + | 4.23090i | 0.180079 | + | 0.311906i | ||||
\(185\) | 14.8755 | + | 8.58836i | 1.09367 | + | 0.631429i | ||||
\(186\) | 11.4029 | + | 19.7503i | 0.836098 | + | 1.44816i | ||||
\(187\) | −1.35907 | − | 1.60579i | −0.0993848 | − | 0.117427i | ||||
\(188\) | 0.102063 | − | 0.176779i | 0.00744373 | − | 0.0128929i | ||||
\(189\) | −35.3621 | −2.57221 | ||||||||
\(190\) | −1.26440 | + | 14.9158i | −0.0917292 | + | 1.08211i | ||||
\(191\) | −9.52305 | −0.689064 | −0.344532 | − | 0.938775i | \(-0.611962\pi\) | ||||
−0.344532 | + | 0.938775i | \(0.611962\pi\) | |||||||
\(192\) | 2.57993 | + | 1.48952i | 0.186191 | + | 0.107497i | ||||
\(193\) | 1.58290 | − | 2.74166i | 0.113939 | − | 0.197349i | −0.803416 | − | 0.595418i | \(-0.796986\pi\) |
0.917355 | + | 0.398070i | \(0.130320\pi\) | |||||||
\(194\) | 0.135282 | − | 0.0781049i | 0.00971266 | − | 0.00560761i | ||||
\(195\) | 6.51665 | + | 3.76239i | 0.466667 | + | 0.269430i | ||||
\(196\) | 5.02503 | + | 8.70360i | 0.358930 | + | 0.621686i | ||||
\(197\) | − | 13.0048i | − | 0.926553i | −0.886214 | − | 0.463277i | \(-0.846674\pi\) | ||
0.886214 | − | 0.463277i | \(-0.153326\pi\) | |||||||
\(198\) | −18.3374 | − | 6.58627i | −1.30318 | − | 0.468066i | ||||
\(199\) | −10.1712 | − | 17.6170i | −0.721017 | − | 1.24884i | −0.960593 | − | 0.277960i | \(-0.910342\pi\) |
0.239576 | − | 0.970878i | \(-0.422992\pi\) | |||||||
\(200\) | 3.39686 | + | 5.88354i | 0.240195 | + | 0.416029i | ||||
\(201\) | 32.0400 | 2.25993 | ||||||||
\(202\) | 7.07769i | 0.497984i | ||||||||
\(203\) | 37.1257 | − | 21.4345i | 2.60571 | − | 1.50441i | ||||
\(204\) | 0.944795 | − | 1.63643i | 0.0661489 | − | 0.114573i | ||||
\(205\) | −16.1397 | − | 27.9548i | −1.12725 | − | 1.95245i | ||||
\(206\) | −10.3290 | − | 5.96347i | −0.719658 | − | 0.415495i | ||||
\(207\) | 14.3503 | − | 24.8554i | 0.997414 | − | 1.72757i | ||||
\(208\) | −0.735513 | −0.0509986 | ||||||||
\(209\) | 8.37412 | + | 11.7845i | 0.579250 | + | 0.815150i | ||||
\(210\) | 42.2441 | 2.91512 | ||||||||
\(211\) | 8.84798 | − | 15.3252i | 0.609120 | − | 1.05503i | −0.382266 | − | 0.924053i | \(-0.624856\pi\) |
0.991386 | − | 0.130975i | \(-0.0418106\pi\) | |||||||
\(212\) | 5.92214 | + | 3.41915i | 0.406734 | + | 0.234828i | ||||
\(213\) | 3.07163 | + | 5.32021i | 0.210464 | + | 0.364535i | ||||
\(214\) | 3.53336 | − | 6.11996i | 0.241536 | − | 0.418352i | ||||
\(215\) | 23.8194 | − | 13.7521i | 1.62447 | − | 0.937887i | ||||
\(216\) | − | 8.56397i | − | 0.582704i | ||||||
\(217\) | −31.6103 | −2.14585 | ||||||||
\(218\) | −2.35983 | − | 4.08734i | −0.159828 | − | 0.276829i | ||||
\(219\) | −1.92722 | − | 3.33804i | −0.130229 | − | 0.225564i | ||||
\(220\) | 10.7195 | + | 3.85014i | 0.722708 | + | 0.259576i | ||||
\(221\) | 0.466531i | 0.0313823i | ||||||||
\(222\) | 7.45011 | + | 12.9040i | 0.500019 | + | 0.866057i | ||||
\(223\) | −14.6912 | − | 8.48197i | −0.983796 | − | 0.567995i | −0.0803821 | − | 0.996764i | \(-0.525614\pi\) |
−0.903414 | + | 0.428769i | \(0.858947\pi\) | |||||||
\(224\) | −3.57597 | + | 2.06459i | −0.238929 | + | 0.137946i | ||||
\(225\) | 19.9557 | − | 34.5642i | 1.33038 | − | 2.30428i | ||||
\(226\) | 3.99540 | + | 2.30674i | 0.265770 | + | 0.153442i | ||||
\(227\) | 19.9304 | 1.32283 | 0.661414 | − | 0.750021i | \(-0.269957\pi\) | ||||
0.661414 | + | 0.750021i | \(0.269957\pi\) | |||||||
\(228\) | −7.41936 | + | 10.6571i | −0.491359 | + | 0.705781i | ||||
\(229\) | 9.97573 | 0.659215 | 0.329607 | − | 0.944118i | \(-0.393084\pi\) | ||||
0.329607 | + | 0.944118i | \(0.393084\pi\) | |||||||
\(230\) | −8.38877 | + | 14.5298i | −0.553139 | + | 0.958065i | ||||
\(231\) | 31.1414 | − | 26.3567i | 2.04895 | − | 1.73414i | ||||
\(232\) | 5.19100 | + | 8.99108i | 0.340806 | + | 0.590293i | ||||
\(233\) | 1.73815 | + | 1.00352i | 0.113870 | + | 0.0657430i | 0.555853 | − | 0.831280i | \(-0.312392\pi\) |
−0.441983 | + | 0.897023i | \(0.645725\pi\) | |||||||
\(234\) | 2.16047 | + | 3.74204i | 0.141234 | + | 0.244625i | ||||
\(235\) | 0.701012 | 0.0457290 | ||||||||
\(236\) | − | 2.12054i | − | 0.138035i | ||||||
\(237\) | −43.6325 | + | 25.1912i | −2.83424 | + | 1.63635i | ||||
\(238\) | 1.30955 | + | 2.26821i | 0.0848857 | + | 0.147026i | ||||
\(239\) | 5.79560i | 0.374886i | 0.982275 | + | 0.187443i | \(0.0600200\pi\) | ||||
−0.982275 | + | 0.187443i | \(0.939980\pi\) | |||||||
\(240\) | 10.2306i | 0.660386i | ||||||||
\(241\) | 7.17589 | + | 12.4290i | 0.462240 | + | 0.800623i | 0.999072 | − | 0.0430661i | \(-0.0137126\pi\) |
−0.536832 | + | 0.843689i | \(0.680379\pi\) | |||||||
\(242\) | 10.3043 | − | 3.84981i | 0.662387 | − | 0.247475i | ||||
\(243\) | 1.89859 | − | 1.09615i | 0.121795 | − | 0.0703183i | ||||
\(244\) | −0.547594 | − | 0.316154i | −0.0350561 | − | 0.0202397i | ||||
\(245\) | −17.2569 | + | 29.8899i | −1.10251 | + | 1.90960i | ||||
\(246\) | − | 28.0013i | − | 1.78529i | ||||||
\(247\) | 0.270800 | − | 3.19457i | 0.0172306 | − | 0.203266i | ||||
\(248\) | − | 7.65537i | − | 0.486116i | ||||||
\(249\) | −4.85053 | + | 8.40137i | −0.307390 | + | 0.532415i | ||||
\(250\) | −3.08001 | + | 5.33474i | −0.194797 | + | 0.337398i | ||||
\(251\) | 3.25298 | + | 5.63433i | 0.205327 | + | 0.355636i | 0.950237 | − | 0.311529i | \(-0.100841\pi\) |
−0.744910 | + | 0.667165i | \(0.767508\pi\) | |||||||
\(252\) | 21.0079 | + | 12.1289i | 1.32337 | + | 0.764048i | ||||
\(253\) | 2.88133 | + | 15.9449i | 0.181148 | + | 1.00245i | ||||
\(254\) | 11.3266 | 0.710691 | ||||||||
\(255\) | 6.48923 | 0.406372 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −6.57841 | + | 3.79805i | −0.410350 | + | 0.236916i | −0.690940 | − | 0.722912i | \(-0.742803\pi\) |
0.280590 | + | 0.959828i | \(0.409470\pi\) | |||||||
\(258\) | 23.8590 | 1.48539 | ||||||||
\(259\) | −20.6527 | −1.28330 | ||||||||
\(260\) | −1.26295 | − | 2.18749i | −0.0783248 | − | 0.135662i | ||||
\(261\) | 30.4958 | − | 52.8202i | 1.88764 | − | 3.26949i | ||||
\(262\) | 0.135724 | − | 0.0783602i | 0.00838505 | − | 0.00484111i | ||||
\(263\) | −7.88375 | − | 4.55169i | −0.486133 | − | 0.280669i | 0.236836 | − | 0.971550i | \(-0.423890\pi\) |
−0.722969 | + | 0.690881i | \(0.757223\pi\) | |||||||
\(264\) | 6.38305 | + | 7.54180i | 0.392850 | + | 0.464166i | ||||
\(265\) | 23.4841i | 1.44261i | ||||||||
\(266\) | −7.65056 | − | 16.2917i | −0.469086 | − | 0.998909i | ||||
\(267\) | −32.9972 | −2.01940 | ||||||||
\(268\) | −9.31419 | − | 5.37755i | −0.568955 | − | 0.328486i | ||||
\(269\) | −18.7841 | − | 10.8450i | −1.14529 | − | 0.661233i | −0.197554 | − | 0.980292i | \(-0.563300\pi\) |
−0.947735 | + | 0.319059i | \(0.896633\pi\) | |||||||
\(270\) | 25.4701 | − | 14.7052i | 1.55006 | − | 0.894930i | ||||
\(271\) | −9.41317 | − | 5.43470i | −0.571809 | − | 0.330134i | 0.186062 | − | 0.982538i | \(-0.440427\pi\) |
−0.757872 | + | 0.652404i | \(0.773761\pi\) | |||||||
\(272\) | −0.549314 | + | 0.317147i | −0.0333071 | + | 0.0192298i | ||||
\(273\) | −9.04754 | −0.547582 | ||||||||
\(274\) | 4.81195 | 0.290700 | ||||||||
\(275\) | 4.00681 | + | 22.1731i | 0.241620 | + | 1.33709i | ||||
\(276\) | −12.6041 | + | 7.27696i | −0.758676 | + | 0.438022i | ||||
\(277\) | 23.4666i | 1.40997i | 0.709221 | + | 0.704987i | \(0.249047\pi\) | ||||
−0.709221 | + | 0.704987i | \(0.750953\pi\) | |||||||
\(278\) | 8.72476i | 0.523276i | ||||||||
\(279\) | −38.9480 | + | 22.4866i | −2.33175 | + | 1.34624i | ||||
\(280\) | −12.2806 | − | 7.09020i | −0.733905 | − | 0.423720i | ||||
\(281\) | 5.68146 | + | 9.84059i | 0.338928 | + | 0.587040i | 0.984231 | − | 0.176886i | \(-0.0566024\pi\) |
−0.645304 | + | 0.763926i | \(0.723269\pi\) | |||||||
\(282\) | 0.526633 | + | 0.304052i | 0.0313605 | + | 0.0181060i | ||||
\(283\) | 10.8002 | + | 6.23551i | 0.642006 | + | 0.370663i | 0.785387 | − | 0.619005i | \(-0.212464\pi\) |
