Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(311,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.311");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.bg (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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 311.7 | ||
Character | \(\chi\) | \(=\) | 546.311 |
Dual form | 546.2.bg.b.467.7 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | −0.924091 | + | 1.46494i | −0.533524 | + | 0.845785i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −3.23425 | + | 1.86729i | −1.44640 | + | 0.835079i | −0.998265 | − | 0.0588875i | \(-0.981245\pi\) |
−0.448134 | + | 0.893966i | \(0.647911\pi\) | |||||||
\(6\) | −1.73072 | − | 0.0678152i | −0.706565 | − | 0.0276854i | ||||
\(7\) | 0.481958 | + | 2.60148i | 0.182163 | + | 0.983268i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.29211 | − | 2.70748i | −0.430704 | − | 0.902493i | ||||
\(10\) | −3.23425 | − | 1.86729i | −1.02276 | − | 0.590490i | ||||
\(11\) | 0.664055 | − | 1.15018i | 0.200220 | − | 0.346791i | −0.748379 | − | 0.663271i | \(-0.769168\pi\) |
0.948599 | + | 0.316480i | \(0.102501\pi\) | |||||||
\(12\) | −0.806632 | − | 1.53276i | −0.232855 | − | 0.442469i | ||||
\(13\) | 0.452687 | − | 3.57702i | 0.125553 | − | 0.992087i | ||||
\(14\) | −2.01197 | + | 1.71813i | −0.537722 | + | 0.459189i | ||||
\(15\) | 0.253262 | − | 6.46353i | 0.0653919 | − | 1.66888i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.49232 | + | 4.31682i | −0.604476 | + | 1.04698i | 0.387658 | + | 0.921803i | \(0.373284\pi\) |
−0.992134 | + | 0.125180i | \(0.960049\pi\) | |||||||
\(18\) | 1.69869 | − | 2.47274i | 0.400385 | − | 0.582831i | ||||
\(19\) | 2.36598 | + | 4.09800i | 0.542793 | + | 0.940145i | 0.998742 | + | 0.0501391i | \(0.0159665\pi\) |
−0.455949 | + | 0.890006i | \(0.650700\pi\) | |||||||
\(20\) | − | 3.73459i | − | 0.835079i | ||||||
\(21\) | −4.25640 | − | 1.69797i | −0.928822 | − | 0.370527i | ||||
\(22\) | 1.32811 | 0.283154 | ||||||||
\(23\) | 1.00204 | − | 0.578526i | 0.208939 | − | 0.120631i | −0.391879 | − | 0.920017i | \(-0.628175\pi\) |
0.600818 | + | 0.799386i | \(0.294842\pi\) | |||||||
\(24\) | 0.924091 | − | 1.46494i | 0.188629 | − | 0.299030i | ||||
\(25\) | 4.47357 | − | 7.74844i | 0.894713 | − | 1.54969i | ||||
\(26\) | 3.32413 | − | 1.39647i | 0.651916 | − | 0.273871i | ||||
\(27\) | 5.16033 | + | 0.609089i | 0.993106 | + | 0.117219i | ||||
\(28\) | −2.49393 | − | 0.883354i | −0.471308 | − | 0.166938i | ||||
\(29\) | − | 6.29862i | − | 1.16962i | −0.811169 | − | 0.584812i | \(-0.801168\pi\) | ||
0.811169 | − | 0.584812i | \(-0.198832\pi\) | |||||||
\(30\) | 5.72421 | − | 3.01244i | 1.04509 | − | 0.549993i | ||||
\(31\) | 1.66752 | − | 2.88823i | 0.299495 | − | 0.518741i | −0.676525 | − | 0.736419i | \(-0.736515\pi\) |
0.976021 | + | 0.217679i | \(0.0698485\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 1.07130 | + | 2.03567i | 0.186489 | + | 0.354365i | ||||
\(34\) | −4.98464 | −0.854858 | ||||||||
\(35\) | −6.41650 | − | 7.51388i | −1.08459 | − | 1.27008i | ||||
\(36\) | 2.99080 | + | 0.234739i | 0.498467 | + | 0.0391231i | ||||
\(37\) | −7.87543 | + | 4.54688i | −1.29471 | + | 0.747503i | −0.979486 | − | 0.201514i | \(-0.935414\pi\) |
−0.315227 | + | 0.949016i | \(0.602081\pi\) | |||||||
\(38\) | −2.36598 | + | 4.09800i | −0.383812 | + | 0.664783i | ||||
\(39\) | 4.82180 | + | 3.96865i | 0.772107 | + | 0.635493i | ||||
\(40\) | 3.23425 | − | 1.86729i | 0.511379 | − | 0.295245i | ||||
\(41\) | 4.38044i | 0.684109i | 0.939680 | + | 0.342055i | \(0.111123\pi\) | ||||
−0.939680 | + | 0.342055i | \(0.888877\pi\) | |||||||
\(42\) | −0.657716 | − | 4.53513i | −0.101488 | − | 0.699786i | ||||
\(43\) | −9.54856 | −1.45614 | −0.728071 | − | 0.685502i | \(-0.759583\pi\) | ||||
−0.728071 | + | 0.685502i | \(0.759583\pi\) | |||||||
\(44\) | 0.664055 | + | 1.15018i | 0.100110 | + | 0.173396i | ||||
\(45\) | 9.23466 | + | 6.34391i | 1.37662 | + | 0.945694i | ||||
\(46\) | 1.00204 | + | 0.578526i | 0.147742 | + | 0.0852990i | ||||
\(47\) | −6.95231 | + | 4.01392i | −1.01410 | + | 0.585490i | −0.912389 | − | 0.409324i | \(-0.865765\pi\) |
−0.101710 | + | 0.994814i | \(0.532431\pi\) | |||||||
\(48\) | 1.73072 | + | 0.0678152i | 0.249808 | + | 0.00978828i | ||||
\(49\) | −6.53543 | + | 2.50761i | −0.933633 | + | 0.358230i | ||||
\(50\) | 8.94713 | 1.26532 | ||||||||
\(51\) | −4.02077 | − | 7.64024i | −0.563020 | − | 1.06985i | ||||
\(52\) | 2.87145 | + | 2.18055i | 0.398198 | + | 0.302388i | ||||
\(53\) | 1.36514 | + | 0.788163i | 0.187516 | + | 0.108263i | 0.590819 | − | 0.806804i | \(-0.298805\pi\) |
−0.403303 | + | 0.915066i | \(0.632138\pi\) | |||||||
\(54\) | 2.05268 | + | 4.77352i | 0.279334 | + | 0.649594i | ||||
\(55\) | 4.95994i | 0.668798i | ||||||||
\(56\) | −0.481958 | − | 2.60148i | −0.0644044 | − | 0.347638i | ||||
\(57\) | −8.18971 | − | 0.320899i | −1.08475 | − | 0.0425041i | ||||
\(58\) | 5.45477 | − | 3.14931i | 0.716246 | − | 0.413525i | ||||
\(59\) | −9.31553 | − | 5.37832i | −1.21278 | − | 0.700198i | −0.249415 | − | 0.968397i | \(-0.580238\pi\) |
−0.963364 | + | 0.268199i | \(0.913572\pi\) | |||||||
\(60\) | 5.47095 | + | 3.45110i | 0.706297 | + | 0.445535i | ||||
\(61\) | 4.85105 | − | 2.80076i | 0.621113 | − | 0.358600i | −0.156189 | − | 0.987727i | \(-0.549921\pi\) |
0.777302 | + | 0.629127i | \(0.216588\pi\) | |||||||
\(62\) | 3.33504 | 0.423550 | ||||||||
\(63\) | 6.42072 | − | 4.66630i | 0.808935 | − | 0.587898i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.21524 | + | 12.4143i | 0.646871 | + | 1.53980i | ||||
\(66\) | −1.22729 | + | 1.94560i | −0.151070 | + | 0.239487i | ||||
\(67\) | −3.51817 | − | 2.03122i | −0.429813 | − | 0.248153i | 0.269454 | − | 0.963013i | \(-0.413157\pi\) |
−0.699267 | + | 0.714861i | \(0.746490\pi\) | |||||||
\(68\) | −2.49232 | − | 4.31682i | −0.302238 | − | 0.523491i | ||||
\(69\) | −0.0784657 | + | 2.00253i | −0.00944616 | + | 0.241077i | ||||
\(70\) | 3.29896 | − | 9.31379i | 0.394301 | − | 1.11321i | ||||
\(71\) | 9.95545 | 1.18150 | 0.590748 | − | 0.806856i | \(-0.298833\pi\) | ||||
0.590748 | + | 0.806856i | \(0.298833\pi\) | |||||||
\(72\) | 1.29211 | + | 2.70748i | 0.152277 | + | 0.319080i | ||||
\(73\) | −7.21154 | + | 12.4907i | −0.844046 | + | 1.46193i | 0.0424005 | + | 0.999101i | \(0.486499\pi\) |
−0.886447 | + | 0.462830i | \(0.846834\pi\) | |||||||
\(74\) | −7.87543 | − | 4.54688i | −0.915500 | − | 0.528564i | ||||
\(75\) | 7.21704 | + | 13.7138i | 0.833352 | + | 1.58353i | ||||
\(76\) | −4.73196 | −0.542793 | ||||||||
\(77\) | 3.31221 | + | 1.17319i | 0.377462 | + | 0.133698i | ||||
\(78\) | −1.02605 | + | 6.16013i | −0.116178 | + | 0.697498i | ||||
\(79\) | 7.22510 | + | 12.5142i | 0.812888 | + | 1.40796i | 0.910835 | + | 0.412771i | \(0.135439\pi\) |
−0.0979473 | + | 0.995192i | \(0.531228\pi\) | |||||||
\(80\) | 3.23425 | + | 1.86729i | 0.361600 | + | 0.208770i | ||||
\(81\) | −5.66090 | + | 6.99673i | −0.628988 | + | 0.777415i | ||||
\(82\) | −3.79357 | + | 2.19022i | −0.418930 | + | 0.241869i | ||||
\(83\) | − | 6.74642i | − | 0.740516i | −0.928929 | − | 0.370258i | \(-0.879269\pi\) | ||
0.928929 | − | 0.370258i | \(-0.120731\pi\) | |||||||
\(84\) | 3.59868 | − | 2.83716i | 0.392648 | − | 0.309560i | ||||
\(85\) | − | 18.6156i | − | 2.01914i | ||||||
\(86\) | −4.77428 | − | 8.26929i | −0.514824 | − | 0.891701i | ||||
\(87\) | 9.22711 | + | 5.82050i | 0.989251 | + | 0.624023i | ||||
\(88\) | −0.664055 | + | 1.15018i | −0.0707885 | + | 0.122609i | ||||
\(89\) | 2.55804 | − | 1.47689i | 0.271152 | − | 0.156550i | −0.358259 | − | 0.933622i | \(-0.616629\pi\) |
0.629411 | + | 0.777072i | \(0.283296\pi\) | |||||||
\(90\) | −0.876652 | + | 11.1694i | −0.0924072 | + | 1.17736i | ||||
\(91\) | 9.52374 | − | 0.546316i | 0.998359 | − | 0.0572695i | ||||
\(92\) | 1.15705i | 0.120631i | ||||||||
\(93\) | 2.69015 | + | 5.11180i | 0.278955 | + | 0.530069i | ||||
\(94\) | −6.95231 | − | 4.01392i | −0.717076 | − | 0.414004i | ||||
\(95\) | −15.3043 | − | 8.83595i | −1.57019 | − | 0.906550i | ||||
\(96\) | 0.806632 | + | 1.53276i | 0.0823265 | + | 0.156436i | ||||
\(97\) | −9.79404 | −0.994434 | −0.497217 | − | 0.867626i | \(-0.665645\pi\) | ||||
−0.497217 | + | 0.867626i | \(0.665645\pi\) | |||||||
\(98\) | −5.43937 | − | 4.40604i | −0.549460 | − | 0.445078i | ||||