−0.143381 | + | 0.989668i | \(0.545797\pi\) | |||||||
\(284\) | − | 2.06215i | − | 0.122366i | ||||||
\(285\) | −44.4350 | − | 3.76671i | −2.63210 | − | 0.223121i | ||||
\(286\) | −2.29582 | − | 0.824596i | −0.135755 | − | 0.0487594i | ||||
\(287\) | 33.6119 | + | 19.4059i | 1.98405 | + | 1.14549i | ||||
\(288\) | −2.93737 | + | 5.08767i | −0.173086 | + | 0.299794i | ||||
\(289\) | −8.29884 | − | 14.3740i | −0.488167 | − | 0.845530i | ||||
\(290\) | −17.8269 | + | 30.8772i | −1.04683 | + | 1.81317i | ||||
\(291\) | 0.232678 | + | 0.403011i | 0.0136398 | + | 0.0236249i | ||||
\(292\) | 1.29385i | 0.0757168i | ||||||||
\(293\) | 27.0106 | 1.57797 | 0.788987 | − | 0.614410i | \(-0.210606\pi\) | ||||
0.788987 | + | 0.614410i | \(0.210606\pi\) | |||||||
\(294\) | −25.9285 | + | 14.9698i | −1.51218 | + | 0.873056i | ||||
\(295\) | 6.30669 | − | 3.64117i | 0.367190 | − | 0.211997i | ||||
\(296\) | − | 5.00167i | − | 0.290716i | ||||||
\(297\) | 9.60122 | − | 26.7315i | 0.557119 | − | 1.55112i | ||||
\(298\) | −3.98778 | + | 2.30235i | −0.231006 | + | 0.133371i | ||||
\(299\) | 1.79665 | − | 3.11188i | 0.103903 | − | 0.179965i | ||||
\(300\) | −17.5274 | + | 10.1194i | −1.01194 | + | 0.584245i | ||||
\(301\) | −16.5351 | + | 28.6396i | −0.953068 | + | 1.65076i | ||||
\(302\) | 6.13483 | − | 10.6258i | 0.353020 | − | 0.611448i | ||||
\(303\) | −21.0848 | −1.21129 | ||||||||
\(304\) | 3.94552 | − | 1.85281i | 0.226291 | − | 0.106266i | ||||
\(305\) | − | 2.17147i | − | 0.124338i | ||||||
\(306\) | 3.22707 | + | 1.86315i | 0.184480 | + | 0.106509i | ||||
\(307\) | 7.21450 | − | 12.4959i | 0.411753 | − | 0.713177i | −0.583328 | − | 0.812236i | \(-0.698250\pi\) |
0.995082 | + | 0.0990590i | \(0.0315833\pi\) | |||||||
\(308\) | −13.4766 | + | 2.43530i | −0.767903 | + | 0.138764i | ||||
\(309\) | 17.7655 | − | 30.7707i | 1.01064 | − | 1.75048i | ||||
\(310\) | 22.7679 | − | 13.1450i | 1.29313 | − | 0.746587i | ||||
\(311\) | −11.7789 | −0.667922 | −0.333961 | − | 0.942587i | \(-0.608385\pi\) | ||||
−0.333961 | + | 0.942587i | \(0.608385\pi\) | |||||||
\(312\) | − | 2.19113i | − | 0.124048i | ||||||
\(313\) | 1.20940 | + | 2.09474i | 0.0683593 | + | 0.118402i | 0.898179 | − | 0.439629i | \(-0.144890\pi\) |
−0.829820 | + | 0.558031i | \(0.811557\pi\) | |||||||
\(314\) | −7.64537 | − | 13.2422i | −0.431453 | − | 0.747299i | ||||
\(315\) | 83.3061i | 4.69376i | ||||||||
\(316\) | 16.9123 | 0.951389 | ||||||||
\(317\) | 21.0959 | − | 12.1797i | 1.18486 | − | 0.684080i | 0.227728 | − | 0.973725i | \(-0.426870\pi\) |
0.957134 | + | 0.289645i | \(0.0935371\pi\) | |||||||
\(318\) | −10.1858 | + | 17.6423i | −0.571192 | + | 0.989333i | ||||
\(319\) | 6.12310 | + | 33.8844i | 0.342828 | + | 1.89716i | ||||
\(320\) | 1.71710 | − | 2.97410i | 0.0959888 | − | 0.166257i | ||||
\(321\) | 18.2317 | + | 10.5261i | 1.01759 | + | 0.587507i | ||||
\(322\) | − | 20.1728i | − | 1.12418i | ||||||
\(323\) | −1.17522 | − | 2.50261i | −0.0653912 | − | 0.139249i | ||||
\(324\) | 7.88829 | 0.438238 | ||||||||
\(325\) | 2.49844 | − | 4.32742i | 0.138588 | − | 0.240042i | ||||
\(326\) | 3.76964 | − | 6.52921i | 0.208781 | − | 0.361619i | ||||
\(327\) | 12.1764 | − | 7.03004i | 0.673355 | − | 0.388762i | ||||
\(328\) | −4.69970 | + | 8.14011i | −0.259497 | + | 0.449463i | ||||
\(329\) | −0.729950 | + | 0.421437i | −0.0402434 | + | 0.0232346i | ||||
\(330\) | −11.4698 | + | 31.9339i | −0.631390 | + | 1.75790i | ||||
\(331\) | 3.41474i | 0.187691i | 0.995587 | + | 0.0938456i | \(0.0299160\pi\) | ||||
−0.995587 | + | 0.0938456i | \(0.970084\pi\) | |||||||
\(332\) | 2.82015 | − | 1.62821i | 0.154776 | − | 0.0893599i | ||||
\(333\) | −25.4468 | + | 14.6917i | −1.39448 | + | 0.805102i | ||||
\(334\) | 5.17832 | 0.283345 | ||||||||
\(335\) | − | 36.9352i | − | 2.01798i | ||||||
\(336\) | −6.15050 | − | 10.6530i | −0.335537 | − | 0.581168i | ||||
\(337\) | 7.30904 | − | 12.6596i | 0.398149 | − | 0.689614i | −0.595349 | − | 0.803467i | \(-0.702986\pi\) |
0.993498 | + | 0.113853i | \(0.0363194\pi\) | |||||||
\(338\) | −6.22951 | − | 10.7898i | −0.338841 | − | 0.586889i | ||||
\(339\) | −6.87190 | + | 11.9025i | −0.373231 | + | 0.646454i | ||||
\(340\) | −1.88645 | − | 1.08915i | −0.102307 | − | 0.0590672i | ||||
\(341\) | 8.58256 | − | 23.8954i | 0.464772 | − | 1.29401i | ||||
\(342\) | −21.0159 | − | 14.6311i | −1.13641 | − | 0.791159i | ||||
\(343\) | − | 12.5942i | − | 0.680022i | ||||||
\(344\) | −6.93593 | − | 4.00446i | −0.373960 | − | 0.215906i | ||||
\(345\) | −43.2849 | − | 24.9905i | −2.33038 | − | 1.34545i | ||||
\(346\) | 3.21632 | + | 5.57082i | 0.172910 | + | 0.299489i | ||||
\(347\) | 12.1315 | + | 7.00412i | 0.651253 | + | 0.376001i | 0.788936 | − | 0.614475i | \(-0.210632\pi\) |
−0.137683 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(348\) | −26.7849 | + | 15.4643i | −1.43582 | + | 0.828971i | ||||
\(349\) | − | 25.2310i | − | 1.35059i | −0.737549 | − | 0.675293i | \(-0.764017\pi\) | ||
0.737549 | − | 0.675293i | \(-0.235983\pi\) | |||||||
\(350\) | − | 28.0525i | − | 1.49947i | ||||||
\(351\) | −5.45502 | + | 3.14946i | −0.291167 | + | 0.168105i | ||||
\(352\) | −0.589780 | − | 3.26376i | −0.0314354 | − | 0.173959i | ||||
\(353\) | −4.82356 | −0.256732 | −0.128366 | − | 0.991727i | \(-0.540973\pi\) | ||||
−0.128366 | + | 0.991727i | \(0.540973\pi\) | |||||||
\(354\) | 6.31718 | 0.335754 | ||||||||
\(355\) | 6.13305 | − | 3.54092i | 0.325509 | − | 0.187933i | ||||
\(356\) | 9.59246 | + | 5.53821i | 0.508399 | + | 0.293524i | ||||
\(357\) | −6.75711 | + | 3.90122i | −0.357624 | + | 0.206475i | ||||
\(358\) | 14.4621 | + | 8.34972i | 0.764348 | + | 0.441296i | ||||
\(359\) | −20.1597 | − | 11.6392i | −1.06399 | − | 0.614293i | −0.137454 | − | 0.990508i | \(-0.543892\pi\) |
−0.926532 | + | 0.376215i | \(0.877225\pi\) | |||||||
\(360\) | −20.1750 | −1.06332 | ||||||||
\(361\) | 6.59469 | + | 17.8188i | 0.347089 | + | 0.937832i | ||||
\(362\) | 1.18830i | 0.0624558i | ||||||||
\(363\) | 11.4688 | + | 30.6971i | 0.601954 | + | 1.61118i | ||||
\(364\) | 2.63017 | + | 1.51853i | 0.137858 | + | 0.0795925i | ||||
\(365\) | −3.84804 | + | 2.22167i | −0.201416 | + | 0.116287i | ||||
\(366\) | 0.941837 | − | 1.63131i | 0.0492306 | − | 0.0852699i | ||||
\(367\) | 8.81137 | + | 15.2617i | 0.459950 | + | 0.796657i | 0.998958 | − | 0.0456442i | \(-0.0145340\pi\) |
−0.539008 | + | 0.842301i | \(0.681201\pi\) | |||||||
\(368\) | 4.88543 | 0.254670 | ||||||||
\(369\) | 55.2189 | 2.87458 | ||||||||
\(370\) | 14.8755 | − | 8.58836i | 0.773340 | − | 0.446488i | ||||
\(371\) | −14.1182 | − | 24.4535i | −0.732983 | − | 1.26956i | ||||
\(372\) | 22.8057 | 1.18242 | ||||||||
\(373\) | −22.3578 | −1.15764 | −0.578821 | − | 0.815455i | \(-0.696487\pi\) | ||||
−0.578821 | + | 0.815455i | \(0.696487\pi\) | |||||||
\(374\) | −2.07018 | + | 0.374094i | −0.107047 | + | 0.0193439i | ||||
\(375\) | −15.8924 | − | 9.17551i | −0.820682 | − | 0.473821i | ||||
\(376\) | −0.102063 | − | 0.176779i | −0.00526351 | − | 0.00911667i | ||||
\(377\) | 3.81805 | − | 6.61306i | 0.196640 | − | 0.340590i | ||||
\(378\) | −17.6811 | + | 30.6245i | −0.909415 | + | 1.57515i | ||||
\(379\) | 8.03980i | 0.412977i | 0.978449 | + | 0.206489i | \(0.0662036\pi\) | ||||
−0.978449 | + | 0.206489i | \(0.933796\pi\) | |||||||
\(380\) | 12.2853 | + | 8.55292i | 0.630222 | + | 0.438756i | ||||
\(381\) | 33.7424i | 1.72867i | ||||||||
\(382\) | −4.76153 | + | 8.24720i | −0.243621 | + | 0.421964i | ||||
\(383\) | −1.35811 | − | 0.784105i | −0.0693962 | − | 0.0400659i | 0.464900 | − | 0.885363i | \(-0.346090\pi\) |
−0.534297 | + | 0.845297i | \(0.679423\pi\) | |||||||
\(384\) | 2.57993 | − | 1.48952i | 0.131657 | − | 0.0760120i | ||||
\(385\) | −30.3836 | − | 35.8993i | −1.54849 | − | 1.82960i | ||||