\(99\) | −3.97212 | − | 0.311759i | −0.399213 | − | 0.0313329i | ||||
\(100\) | 4.47357 | + | 7.74844i | 0.447357 | + | 0.774844i | ||||
\(101\) | −4.68518 | + | 8.11497i | −0.466193 | + | 0.807470i | −0.999254 | − | 0.0386068i | \(-0.987708\pi\) |
0.533062 | + | 0.846076i | \(0.321041\pi\) | |||||||
\(102\) | 4.60626 | − | 7.30220i | 0.456087 | − | 0.723026i | ||||
\(103\) | −0.155999 | + | 0.0900661i | −0.0153710 | + | 0.00887448i | −0.507666 | − | 0.861554i | \(-0.669492\pi\) |
0.492295 | + | 0.870429i | \(0.336158\pi\) | |||||||
\(104\) | −0.452687 | + | 3.57702i | −0.0443896 | + | 0.350756i | ||||
\(105\) | 16.9368 | − | 2.45630i | 1.65287 | − | 0.239710i | ||||
\(106\) | 1.57633i | 0.153106i | ||||||||
\(107\) | −5.15442 | + | 2.97590i | −0.498296 | + | 0.287691i | −0.728010 | − | 0.685567i | \(-0.759554\pi\) |
0.229714 | + | 0.973258i | \(0.426221\pi\) | |||||||
\(108\) | −3.10765 | + | 4.16443i | −0.299034 | + | 0.400723i | ||||
\(109\) | 10.3694 | + | 5.98679i | 0.993211 | + | 0.573431i | 0.906233 | − | 0.422780i | \(-0.138946\pi\) |
0.0869783 | + | 0.996210i | \(0.472279\pi\) | |||||||
\(110\) | −4.29544 | + | 2.47997i | −0.409554 | + | 0.236456i | ||||
\(111\) | 0.616695 | − | 15.7388i | 0.0585341 | − | 1.49386i | ||||
\(112\) | 2.01197 | − | 1.71813i | 0.190113 | − | 0.162348i | ||||
\(113\) | 1.47456i | 0.138714i | 0.997592 | + | 0.0693572i | \(0.0220948\pi\) | ||||
−0.997592 | + | 0.0693572i | \(0.977905\pi\) | |||||||
\(114\) | −3.81695 | − | 7.25294i | −0.357490 | − | 0.679300i | ||||
\(115\) | −2.16055 | + | 3.74219i | −0.201473 | + | 0.348961i | ||||
\(116\) | 5.45477 | + | 3.14931i | 0.506462 | + | 0.292406i | ||||
\(117\) | −10.2696 | + | 3.39627i | −0.949428 | + | 0.313985i | ||||
\(118\) | − | 10.7566i | − | 0.990230i | ||||||
\(119\) | −12.4313 | − | 4.40320i | −1.13958 | − | 0.403640i | ||||
\(120\) | −0.253262 | + | 6.46353i | −0.0231195 | + | 0.590037i | ||||
\(121\) | 4.61806 | + | 7.99872i | 0.419824 | + | 0.727156i | ||||
\(122\) | 4.85105 | + | 2.80076i | 0.439193 | + | 0.253568i | ||||
\(123\) | −6.41709 | − | 4.04792i | −0.578609 | − | 0.364989i | ||||
\(124\) | 1.66752 | + | 2.88823i | 0.149748 | + | 0.259370i | ||||
\(125\) | 14.7409i | 1.31847i | ||||||||
\(126\) | 7.25149 | + | 3.22736i | 0.646014 | + | 0.287516i | ||||
\(127\) | 10.6040 | 0.940957 | 0.470479 | − | 0.882411i | \(-0.344081\pi\) | ||||
0.470479 | + | 0.882411i | \(0.344081\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 8.82373 | − | 13.9881i | 0.776887 | − | 1.23158i | ||||
\(130\) | −8.14345 | + | 10.7237i | −0.714227 | + | 0.940528i | ||||
\(131\) | 0.258515 | + | 0.447761i | 0.0225865 | + | 0.0391210i | 0.877098 | − | 0.480312i | \(-0.159477\pi\) |
−0.854511 | + | 0.519433i | \(0.826143\pi\) | |||||||
\(132\) | −2.29859 | − | 0.0900661i | −0.200067 | − | 0.00783925i | ||||
\(133\) | −9.52057 | + | 8.13012i | −0.825538 | + | 0.704971i | ||||
\(134\) | − | 4.06244i | − | 0.350941i | ||||||
\(135\) | −17.8271 | + | 7.66590i | −1.53431 | + | 0.659776i | ||||
\(136\) | 2.49232 | − | 4.31682i | 0.213714 | − | 0.370164i | ||||
\(137\) | 0.694033 | − | 1.20210i | 0.0592953 | − | 0.102702i | −0.834854 | − | 0.550471i | \(-0.814448\pi\) |
0.894149 | + | 0.447769i | \(0.147781\pi\) | |||||||
\(138\) | −1.77348 | + | 0.933314i | −0.150969 | + | 0.0794490i | ||||
\(139\) | − | 12.9034i | − | 1.09445i | −0.836985 | − | 0.547226i | \(-0.815684\pi\) | ||
0.836985 | − | 0.547226i | \(-0.184316\pi\) | |||||||
\(140\) | 9.71546 | − | 1.79991i | 0.821107 | − | 0.152120i | ||||
\(141\) | 0.544410 | − | 13.8940i | 0.0458476 | − | 1.17008i | ||||
\(142\) | 4.97773 | + | 8.62168i | 0.417722 | + | 0.723515i | ||||
\(143\) | −3.81360 | − | 2.89601i | −0.318909 | − | 0.242176i | ||||
\(144\) | −1.69869 | + | 2.47274i | −0.141558 | + | 0.206062i | ||||
\(145\) | 11.7614 | + | 20.3713i | 0.976729 | + | 1.69174i | ||||
\(146\) | −14.4231 | −1.19366 | ||||||||
\(147\) | 2.36583 | − | 11.8913i | 0.195130 | − | 0.980777i | ||||
\(148\) | − | 9.09376i | − | 0.747503i | ||||||
\(149\) | −4.15260 | − | 7.19252i | −0.340194 | − | 0.589234i | 0.644274 | − | 0.764795i | \(-0.277160\pi\) |
−0.984469 | + | 0.175561i | \(0.943826\pi\) | |||||||
\(150\) | −8.26796 | + | 13.1070i | −0.675076 | + | 1.07018i | ||||
\(151\) | 1.12265 | + | 0.648163i | 0.0913600 | + | 0.0527467i | 0.544984 | − | 0.838446i | \(-0.316536\pi\) |
−0.453624 | + | 0.891193i | \(0.649869\pi\) | |||||||
\(152\) | −2.36598 | − | 4.09800i | −0.191906 | − | 0.332391i | ||||
\(153\) | 14.9081 | + | 1.17009i | 1.20525 | + | 0.0945959i | ||||
\(154\) | 0.640093 | + | 3.45506i | 0.0515802 | + | 0.278416i | ||||
\(155\) | 12.4550i | 1.00041i | ||||||||
\(156\) | −5.84786 | + | 2.19148i | −0.468203 | + | 0.175459i | ||||
\(157\) | 15.2700 | + | 8.81616i | 1.21868 | + | 0.703606i | 0.964636 | − | 0.263586i | \(-0.0849053\pi\) |
0.254046 | + | 0.967192i | \(0.418239\pi\) | |||||||
\(158\) | −7.22510 | + | 12.5142i | −0.574798 | + | 0.995580i | ||||
\(159\) | −2.41613 | + | 1.27151i | −0.191611 | + | 0.100838i | ||||
\(160\) | 3.73459i | 0.295245i | ||||||||
\(161\) | 1.98796 | + | 2.32795i | 0.156674 | + | 0.183469i | ||||
\(162\) | −8.88980 | − | 1.40411i | −0.698448 | − | 0.110318i | ||||
\(163\) | 5.82554 | − | 3.36338i | 0.456292 | − | 0.263440i | −0.254192 | − | 0.967154i | \(-0.581810\pi\) |
0.710484 | + | 0.703714i | \(0.248476\pi\) | |||||||
\(164\) | −3.79357 | − | 2.19022i | −0.296228 | − | 0.171027i | ||||
\(165\) | −7.26603 | − | 4.58344i | −0.565660 | − | 0.356820i | ||||
\(166\) | 5.84258 | − | 3.37321i | 0.453472 | − | 0.261812i | ||||
\(167\) | 1.39818i | 0.108194i | 0.998536 | + | 0.0540972i | \(0.0172281\pi\) | ||||
−0.998536 | + | 0.0540972i | \(0.982772\pi\) | |||||||
\(168\) | 4.25640 | + | 1.69797i | 0.328388 | + | 0.131001i | ||||
\(169\) | −12.5901 | − | 3.23854i | −0.968473 | − | 0.249119i | ||||
\(170\) | 16.1215 | − | 9.30778i | 1.23647 | − | 0.713874i | ||||
\(171\) | 8.03813 | − | 11.7009i | 0.614691 | − | 0.894791i | ||||
\(172\) | 4.77428 | − | 8.26929i | 0.364035 | − | 0.630528i | ||||
\(173\) | 11.0767 | + | 19.1854i | 0.842145 | + | 1.45864i | 0.888078 | + | 0.459693i | \(0.152040\pi\) |
−0.0459336 | + | 0.998944i | \(0.514626\pi\) | |||||||
\(174\) | −0.427142 | + | 10.9012i | −0.0323816 | + | 0.826415i | ||||
\(175\) | 22.3135 | + | 7.90348i | 1.68674 | + | 0.597447i | ||||
\(176\) | −1.32811 | −0.100110 | ||||||||
\(177\) | 16.4873 | − | 8.67665i | 1.23926 | − | 0.652177i | ||||
\(178\) | 2.55804 | + | 1.47689i | 0.191734 | + | 0.110697i | ||||
\(179\) | −21.0472 | − | 12.1516i | −1.57314 | − | 0.908253i | −0.995781 | − | 0.0917629i | \(-0.970750\pi\) |
−0.577359 | − | 0.816490i | \(-0.695917\pi\) | |||||||
\(180\) | −10.1113 | + | 4.82550i | −0.753653 | + | 0.359672i | ||||
\(181\) | 14.4139i | 1.07137i | 0.844417 | + | 0.535687i | \(0.179947\pi\) | ||||
−0.844417 | + | 0.535687i | \(0.820053\pi\) | |||||||
\(182\) | 5.23499 | + | 7.97464i | 0.388043 | + | 0.591120i | ||||
\(183\) | −0.379868 | + | 9.69466i | −0.0280806 | + | 0.716650i | ||||
\(184\) | −1.00204 | + | 0.578526i | −0.0738711 | + | 0.0426495i | ||||
\(185\) | 16.9807 | − | 29.4115i | 1.24845 | − | 2.16237i | ||||
\(186\) | −3.08188 | + | 4.88564i | −0.225974 | + | 0.358232i | ||||
\(187\) | 3.31007 | + | 5.73321i | 0.242057 | + | 0.419254i | ||||
\(188\) | − | 8.02784i | − | 0.585490i | ||||||
\(189\) | 0.902527 | + | 13.7181i | 0.0656491 | + | 0.997843i | ||||
\(190\) | − | 17.6719i | − | 1.28205i | ||||||
\(191\) | 0.358267 | − | 0.206846i | 0.0259233 | − | 0.0149668i | −0.486982 | − | 0.873412i | \(-0.661902\pi\) |
0.512906 | + | 0.858445i | \(0.328569\pi\) | |||||||
\(192\) | −0.924091 | + | 1.46494i | −0.0666905 | + | 0.105723i | ||||
\(193\) | 6.58304 | + | 3.80072i | 0.473857 | + | 0.273582i | 0.717853 | − | 0.696195i | \(-0.245125\pi\) |
−0.243996 | + | 0.969776i | \(0.578458\pi\) | |||||||
\(194\) | −4.89702 | − | 8.48189i | −0.351586 | − | 0.608964i | ||||
\(195\) | −23.0055 | − | 3.83188i | −1.64746 | − | 0.274407i | ||||
\(196\) | 1.09606 | − | 6.91366i | 0.0782901 | − | 0.493833i | ||||
\(197\) | −6.65182 | −0.473922 | −0.236961 | − | 0.971519i | \(-0.576151\pi\) | ||||
−0.236961 | + | 0.971519i | \(0.576151\pi\) | |||||||
\(198\) | −1.71607 | − | 3.59583i | −0.121956 | − | 0.255545i | ||||
\(199\) | −13.0997 | − | 7.56314i | −0.928616 | − | 0.536137i | −0.0422423 | − | 0.999107i | \(-0.513450\pi\) |
−0.886374 | + | 0.462971i | \(0.846783\pi\) | |||||||
\(200\) | −4.47357 | + | 7.74844i | −0.316329 | + | 0.547898i | ||||
\(201\) | 6.22673 | − | 3.27689i | 0.439200 | − | 0.231134i | ||||
\(202\) | −9.37036 | −0.659296 | ||||||||
\(203\) | 16.3858 | − | 3.03567i | 1.15005 | − | 0.213062i | ||||
\(204\) | 8.62702 | + | 0.338034i | 0.604012 | + | 0.0236671i | ||||
\(205\) | −8.17956 | − | 14.1674i | −0.571285 | − | 0.989495i | ||||
\(206\) | −0.155999 | − | 0.0900661i | −0.0108690 | − | 0.00627520i | ||||
\(207\) | −2.86109 | − | 1.96547i | −0.198859 | − | 0.136610i | ||||
\(208\) | −3.32413 | + | 1.39647i | −0.230487 | + | 0.0968279i | ||||
\(209\) | 6.28456 | 0.434712 | ||||||||
\(210\) | 10.5956 | + | 13.4396i | 0.731168 | + | 0.927419i | ||||
\(211\) | −10.2354 | −0.704635 | −0.352318 | − | 0.935880i | \(-0.614606\pi\) | ||||
−0.352318 | + | 0.935880i | \(0.614606\pi\) | |||||||
\(212\) | −1.36514 | + | 0.788163i | −0.0937581 | + | 0.0541313i | ||||
\(213\) | −9.19975 | + | 14.5842i | −0.630356 | + | 0.999291i | ||||
\(214\) | −5.15442 | − | 2.97590i | −0.352349 | − | 0.203429i | ||||
\(215\) | 30.8824 | − | 17.8300i | 2.10616 | − | 1.21599i | ||||
\(216\) | −5.16033 | − | 0.609089i | −0.351116 | − | 0.0414433i | ||||
\(217\) | 8.31735 | + | 2.94602i | 0.564618 | + | 0.199989i | ||||
\(218\) | 11.9736i | 0.810953i | ||||||||
\(219\) | −11.6341 | − | 22.1071i | −0.786160 | − | 1.49386i | ||||
\(220\) | −4.29544 | − | 2.47997i | −0.289598 | − | 0.167200i | ||||
\(221\) | 14.3131 | + | 10.8692i | 0.962804 | + | 0.731144i | ||||
\(222\) | 13.9385 | − | 7.33532i | 0.935493 | − | 0.492314i | ||||
\(223\) | −21.3728 | −1.43123 | −0.715616 | − | 0.698494i | \(-0.753854\pi\) | ||||
−0.715616 | + | 0.698494i | \(0.753854\pi\) | |||||||
\(224\) | 2.49393 | + | 0.883354i | 0.166633 | + | 0.0590216i | ||||
\(225\) | −26.7591 | − | 2.10024i | −1.78394 | − | 0.140016i | ||||
\(226\) | −1.27700 | + | 0.737278i | −0.0849449 | + | 0.0490430i | ||||
\(227\) | −13.1596 | − | 7.59771i | −0.873434 | − | 0.504278i | −0.00494636 | − | 0.999988i | \(-0.501574\pi\) |
−0.868488 | + | 0.495710i | \(0.834908\pi\) | |||||||
\(228\) | 4.37276 | − | 6.93205i | 0.289593 | − | 0.459086i | ||||
\(229\) | −10.7812 | − | 18.6737i | −0.712445 | − | 1.23399i | −0.963937 | − | 0.266131i | \(-0.914255\pi\) |
0.251492 | − | 0.967859i | \(-0.419079\pi\) | |||||||
\(230\) | −4.32111 | −0.284925 | ||||||||
\(231\) | −4.77944 | + | 3.76807i | −0.314464 | + | 0.247921i | ||||
\(232\) | 6.29862i | 0.413525i | ||||||||
\(233\) | −23.8631 | + | 13.7774i | −1.56332 | + | 0.902586i | −0.566407 | + | 0.824126i | \(0.691667\pi\) |
−0.996917 | + | 0.0784603i | \(0.975000\pi\) | |||||||
\(234\) | −8.07607 | − | 7.19563i | −0.527949 | − | 0.470393i | ||||
\(235\) | 14.9903 | − | 25.9640i | 0.977861 | − | 1.69371i | ||||
\(236\) | 9.31553 | − | 5.37832i | 0.606389 | − | 0.350099i | ||||
\(237\) | −25.0093 | − | 0.979944i | −1.62453 | − | 0.0636542i | ||||
\(238\) | −2.40239 | − | 12.9674i | −0.155724 | − | 0.840555i | ||||
\(239\) | 12.0981 | 0.782563 | 0.391282 | − | 0.920271i | \(-0.372032\pi\) | ||||
0.391282 | + | 0.920271i | \(0.372032\pi\) | |||||||
\(240\) | −5.72421 | + | 3.01244i | −0.369496 | + | 0.194452i | ||||
\(241\) | −1.76152 | + | 3.05105i | −0.113470 | + | 0.196535i | −0.917167 | − | 0.398503i | \(-0.869530\pi\) |
0.803697 | + | 0.595038i | \(0.202863\pi\) | |||||||
\(242\) | −4.61806 | + | 7.99872i | −0.296860 | + | 0.514177i | ||||
\(243\) | −5.01862 | − | 14.7585i | −0.321945 | − | 0.946758i | ||||
\(244\) | 5.60151i | 0.358600i | ||||||||
\(245\) | 16.4548 | − | 20.3138i | 1.05126 | − | 1.29780i | ||||
\(246\) | 0.297060 | − | 7.58132i | 0.0189399 | − | 0.483367i | ||||
\(247\) | 15.7297 | − | 6.60805i | 1.00085 | − | 0.420460i | ||||
\(248\) | −1.66752 | + | 2.88823i | −0.105887 | + | 0.183403i | ||||
\(249\) | 9.88312 | + | 6.23431i | 0.626317 | + | 0.395083i | ||||
\(250\) | −12.7660 | + | 7.37045i | −0.807392 | + | 0.466148i | ||||
\(251\) | 18.9499 | 1.19611 | 0.598053 | − | 0.801457i | \(-0.295941\pi\) | ||||
0.598053 | + | 0.801457i | \(0.295941\pi\) | |||||||
\(252\) | 0.830772 | + | 7.89366i | 0.0523337 | + | 0.497254i | ||||
\(253\) | − | 1.53669i | − | 0.0966110i | ||||||
\(254\) | 5.30202 | + | 9.18338i | 0.332679 | + | 0.576216i | ||||
\(255\) | 27.2707 | + | 17.2025i | 1.70776 | + | 1.07726i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −0.299289 | − | 0.518384i | −0.0186692 | − | 0.0323359i | 0.856540 | − | 0.516081i | \(-0.172610\pi\) |
−0.875209 | + | 0.483745i | \(0.839276\pi\) | |||||||
\(258\) | 16.5259 | + | 0.647537i | 1.02886 | + | 0.0403139i | ||||
\(259\) | −15.6243 | − | 18.2964i | −0.970844 | − | 1.13688i | ||||
\(260\) | −13.3587 | − | 1.69060i | −0.828471 | − | 0.104846i | ||||
\(261\) | −17.0534 | + | 8.13852i | −1.05558 | + | 0.503762i | ||||
\(262\) | −0.258515 | + | 0.447761i | −0.0159711 | + | 0.0276627i | ||||
\(263\) | 23.1551 | + | 13.3686i | 1.42781 | + | 0.824344i | 0.996947 | − | 0.0780752i | \(-0.0248774\pi\) |
0.430859 | + | 0.902419i | \(0.358211\pi\) | |||||||
\(264\) | −1.07130 | − | 2.03567i | −0.0659337 | − | 0.125287i | ||||
\(265\) | −5.88693 | −0.361631 | ||||||||
\(266\) | −11.8012 | − | 4.17999i | −0.723576 | − | 0.256292i | ||||
\(267\) | −0.200311 | + | 5.11217i | −0.0122588 | + | 0.312860i | ||||
\(268\) | 3.51817 | − | 2.03122i | 0.214907 | − | 0.124076i | ||||
\(269\) | −5.72442 | + | 9.91498i | −0.349024 | + | 0.604527i | −0.986076 | − | 0.166293i | \(-0.946820\pi\) |
0.637052 | + | 0.770820i | \(0.280153\pi\) | |||||||
\(270\) | −15.5524 | − | 11.6058i | −0.946491 | − | 0.706306i | ||||
\(271\) | 12.6383 | + | 21.8902i | 0.767723 | + | 1.32974i | 0.938795 | + | 0.344477i | \(0.111944\pi\) |
−0.171072 | + | 0.985259i | \(0.554723\pi\) | |||||||
\(272\) | 4.98464 | 0.302238 | ||||||||
\(273\) | −8.00048 | + | 14.4566i | −0.484211 | + | 0.874951i | ||||
\(274\) | 1.38807 | 0.0838562 | ||||||||
\(275\) | −5.94139 | − | 10.2908i | −0.358279 | − | 0.620558i | ||||
\(276\) | −1.69501 | − | 1.06922i | −0.102028 | − | 0.0643595i | ||||
\(277\) | −2.29715 | + | 3.97877i | −0.138022 | + | 0.239061i | −0.926748 | − | 0.375684i | \(-0.877408\pi\) |
0.788726 | + | 0.614745i | \(0.210741\pi\) | |||||||
\(278\) | 11.1747 | − | 6.45170i | 0.670213 | − | 0.386947i | ||||
\(279\) | −9.97443 | − | 0.782862i | −0.597154 | − | 0.0468687i | ||||
\(280\) | 6.41650 | + | 7.51388i | 0.383459 | + | 0.449040i | ||||
\(281\) | 22.5191 | 1.34338 | 0.671689 | − | 0.740834i | \(-0.265569\pi\) | ||||
0.671689 | + | 0.740834i | \(0.265569\pi\) | |||||||
\(282\) | 12.3047 | − | 6.47551i | 0.732736 | − | 0.385611i | ||||
\(283\) | 6.47259 | + | 3.73695i | 0.384756 | + | 0.222139i | 0.679885 | − | 0.733318i | \(-0.262030\pi\) |
−0.295130 | + | 0.955457i | \(0.595363\pi\) | |||||||
\(284\) | −4.97773 | + | 8.62168i | −0.295374 | + | 0.511602i | ||||
\(285\) | 27.0867 | − | 14.2547i | 1.60448 | − | 0.844377i | ||||
\(286\) | 0.601218 | − | 4.75068i | 0.0355508 | − | 0.280913i | ||||
\(287\) | −11.3956 | + | 2.11119i | −0.672663 | + | 0.124619i | ||||
\(288\) | −2.99080 | − | 0.234739i | −0.176235 | − | 0.0138321i | ||||
\(289\) | −3.92330 | − | 6.79535i | −0.230782 | − | 0.399726i | ||||
\(290\) | −11.7614 | + | 20.3713i | −0.690651 | + | 1.19624i | ||||
\(291\) | 9.05058 | − | 14.3477i | 0.530555 | − | 0.841077i | ||||
\(292\) | −7.21154 | − | 12.4907i | −0.422023 | − | 0.730966i | ||||
\(293\) | 14.6089i | 0.853460i | 0.904379 | + | 0.426730i | \(0.140334\pi\) | ||||
−0.904379 | + | 0.426730i | \(0.859666\pi\) | |||||||
\(294\) | 11.4811 | − | 3.89678i | 0.669590 | − | 0.227265i | ||||
\(295\) | 40.1716 | 2.33888 | ||||||||
\(296\) | 7.87543 | − | 4.54688i | 0.457750 | − | 0.264282i | ||||
\(297\) | 4.12730 | − | 5.53083i | 0.239491 | − | 0.320931i | ||||
\(298\) | 4.15260 | − | 7.19252i | 0.240554 | − | 0.416651i | ||||
\(299\) | −1.61579 | − | 3.84619i | −0.0934435 | − | 0.222431i | ||||
\(300\) | −15.4850 | − | 0.606752i | −0.894027 | − | 0.0350308i | ||||
\(301\) | −4.60200 | − | 24.8404i | −0.265255 | − | 1.43178i | ||||
\(302\) | 1.29633i | 0.0745952i | ||||||||
\(303\) | −7.55843 | − | 14.3625i | −0.434220 | − | 0.825103i | ||||
\(304\) | 2.36598 | − | 4.09800i | 0.135698 | − | 0.235036i | ||||
\(305\) | −10.4597 | + | 18.1167i | −0.598918 | + | 1.03736i | ||||