\(386\) | −1.58290 | − | 2.74166i | −0.0805672 | − | 0.139547i | ||||
\(387\) | 47.0503i | 2.39170i | ||||||||
\(388\) | − | 0.156210i | − | 0.00793035i | ||||||
\(389\) | 7.27802 | + | 12.6059i | 0.369010 | + | 0.639144i | 0.989411 | − | 0.145141i | \(-0.0463634\pi\) |
−0.620401 | + | 0.784285i | \(0.713030\pi\) | |||||||
\(390\) | 6.51665 | − | 3.76239i | 0.329983 | − | 0.190516i | ||||
\(391\) | − | 3.09879i | − | 0.156713i | ||||||
\(392\) | 10.0501 | 0.507604 | ||||||||
\(393\) | 0.233439 | + | 0.404328i | 0.0117754 | + | 0.0203957i | ||||
\(394\) | −11.2625 | − | 6.50240i | −0.567396 | − | 0.327586i | ||||
\(395\) | 29.0400 | + | 50.2988i | 1.46116 | + | 2.53081i | ||||
\(396\) | −14.8726 | + | 12.5875i | −0.747374 | + | 0.632545i | ||||
\(397\) | −14.6884 | + | 25.4411i | −0.737190 | + | 1.27685i | 0.216566 | + | 0.976268i | \(0.430514\pi\) |
−0.953756 | + | 0.300583i | \(0.902819\pi\) | |||||||
\(398\) | −20.3424 | −1.01967 | ||||||||
\(399\) | 48.5338 | − | 22.7914i | 2.42973 | − | 1.14100i | ||||
\(400\) | 6.79373 | 0.339686 | ||||||||
\(401\) | 23.3032 | + | 13.4541i | 1.16371 | + | 0.671865i | 0.952189 | − | 0.305509i | \(-0.0988266\pi\) |
0.211516 | + | 0.977375i | \(0.432160\pi\) | |||||||
\(402\) | 16.0200 | − | 27.7474i | 0.799004 | − | 1.38392i | ||||
\(403\) | −4.87626 | + | 2.81531i | −0.242904 | + | 0.140241i | ||||
\(404\) | 6.12946 | + | 3.53884i | 0.304952 | + | 0.176064i | ||||
\(405\) | 13.5450 | + | 23.4606i | 0.673056 | + | 1.16577i | ||||
\(406\) | − | 42.8691i | − | 2.12756i | ||||||
\(407\) | 5.60746 | − | 15.6122i | 0.277951 | − | 0.773867i | ||||
\(408\) | −0.944795 | − | 1.63643i | −0.0467743 | − | 0.0810155i | ||||
\(409\) | −3.80335 | − | 6.58759i | −0.188063 | − | 0.325735i | 0.756541 | − | 0.653946i | \(-0.226888\pi\) |
−0.944605 | + | 0.328211i | \(0.893554\pi\) | |||||||
\(410\) | −32.2794 | −1.59417 | ||||||||
\(411\) | 14.3350i | 0.707095i | ||||||||
\(412\) | −10.3290 | + | 5.96347i | −0.508875 | + | 0.293799i | ||||
\(413\) | −4.37803 | + | 7.58296i | −0.215429 | + | 0.373133i | ||||
\(414\) | −14.3503 | − | 24.8554i | −0.705278 | − | 1.22158i | ||||
\(415\) | 9.68496 | + | 5.59161i | 0.475416 | + | 0.274482i | ||||
\(416\) | −0.367756 | + | 0.636973i | −0.0180307 | + | 0.0312302i | ||||
\(417\) | −25.9915 | −1.27281 | ||||||||
\(418\) | 14.3927 | − | 1.35996i | 0.703971 | − | 0.0665177i | ||||
\(419\) | 0.944008 | 0.0461178 | 0.0230589 | − | 0.999734i | \(-0.492659\pi\) | ||||
0.0230589 | + | 0.999734i | \(0.492659\pi\) | |||||||
\(420\) | 21.1221 | − | 36.5845i | 1.03065 | − | 1.78514i | ||||
\(421\) | −2.12809 | − | 1.22866i | −0.103717 | − | 0.0598810i | 0.447244 | − | 0.894412i | \(-0.352405\pi\) |
−0.550961 | + | 0.834531i | \(0.685739\pi\) | |||||||
\(422\) | −8.84798 | − | 15.3252i | −0.430713 | − | 0.746017i | ||||
\(423\) | −0.599595 | + | 1.03853i | −0.0291533 | + | 0.0504950i | ||||
\(424\) | 5.92214 | − | 3.41915i | 0.287604 | − | 0.166048i | ||||
\(425\) | − | 4.30922i | − | 0.209028i | ||||||
\(426\) | 6.14325 | 0.297641 | ||||||||
\(427\) | 1.30545 | + | 2.26111i | 0.0631753 | + | 0.109423i | ||||
\(428\) | −3.53336 | − | 6.11996i | −0.170792 | − | 0.295820i | ||||
\(429\) | 2.45651 | − | 6.83937i | 0.118602 | − | 0.330208i | ||||
\(430\) | − | 27.5042i | − | 1.32637i | ||||||
\(431\) | 5.91070 | + | 10.2376i | 0.284708 | + | 0.493130i | 0.972538 | − | 0.232742i | \(-0.0747699\pi\) |
−0.687830 | + | 0.725872i | \(0.741437\pi\) | |||||||
\(432\) | −7.41662 | − | 4.28199i | −0.356832 | − | 0.206017i | ||||
\(433\) | 1.30372 | − | 0.752706i | 0.0626530 | − | 0.0361727i | −0.468346 | − | 0.883545i | \(-0.655150\pi\) |
0.530999 | + | 0.847372i | \(0.321817\pi\) | |||||||
\(434\) | −15.8052 | + | 27.3753i | −0.758672 | + | 1.31406i | ||||
\(435\) | −91.9846 | − | 53.1073i | −4.41032 | − | 2.54630i | ||||
\(436\) | −4.71965 | −0.226030 | ||||||||
\(437\) | −1.79871 | + | 21.2190i | −0.0860440 | + | 1.01504i | ||||
\(438\) | −3.85444 | −0.184172 | ||||||||
\(439\) | 16.0679 | − | 27.8305i | 0.766881 | − | 1.32828i | −0.172365 | − | 0.985033i | \(-0.555141\pi\) |
0.939246 | − | 0.343244i | \(-0.111526\pi\) | |||||||
\(440\) | 8.69406 | − | 7.35828i | 0.414473 | − | 0.350792i | ||||
\(441\) | −29.5207 | − | 51.1313i | −1.40575 | − | 2.43483i | ||||
\(442\) | 0.404028 | + | 0.233265i | 0.0192176 | + | 0.0110953i | ||||
\(443\) | −20.5472 | − | 35.5888i | −0.976228 | − | 1.69088i | −0.675821 | − | 0.737066i | \(-0.736211\pi\) |
−0.300407 | − | 0.953811i | \(-0.597123\pi\) | |||||||
\(444\) | 14.9002 | 0.707133 | ||||||||
\(445\) | 38.0386i | 1.80320i | ||||||||
\(446\) | −14.6912 | + | 8.48197i | −0.695649 | + | 0.401633i | ||||
\(447\) | −6.85880 | − | 11.8798i | −0.324410 | − | 0.561895i | ||||
\(448\) | 4.12917i | 0.195085i | ||||||||
\(449\) | − | 8.43791i | − | 0.398210i | −0.979978 | − | 0.199105i | \(-0.936197\pi\) | ||
0.979978 | − | 0.199105i | \(-0.0638034\pi\) | |||||||
\(450\) | −19.9557 | − | 34.5642i | −0.940719 | − | 1.62937i | ||||
\(451\) | −23.7956 | + | 20.1396i | −1.12049 | + | 0.948336i | ||||
\(452\) | 3.99540 | − | 2.30674i | 0.187928 | − | 0.108500i | ||||
\(453\) | 31.6549 | + | 18.2760i | 1.48728 | + | 0.858680i | ||||
\(454\) | 9.96521 | − | 17.2602i | 0.467690 | − | 0.810064i | ||||
\(455\) | 10.4299i | 0.488960i | ||||||||
\(456\) | 5.51961 | + | 11.7539i | 0.258479 | + | 0.550426i | ||||
\(457\) | − | 37.1348i | − | 1.73709i | −0.495608 | − | 0.868546i | \(-0.665055\pi\) | ||
0.495608 | − | 0.868546i | \(-0.334945\pi\) | |||||||
\(458\) | 4.98787 | − | 8.63924i | 0.233068 | − | 0.403685i | ||||
\(459\) | −2.71604 | + | 4.70431i | −0.126774 | + | 0.219578i | ||||
\(460\) | 8.38877 | + | 14.5298i | 0.391128 | + | 0.677454i | ||||
\(461\) | −3.51316 | − | 2.02833i | −0.163624 | − | 0.0944686i | 0.415952 | − | 0.909387i | \(-0.363449\pi\) |
−0.579576 | + | 0.814918i | \(0.696782\pi\) | |||||||
\(462\) | −7.25489 | − | 40.1476i | −0.337528 | − | 1.86783i | ||||
\(463\) | −22.7991 | −1.05957 | −0.529783 | − | 0.848134i | \(-0.677726\pi\) | ||||
−0.529783 | + | 0.848134i | \(0.677726\pi\) | |||||||
\(464\) | 10.3820 | 0.481973 | ||||||||
\(465\) | 39.1597 | + | 67.8266i | 1.81599 | + | 3.14538i | ||||
\(466\) | 1.73815 | − | 1.00352i | 0.0805184 | − | 0.0464873i | ||||
\(467\) | −32.2303 | −1.49144 | −0.745719 | − | 0.666260i | \(-0.767894\pi\) | ||||
−0.745719 | + | 0.666260i | \(0.767894\pi\) | |||||||
\(468\) | 4.32094 | 0.199736 | ||||||||
\(469\) | 22.2048 | + | 38.4599i | 1.02532 | + | 1.77591i | ||||
\(470\) | 0.350506 | − | 0.607094i | 0.0161676 | − | 0.0280032i | ||||
\(471\) | 39.4491 | − | 22.7759i | 1.81772 | − | 1.04946i | ||||
\(472\) | −1.83644 | − | 1.06027i | −0.0845289 | − | 0.0488028i | ||||
\(473\) | −17.1603 | − | 20.2755i | −0.789031 | − | 0.932268i | ||||
\(474\) | 50.3825i | 2.31414i | ||||||||
\(475\) | −2.50131 | + | 29.5074i | −0.114768 | + | 1.35389i | ||||
\(476\) | 2.61911 | 0.120047 | ||||||||
\(477\) | −34.7910 | − | 20.0866i | −1.59297 | − | 0.919701i | ||||
\(478\) | 5.01914 | + | 2.89780i | 0.229570 | + | 0.132542i | ||||
\(479\) | −31.3786 | + | 18.1165i | −1.43373 | + | 0.827762i | −0.997403 | − | 0.0720284i | \(-0.977053\pi\) |
−0.436323 | + | 0.899790i | \(0.643719\pi\) | |||||||
\(480\) | 8.86000 | + | 5.11532i | 0.404402 | + | 0.233482i | ||||
\(481\) | −3.18593 | + | 1.83940i | −0.145266 | + | 0.0838692i | ||||
\(482\) | 14.3518 | 0.653706 | ||||||||
\(483\) | 60.0956 | 2.73445 | ||||||||
\(484\) | 1.81813 | − | 10.8487i | 0.0826421 | − | 0.493123i | ||||
\(485\) | 0.464584 | − | 0.268228i | 0.0210957 | − | 0.0121796i | ||||
\(486\) | − | 2.19231i | − | 0.0994451i | ||||||
\(487\) | 12.9021i | 0.584651i | 0.956319 | + | 0.292326i | \(0.0944291\pi\) | ||||
−0.956319 | + | 0.292326i | \(0.905571\pi\) | |||||||