\(306\) | 6.44070 | + | 13.4958i | 0.368191 | + | 0.771504i | ||||
\(307\) | −5.52889 | −0.315550 | −0.157775 | − | 0.987475i | \(-0.550432\pi\) | ||||
−0.157775 | + | 0.987475i | \(0.550432\pi\) | |||||||
\(308\) | −2.67212 | + | 2.28187i | −0.152258 | + | 0.130021i | ||||
\(309\) | 0.0122157 | − | 0.311759i | 0.000694927 | − | 0.0177353i | ||||
\(310\) | −10.7863 | + | 6.22749i | −0.612622 | + | 0.353698i | ||||
\(311\) | 12.5077 | − | 21.6640i | 0.709247 | − | 1.22845i | −0.255890 | − | 0.966706i | \(-0.582368\pi\) |
0.965137 | − | 0.261746i | \(-0.0842982\pi\) | |||||||
\(312\) | −4.82180 | − | 3.96865i | −0.272981 | − | 0.224681i | ||||
\(313\) | 12.4242 | − | 7.17314i | 0.702260 | − | 0.405450i | −0.105929 | − | 0.994374i | \(-0.533782\pi\) |
0.808189 | + | 0.588924i | \(0.200448\pi\) | |||||||
\(314\) | 17.6323i | 0.995049i | ||||||||
\(315\) | −12.0528 | + | 27.0813i | −0.679101 | + | 1.52586i | ||||
\(316\) | −14.4502 | −0.812888 | ||||||||
\(317\) | 7.58692 | + | 13.1409i | 0.426124 | + | 0.738068i | 0.996525 | − | 0.0832983i | \(-0.0265454\pi\) |
−0.570401 | + | 0.821367i | \(0.693212\pi\) | |||||||
\(318\) | −2.30923 | − | 1.45667i | −0.129495 | − | 0.0816860i | ||||
\(319\) | −7.24453 | − | 4.18263i | −0.405616 | − | 0.234182i | ||||
\(320\) | −3.23425 | + | 1.86729i | −0.180800 | + | 0.104385i | ||||
\(321\) | 0.403623 | − | 10.3009i | 0.0225280 | − | 0.574942i | ||||
\(322\) | −1.02209 | + | 2.88560i | −0.0569586 | + | 0.160808i | ||||
\(323\) | −23.5871 | −1.31242 | ||||||||
\(324\) | −3.22890 | − | 8.40085i | −0.179383 | − | 0.466714i | ||||
\(325\) | −25.6912 | − | 19.5097i | −1.42509 | − | 1.08220i | ||||
\(326\) | 5.82554 | + | 3.36338i | 0.322647 | + | 0.186280i | ||||
\(327\) | −18.3526 | + | 9.65827i | −1.01490 | + | 0.534104i | ||||
\(328\) | − | 4.38044i | − | 0.241869i | ||||||
\(329\) | −13.7929 | − | 16.1518i | −0.760425 | − | 0.890477i | ||||
\(330\) | 0.336360 | − | 8.58428i | 0.0185160 | − | 0.472549i | ||||
\(331\) | −25.2714 | + | 14.5904i | −1.38904 | + | 0.801963i | −0.993207 | − | 0.116360i | \(-0.962878\pi\) |
−0.395833 | + | 0.918322i | \(0.629544\pi\) | |||||||
\(332\) | 5.84258 | + | 3.37321i | 0.320653 | + | 0.185129i | ||||
\(333\) | 22.4865 | + | 15.4475i | 1.23225 | + | 0.846517i | ||||
\(334\) | −1.21086 | + | 0.699090i | −0.0662553 | + | 0.0382525i | ||||
\(335\) | 15.1715 | 0.828908 | ||||||||
\(336\) | 0.657716 | + | 4.53513i | 0.0358813 | + | 0.247412i | ||||
\(337\) | 21.8314 | 1.18923 | 0.594615 | − | 0.804011i | \(-0.297305\pi\) | ||||
0.594615 | + | 0.804011i | \(0.297305\pi\) | |||||||
\(338\) | −3.49042 | − | 12.5227i | −0.189854 | − | 0.681143i | ||||
\(339\) | −2.16014 | − | 1.36262i | −0.117323 | − | 0.0740075i | ||||
\(340\) | 16.1215 | + | 9.30778i | 0.874313 | + | 0.504785i | ||||
\(341\) | −2.21465 | − | 3.83588i | −0.119930 | − | 0.207725i | ||||
\(342\) | 14.1524 | + | 1.11077i | 0.765271 | + | 0.0600638i | ||||
\(343\) | −9.67332 | − | 15.7933i | −0.522310 | − | 0.852756i | ||||
\(344\) | 9.54856 | 0.514824 | ||||||||
\(345\) | −3.48554 | − | 6.62321i | −0.187655 | − | 0.356582i | ||||
\(346\) | −11.0767 | + | 19.1854i | −0.595486 | + | 1.03141i | ||||
\(347\) | 24.0903 | + | 13.9086i | 1.29324 | + | 0.746651i | 0.979227 | − | 0.202768i | \(-0.0649938\pi\) |
0.314011 | + | 0.949419i | \(0.398327\pi\) | |||||||
\(348\) | −9.65426 | + | 5.08067i | −0.517522 | + | 0.272352i | ||||
\(349\) | −4.54691 | −0.243391 | −0.121695 | − | 0.992567i | \(-0.538833\pi\) | ||||
−0.121695 | + | 0.992567i | \(0.538833\pi\) | |||||||
\(350\) | 4.31214 | + | 23.2758i | 0.230494 | + | 1.24414i | ||||
\(351\) | 4.51474 | − | 18.1829i | 0.240979 | − | 0.970530i | ||||
\(352\) | −0.664055 | − | 1.15018i | −0.0353943 | − | 0.0613047i | ||||
\(353\) | −7.21102 | − | 4.16329i | −0.383804 | − | 0.221589i | 0.295668 | − | 0.955291i | \(-0.404458\pi\) |
−0.679472 | + | 0.733701i | \(0.737791\pi\) | |||||||
\(354\) | 15.7579 | + | 9.94012i | 0.837521 | + | 0.528311i | ||||
\(355\) | −32.1984 | + | 18.5897i | −1.70891 | + | 0.986641i | ||||
\(356\) | 2.95378i | 0.156550i | ||||||||
\(357\) | 17.9381 | − | 14.1422i | 0.949386 | − | 0.748486i | ||||
\(358\) | − | 24.3032i | − | 1.28446i | ||||||
\(359\) | 7.10506 | + | 12.3063i | 0.374991 | + | 0.649503i | 0.990326 | − | 0.138763i | \(-0.0443126\pi\) |
−0.615335 | + | 0.788266i | \(0.710979\pi\) | |||||||
\(360\) | −9.23466 | − | 6.34391i | −0.486710 | − | 0.334353i | ||||
\(361\) | −1.69571 | + | 2.93706i | −0.0892481 | + | 0.154582i | ||||
\(362\) | −12.4828 | + | 7.20693i | −0.656080 | + | 0.378788i | ||||
\(363\) | −15.9852 | − | 0.626350i | −0.839004 | − | 0.0328748i | ||||
\(364\) | −4.28874 | + | 8.52095i | −0.224791 | + | 0.446619i | ||||
\(365\) | − | 53.8642i | − | 2.81938i | ||||||
\(366\) | −8.58576 | + | 4.51836i | −0.448785 | + | 0.236178i | ||||
\(367\) | 2.05984 | + | 1.18925i | 0.107523 | + | 0.0620782i | 0.552797 | − | 0.833316i | \(-0.313561\pi\) |
−0.445274 | + | 0.895394i | \(0.646894\pi\) | |||||||
\(368\) | −1.00204 | − | 0.578526i | −0.0522347 | − | 0.0301577i | ||||
\(369\) | 11.8599 | − | 5.66001i | 0.617404 | − | 0.294648i | ||||
\(370\) | 33.9614 | 1.76557 | ||||||||
\(371\) | −1.39245 | + | 3.93125i | −0.0722926 | + | 0.204100i | ||||
\(372\) | −5.77202 | − | 0.226166i | −0.299265 | − | 0.0117262i | ||||
\(373\) | −11.7785 | − | 20.4010i | −0.609869 | − | 1.05632i | −0.991262 | − | 0.131911i | \(-0.957889\pi\) |
0.381392 | − | 0.924413i | \(-0.375445\pi\) | |||||||
\(374\) | −3.31007 | + | 5.73321i | −0.171160 | + | 0.296457i | ||||
\(375\) | −21.5946 | − | 13.6219i | −1.11514 | − | 0.703434i | ||||
\(376\) | 6.95231 | − | 4.01392i | 0.358538 | − | 0.207002i | ||||
\(377\) | −22.5303 | − | 2.85130i | −1.16037 | − | 0.146850i | ||||
\(378\) | −11.4289 | + | 7.64065i | −0.587841 | + | 0.392992i | ||||
\(379\) | 18.0896i | 0.929201i | 0.885520 | + | 0.464601i | \(0.153802\pi\) | ||||
−0.885520 | + | 0.464601i | \(0.846198\pi\) | |||||||
\(380\) | 15.3043 | − | 8.83595i | 0.785095 | − | 0.453275i | ||||
\(381\) | −9.79911 | + | 15.5343i | −0.502023 | + | 0.795847i | ||||
\(382\) | 0.358267 | + | 0.206846i | 0.0183306 | + | 0.0105831i | ||||
\(383\) | 6.97099 | − | 4.02470i | 0.356201 | − | 0.205653i | −0.311212 | − | 0.950340i | \(-0.600735\pi\) |
0.667413 | + | 0.744688i | \(0.267402\pi\) | |||||||
\(384\) | −1.73072 | − | 0.0678152i | −0.0883206 | − | 0.00346068i | ||||
\(385\) | −12.9032 | + | 2.39048i | −0.657608 | + | 0.121830i | ||||
\(386\) | 7.60143i | 0.386903i | ||||||||
\(387\) | 12.3378 | + | 25.8525i | 0.627166 | + | 1.31416i | ||||
\(388\) | 4.89702 | − | 8.48189i | 0.248609 | − | 0.430603i | ||||
\(389\) | 27.5356 | + | 15.8977i | 1.39611 | + | 0.806045i | 0.993983 | − | 0.109539i | \(-0.0349373\pi\) |
0.402128 | + | 0.915583i | \(0.368271\pi\) | |||||||
\(390\) | −8.18426 | − | 21.8393i | −0.414426 | − | 1.10588i | ||||
\(391\) | 5.76748i | 0.291674i | ||||||||
\(392\) | 6.53543 | − | 2.50761i | 0.330089 | − | 0.126654i | ||||
\(393\) | −0.894835 | − | 0.0350625i | −0.0451384 | − | 0.00176867i | ||||
\(394\) | −3.32591 | − | 5.76064i | −0.167557 | − | 0.290217i | ||||
\(395\) | −46.7355 | − | 26.9828i | −2.35152 | − | 1.35765i | ||||
\(396\) | 2.25605 | − | 3.28407i | 0.113371 | − | 0.165031i | ||||
\(397\) | −13.5400 | − | 23.4520i | −0.679555 | − | 1.17702i | −0.975115 | − | 0.221700i | \(-0.928840\pi\) |
0.295560 | − | 0.955324i | \(-0.404494\pi\) | |||||||
\(398\) | − | 15.1263i | − | 0.758212i | ||||||
\(399\) | −3.11228 | − | 21.4600i | −0.155809 | − | 1.07435i | ||||
\(400\) | −8.94713 | −0.447357 | ||||||||
\(401\) | −7.51128 | − | 13.0099i | −0.375095 | − | 0.649684i | 0.615246 | − | 0.788335i | \(-0.289057\pi\) |
−0.990341 | + | 0.138651i | \(0.955723\pi\) | |||||||
\(402\) | 5.95123 | + | 3.75406i | 0.296821 | + | 0.187235i | ||||
\(403\) | −9.57638 | − | 7.27221i | −0.477033 | − | 0.362254i | ||||
\(404\) | −4.68518 | − | 8.11497i | −0.233096 | − | 0.403735i | ||||
\(405\) | 5.24378 | − | 33.1997i | 0.260566 | − | 1.64971i | ||||
\(406\) | 10.8218 | + | 12.6726i | 0.537079 | + | 0.628933i | ||||
\(407\) | 12.0775i | 0.598660i | ||||||||
\(408\) | 4.02077 | + | 7.64024i | 0.199058 | + | 0.378248i | ||||
\(409\) | −9.71830 | + | 16.8326i | −0.480539 | + | 0.832318i | −0.999751 | − | 0.0223276i | \(-0.992892\pi\) |