\(488\) | −0.547594 | + | 0.316154i | −0.0247884 | + | 0.0143116i | ||||
\(489\) | 19.4508 | + | 11.2299i | 0.879597 | + | 0.507836i | ||||
\(490\) | 17.2569 | + | 29.8899i | 0.779589 | + | 1.35029i | ||||
\(491\) | −20.6492 | − | 11.9218i | −0.931886 | − | 0.538025i | −0.0444785 | − | 0.999010i | \(-0.514163\pi\) |
−0.887408 | + | 0.460986i | \(0.847496\pi\) | |||||||
\(492\) | −24.2498 | − | 14.0006i | −1.09327 | − | 0.631197i | ||||
\(493\) | − | 6.58524i | − | 0.296584i | ||||||
\(494\) | −2.63118 | − | 1.83180i | −0.118382 | − | 0.0824168i | ||||
\(495\) | −62.9741 | − | 22.6186i | −2.83048 | − | 1.01663i | ||||
\(496\) | −6.62974 | − | 3.82768i | −0.297684 | − | 0.171868i | ||||
\(497\) | −4.25749 | + | 7.37419i | −0.190974 | + | 0.330777i | ||||
\(498\) | 4.85053 | + | 8.40137i | 0.217357 | + | 0.376474i | ||||
\(499\) | 15.5326 | − | 26.9032i | 0.695333 | − | 1.20435i | −0.274736 | − | 0.961520i | \(-0.588590\pi\) |
0.970068 | − | 0.242832i | \(-0.0780763\pi\) | |||||||
\(500\) | 3.08001 | + | 5.33474i | 0.137742 | + | 0.238577i | ||||
\(501\) | 15.4265i | 0.689204i | ||||||||
\(502\) | 6.50597 | 0.290376 | ||||||||
\(503\) | −34.4433 | + | 19.8858i | −1.53575 | + | 0.886665i | −0.536669 | + | 0.843793i | \(0.680317\pi\) |
−0.999081 | + | 0.0428721i | \(0.986349\pi\) | |||||||
\(504\) | 21.0079 | − | 12.1289i | 0.935764 | − | 0.540264i | ||||
\(505\) | 24.3062i | 1.08161i | ||||||||
\(506\) | 15.2493 | + | 5.47714i | 0.677916 | + | 0.243488i | ||||
\(507\) | 32.1434 | − | 18.5580i | 1.42754 | − | 0.824190i | ||||
\(508\) | 5.66328 | − | 9.80908i | 0.251267 | − | 0.435208i | ||||
\(509\) | 10.9259 | − | 6.30810i | 0.484284 | − | 0.279602i | −0.237916 | − | 0.971286i | \(-0.576464\pi\) |
0.722200 | + | 0.691684i | \(0.243131\pi\) | |||||||
\(510\) | 3.24462 | − | 5.61984i | 0.143674 | − | 0.248851i | ||||
\(511\) | 2.67126 | − | 4.62676i | 0.118170 | − | 0.204676i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 21.3287 | − | 30.6362i | 0.941684 | − | 1.35262i | ||||
\(514\) | 7.59610i | 0.335050i | ||||||||
\(515\) | −35.4720 | − | 20.4798i | −1.56308 | − | 0.902446i | ||||
\(516\) | 11.9295 | − | 20.6625i | 0.525166 | − | 0.909615i | ||||
\(517\) | −0.120390 | − | 0.666221i | −0.00529474 | − | 0.0293004i | ||||
\(518\) | −10.3264 | + | 17.8858i | −0.453715 | + | 0.785857i | ||||
\(519\) | −16.5958 | + | 9.58156i | −0.728473 | + | 0.420584i | ||||
\(520\) | −2.52590 | −0.110768 | ||||||||
\(521\) | 13.9715i | 0.612102i | 0.952015 | + | 0.306051i | \(0.0990078\pi\) | ||||
−0.952015 | + | 0.306051i | \(0.900992\pi\) | |||||||
\(522\) | −30.4958 | − | 52.8202i | −1.33476 | − | 2.31188i | ||||
\(523\) | 7.25617 | + | 12.5681i | 0.317290 | + | 0.549563i | 0.979922 | − | 0.199383i | \(-0.0638938\pi\) |
−0.662632 | + | 0.748946i | \(0.730560\pi\) | |||||||
\(524\) | − | 0.156720i | − | 0.00684637i | ||||||
\(525\) | 83.5697 | 3.64728 | ||||||||
\(526\) | −7.88375 | + | 4.55169i | −0.343748 | + | 0.198463i | ||||
\(527\) | −2.42787 | + | 4.20520i | −0.105760 | + | 0.183181i | ||||
\(528\) | 9.72291 | − | 1.75698i | 0.423136 | − | 0.0764630i | ||||
\(529\) | −0.433698 | + | 0.751187i | −0.0188564 | + | 0.0326603i | ||||
\(530\) | 20.3378 | + | 11.7420i | 0.883417 | + | 0.510041i | ||||
\(531\) | 12.4576i | 0.540613i | ||||||||
\(532\) | −17.9343 | − | 1.52027i | −0.777551 | − | 0.0659122i | ||||
\(533\) | 6.91337 | 0.299451 | ||||||||
\(534\) | −16.4986 | + | 28.5764i | −0.713964 | + | 1.23662i | ||||
\(535\) | 12.1343 | − | 21.0172i | 0.524610 | − | 0.908652i | ||||
\(536\) | −9.31419 | + | 5.37755i | −0.402312 | + | 0.232275i | ||||
\(537\) | −24.8742 | + | 43.0834i | −1.07340 | + | 1.85919i | ||||
\(538\) | −18.7841 | + | 10.8450i | −0.809841 | + | 0.467562i | ||||
\(539\) | 31.3702 | + | 11.2673i | 1.35121 | + | 0.485316i | ||||
\(540\) | − | 29.4104i | − | 1.26562i | ||||||
\(541\) | −4.91487 | + | 2.83760i | −0.211307 | + | 0.121998i | −0.601919 | − | 0.798557i | \(-0.705597\pi\) |
0.390612 | + | 0.920556i | \(0.372264\pi\) | |||||||
\(542\) | −9.41317 | + | 5.43470i | −0.404330 | + | 0.233440i | ||||
\(543\) | −3.54001 | −0.151916 | ||||||||
\(544\) | 0.634293i | 0.0271951i | ||||||||
\(545\) | −8.10411 | − | 14.0367i | −0.347142 | − | 0.601268i | ||||
\(546\) | −4.52377 | + | 7.83540i | −0.193600 | + | 0.335324i | ||||
\(547\) | −18.1766 | − | 31.4828i | −0.777176 | − | 1.34611i | −0.933564 | − | 0.358412i | \(-0.883318\pi\) |
0.156388 | − | 0.987696i | \(-0.450015\pi\) | |||||||
\(548\) | 2.40597 | − | 4.16727i | 0.102778 | − | 0.178017i | ||||
\(549\) | 3.21697 | + | 1.85732i | 0.137297 | + | 0.0792684i | ||||
\(550\) | 21.2059 | + | 7.61657i | 0.904223 | + | 0.324772i | ||||
\(551\) | −3.82244 | + | 45.0924i | −0.162841 | + | 1.92100i | ||||
\(552\) | 14.5539i | 0.619456i | ||||||||
\(553\) | −60.4777 | − | 34.9168i | −2.57177 | − | 1.48481i | ||||
\(554\) | 20.3227 | + | 11.7333i | 0.863429 | + | 0.498501i | ||||
\(555\) | 25.5852 | + | 44.3148i | 1.08603 | + | 1.88106i | ||||
\(556\) | 7.55586 | + | 4.36238i | 0.320440 | + | 0.185006i | ||||
\(557\) | −28.3779 | + | 16.3840i | −1.20241 | + | 0.694212i | −0.961091 | − | 0.276233i | \(-0.910914\pi\) |
−0.241321 | + | 0.970445i | \(0.577581\pi\) | |||||||
\(558\) | 44.9732i | 1.90387i | ||||||||
\(559\) | 5.89066i | 0.249149i | ||||||||
\(560\) | −12.2806 | + | 7.09020i | −0.518949 | + | 0.299616i | ||||
\(561\) | −1.11444 | − | 6.16718i | −0.0470519 | − | 0.260379i | ||||
\(562\) | 11.3629 | 0.479316 | ||||||||
\(563\) | −0.410088 | −0.0172832 | −0.00864158 | − | 0.999963i | \(-0.502751\pi\) | ||||
−0.00864158 | + | 0.999963i | \(0.502751\pi\) | |||||||
\(564\) | 0.526633 | − | 0.304052i | 0.0221752 | − | 0.0128029i | ||||
\(565\) | 13.7210 | + | 7.92182i | 0.577247 | + | 0.333273i | ||||
\(566\) | 10.8002 | − | 6.23551i | 0.453967 | − | 0.262098i | ||||
\(567\) | −28.2083 | − | 16.2861i | −1.18464 | − | 0.683950i | ||||
\(568\) | −1.78588 | − | 1.03108i | −0.0749337 | − | 0.0432630i | ||||
\(569\) | −19.7430 | −0.827669 | −0.413834 | − | 0.910352i | \(-0.635811\pi\) | ||||
−0.413834 | + | 0.910352i | \(0.635811\pi\) | |||||||
\(570\) | −25.4796 | + | 36.5985i | −1.06722 | + | 1.53294i | ||||
\(571\) | 31.9660i | 1.33773i | 0.743382 | + | 0.668867i | \(0.233221\pi\) | ||||
−0.743382 | + | 0.668867i | \(0.766779\pi\) | |||||||
\(572\) | −1.86203 | + | 1.57594i | −0.0778555 | + | 0.0658935i | ||||
\(573\) | −24.5688 | − | 14.1848i | −1.02638 | − | 0.592579i | ||||
\(574\) | 33.6119 | − | 19.4059i | 1.40293 | − | 0.809985i | ||||
\(575\) | −16.5951 | + | 28.7436i | −0.692065 | + | 1.19869i | ||||
\(576\) | 2.93737 | + | 5.08767i | 0.122390 | + | 0.211986i | ||||
\(577\) | −16.6632 | −0.693697 | −0.346848 | − | 0.937921i | \(-0.612748\pi\) | ||||
−0.346848 | + | 0.937921i | \(0.612748\pi\) | |||||||
\(578\) | −16.5977 | −0.690372 | ||||||||
\(579\) | 8.16753 | − | 4.71552i | 0.339431 | − | 0.195970i | ||||
\(580\) | 17.8269 | + | 30.8772i | 0.740224 | + | 1.28210i | ||||
\(581\) | −13.4464 | −0.557849 | ||||||||
\(582\) | 0.465357 | 0.0192897 | ||||||||
\(583\) | 22.3186 | − | 4.03309i | 0.924341 | − | 0.167034i | ||||
\(584\) | 1.12051 | + | 0.646925i | 0.0463669 | + | 0.0267699i | ||||
\(585\) | 7.41949 | + | 12.8509i | 0.306758 | + | 0.531321i | ||||
\(586\) | 13.5053 | − | 23.3918i | 0.557898 | − | 0.966308i | ||||
\(587\) | 2.70860 | − | 4.69142i | 0.111796 | − | 0.193636i | −0.804699 | − | 0.593684i | \(-0.797673\pi\) |
0.916494 | + | 0.400048i | \(0.131006\pi\) | |||||||
\(588\) | 29.9396i | 1.23469i | ||||||||
\(589\) | 19.0658 | − | 27.3858i | 0.785592 | − | 1.12841i | ||||
\(590\) | − | 7.28234i | − | 0.299809i | ||||||
\(591\) | 19.3710 | − | 33.5515i | 0.796815 | − | 1.38012i | ||||
\(592\) | −4.33157 | − | 2.50083i | −0.178027 | − | 0.102784i | ||||