0.519212 | + | 0.854646i | \(0.326226\pi\) | |||||||
\(410\) | 8.17956 | − | 14.1674i | 0.403960 | − | 0.699679i | ||||
\(411\) | 1.11966 | + | 2.12757i | 0.0552287 | + | 0.104945i | ||||
\(412\) | − | 0.180132i | − | 0.00887448i | ||||||
\(413\) | 9.50193 | − | 26.8263i | 0.467559 | − | 1.32004i | ||||
\(414\) | 0.271605 | − | 3.46051i | 0.0133486 | − | 0.170075i | ||||
\(415\) | 12.5976 | + | 21.8196i | 0.618389 | + | 1.07108i | ||||
\(416\) | −2.87145 | − | 2.18055i | −0.140784 | − | 0.106910i | ||||
\(417\) | 18.9027 | + | 11.9239i | 0.925672 | + | 0.583917i | ||||
\(418\) | 3.14228 | + | 5.44259i | 0.153694 | + | 0.266206i | ||||
\(419\) | 11.9628 | 0.584422 | 0.292211 | − | 0.956354i | \(-0.405609\pi\) | ||||
0.292211 | + | 0.956354i | \(0.405609\pi\) | |||||||
\(420\) | −6.34120 | + | 15.8959i | −0.309419 | + | 0.775639i | ||||
\(421\) | 8.12436i | 0.395957i | 0.980206 | + | 0.197979i | \(0.0634377\pi\) | ||||
−0.980206 | + | 0.197979i | \(0.936562\pi\) | |||||||
\(422\) | −5.11771 | − | 8.86413i | −0.249126 | − | 0.431499i | ||||
\(423\) | 19.8508 | + | 13.6368i | 0.965177 | + | 0.663045i | ||||
\(424\) | −1.36514 | − | 0.788163i | −0.0662970 | − | 0.0382766i | ||||
\(425\) | 22.2991 | + | 38.6232i | 1.08166 | + | 1.87350i | ||||
\(426\) | −17.2301 | − | 0.675131i | −0.834803 | − | 0.0327102i | ||||
\(427\) | 9.62412 | + | 11.2701i | 0.465744 | + | 0.545397i | ||||
\(428\) | − | 5.95181i | − | 0.287691i | ||||||
\(429\) | 7.76660 | − | 2.91053i | 0.374975 | − | 0.140521i | ||||
\(430\) | 30.8824 | + | 17.8300i | 1.48928 | + | 0.859837i | ||||
\(431\) | 4.94182 | − | 8.55948i | 0.238039 | − | 0.412296i | −0.722112 | − | 0.691776i | \(-0.756829\pi\) |
0.960152 | + | 0.279480i | \(0.0901620\pi\) | |||||||
\(432\) | −2.05268 | − | 4.77352i | −0.0987595 | − | 0.229666i | ||||
\(433\) | 14.2606i | 0.685321i | 0.939459 | + | 0.342661i | \(0.111328\pi\) | ||||
−0.939459 | + | 0.342661i | \(0.888672\pi\) | |||||||
\(434\) | 1.60735 | + | 8.67604i | 0.0771551 | + | 0.416463i | ||||
\(435\) | −40.7113 | − | 1.59520i | −1.95196 | − | 0.0764840i | ||||
\(436\) | −10.3694 | + | 5.98679i | −0.496605 | + | 0.286715i | ||||
\(437\) | 4.74159 | + | 2.73756i | 0.226821 | + | 0.130955i | ||||
\(438\) | 13.3282 | − | 21.1290i | 0.636847 | − | 1.00958i | ||||
\(439\) | −17.7811 | + | 10.2659i | −0.848646 | + | 0.489966i | −0.860194 | − | 0.509968i | \(-0.829657\pi\) |
0.0115480 | + | 0.999933i | \(0.496324\pi\) | |||||||
\(440\) | − | 4.95994i | − | 0.236456i | ||||||
\(441\) | 15.2338 | + | 14.4544i | 0.725420 | + | 0.688307i | ||||
\(442\) | −2.25648 | + | 17.8301i | −0.107330 | + | 0.848093i | ||||
\(443\) | 0.915950 | − | 0.528824i | 0.0435181 | − | 0.0251252i | −0.478083 | − | 0.878315i | \(-0.658668\pi\) |
0.521601 | + | 0.853189i | \(0.325335\pi\) | |||||||
\(444\) | 13.3218 | + | 8.40346i | 0.632226 | + | 0.398811i | ||||
\(445\) | −5.51556 | + | 9.55324i | −0.261463 | + | 0.452867i | ||||
\(446\) | −10.6864 | − | 18.5094i | −0.506017 | − | 0.876447i | ||||
\(447\) | 14.3740 | + | 0.563219i | 0.679867 | + | 0.0266394i | ||||
\(448\) | 0.481958 | + | 2.60148i | 0.0227704 | + | 0.122909i | ||||
\(449\) | −7.60160 | −0.358742 | −0.179371 | − | 0.983782i | \(-0.557406\pi\) | ||||
−0.179371 | + | 0.983782i | \(0.557406\pi\) | |||||||
\(450\) | −11.5607 | − | 24.2242i | −0.544976 | − | 1.14194i | ||||
\(451\) | 5.03828 | + | 2.90885i | 0.237243 | + | 0.136972i | ||||
\(452\) | −1.27700 | − | 0.737278i | −0.0600651 | − | 0.0346786i | ||||
\(453\) | −1.98695 | + | 1.04566i | −0.0933552 | + | 0.0491293i | ||||
\(454\) | − | 15.1954i | − | 0.713156i | ||||||
\(455\) | −29.7820 | + | 19.5505i | −1.39620 | + | 0.916543i | ||||
\(456\) | 8.18971 | + | 0.320899i | 0.383518 | + | 0.0150275i | ||||
\(457\) | 9.27260 | − | 5.35354i | 0.433754 | − | 0.250428i | −0.267191 | − | 0.963644i | \(-0.586095\pi\) |
0.700945 | + | 0.713216i | \(0.252762\pi\) | |||||||
\(458\) | 10.7812 | − | 18.6737i | 0.503775 | − | 0.872563i | ||||
\(459\) | −15.4905 | + | 20.7582i | −0.723035 | + | 0.968909i | ||||
\(460\) | −2.16055 | − | 3.74219i | −0.100736 | − | 0.174480i | ||||
\(461\) | 9.51862i | 0.443326i | 0.975123 | + | 0.221663i | \(0.0711485\pi\) | ||||
−0.975123 | + | 0.221663i | \(0.928851\pi\) | |||||||
\(462\) | −5.65296 | − | 2.25509i | −0.263000 | − | 0.104916i | ||||
\(463\) | 17.7463i | 0.824742i | 0.911016 | + | 0.412371i | \(0.135299\pi\) | ||||
−0.911016 | + | 0.412371i | \(0.864701\pi\) | |||||||
\(464\) | −5.45477 | + | 3.14931i | −0.253231 | + | 0.146203i | ||||
\(465\) | −18.2458 | − | 11.5095i | −0.846130 | − | 0.533742i | ||||
\(466\) | −23.8631 | − | 13.7774i | −1.10544 | − | 0.638225i | ||||
\(467\) | −2.60380 | − | 4.50991i | −0.120489 | − | 0.208694i | 0.799471 | − | 0.600704i | \(-0.205113\pi\) |
−0.919961 | + | 0.392010i | \(0.871780\pi\) | |||||||
\(468\) | 2.19356 | − | 10.5919i | 0.101397 | − | 0.489611i | ||||
\(469\) | 3.58857 | − | 10.1314i | 0.165705 | − | 0.467826i | ||||
\(470\) | 29.9807 | 1.38290 | ||||||||
\(471\) | −27.0261 | + | 14.2228i | −1.24530 | + | 0.655352i | ||||
\(472\) | 9.31553 | + | 5.37832i | 0.428782 | + | 0.247557i | ||||
\(473\) | −6.34077 | + | 10.9825i | −0.291549 | + | 0.504977i | ||||
\(474\) | −11.6560 | − | 22.1487i | −0.535378 | − | 1.01732i | ||||
\(475\) | 42.3375 | 1.94258 | ||||||||
\(476\) | 10.0289 | − | 8.56425i | 0.459676 | − | 0.392542i | ||||
\(477\) | 0.370025 | − | 4.71448i | 0.0169423 | − | 0.215861i | ||||
\(478\) | 6.04907 | + | 10.4773i | 0.276678 | + | 0.479220i | ||||
\(479\) | 15.3659 | + | 8.87151i | 0.702086 | + | 0.405350i | 0.808124 | − | 0.589012i | \(-0.200483\pi\) |
−0.106038 | + | 0.994362i | \(0.533816\pi\) | |||||||
\(480\) | −5.47095 | − | 3.45110i | −0.249714 | − | 0.157520i | ||||
\(481\) | 12.6992 | + | 30.2289i | 0.579033 | + | 1.37832i | ||||
\(482\) | −3.52305 | −0.160470 | ||||||||
\(483\) | −5.24738 | + | 0.761011i | −0.238764 | + | 0.0346272i | ||||
\(484\) | −9.23612 | −0.419824 | ||||||||
\(485\) | 31.6763 | − | 18.2883i | 1.43835 | − | 0.830431i | ||||
\(486\) | 10.2719 | − | 11.7255i | 0.465944 | − | 0.531880i | ||||
\(487\) | 18.9701 | + | 10.9524i | 0.859616 | + | 0.496299i | 0.863884 | − | 0.503691i | \(-0.168025\pi\) |
−0.00426783 | + | 0.999991i | \(0.501358\pi\) | |||||||
\(488\) | −4.85105 | + | 2.80076i | −0.219597 | + | 0.126784i | ||||
\(489\) | −0.456176 | + | 11.6421i | −0.0206290 | + | 0.526476i | ||||
\(490\) | 25.8196 | + | 4.09333i | 1.16641 | + | 0.184918i | ||||
\(491\) | − | 3.60049i | − | 0.162488i | −0.996694 | − | 0.0812438i | \(-0.974111\pi\) | ||
0.996694 | − | 0.0812438i | \(-0.0258893\pi\) | |||||||
\(492\) | 6.71415 | − | 3.53340i | 0.302697 | − | 0.159298i | ||||
\(493\) | 27.1900 | + | 15.6982i | 1.22458 | + | 0.707010i | ||||
\(494\) | 13.5876 | + | 10.3183i | 0.611334 | + | 0.464241i | ||||
\(495\) | 13.4289 | − | 6.40880i | 0.603586 | − | 0.288054i | ||||
\(496\) | −3.33504 | −0.149748 | ||||||||
\(497\) | 4.79811 | + | 25.8990i | 0.215225 | + | 1.16173i | ||||
\(498\) | −0.457510 | + | 11.6762i | −0.0205015 | + | 0.523223i | ||||
\(499\) | 6.88661 | − | 3.97599i | 0.308287 | − | 0.177990i | −0.337873 | − | 0.941192i | \(-0.609707\pi\) |
0.646160 | + | 0.763202i | \(0.276374\pi\) | |||||||
\(500\) | −12.7660 | − | 7.37045i | −0.570913 | − | 0.329617i | ||||
\(501\) | −2.04825 | − | 1.29205i | −0.0915092 | − | 0.0577243i | ||||
\(502\) | 9.47494 | + | 16.4111i | 0.422887 | + | 0.732462i | ||||
\(503\) | 10.7862 | 0.480934 | 0.240467 | − | 0.970657i | \(-0.422699\pi\) | ||||
0.240467 | + | 0.970657i | \(0.422699\pi\) | |||||||
\(504\) | −6.42072 | + | 4.66630i | −0.286002 | + | 0.207853i | ||||
\(505\) | − | 34.9944i | − | 1.55723i | ||||||
\(506\) | 1.33081 | − | 0.768346i | 0.0591619 | − | 0.0341571i | ||||
\(507\) | 16.3787 | − | 15.4511i | 0.727404 | − | 0.686209i | ||||
\(508\) | −5.30202 | + | 9.18338i | −0.235239 | + | 0.407446i | ||||
\(509\) | −14.3853 | + | 8.30537i | −0.637618 | + | 0.368129i | −0.783696 | − | 0.621144i | \(-0.786668\pi\) |
0.146078 | + | 0.989273i | \(0.453335\pi\) | |||||||
\(510\) | −1.26242 | + | 32.2184i | −0.0559008 | + | 1.42665i | ||||
\(511\) | −35.9701 | − | 12.7407i | −1.59122 | − | 0.563614i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 9.71319 | + | 22.5881i | 0.428848 | + | 0.997289i | ||||
\(514\) | 0.299289 | − | 0.518384i | 0.0132011 | − | 0.0228650i | ||||