\(593\) | −2.17337 | + | 1.25479i | −0.0892494 | + | 0.0515282i | −0.543960 | − | 0.839111i | \(-0.683076\pi\) |
0.454711 | + | 0.890639i | \(0.349743\pi\) | |||||||
\(594\) | −18.3496 | − | 21.6807i | −0.752892 | − | 0.889568i | ||||
\(595\) | 4.49727 | + | 7.78949i | 0.184370 | + | 0.319338i | ||||
\(596\) | 4.60469i | 0.188615i | ||||||||
\(597\) | − | 60.6010i | − | 2.48023i | ||||||
\(598\) | −1.79665 | − | 3.11188i | −0.0734704 | − | 0.127254i | ||||
\(599\) | −32.4401 | + | 18.7293i | −1.32546 | + | 0.765257i | −0.984595 | − | 0.174853i | \(-0.944055\pi\) |
−0.340870 | + | 0.940110i | \(0.610722\pi\) | |||||||
\(600\) | 20.2389i | 0.826248i | ||||||||
\(601\) | 15.4119 | 0.628665 | 0.314333 | − | 0.949313i | \(-0.398219\pi\) | ||||
0.314333 | + | 0.949313i | \(0.398219\pi\) | |||||||
\(602\) | 16.5351 | + | 28.6396i | 0.673921 | + | 1.16726i | ||||
\(603\) | 54.7184 | + | 31.5917i | 2.22830 | + | 1.28651i | ||||
\(604\) | −6.13483 | − | 10.6258i | −0.249623 | − | 0.432359i | ||||
\(605\) | 35.3871 | − | 13.2210i | 1.43869 | − | 0.537511i | ||||
\(606\) | −10.5424 | + | 18.2600i | −0.428255 | + | 0.741760i | ||||
\(607\) | −35.9601 | −1.45958 | −0.729788 | − | 0.683674i | \(-0.760381\pi\) | ||||
−0.729788 | + | 0.683674i | \(0.760381\pi\) | |||||||
\(608\) | 0.368179 | − | 4.34332i | 0.0149316 | − | 0.176145i | ||||
\(609\) | 127.709 | 5.17503 | ||||||||
\(610\) | −1.88055 | − | 1.08573i | −0.0761411 | − | 0.0439601i | ||||
\(611\) | −0.0750689 | + | 0.130023i | −0.00303696 | + | 0.00526017i | ||||
\(612\) | 3.22707 | − | 1.86315i | 0.130447 | − | 0.0753135i | ||||
\(613\) | −21.3094 | − | 12.3030i | −0.860678 | − | 0.496913i | 0.00356133 | − | 0.999994i | \(-0.498866\pi\) |
−0.864239 | + | 0.503081i | \(0.832200\pi\) | |||||||
\(614\) | −7.21450 | − | 12.4959i | −0.291153 | − | 0.504293i | ||||
\(615\) | − | 96.1619i | − | 3.87762i | ||||||
\(616\) | −4.62929 | + | 12.8888i | −0.186519 | + | 0.519303i | ||||
\(617\) | 23.3744 | + | 40.4856i | 0.941017 | + | 1.62989i | 0.763536 | + | 0.645766i | \(0.223462\pi\) |
0.177482 | + | 0.984124i | \(0.443205\pi\) | |||||||
\(618\) | −17.7655 | − | 30.7707i | −0.714632 | − | 1.23778i | ||||
\(619\) | 18.1190 | 0.728263 | 0.364132 | − | 0.931347i | \(-0.381366\pi\) | ||||
0.364132 | + | 0.931347i | \(0.381366\pi\) | |||||||
\(620\) | − | 26.2901i | − | 1.05583i | ||||||
\(621\) | 36.2333 | − | 20.9193i | 1.45399 | − | 0.839464i | ||||
\(622\) | −5.88946 | + | 10.2009i | −0.236146 | + | 0.409017i | ||||
\(623\) | −22.8682 | − | 39.6089i | −0.916196 | − | 1.58690i | ||||
\(624\) | −1.89757 | − | 1.09556i | −0.0759637 | − | 0.0438577i | ||||
\(625\) | 6.40695 | − | 11.0972i | 0.256278 | − | 0.443886i | ||||
\(626\) | 2.41880 | 0.0966747 | ||||||||
\(627\) | 4.05138 | + | 42.8766i | 0.161796 | + | 1.71233i | ||||
\(628\) | −15.2907 | −0.610167 | ||||||||
\(629\) | −1.58626 | + | 2.74749i | −0.0632484 | + | 0.109549i | ||||
\(630\) | 72.1452 | + | 41.6530i | 2.87433 | + | 1.65950i | ||||
\(631\) | 20.6881 | + | 35.8328i | 0.823578 | + | 1.42648i | 0.903001 | + | 0.429639i | \(0.141359\pi\) |
−0.0794225 | + | 0.996841i | \(0.525308\pi\) | |||||||
\(632\) | 8.45613 | − | 14.6465i | 0.336367 | − | 0.582605i | ||||
\(633\) | 45.6544 | − | 26.3586i | 1.81460 | − | 1.04766i | ||||
\(634\) | − | 24.3594i | − | 0.967436i | ||||||
\(635\) | 38.8976 | 1.54361 | ||||||||
\(636\) | 10.1858 | + | 17.6423i | 0.403893 | + | 0.699564i | ||||
\(637\) | −3.69597 | − | 6.40161i | −0.146440 | − | 0.253641i | ||||
\(638\) | 32.4063 | + | 11.6394i | 1.28298 | + | 0.460810i | ||||
\(639\) | 12.1146i | 0.479246i | ||||||||
\(640\) | −1.71710 | − | 2.97410i | −0.0678743 | − | 0.117562i | ||||
\(641\) | −33.7828 | − | 19.5045i | −1.33434 | − | 0.770382i | −0.348379 | − | 0.937354i | \(-0.613268\pi\) |
−0.985962 | + | 0.166972i | \(0.946601\pi\) | |||||||
\(642\) | 18.2317 | − | 10.5261i | 0.719547 | − | 0.415430i | ||||
\(643\) | −9.51128 | + | 16.4740i | −0.375088 | + | 0.649672i | −0.990340 | − | 0.138658i | \(-0.955721\pi\) |
0.615252 | + | 0.788331i | \(0.289054\pi\) | |||||||
\(644\) | −17.4701 | − | 10.0864i | −0.688419 | − | 0.397459i | ||||
\(645\) | 81.9365 | 3.22625 | ||||||||
\(646\) | −2.75494 | − | 0.233533i | −0.108392 | − | 0.00918825i | ||||
\(647\) | −31.4269 | −1.23552 | −0.617759 | − | 0.786368i | \(-0.711959\pi\) | ||||
−0.617759 | + | 0.786368i | \(0.711959\pi\) | |||||||
\(648\) | 3.94415 | − | 6.83146i | 0.154941 | − | 0.268365i | ||||
\(649\) | −4.54356 | − | 5.36837i | −0.178350 | − | 0.210727i | ||||
\(650\) | −2.49844 | − | 4.32742i | −0.0979968 | − | 0.169735i | ||||
\(651\) | −81.5525 | − | 47.0843i | −3.19629 | − | 1.84538i | ||||
\(652\) | −3.76964 | − | 6.52921i | −0.147630 | − | 0.255704i | ||||
\(653\) | −13.4292 | −0.525524 | −0.262762 | − | 0.964861i | \(-0.584633\pi\) | ||||
−0.262762 | + | 0.964861i | \(0.584633\pi\) | |||||||
\(654\) | − | 14.0601i | − | 0.549792i | ||||||
\(655\) | 0.466103 | − | 0.269105i | 0.0182122 | − | 0.0105148i | ||||
\(656\) | 4.69970 | + | 8.14011i | 0.183492 | + | 0.317818i | ||||
\(657\) | − | 7.60102i | − | 0.296544i | ||||||
\(658\) | 0.842874i | 0.0328586i | ||||||||
\(659\) | −12.1545 | − | 21.0522i | −0.473473 | − | 0.820079i | 0.526066 | − | 0.850444i | \(-0.323666\pi\) |
−0.999539 | + | 0.0303646i | \(0.990333\pi\) | |||||||
\(660\) | 21.9207 | + | 25.9000i | 0.853261 | + | 1.00816i | ||||
\(661\) | 39.3706 | − | 22.7306i | 1.53134 | − | 0.884119i | 0.532038 | − | 0.846721i | \(-0.321426\pi\) |
0.999300 | − | 0.0373979i | \(-0.0119069\pi\) | |||||||
\(662\) | 2.95725 | + | 1.70737i | 0.114937 | + | 0.0663588i | ||||
\(663\) | −0.694909 | + | 1.20362i | −0.0269880 | + | 0.0467446i | ||||
\(664\) | − | 3.25643i | − | 0.126374i | ||||||
\(665\) | −26.2736 | − | 55.9490i | −1.01885 | − | 2.16961i | ||||
\(666\) | 29.3835i | 1.13859i | ||||||||
\(667\) | −25.3603 | + | 43.9253i | −0.981953 | + | 1.70079i | ||||
\(668\) | 2.58916 | − | 4.48456i | 0.100178 | − | 0.173513i | ||||
\(669\) | −25.2682 | − | 43.7658i | −0.976926 | − | 1.69209i | ||||
\(670\) | −31.9868 | − | 18.4676i | −1.23576 | − | 0.713465i | ||||
\(671\) | −2.06370 | + | 0.372922i | −0.0796683 | + | 0.0143965i | ||||
\(672\) | −12.3010 | −0.474521 | ||||||||
\(673\) | −3.32009 | −0.127980 | −0.0639901 | − | 0.997951i | \(-0.520383\pi\) | ||||
−0.0639901 | + | 0.997951i | \(0.520383\pi\) | |||||||
\(674\) | −7.30904 | − | 12.6596i | −0.281534 | − | 0.487631i | ||||
\(675\) | 50.3865 | − | 29.0907i | 1.93938 | − | 1.11970i | ||||
\(676\) | −12.4590 | −0.479193 | ||||||||
\(677\) | 26.3040 | 1.01095 | 0.505473 | − | 0.862842i | \(-0.331318\pi\) | ||||
0.505473 | + | 0.862842i | \(0.331318\pi\) | |||||||
\(678\) | 6.87190 | + | 11.9025i | 0.263914 | + | 0.457112i | ||||
\(679\) | −0.322509 | + | 0.558601i | −0.0123767 | + | 0.0214371i | ||||
\(680\) | −1.88645 | + | 1.08915i | −0.0723422 | + | 0.0417668i | ||||
\(681\) | 51.4191 | + | 29.6868i | 1.97039 | + | 1.13760i | ||||
\(682\) | −16.4027 | − | 19.3804i | −0.628094 | − | 0.742115i | ||||
\(683\) | − | 40.9395i | − | 1.56651i | −0.621703 | − | 0.783253i | \(-0.713559\pi\) | ||
0.621703 | − | 0.783253i | \(-0.286441\pi\) | |||||||
\(684\) | −23.1789 | + | 10.8848i | −0.886266 | + | 0.416189i | ||||
\(685\) | 16.5252 | 0.631395 | ||||||||
\(686\) | −10.9069 | − | 6.29709i | −0.416427 | − | 0.240424i | ||||
\(687\) | 25.7367 | + | 14.8591i | 0.981917 | + | 0.566910i | ||||
\(688\) | −6.93593 | + | 4.00446i | −0.264430 | + | 0.152669i | ||||
\(689\) | −4.35581 | − | 2.51483i | −0.165943 | − | 0.0958072i | ||||
\(690\) | −43.2849 | + | 24.9905i | −1.64783 | + | 0.951374i | ||||
\(691\) | 16.5403 | 0.629222 | 0.314611 | − | 0.949221i | \(-0.398126\pi\) | ||||
0.314611 | + | 0.949221i | \(0.398126\pi\) | |||||||
\(692\) | 6.43263 | 0.244532 | ||||||||
\(693\) | 79.1717 | − | 14.3068i | 3.00748 | − | 0.543469i | ||||
\(694\) | 12.1315 | − | 7.00412i | 0.460505 | − | 0.265873i | ||||
\(695\) | 29.9626i | 1.13654i | ||||||||
\(696\) | 30.9285i | 1.17234i | ||||||||
\(697\) | 5.16322 | − | 2.98099i | 0.195571 | − | 0.112913i | ||||
\(698\) | −21.8507 | − | 12.6155i | −0.827062 | − | 0.477504i | ||||
\(699\) | 2.98955 | + | 5.17805i | 0.113075 | + | 0.195852i | ||||
\(700\) | −24.2941 | − | 14.0262i | −0.918233 | − | 0.530142i | ||||
\(701\) | 23.5769 | + | 13.6121i | 0.890488 | + | 0.514123i | 0.874102 | − | 0.485742i | \(-0.161451\pi\) |
0.0163858 | + | 0.999866i | \(0.494784\pi\) | |||||||
\(702\) | 6.29891i | 0.237737i | ||||||||
\(703\) | 12.4567 | − | 17.8927i | 0.469814 | − | 0.674834i | ||||
\(704\) | −3.12139 | − | 1.12112i | −0.117642 | − | 0.0422537i | ||||
\(705\) | 1.80856 | + | 1.04417i | 0.0681144 | + | 0.0393259i | ||||
\(706\) | −2.41178 | + | 4.17732i | −0.0907685 | + | 0.157216i | ||||
\(707\) | −14.6125 | − | 25.3096i | −0.549559 | − | 0.951865i | ||||
\(708\) | 3.15859 | − | 5.47084i | 0.118707 | − | 0.205607i | ||||
\(709\) | −11.9147 | − | 20.6368i | −0.447465 | − | 0.775033i | 0.550755 | − | 0.834667i | \(-0.314340\pi\) |
−0.998220 | + | 0.0596342i | \(0.981007\pi\) | |||||||
\(710\) | − | 7.08184i | − | 0.265777i | ||||||
\(711\) | −99.3550 | −3.72611 | ||||||||
\(712\) | 9.59246 | − | 5.53821i | 0.359493 | − | 0.207553i | ||||
\(713\) | 32.3891 | − | 18.6999i | 1.21298 | − | 0.700315i | ||||
\(714\) | 7.80244i | 0.291999i | ||||||||
\(715\) | −7.88432 | − | 2.83183i | −0.294857 | − | 0.105904i | ||||
\(716\) | 14.4621 | − | 8.34972i | 0.540475 | − | 0.312044i | ||||
\(717\) | −8.63269 | + | 14.9523i | −0.322394 | + | 0.558402i | ||||
\(718\) | −20.1597 | + | 11.6392i | −0.752352 | + | 0.434371i | ||||
\(719\) | 13.1560 | − | 22.7868i | 0.490635 | − | 0.849806i | −0.509306 | − | 0.860585i | \(-0.670098\pi\) |
0.999942 | + | 0.0107797i | \(0.00343135\pi\) | |||||||
\(720\) | −10.0875 | + | 17.4721i | −0.375939 | + | 0.651146i | ||||
\(721\) | 49.2484 | 1.83411 | ||||||||
\(722\) | 18.7289 | + | 3.19824i | 0.697017 | + | 0.119026i | ||||
\(723\) | 42.7547i | 1.59006i | ||||||||
\(724\) | 1.02910 | + | 0.594151i | 0.0382462 | + | 0.0220815i | ||||
\(725\) | −35.2663 | + | 61.0830i | −1.30976 | + | 2.26856i | ||||
\(726\) | 32.3188 | + | 5.41629i | 1.19946 | + | 0.201017i | ||||
\(727\) | 9.14811 | − | 15.8450i | 0.339285 | − | 0.587658i | −0.645014 | − | 0.764171i | \(-0.723148\pi\) |
0.984298 | + | 0.176513i | \(0.0564817\pi\) | |||||||
\(728\) | 2.63017 | − | 1.51853i | 0.0974806 | − | 0.0562804i | ||||
\(729\) | 30.1959 | 1.11837 | ||||||||
\(730\) | 4.44334i | 0.164455i | ||||||||
\(731\) | 2.54000 | + | 4.39941i | 0.0939454 | + | 0.162718i | ||||
\(732\) | −0.941837 | − | 1.63131i | −0.0348113 | − | 0.0602949i | ||||
\(733\) | 18.1630i | 0.670864i | 0.942064 | + | 0.335432i | \(0.108882\pi\) | ||||
−0.942064 | + | 0.335432i | \(0.891118\pi\) | |||||||
\(734\) | 17.6227 | 0.650467 | ||||||||
\(735\) | −89.0435 | + | 51.4093i | −3.28442 | + | 1.89626i | ||||
\(736\) | 2.44271 | − | 4.23090i | 0.0900396 | − | 0.155953i | ||||
\(737\) | −35.1021 | + | 6.34315i | −1.29300 | + | 0.233653i | ||||
\(738\) | 27.6095 | − | 47.8210i | 1.01632 | − | 1.76032i | ||||
\(739\) | 36.5704 | + | 21.1140i | 1.34527 | + | 0.776689i | 0.987575 | − | 0.157151i | \(-0.0502308\pi\) |
0.357691 | + | 0.933840i | \(0.383564\pi\) | |||||||
\(740\) | − | 17.1767i | − | 0.631429i | ||||||
\(741\) | 5.45703 | − | 7.83841i | 0.200469 | − | 0.287951i | ||||
\(742\) | −28.2365 | −1.03659 | ||||||||
\(743\) | 6.55547 | − | 11.3544i | 0.240497 | − | 0.416553i | −0.720359 | − | 0.693601i | \(-0.756023\pi\) |
0.960856 | + | 0.277049i | \(0.0893563\pi\) | |||||||
\(744\) | 11.4029 | − | 19.7503i | 0.418049 | − | 0.724082i | ||||
\(745\) | −13.6948 | + | 7.90671i | −0.501740 | + | 0.289680i | ||||
\(746\) | −11.1789 | + | 19.3624i | −0.409288 | + | 0.708908i | ||||
\(747\) | −16.5676 | + | 9.56533i | −0.606178 | + | 0.349977i | ||||
\(748\) | −0.711117 | + | 1.97988i | −0.0260010 | + | 0.0723915i | ||||
\(749\) | 29.1797i | 1.06620i | ||||||||
\(750\) | −15.8924 | + | 9.17551i | −0.580310 | + | 0.335042i | ||||
\(751\) | −8.72509 | + | 5.03743i | −0.318383 | + | 0.183819i | −0.650672 | − | 0.759359i | \(-0.725513\pi\) |
0.332289 | + | 0.943178i | \(0.392179\pi\) | |||||||
\(752\) | −0.204127 | −0.00744373 | ||||||||
\(753\) | 19.3816i | 0.706305i | ||||||||
\(754\) | −3.81805 | − | 6.61306i | −0.139045 | − | 0.240833i | ||||
\(755\) | 21.0682 | − | 36.4913i | 0.766752 | − | 1.32805i | ||||
\(756\) | 17.6811 | + | 30.6245i | 0.643054 | + | 1.11380i | ||||
\(757\) | −11.2096 | + | 19.4156i | −0.407419 | + | 0.705670i | −0.994600 | − | 0.103785i | \(-0.966904\pi\) |
0.587181 | + | 0.809456i | \(0.300238\pi\) | |||||||
\(758\) | 6.96267 | + | 4.01990i | 0.252896 | + | 0.146009i | ||||
\(759\) | −16.3167 | + | 45.4285i | −0.592257 | + | 1.64895i | ||||
\(760\) | 13.5497 | − | 6.36291i | 0.491499 | − | 0.230807i | ||||
\(761\) | − | 16.8910i | − | 0.612298i | −0.951984 | − | 0.306149i | \(-0.900959\pi\) | ||
0.951984 | − | 0.306149i | \(-0.0990406\pi\) | |||||||
\(762\) | 29.2217 | + | 16.8712i | 1.05859 | + | 0.611178i | ||||
\(763\) | 16.8773 | + | 9.74412i | 0.611000 | + | 0.352761i | ||||
\(764\) | 4.76153 | + | 8.24720i | 0.172266 | + | 0.298373i | ||||
\(765\) | 11.0824 | + | 6.39844i | 0.400686 | + | 0.231336i | ||||
\(766\) | −1.35811 | + | 0.784105i | −0.0490705 | + | 0.0283309i | ||||
\(767\) | 1.55968i | 0.0563168i | ||||||||
\(768\) | − | 2.97905i | − | 0.107497i | ||||||
\(769\) | −39.0784 | + | 22.5619i | −1.40920 | + | 0.813604i | −0.995311 | − | 0.0967223i | \(-0.969164\pi\) |
−0.413892 | + | 0.910326i | \(0.635831\pi\) | |||||||
\(770\) | −46.2815 | + | 8.36332i | −1.66787 | + | 0.301393i | ||||
\(771\) | −22.6292 | −0.814969 | ||||||||
\(772\) | −3.16579 | −0.113939 | ||||||||
\(773\) | 17.1073 | − | 9.87688i | 0.615305 | − | 0.355247i | −0.159734 | − | 0.987160i | \(-0.551064\pi\) |
0.775039 | + | 0.631913i | \(0.217730\pi\) | |||||||
\(774\) | 40.7467 | + | 23.5251i | 1.46461 | + | 0.845594i | ||||
\(775\) | 45.0407 | − | 26.0042i | 1.61791 | − | 0.934100i | ||||
\(776\) | −0.135282 | − | 0.0781049i | −0.00485633 | − | 0.00280380i | ||||
\(777\) | −53.2827 | − | 30.7628i | −1.91151 | − | 1.10361i | ||||
\(778\) | 14.5560 | 0.521859 | ||||||||
\(779\) | −37.0855 | + | 17.4153i | −1.32872 | + | 0.623967i | ||||
\(780\) | − | 7.52477i | − | 0.269430i | ||||||
\(781\) | −4.41846 | − | 5.22057i | −0.158105 | − | 0.186807i | ||||
\(782\) | −2.68363 | − | 1.54940i | −0.0959666 | − | 0.0554063i | ||||
\(783\) | 76.9994 | − | 44.4556i | 2.75173 | − | 1.58871i | ||||
\(784\) | 5.02503 | − | 8.70360i | 0.179465 | − | 0.310843i | ||||
\(785\) | −26.2557 | − | 45.4763i | −0.937108 | − | 1.62312i | ||||
\(786\) | 0.466878 | 0.0166530 | ||||||||
\(787\) | −27.7256 | −0.988312 | −0.494156 | − | 0.869373i | \(-0.664523\pi\) | ||||
−0.494156 | + | 0.869373i | \(0.664523\pi\) | |||||||
\(788\) | −11.2625 | + | 6.50240i | −0.401209 | + | 0.231638i | ||||
\(789\) | −13.5597 | − | 23.4861i | −0.482738 | − | 0.836127i | ||||
\(790\) | 58.0801 | 2.06640 | ||||||||
\(791\) | −19.0499 | −0.677336 | ||||||||
\(792\) | 3.46480 | + | 19.1737i | 0.123116 | + | 0.681309i | ||||
\(793\) | 0.402762 | + | 0.232535i | 0.0143025 | + | 0.00825756i | ||||
\(794\) | 14.6884 | + | 25.4411i | 0.521272 | + | 0.902870i | ||||
\(795\) | −34.9801 | + | 60.5873i | −1.24062 | + | 2.14881i | ||||
\(796\) | −10.1712 | + | 17.6170i | −0.360508 | + | 0.624419i | ||||
\(797\) | − | 10.0338i | − | 0.355417i | −0.984083 | − | 0.177709i | \(-0.943132\pi\) | ||
0.984083 | − | 0.177709i | \(-0.0568684\pi\) | |||||||