\(515\) | 0.336360 | − | 0.582592i | 0.0148218 | − | 0.0256721i | ||||
\(516\) | 7.70217 | + | 14.6356i | 0.339069 | + | 0.644297i | ||||
\(517\) | 10.6619i | 0.468908i | ||||||||
\(518\) | 8.03301 | − | 22.6792i | 0.352950 | − | 0.996467i | ||||
\(519\) | −38.3413 | − | 1.50234i | −1.68300 | − | 0.0659452i | ||||
\(520\) | −5.21524 | − | 12.4143i | −0.228704 | − | 0.544401i | ||||
\(521\) | −1.55866 | + | 2.69969i | −0.0682863 | + | 0.118275i | −0.898147 | − | 0.439695i | \(-0.855086\pi\) |
0.829861 | + | 0.557971i | \(0.188420\pi\) | |||||||
\(522\) | −15.5749 | − | 10.6994i | −0.681693 | − | 0.468300i | ||||
\(523\) | −10.9887 | + | 6.34431i | −0.480501 | + | 0.277417i | −0.720625 | − | 0.693325i | \(-0.756145\pi\) |
0.240124 | + | 0.970742i | \(0.422812\pi\) | |||||||
\(524\) | −0.517030 | −0.0225865 | ||||||||
\(525\) | −32.1979 | + | 25.3845i | −1.40523 | + | 1.10787i | ||||
\(526\) | 26.7372i | 1.16580i | ||||||||
\(527\) | 8.31197 | + | 14.3968i | 0.362075 | + | 0.627132i | ||||
\(528\) | 1.22729 | − | 1.94560i | 0.0534112 | − | 0.0846716i | ||||
\(529\) | −10.8306 | + | 18.7592i | −0.470896 | + | 0.815616i | ||||
\(530\) | −2.94346 | − | 5.09823i | −0.127856 | − | 0.221453i | ||||
\(531\) | −2.52500 | + | 32.1710i | −0.109576 | + | 1.39610i | ||||
\(532\) | −2.28061 | − | 12.3101i | −0.0988768 | − | 0.533711i | ||||
\(533\) | 15.6689 | + | 1.98297i | 0.678696 | + | 0.0858918i | ||||
\(534\) | −4.52742 | + | 2.38261i | −0.195921 | + | 0.103106i | ||||
\(535\) | 11.1138 | − | 19.2496i | 0.480490 | − | 0.832233i | ||||
\(536\) | 3.51817 | + | 2.03122i | 0.151962 | + | 0.0877352i | ||||
\(537\) | 37.2509 | − | 19.6037i | 1.60750 | − | 0.845963i | ||||
\(538\) | −11.4488 | −0.493594 | ||||||||
\(539\) | −1.45569 | + | 9.18210i | −0.0627010 | + | 0.395501i | ||||
\(540\) | 2.27470 | − | 19.2717i | 0.0978874 | − | 0.829322i | ||||
\(541\) | 0.286703 | − | 0.165528i | 0.0123263 | − | 0.00711660i | −0.493824 | − | 0.869562i | \(-0.664401\pi\) |
0.506150 | + | 0.862445i | \(0.331068\pi\) | |||||||
\(542\) | −12.6383 | + | 21.8902i | −0.542862 | + | 0.940265i | ||||
\(543\) | −21.1155 | − | 13.3197i | −0.906151 | − | 0.571604i | ||||
\(544\) | 2.49232 | + | 4.31682i | 0.106857 | + | 0.185082i | ||||
\(545\) | −44.7164 | −1.91544 | ||||||||
\(546\) | −16.5200 | + | 0.299667i | −0.706990 | + | 0.0128246i | ||||
\(547\) | 21.1593 | 0.904707 | 0.452354 | − | 0.891839i | \(-0.350584\pi\) | ||||
0.452354 | + | 0.891839i | \(0.350584\pi\) | |||||||
\(548\) | 0.694033 | + | 1.20210i | 0.0296476 | + | 0.0513512i | ||||
\(549\) | −13.8511 | − | 9.51523i | −0.591150 | − | 0.406100i | ||||
\(550\) | 5.94139 | − | 10.2908i | 0.253342 | − | 0.438801i | ||||
\(551\) | 25.8117 | − | 14.9024i | 1.09962 | − | 0.634864i | ||||
\(552\) | 0.0784657 | − | 2.00253i | 0.00333972 | − | 0.0852335i | ||||
\(553\) | −29.0734 | + | 24.8273i | −1.23633 | + | 1.05577i | ||||
\(554\) | −4.59429 | −0.195193 | ||||||||
\(555\) | 27.3944 | + | 52.0546i | 1.16283 | + | 2.20960i | ||||
\(556\) | 11.1747 | + | 6.45170i | 0.473912 | + | 0.273613i | ||||
\(557\) | −10.1206 | + | 17.5294i | −0.428823 | + | 0.742743i | −0.996769 | − | 0.0803231i | \(-0.974405\pi\) |
0.567946 | + | 0.823066i | \(0.307738\pi\) | |||||||
\(558\) | −4.30924 | − | 9.02954i | −0.182425 | − | 0.382251i | ||||
\(559\) | −4.32251 | + | 34.1554i | −0.182823 | + | 1.44462i | ||||
\(560\) | −3.29896 | + | 9.31379i | −0.139407 | + | 0.393580i | ||||
\(561\) | −11.4576 | − | 0.448947i | −0.483742 | − | 0.0189545i | ||||
\(562\) | 11.2596 | + | 19.5021i | 0.474956 | + | 0.822647i | ||||
\(563\) | −16.4117 | + | 28.4259i | −0.691670 | + | 1.19801i | 0.279621 | + | 0.960111i | \(0.409791\pi\) |
−0.971290 | + | 0.237897i | \(0.923542\pi\) | |||||||
\(564\) | 11.7603 | + | 7.41845i | 0.495199 | + | 0.312373i | ||||
\(565\) | −2.75343 | − | 4.76907i | −0.115838 | − | 0.200636i | ||||
\(566\) | 7.47391i | 0.314152i | ||||||||
\(567\) | −20.9302 | − | 11.3546i | −0.878986 | − | 0.476848i | ||||
\(568\) | −9.95545 | −0.417722 | ||||||||
\(569\) | −36.2966 | + | 20.9559i | −1.52163 | + | 0.878515i | −0.521959 | + | 0.852971i | \(0.674799\pi\) |
−0.999674 | + | 0.0255443i | \(0.991868\pi\) | |||||||
\(570\) | 25.8883 | + | 16.3304i | 1.08434 | + | 0.684007i | ||||
\(571\) | −3.99051 | + | 6.91177i | −0.166998 | + | 0.289248i | −0.937363 | − | 0.348354i | \(-0.886741\pi\) |
0.770365 | + | 0.637603i | \(0.220074\pi\) | |||||||
\(572\) | 4.41482 | − | 1.85467i | 0.184593 | − | 0.0775476i | ||||
\(573\) | −0.0280546 | + | 0.715985i | −0.00117200 | + | 0.0299107i | ||||
\(574\) | −7.52616 | − | 8.81332i | −0.314136 | − | 0.367861i | ||||
\(575\) | − | 10.3523i | − | 0.431720i | ||||||
\(576\) | −1.29211 | − | 2.70748i | −0.0538380 | − | 0.112812i | ||||
\(577\) | 6.63093 | − | 11.4851i | 0.276049 | − | 0.478131i | −0.694350 | − | 0.719637i | \(-0.744308\pi\) |
0.970399 | + | 0.241506i | \(0.0776414\pi\) | |||||||
\(578\) | 3.92330 | − | 6.79535i | 0.163188 | − | 0.282649i | ||||
\(579\) | −11.6512 | + | 6.13156i | −0.484205 | + | 0.254819i | ||||
\(580\) | −23.5227 | −0.976729 | ||||||||
\(581\) | 17.5507 | − | 3.25149i | 0.728126 | − | 0.134895i | ||||
\(582\) | 16.9508 | + | 0.664185i | 0.702632 | + | 0.0275314i | ||||
\(583\) | 1.81306 | − | 1.04677i | 0.0750891 | − | 0.0433527i | ||||
\(584\) | 7.21154 | − | 12.4907i | 0.298415 | − | 0.516871i | ||||
\(585\) | 26.8727 | − | 30.1608i | 1.11105 | − | 1.24699i | ||||
\(586\) | −12.6517 | + | 7.30444i | −0.522635 | + | 0.301744i | ||||
\(587\) | 9.45396i | 0.390207i | 0.980783 | + | 0.195103i | \(0.0625043\pi\) | ||||
−0.980783 | + | 0.195103i | \(0.937496\pi\) | |||||||
\(588\) | 9.11525 | + | 7.99451i | 0.375906 | + | 0.329688i | ||||
\(589\) | 15.7813 | 0.650255 | ||||||||
\(590\) | 20.0858 | + | 34.7896i | 0.826920 | + | 1.43227i | ||||
\(591\) | 6.14689 | − | 9.74453i | 0.252849 | − | 0.400836i | ||||
\(592\) | 7.87543 | + | 4.54688i | 0.323678 | + | 0.186876i | ||||
\(593\) | −30.1356 | + | 17.3988i | −1.23752 | + | 0.714482i | −0.968587 | − | 0.248677i | \(-0.920004\pi\) |
−0.268933 | + | 0.963159i | \(0.586671\pi\) | |||||||
\(594\) | 6.85349 | + | 0.808938i | 0.281202 | + | 0.0331911i | ||||
\(595\) | 48.4280 | − | 8.97191i | 1.98536 | − | 0.367813i | ||||
\(596\) | 8.30520 | 0.340194 | ||||||||
\(597\) | 23.1849 | − | 12.2013i | 0.948895 | − | 0.499367i | ||||
\(598\) | 2.52301 | − | 3.32241i | 0.103173 | − | 0.135864i | ||||
\(599\) | 3.32776 | + | 1.92128i | 0.135969 | + | 0.0785016i | 0.566441 | − | 0.824102i | \(-0.308320\pi\) |
−0.430473 | + | 0.902604i | \(0.641653\pi\) | |||||||
\(600\) | −7.21704 | − | 13.7138i | −0.294634 | − | 0.559863i | ||||
\(601\) | − | 24.4368i | − | 0.996796i | −0.866948 | − | 0.498398i | \(-0.833922\pi\) | ||
0.866948 | − | 0.498398i | \(-0.166078\pi\) | |||||||
\(602\) | 19.2114 | − | 16.4057i | 0.782999 | − | 0.668645i | ||||
\(603\) | −0.953611 | + | 12.1499i | −0.0388340 | + | 0.494784i | ||||
\(604\) | −1.12265 | + | 0.648163i | −0.0456800 | + | 0.0263734i | ||||
\(605\) | −29.8719 | − | 17.2465i | −1.21447 | − | 0.701172i | ||||
\(606\) | 8.65907 | − | 13.7270i | 0.351750 | − | 0.557623i | ||||
\(607\) | 25.3256 | − | 14.6218i | 1.02794 | − | 0.593479i | 0.111543 | − | 0.993760i | \(-0.464421\pi\) |
0.916393 | + | 0.400281i | \(0.131087\pi\) | |||||||
\(608\) | 4.73196 | 0.191906 | ||||||||
\(609\) | −10.6948 | + | 26.8094i | −0.433377 | + | 1.08637i | ||||
\(610\) | −20.9193 | −0.846999 | ||||||||
\(611\) | 11.2107 | + | 26.6856i | 0.453534 | + | 1.07958i | ||||
\(612\) | −8.46735 | + | 12.3257i | −0.342273 | + | 0.498237i | ||||
\(613\) | −7.85345 | − | 4.53419i | −0.317198 | − | 0.183134i | 0.332945 | − | 0.942946i | \(-0.391958\pi\) |
−0.650143 | + | 0.759812i | \(0.725291\pi\) | |||||||
\(614\) | −2.76445 | − | 4.78816i | −0.111564 | − | 0.193234i | ||||
\(615\) | 28.3131 | + | 1.10940i | 1.14169 | + | 0.0447352i | ||||
\(616\) | −3.31221 | − | 1.17319i | −0.133453 | − | 0.0472692i | ||||
\(617\) | 47.4218 | 1.90913 | 0.954565 | − | 0.298002i | \(-0.0963202\pi\) | ||||
0.954565 | + | 0.298002i | \(0.0963202\pi\) | |||||||
\(618\) | 0.276099 | − | 0.145300i | 0.0111063 | − | 0.00584484i | ||||
\(619\) | 20.7977 | − | 36.0226i | 0.835929 | − | 1.44787i | −0.0573430 | − | 0.998355i | \(-0.518263\pi\) |
0.893272 | − | 0.449517i | \(-0.148404\pi\) | |||||||