\(798\) | 4.52897 | − | 53.4272i | 0.160324 | − | 1.89130i | ||||
\(799\) | 0.129476i | 0.00458054i | ||||||||
\(800\) | 3.39686 | − | 5.88354i | 0.120097 | − | 0.208015i | ||||
\(801\) | −56.3531 | − | 32.5355i | −1.99114 | − | 1.14959i | ||||
\(802\) | 23.3032 | − | 13.4541i | 0.822864 | − | 0.475081i | ||||
\(803\) | 2.77226 | + | 3.27552i | 0.0978310 | + | 0.115591i | ||||
\(804\) | −16.0200 | − | 27.7474i | −0.564981 | − | 0.978576i | ||||
\(805\) | − | 69.2773i | − | 2.44170i | ||||||
\(806\) | 5.63062i | 0.198330i | ||||||||
\(807\) | −32.3079 | − | 55.9588i | −1.13729 | − | 1.96984i | ||||
\(808\) | 6.12946 | − | 3.53884i | 0.215634 | − | 0.124496i | ||||
\(809\) | − | 27.0058i | − | 0.949473i | −0.880128 | − | 0.474736i | \(-0.842543\pi\) | ||
0.880128 | − | 0.474736i | \(-0.157457\pi\) | |||||||
\(810\) | 27.0900 | 0.951845 | ||||||||
\(811\) | 11.5563 | + | 20.0161i | 0.405797 | + | 0.702861i | 0.994414 | − | 0.105551i | \(-0.0336606\pi\) |
−0.588617 | + | 0.808412i | \(0.700327\pi\) | |||||||
\(812\) | −37.1257 | − | 21.4345i | −1.30286 | − | 0.752205i | ||||
\(813\) | −16.1902 | − | 28.0423i | −0.567816 | − | 0.983486i | ||||
\(814\) | −10.7168 | − | 12.6623i | −0.375624 | − | 0.443813i | ||||
\(815\) | 12.9457 | − | 22.4226i | 0.453468 | − | 0.785430i | ||||
\(816\) | −1.88959 | −0.0661489 | ||||||||
\(817\) | −14.8390 | − | 31.5993i | −0.519151 | − | 1.10552i | ||||
\(818\) | −7.60669 | −0.265962 | ||||||||
\(819\) | −15.4515 | − | 8.92095i | −0.539921 | − | 0.311723i | ||||
\(820\) | −16.1397 | + | 27.9548i | −0.563623 | + | 0.976223i | ||||
\(821\) | −3.39258 | + | 1.95871i | −0.118402 | + | 0.0683594i | −0.558031 | − | 0.829820i | \(-0.688443\pi\) |
0.439629 | + | 0.898179i | \(0.355110\pi\) | |||||||
\(822\) | 12.4145 | + | 7.16751i | 0.433005 | + | 0.249996i | ||||
\(823\) | −2.98812 | − | 5.17557i | −0.104159 | − | 0.180409i | 0.809235 | − | 0.587485i | \(-0.199882\pi\) |
−0.913394 | + | 0.407076i | \(0.866548\pi\) | |||||||
\(824\) | 11.9269i | 0.415495i | ||||||||
\(825\) | −22.6901 | + | 63.1734i | −0.789969 | + | 2.19942i | ||||
\(826\) | 4.37803 | + | 7.58296i | 0.152331 | + | 0.263845i | ||||
\(827\) | −0.687493 | − | 1.19077i | −0.0239065 | − | 0.0414073i | 0.853825 | − | 0.520561i | \(-0.174277\pi\) |
−0.877731 | + | 0.479153i | \(0.840944\pi\) | |||||||
\(828\) | −28.7006 | −0.997414 | ||||||||
\(829\) | 26.3859i | 0.916419i | 0.888844 | + | 0.458210i | \(0.151509\pi\) | ||||
−0.888844 | + | 0.458210i | \(0.848491\pi\) | |||||||
\(830\) | 9.68496 | − | 5.59161i | 0.336170 | − | 0.194088i | ||||
\(831\) | −34.9541 | + | 60.5423i | −1.21255 | + | 2.10019i | ||||
\(832\) | 0.367756 | + | 0.636973i | 0.0127497 | + | 0.0220831i | ||||
\(833\) | −5.52064 | − | 3.18734i | −0.191279 | − | 0.110435i | ||||
\(834\) | −12.9957 | + | 22.5093i | −0.450006 | + | 0.779433i | ||||
\(835\) | 17.7834 | 0.615419 | ||||||||
\(836\) | 6.01861 | − | 13.1444i | 0.208158 | − | 0.454610i | ||||
\(837\) | −65.5603 | −2.26610 | ||||||||
\(838\) | 0.472004 | − | 0.817535i | 0.0163051 | − | 0.0282413i | ||||
\(839\) | 12.1495 | + | 7.01452i | 0.419448 | + | 0.242168i | 0.694841 | − | 0.719163i | \(-0.255475\pi\) |
−0.275393 | + | 0.961332i | \(0.588808\pi\) | |||||||
\(840\) | −21.1221 | − | 36.5845i | −0.728780 | − | 1.26228i | ||||
\(841\) | −39.3930 | + | 68.2307i | −1.35838 | + | 2.35278i | ||||
\(842\) | −2.12809 | + | 1.22866i | −0.0733390 | + | 0.0423423i | ||||
\(843\) | 33.8507i | 1.16588i | ||||||||
\(844\) | −17.6960 | −0.609120 | ||||||||
\(845\) | −21.3934 | − | 37.0544i | −0.735955 | − | 1.27471i | ||||
\(846\) | 0.599595 | + | 1.03853i | 0.0206145 | + | 0.0357053i | ||||
\(847\) | −28.8996 | + | 35.0409i | −0.993003 | + | 1.20402i | ||||
\(848\) | − | 6.83829i | − | 0.234828i | ||||||
\(849\) | 18.5759 | + | 32.1744i | 0.637523 | + | 1.10422i | ||||
\(850\) | −3.73189 | − | 2.15461i | −0.128003 | − | 0.0739025i | ||||
\(851\) | 21.1616 | − | 12.2176i | 0.725410 | − | 0.418815i | ||||
\(852\) | 3.07163 | − | 5.32021i | 0.105232 | − | 0.182267i | ||||
\(853\) | −18.5660 | − | 10.7191i | −0.635689 | − | 0.367015i | 0.147263 | − | 0.989097i | \(-0.452954\pi\) |
−0.782952 | + | 0.622082i | \(0.786287\pi\) | |||||||
\(854\) | 2.61090 | 0.0893433 | ||||||||
\(855\) | −72.1728 | − | 50.2461i | −2.46826 | − | 1.71838i | ||||
\(856\) | −7.06672 | −0.241536 | ||||||||
\(857\) | 4.06824 | − | 7.04639i | 0.138968 | − | 0.240700i | −0.788138 | − | 0.615499i | \(-0.788955\pi\) |
0.927106 | + | 0.374798i | \(0.122288\pi\) | |||||||
\(858\) | −4.69482 | − | 5.54709i | −0.160278 | − | 0.189375i | ||||
\(859\) | −4.87037 | − | 8.43573i | −0.166175 | − | 0.287823i | 0.770897 | − | 0.636960i | \(-0.219808\pi\) |
−0.937072 | + | 0.349136i | \(0.886475\pi\) | |||||||
\(860\) | −23.8194 | − | 13.7521i | −0.812234 | − | 0.468943i | ||||
\(861\) | 57.8110 | + | 100.132i | 1.97019 | + | 3.41247i | ||||
\(862\) | 11.8214 | 0.402639 | ||||||||
\(863\) | 13.0390i | 0.443852i | 0.975063 | + | 0.221926i | \(0.0712344\pi\) | ||||
−0.975063 | + | 0.221926i | \(0.928766\pi\) | |||||||
\(864\) | −7.41662 | + | 4.28199i | −0.252318 | + | 0.145676i | ||||
\(865\) | 11.0455 | + | 19.1313i | 0.375557 | + | 0.650484i | ||||
\(866\) | − | 1.50541i | − | 0.0511560i | ||||||
\(867\) | − | 49.4453i | − | 1.67925i | ||||||
\(868\) | 15.8052 | + | 27.3753i | 0.536462 | + | 0.929179i | ||||
\(869\) | 42.8153 | − | 36.2370i | 1.45241 | − | 1.22926i | ||||
\(870\) | −91.9846 | + | 53.1073i | −3.11857 | + | 1.80051i | ||||
\(871\) | 6.85071 | + | 3.95526i | 0.232127 | + | 0.134019i | ||||
\(872\) | −2.35983 | + | 4.08734i | −0.0799138 | + | 0.138415i | ||||
\(873\) | 0.917691i | 0.0310591i | ||||||||
\(874\) | 17.4768 | + | 12.1672i | 0.591162 | + | 0.411562i | ||||
\(875\) | − | 25.4358i | − | 0.859887i | ||||||
\(876\) | −1.92722 | + | 3.33804i | −0.0651147 | + | 0.112782i | ||||
\(877\) | 8.53286 | − | 14.7794i | 0.288134 | − | 0.499063i | −0.685230 | − | 0.728327i | \(-0.740298\pi\) |
0.973364 | + | 0.229263i | \(0.0736317\pi\) | |||||||
\(878\) | −16.0679 | − | 27.8305i | −0.542267 | − | 0.939234i | ||||
\(879\) | 69.6854 | + | 40.2329i | 2.35043 | + | 1.35702i | ||||
\(880\) | −2.02542 | − | 11.2084i | −0.0682770 | − | 0.377836i | ||||
\(881\) | −5.88549 | −0.198287 | −0.0991437 | − | 0.995073i | \(-0.531610\pi\) | ||||
−0.0991437 | + | 0.995073i | \(0.531610\pi\) | |||||||
\(882\) | −59.0414 | −1.98803 | ||||||||
\(883\) | 23.8598 | + | 41.3263i | 0.802945 | + | 1.39074i | 0.917670 | + | 0.397344i | \(0.130068\pi\) |
−0.114725 | + | 0.993397i | \(0.536599\pi\) | |||||||
\(884\) | 0.404028 | − | 0.233265i | 0.0135889 | − | 0.00784557i | ||||
\(885\) | 21.6945 | 0.729251 | ||||||||
\(886\) | −41.0945 | −1.38060 | ||||||||
\(887\) | 7.07336 | + | 12.2514i | 0.237500 | + | 0.411362i | 0.959996 | − | 0.280012i | \(-0.0903386\pi\) |
−0.722496 | + | 0.691375i | \(0.757005\pi\) | |||||||
\(888\) | 7.45011 | − | 12.9040i | 0.250009 | − | 0.433029i | ||||
\(889\) | −40.5034 | + | 23.3846i | −1.35844 | + | 0.784296i | ||||
\(890\) | 32.9424 | + | 19.0193i | 1.10423 | + | 0.637529i | ||||
\(891\) | 19.9701 | − | 16.9018i | 0.669024 | − | 0.566232i | ||||
\(892\) | 16.9639i | 0.567995i | ||||||||
\(893\) | 0.0751551 | − | 0.886588i | 0.00251497 | − | 0.0296685i | ||||
\(894\) | −13.7176 | −0.458785 | ||||||||
\(895\) | 49.6659 | + | 28.6746i | 1.66015 | + | 0.958486i | ||||
\(896\) | 3.57597 | + | 2.06459i | 0.119465 | + | 0.0689730i | ||||
\(897\) | 9.27045 | − | 5.35230i | 0.309531 | − | 0.178708i | ||||
\(898\) | −7.30745 | − | 4.21896i | −0.243853 | − | 0.140788i | ||||
\(899\) | 68.8300 | − | 39.7390i | 2.29561 | − | 1.32537i | ||||
\(900\) | −39.9113 | −1.33038 | ||||||||
\(901\) | −4.33748 | −0.144503 | ||||||||
\(902\) | 5.54358 | + | 30.6774i | 0.184581 | + | 1.02145i | ||||