\(620\) | −10.7863 | − | 6.22749i | −0.433189 | − | 0.250102i | ||||
\(621\) | 5.52321 | − | 2.37505i | 0.221639 | − | 0.0953076i | ||||
\(622\) | 25.0154 | 1.00303 | ||||||||
\(623\) | 5.07497 | + | 5.94291i | 0.203324 | + | 0.238098i | ||||
\(624\) | 1.02605 | − | 6.16013i | 0.0410750 | − | 0.246603i | ||||
\(625\) | −5.15775 | − | 8.93348i | −0.206310 | − | 0.357339i | ||||
\(626\) | 12.4242 | + | 7.17314i | 0.496573 | + | 0.286696i | ||||
\(627\) | −5.80751 | + | 9.20652i | −0.231930 | + | 0.367673i | ||||
\(628\) | −15.2700 | + | 8.81616i | −0.609341 | + | 0.351803i | ||||
\(629\) | − | 45.3291i | − | 1.80739i | ||||||
\(630\) | −29.4795 | + | 3.10259i | −1.17449 | + | 0.123610i | ||||
\(631\) | − | 2.35427i | − | 0.0937218i | −0.998901 | − | 0.0468609i | \(-0.985078\pi\) | ||
0.998901 | − | 0.0468609i | \(-0.0149218\pi\) | |||||||
\(632\) | −7.22510 | − | 12.5142i | −0.287399 | − | 0.497790i | ||||
\(633\) | 9.45846 | − | 14.9943i | 0.375940 | − | 0.595970i | ||||
\(634\) | −7.58692 | + | 13.1409i | −0.301315 | + | 0.521893i | ||||
\(635\) | −34.2961 | + | 19.8009i | −1.36100 | + | 0.785773i | ||||
\(636\) | 0.106899 | − | 2.72818i | 0.00423882 | − | 0.108180i | ||||
\(637\) | 6.01127 | + | 24.5125i | 0.238175 | + | 0.971222i | ||||
\(638\) | − | 8.36526i | − | 0.331184i | ||||||
\(639\) | −12.8636 | − | 26.9542i | −0.508874 | − | 1.06629i | ||||
\(640\) | −3.23425 | − | 1.86729i | −0.127845 | − | 0.0738112i | ||||
\(641\) | −14.3753 | − | 8.29956i | −0.567789 | − | 0.327813i | 0.188477 | − | 0.982078i | \(-0.439645\pi\) |
−0.756266 | + | 0.654265i | \(0.772978\pi\) | |||||||
\(642\) | 9.12268 | − | 4.80092i | 0.360043 | − | 0.189477i | ||||
\(643\) | 5.87699 | 0.231766 | 0.115883 | − | 0.993263i | \(-0.463030\pi\) | ||||
0.115883 | + | 0.993263i | \(0.463030\pi\) | |||||||
\(644\) | −3.01005 | + | 0.557650i | −0.118613 | + | 0.0219745i | ||||
\(645\) | −2.41828 | + | 61.7174i | −0.0952198 | + | 2.43012i | ||||
\(646\) | −11.7935 | − | 20.4270i | −0.464011 | − | 0.803690i | ||||
\(647\) | 14.9475 | − | 25.8898i | 0.587645 | − | 1.01783i | −0.406895 | − | 0.913475i | \(-0.633388\pi\) |
0.994540 | − | 0.104356i | \(-0.0332783\pi\) | |||||||
\(648\) | 5.66090 | − | 6.99673i | 0.222381 | − | 0.274858i | ||||
\(649\) | −12.3721 | + | 7.14301i | −0.485645 | + | 0.280388i | ||||
\(650\) | 4.05025 | − | 32.0041i | 0.158864 | − | 1.25530i | ||||
\(651\) | −12.0017 | + | 9.46204i | −0.470385 | + | 0.370847i | ||||
\(652\) | 6.72676i | 0.263440i | ||||||||
\(653\) | 6.48294 | − | 3.74293i | 0.253697 | − | 0.146472i | −0.367759 | − | 0.929921i | \(-0.619875\pi\) |
0.621456 | + | 0.783449i | \(0.286541\pi\) | |||||||
\(654\) | −17.5406 | − | 11.0647i | −0.685892 | − | 0.432663i | ||||
\(655\) | −1.67220 | − | 0.965446i | −0.0653383 | − | 0.0377231i | ||||
\(656\) | 3.79357 | − | 2.19022i | 0.148114 | − | 0.0855137i | ||||
\(657\) | 43.1365 | + | 3.38565i | 1.68292 | + | 0.132087i | ||||
\(658\) | 7.09142 | − | 20.0209i | 0.276452 | − | 0.780495i | ||||
\(659\) | 32.6856i | 1.27325i | 0.771174 | + | 0.636624i | \(0.219670\pi\) | ||||
−0.771174 | + | 0.636624i | \(0.780330\pi\) | |||||||
\(660\) | 7.60239 | − | 4.00085i | 0.295923 | − | 0.155733i | ||||
\(661\) | 2.68538 | − | 4.65121i | 0.104449 | − | 0.180911i | −0.809064 | − | 0.587721i | \(-0.800025\pi\) |
0.913513 | + | 0.406809i | \(0.133359\pi\) | |||||||
\(662\) | −25.2714 | − | 14.5904i | −0.982200 | − | 0.567073i | ||||
\(663\) | −29.1494 | + | 10.9237i | −1.13207 | + | 0.424242i | ||||
\(664\) | 6.74642i | 0.261812i | ||||||||
\(665\) | 15.6105 | − | 44.0725i | 0.605351 | − | 1.70906i | ||||
\(666\) | −2.13466 | + | 27.1976i | −0.0827163 | + | 1.05389i | ||||
\(667\) | −3.64391 | − | 6.31144i | −0.141093 | − | 0.244380i | ||||
\(668\) | −1.21086 | − | 0.699090i | −0.0468496 | − | 0.0270486i | ||||
\(669\) | 19.7505 | − | 31.3100i | 0.763597 | − | 1.21051i | ||||
\(670\) | 7.58576 | + | 13.1389i | 0.293063 | + | 0.507601i | ||||
\(671\) | − | 7.43942i | − | 0.287196i | ||||||
\(672\) | −3.59868 | + | 2.83716i | −0.138822 | + | 0.109446i | ||||
\(673\) | −27.9654 | −1.07799 | −0.538994 | − | 0.842310i | \(-0.681195\pi\) | ||||
−0.538994 | + | 0.842310i | \(0.681195\pi\) | |||||||
\(674\) | 10.9157 | + | 18.9065i | 0.420456 | + | 0.728251i | ||||
\(675\) | 27.8046 | − | 37.2597i | 1.07020 | − | 1.43413i | ||||
\(676\) | 9.09973 | − | 9.28412i | 0.349990 | − | 0.357081i | ||||
\(677\) | −17.5946 | − | 30.4747i | −0.676214 | − | 1.17124i | −0.976112 | − | 0.217266i | \(-0.930286\pi\) |
0.299898 | − | 0.953971i | \(-0.403047\pi\) | |||||||
\(678\) | 0.0999973 | − | 2.55205i | 0.00384037 | − | 0.0980107i | ||||
\(679\) | −4.72032 | − | 25.4790i | −0.181149 | − | 0.977796i | ||||
\(680\) | 18.6156i | 0.713874i | ||||||||
\(681\) | 23.2909 | − | 12.2571i | 0.892509 | − | 0.469693i | ||||
\(682\) | 2.21465 | − | 3.83588i | 0.0848032 | − | 0.146884i | ||||
\(683\) | −15.0441 | + | 26.0572i | −0.575648 | + | 0.997052i | 0.420323 | + | 0.907375i | \(0.361917\pi\) |
−0.995971 | + | 0.0896770i | \(0.971417\pi\) | |||||||
\(684\) | 6.11422 | + | 12.8117i | 0.233783 | + | 0.489867i | ||||
\(685\) | 5.18385i | 0.198065i | ||||||||
\(686\) | 8.84070 | − | 16.2740i | 0.337540 | − | 0.621343i | ||||
\(687\) | 37.3187 | + | 1.46227i | 1.42380 | + | 0.0557889i | ||||
\(688\) | 4.77428 | + | 8.26929i | 0.182018 | + | 0.315264i | ||||
\(689\) | 3.43726 | − | 4.52634i | 0.130949 | − | 0.172440i | ||||
\(690\) | 3.99310 | − | 6.33017i | 0.152015 | − | 0.240986i | ||||
\(691\) | −11.4256 | − | 19.7898i | −0.434651 | − | 0.752838i | 0.562616 | − | 0.826719i | \(-0.309795\pi\) |
−0.997267 | + | 0.0738803i | \(0.976462\pi\) | |||||||
\(692\) | −22.1534 | −0.842145 | ||||||||
\(693\) | −1.10336 | − | 10.4836i | −0.0419131 | − | 0.398241i | ||||
\(694\) | 27.8171i | 1.05592i | ||||||||
\(695\) | 24.0944 | + | 41.7328i | 0.913954 | + | 1.58302i | ||||
\(696\) | −9.22711 | − | 5.82050i | −0.349753 | − | 0.220625i | ||||
\(697\) | −18.9096 | − | 10.9174i | −0.716251 | − | 0.413528i | ||||
\(698\) | −2.27346 | − | 3.93774i | −0.0860516 | − | 0.149046i | ||||
\(699\) | 1.86863 | − | 47.6896i | 0.0706781 | − | 1.80379i | ||||
\(700\) | −18.0014 | + | 15.3723i | −0.680388 | + | 0.581020i | ||||
\(701\) | 31.5577i | 1.19192i | 0.803015 | + | 0.595959i | \(0.203228\pi\) | ||||
−0.803015 | + | 0.595959i | \(0.796772\pi\) | |||||||
\(702\) | 18.0042 | − | 5.18156i | 0.679525 | − | 0.195565i | ||||
\(703\) | −37.2662 | − | 21.5156i | −1.40552 | − | 0.811478i | ||||
\(704\) | 0.664055 | − | 1.15018i | 0.0250275 | − | 0.0433489i | ||||
\(705\) | 24.1833 | + | 45.9531i | 0.910797 | + | 1.73069i | ||||
\(706\) | − | 8.32657i | − | 0.313375i | ||||||
\(707\) | −23.3690 | − | 8.27734i | −0.878882 | − | 0.311302i | ||||
\(708\) | −0.729464 | + | 18.6168i | −0.0274150 | + | 0.699661i | ||||
\(709\) | −14.1878 | + | 8.19131i | −0.532833 | + | 0.307631i | −0.742169 | − | 0.670213i | \(-0.766203\pi\) |
0.209336 | + | 0.977844i | \(0.432870\pi\) | |||||||
\(710\) | −32.1984 | − | 18.5897i | −1.20838 | − | 0.697661i | ||||
\(711\) | 24.5464 | − | 35.7316i | 0.920563 | − | 1.34004i | ||||
\(712\) | −2.55804 | + | 1.47689i | −0.0958668 | + | 0.0553487i | ||||
\(713\) | − | 3.85881i | − | 0.144513i | ||||||
\(714\) | 21.2166 | + | 8.46375i | 0.794011 | + | 0.316748i | ||||
\(715\) | 17.7418 | + | 2.24530i | 0.663506 | + | 0.0839695i | ||||
\(716\) | 21.0472 | − | 12.1516i | 0.786570 | − | 0.454126i | ||||
\(717\) | −11.1798 | + | 17.7231i | −0.417516 | + | 0.661880i | ||||
\(718\) | −7.10506 | + | 12.3063i | −0.265158 | + | 0.459268i | ||||
\(719\) | 8.08537 | + | 14.0043i | 0.301533 | + | 0.522271i | 0.976483 | − | 0.215592i | \(-0.0691682\pi\) |
−0.674950 | + | 0.737863i | \(0.735835\pi\) | |||||||
\(720\) | 0.876652 | − | 11.1694i | 0.0326709 | − | 0.416259i | ||||
\(721\) | −0.309490 | − | 0.362421i | −0.0115260 | − | 0.0134973i | ||||
\(722\) | −3.39143 | −0.126216 | ||||||||
\(723\) | −2.84180 | − | 5.39998i | −0.105688 | − | 0.200827i | ||||
\(724\) | −12.4828 | − | 7.20693i | −0.463918 | − | 0.267843i | ||||
\(725\) | −48.8045 | − | 28.1773i | −1.81255 | − | 1.04648i | ||||
\(726\) | −7.45015 | − | 14.1567i | −0.276501 | − | 0.525406i | ||||
\(727\) | − | 16.3582i | − | 0.606692i | −0.952880 | − | 0.303346i | \(-0.901896\pi\) | ||
0.952880 | − | 0.303346i | \(-0.0981038\pi\) | |||||||