\(903\) | −85.3189 | + | 49.2589i | −2.83924 | + | 1.63923i | ||||
\(904\) | − | 4.61349i | − | 0.153442i | ||||||
\(905\) | 4.08087i | 0.135653i | ||||||||
\(906\) | 31.6549 | − | 18.2760i | 1.05166 | − | 0.607178i | ||||
\(907\) | −22.5638 | − | 13.0272i | −0.749219 | − | 0.432562i | 0.0761925 | − | 0.997093i | \(-0.475724\pi\) |
−0.825412 | + | 0.564531i | \(0.809057\pi\) | |||||||
\(908\) | −9.96521 | − | 17.2602i | −0.330707 | − | 0.572801i | ||||
\(909\) | −36.0089 | − | 20.7898i | −1.19434 | − | 0.689553i | ||||
\(910\) | 9.03253 | + | 5.21493i | 0.299425 | + | 0.172873i | ||||
\(911\) | − | 9.90289i | − | 0.328097i | −0.986452 | − | 0.164049i | \(-0.947545\pi\) | ||
0.986452 | − | 0.164049i | \(-0.0524554\pi\) | |||||||
\(912\) | 12.9390 | + | 1.09682i | 0.428452 | + | 0.0363194i | ||||
\(913\) | 3.65084 | − | 10.1646i | 0.120825 | − | 0.336399i | ||||
\(914\) | −32.1597 | − | 18.5674i | −1.06375 | − | 0.614155i | ||||
\(915\) | 3.23446 | − | 5.60224i | 0.106928 | − | 0.185204i | ||||
\(916\) | −4.98787 | − | 8.63924i | −0.164804 | − | 0.285448i | ||||
\(917\) | −0.323563 | + | 0.560427i | −0.0106850 | + | 0.0185069i | ||||
\(918\) | 2.71604 | + | 4.70431i | 0.0896425 | + | 0.155265i | ||||
\(919\) | 15.2439i | 0.502849i | 0.967877 | + | 0.251425i | \(0.0808991\pi\) | ||||
−0.967877 | + | 0.251425i | \(0.919101\pi\) | |||||||
\(920\) | 16.7775 | 0.553139 | ||||||||
\(921\) | 37.2258 | − | 21.4923i | 1.22663 | − | 0.708197i | ||||
\(922\) | −3.51316 | + | 2.02833i | −0.115700 | + | 0.0667994i | ||||
\(923\) | 1.51674i | 0.0499241i | ||||||||
\(924\) | −38.3963 | − | 13.7909i | −1.26314 | − | 0.453686i | ||||
\(925\) | 29.4275 | − | 16.9900i | 0.967571 | − | 0.558627i | ||||
\(926\) | −11.3996 | + | 19.7446i | −0.374613 | + | 0.648848i | ||||
\(927\) | 60.6803 | − | 35.0338i | 1.99300 | − | 1.15066i | ||||
\(928\) | 5.19100 | − | 8.99108i | 0.170403 | − | 0.295147i | ||||
\(929\) | −0.0461593 | + | 0.0799502i | −0.00151444 | + | 0.00262308i | −0.866782 | − | 0.498688i | \(-0.833815\pi\) |
0.865267 | + | 0.501311i | \(0.167149\pi\) | |||||||
\(930\) | 78.3194 | 2.56819 | ||||||||
\(931\) | 35.9524 | + | 25.0298i | 1.17829 | + | 0.820318i | ||||
\(932\) | − | 2.00705i | − | 0.0657430i | ||||||
\(933\) | −30.3888 | − | 17.5450i | −0.994886 | − | 0.574398i | ||||
\(934\) | −16.1151 | + | 27.9122i | −0.527303 | + | 0.913316i | ||||
\(935\) | −7.10943 | + | 1.28471i | −0.232503 | + | 0.0420146i | ||||
\(936\) | 2.16047 | − | 3.74204i | 0.0706172 | − | 0.122313i | ||||
\(937\) | −20.6527 | + | 11.9238i | −0.674694 | + | 0.389535i | −0.797853 | − | 0.602852i | \(-0.794031\pi\) |
0.123159 | + | 0.992387i | \(0.460697\pi\) | |||||||
\(938\) | 44.4096 | 1.45003 | ||||||||
\(939\) | 7.20572i | 0.235150i | ||||||||
\(940\) | −0.350506 | − | 0.607094i | −0.0114322 | − | 0.0198012i | ||||
\(941\) | 24.7278 | + | 42.8298i | 0.806103 | + | 1.39621i | 0.915544 | + | 0.402218i | \(0.131761\pi\) |
−0.109440 | + | 0.993993i | \(0.534906\pi\) | |||||||
\(942\) | − | 45.5519i | − | 1.48416i | ||||||
\(943\) | −45.9201 | −1.49536 | ||||||||
\(944\) | −1.83644 | + | 1.06027i | −0.0597709 | + | 0.0345088i | ||||
\(945\) | −60.7203 | + | 105.171i | −1.97523 | + | 3.42120i | ||||
\(946\) | −26.1392 | + | 4.72351i | −0.849860 | + | 0.153574i | ||||
\(947\) | −10.3059 | + | 17.8503i | −0.334896 | + | 0.580056i | −0.983465 | − | 0.181099i | \(-0.942034\pi\) |
0.648569 | + | 0.761156i | \(0.275368\pi\) | |||||||
\(948\) | 43.6325 | + | 25.1912i | 1.41712 | + | 0.818173i | ||||
\(949\) | − | 0.951642i | − | 0.0308916i | ||||||
\(950\) | 24.3035 | + | 16.9199i | 0.788508 | + | 0.548953i | ||||
\(951\) | 72.5679 | 2.35317 | ||||||||
\(952\) | 1.30955 | − | 2.26821i | 0.0424428 | − | 0.0735132i | ||||
\(953\) | −9.64182 | + | 16.7001i | −0.312329 | + | 0.540970i | −0.978866 | − | 0.204502i | \(-0.934443\pi\) |
0.666537 | + | 0.745472i | \(0.267776\pi\) | |||||||
\(954\) | −34.7910 | + | 20.0866i | −1.12640 | + | 0.650327i | ||||
\(955\) | −16.3520 | + | 28.3226i | −0.529139 | + | 0.916496i | ||||
\(956\) | 5.01914 | − | 2.89780i | 0.162330 | − | 0.0937215i | ||||
\(957\) | −34.6745 | + | 96.5400i | −1.12087 | + | 3.12070i | ||||
\(958\) | 36.2329i | 1.17063i | ||||||||
\(959\) | −17.2074 | + | 9.93467i | −0.555655 | + | 0.320807i | ||||
\(960\) | 8.86000 | − | 5.11532i | 0.285955 | − | 0.165096i | ||||
\(961\) | −27.6046 | −0.890472 | ||||||||
\(962\) | 3.67879i | 0.118609i | ||||||||
\(963\) | 20.7576 | + | 35.9531i | 0.668903 | + | 1.15857i | ||||
\(964\) | 7.17589 | − | 12.4290i | 0.231120 | − | 0.400311i | ||||
\(965\) | −5.43598 | − | 9.41539i | −0.174990 | − | 0.303092i | ||||
\(966\) | 30.0478 | − | 52.0444i | 0.966773 | − | 1.67450i | ||||
\(967\) | 13.6347 | + | 7.87200i | 0.438463 | + | 0.253147i | 0.702945 | − | 0.711244i | \(-0.251868\pi\) |
−0.264483 | + | 0.964390i | \(0.585201\pi\) | |||||||
\(968\) | −8.48619 | − | 6.99890i | −0.272757 | − | 0.224953i | ||||
\(969\) | 0.695708 | − | 8.20710i | 0.0223494 | − | 0.263650i | ||||
\(970\) | − | 0.536456i | − | 0.0172246i | ||||||
\(971\) | 42.3187 | + | 24.4327i | 1.35807 | + | 0.784084i | 0.989364 | − | 0.145461i | \(-0.0464666\pi\) |
0.368709 | + | 0.929545i | \(0.379800\pi\) | |||||||
\(972\) | −1.89859 | − | 1.09615i | −0.0608974 | − | 0.0351591i | ||||
\(973\) | −18.0130 | − | 31.1994i | −0.577470 | − | 1.00021i | ||||
\(974\) | 11.1736 | + | 6.45106i | 0.358024 | + | 0.206705i | ||||
\(975\) | 12.8916 | − | 7.44297i | 0.412862 | − | 0.238366i | ||||
\(976\) | 0.632307i | 0.0202397i | ||||||||
\(977\) | − | 18.8540i | − | 0.603192i | −0.953436 | − | 0.301596i | \(-0.902481\pi\) | ||
0.953436 | − | 0.301596i | \(-0.0975194\pi\) | |||||||
\(978\) | 19.4508 | − | 11.2299i | 0.621969 | − | 0.359094i | ||||
\(979\) | 36.1508 | − | 6.53265i | 1.15539 | − | 0.208785i | ||||
\(980\) | 34.5139 | 1.10251 | ||||||||
\(981\) | 27.7267 | 0.885245 | ||||||||
\(982\) | −20.6492 | + | 11.9218i | −0.658943 | + | 0.380441i | ||||
\(983\) | −0.516306 | − | 0.298089i | −0.0164676 | − | 0.00950757i | 0.491744 | − | 0.870740i | \(-0.336360\pi\) |
−0.508211 | + | 0.861232i | \(0.669693\pi\) | |||||||
\(984\) | −24.2498 | + | 14.0006i | −0.773055 | + | 0.446324i | ||||
\(985\) | −38.6776 | − | 22.3305i | −1.23237 | − | 0.711510i | ||||
\(986\) | −5.70298 | − | 3.29262i | −0.181620 | − | 0.104858i | ||||
\(987\) | −2.51096 | −0.0799248 | ||||||||
\(988\) | −2.90198 | + | 1.36276i | −0.0923242 | + | 0.0433553i | ||||
\(989\) | − | 39.1270i | − | 1.24417i | ||||||
\(990\) | −51.0753 | + | 43.2279i | −1.62328 | + | 1.37387i | ||||
\(991\) | −29.9960 | − | 17.3182i | −0.952853 | − | 0.550130i | −0.0588870 | − | 0.998265i | \(-0.518755\pi\) |
−0.893966 | + | 0.448135i | \(0.852089\pi\) | |||||||
\(992\) | −6.62974 | + | 3.82768i | −0.210494 | + | 0.121529i | ||||
\(993\) | −5.08634 | + | 8.80980i | −0.161410 | + | 0.279571i | ||||
\(994\) | 4.25749 | + | 7.37419i | 0.135039 | + | 0.233895i | ||||
\(995\) | −69.8598 | −2.21471 | ||||||||
\(996\) | 9.70106 | 0.307390 | ||||||||
\(997\) | −35.5996 | + | 20.5534i | −1.12745 | + | 0.650934i | −0.943293 | − | 0.331962i | \(-0.892289\pi\) |
−0.184158 | + | 0.982897i | \(0.558956\pi\) | |||||||
\(998\) | −15.5326 | − | 26.9032i | −0.491674 | − | 0.851605i | ||||
\(999\) | −42.8341 | −1.35521 |
(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 | 418.2.h.b.65.10 | yes | 20 | |
11.10 | odd | 2 | 418.2.h.a.65.10 | ✓ | 20 | ||
19.12 | odd | 6 | 418.2.h.a.373.10 | yes | 20 | ||
209.164 | even | 6 | inner | 418.2.h.b.373.10 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.h.a.65.10 | ✓ | 20 | 11.10 | odd | 2 | ||
418.2.h.a.373.10 | yes | 20 | 19.12 | odd | 6 | ||
418.2.h.b.65.10 | yes | 20 | 1.1 | even | 1 | trivial | |
418.2.h.b.373.10 | yes | 20 | 209.164 | even | 6 | inner |