\(728\) | −9.52374 | + | 0.546316i | −0.352973 | + | 0.0202478i | ||||
\(729\) | 26.2580 | + | 6.28621i | 0.972519 | + | 0.232822i | ||||
\(730\) | 46.6478 | − | 26.9321i | 1.72651 | − | 0.996802i | ||||
\(731\) | 23.7980 | − | 41.2194i | 0.880202 | − | 1.52455i | ||||
\(732\) | −8.20589 | − | 5.17631i | −0.303298 | − | 0.191322i | ||||
\(733\) | −25.9026 | − | 44.8646i | −0.956734 | − | 1.65711i | −0.730348 | − | 0.683075i | \(-0.760642\pi\) |
−0.226386 | − | 0.974038i | \(-0.572691\pi\) | |||||||
\(734\) | 2.37849i | 0.0877918i | ||||||||
\(735\) | 14.5529 | + | 42.8771i | 0.536790 | + | 1.58154i | ||||
\(736\) | − | 1.15705i | − | 0.0426495i | ||||||
\(737\) | −4.67252 | + | 2.69768i | −0.172115 | + | 0.0993704i | ||||
\(738\) | 10.8317 | + | 7.44101i | 0.398720 | + | 0.273907i | ||||
\(739\) | 13.0157 | + | 7.51460i | 0.478789 | + | 0.276429i | 0.719912 | − | 0.694066i | \(-0.244182\pi\) |
−0.241123 | + | 0.970495i | \(0.577516\pi\) | |||||||
\(740\) | 16.9807 | + | 29.4115i | 0.624224 | + | 1.08119i | ||||
\(741\) | −4.85524 | + | 29.1495i | −0.178362 | + | 1.07083i | ||||
\(742\) | −4.10079 | + | 0.759723i | −0.150545 | + | 0.0278903i | ||||
\(743\) | 22.4238 | 0.822651 | 0.411326 | − | 0.911489i | \(-0.365066\pi\) | ||||
0.411326 | + | 0.911489i | \(0.365066\pi\) | |||||||
\(744\) | −2.69015 | − | 5.11180i | −0.0986255 | − | 0.187408i | ||||
\(745\) | 26.8611 | + | 15.5082i | 0.984114 | + | 0.568178i | ||||
\(746\) | 11.7785 | − | 20.4010i | 0.431243 | − | 0.746934i | ||||
\(747\) | −18.2658 | + | 8.71713i | −0.668311 | + | 0.318943i | ||||
\(748\) | −6.62015 | −0.242057 | ||||||||
\(749\) | −10.2260 | − | 11.9749i | −0.373649 | − | 0.437552i | ||||
\(750\) | 0.999657 | − | 25.5124i | 0.0365023 | − | 0.931581i | ||||
\(751\) | −13.6135 | − | 23.5793i | −0.496765 | − | 0.860422i | 0.503228 | − | 0.864154i | \(-0.332146\pi\) |
−0.999993 | + | 0.00373163i | \(0.998812\pi\) | |||||||
\(752\) | 6.95231 | + | 4.01392i | 0.253525 | + | 0.146373i | ||||
\(753\) | −17.5114 | + | 27.7605i | −0.638152 | + | 1.01165i | ||||
\(754\) | −8.79585 | − | 20.9375i | −0.320326 | − | 0.762497i | ||||
\(755\) | −4.84124 | −0.176191 | ||||||||
\(756\) | −12.3315 | − | 6.07742i | −0.448491 | − | 0.221034i | ||||
\(757\) | 4.76540 | 0.173201 | 0.0866007 | − | 0.996243i | \(-0.472400\pi\) | ||||
0.0866007 | + | 0.996243i | \(0.472400\pi\) | |||||||
\(758\) | −15.6661 | + | 9.04481i | −0.569017 | + | 0.328522i | ||||
\(759\) | 2.25116 | + | 1.42004i | 0.0817121 | + | 0.0515443i | ||||
\(760\) | 15.3043 | + | 8.83595i | 0.555146 | + | 0.320514i | ||||
\(761\) | −29.7410 | + | 17.1710i | −1.07811 | + | 0.622448i | −0.930386 | − | 0.366580i | \(-0.880529\pi\) |
−0.147725 | + | 0.989028i | \(0.547195\pi\) | |||||||
\(762\) | −18.3527 | − | 0.719116i | −0.664847 | − | 0.0260508i | ||||
\(763\) | −10.5769 | + | 29.8613i | −0.382910 | + | 1.08105i | ||||
\(764\) | 0.413691i | 0.0149668i | ||||||||
\(765\) | −50.4012 | + | 24.0534i | −1.82226 | + | 0.869651i | ||||
\(766\) | 6.97099 | + | 4.02470i | 0.251872 | + | 0.145418i | ||||
\(767\) | −23.4554 | + | 30.8871i | −0.846925 | + | 1.11527i | ||||
\(768\) | −0.806632 | − | 1.53276i | −0.0291068 | − | 0.0553086i | ||||
\(769\) | −22.9273 | −0.826779 | −0.413390 | − | 0.910554i | \(-0.635655\pi\) | ||||
−0.413390 | + | 0.910554i | \(0.635655\pi\) | |||||||
\(770\) | −8.52182 | − | 9.97926i | −0.307105 | − | 0.359628i | ||||
\(771\) | 1.03597 | + | 0.0405927i | 0.0373097 | + | 0.00146191i | ||||
\(772\) | −6.58304 | + | 3.80072i | −0.236929 | + | 0.136791i | ||||
\(773\) | 35.9806 | + | 20.7734i | 1.29413 | + | 0.747168i | 0.979384 | − | 0.202007i | \(-0.0647465\pi\) |
0.314748 | + | 0.949175i | \(0.398080\pi\) | |||||||
\(774\) | −16.2200 | + | 23.6111i | −0.583017 | + | 0.848684i | ||||
\(775\) | −14.9195 | − | 25.8413i | −0.535924 | − | 0.928248i | ||||
\(776\) | 9.79404 | 0.351586 | ||||||||
\(777\) | 41.2414 | − | 5.98111i | 1.47953 | − | 0.214571i | ||||
\(778\) | 31.7954i | 1.13992i | ||||||||
\(779\) | −17.9510 | + | 10.3640i | −0.643162 | + | 0.371330i | ||||
\(780\) | 14.8213 | − | 18.0074i | 0.530687 | − | 0.644770i | ||||
\(781\) | 6.61097 | − | 11.4505i | 0.236559 | − | 0.409732i | ||||
\(782\) | −4.99478 | + | 2.88374i | −0.178613 | + | 0.103122i | ||||
\(783\) | 3.83642 | − | 32.5030i | 0.137103 | − | 1.16156i | ||||
\(784\) | 5.43937 | + | 4.40604i | 0.194263 | + | 0.157359i | ||||
\(785\) | −65.8494 | −2.35027 | ||||||||
\(786\) | −0.417052 | − | 0.792481i | −0.0148758 | − | 0.0282669i | ||||
\(787\) | −6.06775 | + | 10.5097i | −0.216292 | + | 0.374629i | −0.953671 | − | 0.300850i | \(-0.902730\pi\) |
0.737379 | + | 0.675479i | \(0.236063\pi\) | |||||||
\(788\) | 3.32591 | − | 5.76064i | 0.118481 | − | 0.205214i | ||||
\(789\) | −40.9817 | + | 21.5671i | −1.45899 | + | 0.767809i | ||||
\(790\) | − | 53.9655i | − | 1.92001i | ||||||
\(791\) | −3.83603 | + | 0.710674i | −0.136394 | + | 0.0252686i | ||||
\(792\) | 3.97212 | + | 0.311759i | 0.141143 | + | 0.0110779i | ||||
\(793\) | −7.82235 | − | 18.6202i | −0.277780 | − | 0.661222i | ||||
\(794\) | 13.5400 | − | 23.4520i | 0.480518 | − | 0.832282i | ||||
\(795\) | 5.44006 | − | 8.62401i | 0.192939 | − | 0.305862i | ||||
\(796\) | 13.0997 | − | 7.56314i | 0.464308 | − | 0.268068i | ||||
\(797\) | 29.6346 | 1.04971 | 0.524856 | − | 0.851191i | \(-0.324119\pi\) | ||||
0.524856 | + | 0.851191i | \(0.324119\pi\) | |||||||
\(798\) | 17.0288 | − | 13.4253i | 0.602813 | − | 0.475252i | ||||
\(799\) | − | 40.0159i | − | 1.41566i | ||||||
\(800\) | −4.47357 | − | 7.74844i | −0.158164 | − | 0.273949i | ||||
\(801\) | −7.30392 | − | 5.01755i | −0.258071 | − | 0.177286i | ||||
\(802\) | 7.51128 | − | 13.0099i | 0.265233 | − | 0.459396i | ||||
\(803\) | 9.57771 | + | 16.5891i | 0.337990 | + | 0.585416i | ||||
\(804\) | −0.275495 | + | 7.03095i | −0.00971596 | + | 0.247962i | ||||
\(805\) | −10.7765 | − | 3.81707i | −0.379823 | − | 0.134534i | ||||
\(806\) | 1.50973 | − | 11.9295i | 0.0531779 | − | 0.420198i | ||||
\(807\) | −9.23499 | − | 17.5483i | −0.325087 | − | 0.617729i | ||||
\(808\) | 4.68518 | − | 8.11497i | 0.164824 | − | 0.285484i | ||||
\(809\) | 2.60344 | + | 1.50310i | 0.0915320 | + | 0.0528460i | 0.545067 | − | 0.838392i | \(-0.316504\pi\) |
−0.453535 | + | 0.891238i | \(0.649837\pi\) | |||||||
\(810\) | 31.3737 | − | 12.0586i | 1.10236 | − | 0.423696i | ||||
\(811\) | 26.5609 | 0.932679 | 0.466339 | − | 0.884606i | \(-0.345573\pi\) | ||||
0.466339 | + | 0.884606i | \(0.345573\pi\) | |||||||
\(812\) | −5.56391 | + | 15.7083i | −0.195255 | + | 0.551254i | ||||
\(813\) | −43.7469 | − | 1.71414i | −1.53427 | − | 0.0601175i | ||||
\(814\) | −10.4594 | + | 6.03876i | −0.366603 | + | 0.211658i | ||||
\(815\) | −12.5608 | + | 21.7560i | −0.439986 | + | 0.762079i | ||||
\(816\) | −4.60626 | + | 7.30220i | −0.161251 | + | 0.255628i | ||||
\(817\) | −22.5917 | − | 39.1299i | −0.790383 | − | 1.36898i | ||||
\(818\) | −19.4366 | −0.679585 | ||||||||
\(819\) | −13.7849 | − | 25.0794i | −0.481682 | − | 0.876346i | ||||
\(820\) | 16.3591 | 0.571285 | ||||||||
\(821\) | −15.3289 | − | 26.5504i | −0.534982 | − | 0.926617i | −0.999164 | − | 0.0408767i | \(-0.986985\pi\) |
0.464182 | − | 0.885740i | \(-0.346348\pi\) | |||||||
\(822\) | −1.28270 | + | 2.03344i | −0.0447393 | + | 0.0709243i | ||||
\(823\) | 14.7584 | − | 25.5624i | 0.514447 | − | 0.891048i | −0.485413 | − | 0.874285i | \(-0.661331\pi\) |
0.999859 | − | 0.0167629i | \(-0.00533605\pi\) | |||||||
\(824\) | 0.155999 | − | 0.0900661i | 0.00543448 | − | 0.00313760i | ||||
\(825\) | 20.5658 | + | 0.805833i | 0.716009 | + | 0.0280555i | ||||
\(826\) | 27.9832 | − | 5.18425i | 0.973661 | − | 0.180383i | ||||
\(827\) | 15.9435 | 0.554408 | 0.277204 | − | 0.960811i | \(-0.410592\pi\) | ||||
0.277204 | + | 0.960811i | \(0.410592\pi\) | |||||||
\(828\) | 3.13269 | − | 1.49504i | 0.108869 | − | 0.0519562i | ||||
\(829\) | −34.3579 | − | 19.8365i | −1.19330 | − | 0.688952i | −0.234246 | − | 0.972177i | \(-0.575262\pi\) |
−0.959053 | + | 0.283226i | \(0.908595\pi\) | |||||||
\(830\) | −12.5976 | + | 21.8196i | −0.437267 | + | 0.757369i | ||||
\(831\) | −3.70590 | − | 7.04194i | −0.128556 | − | 0.244282i | ||||
\(832\) | 0.452687 | − | 3.57702i | 0.0156941 | − | 0.124011i | ||||
\(833\) | 5.46346 | − | 34.4621i | 0.189298 | − | 1.19404i | ||||
\(834\) | −0.875047 | + | 22.3322i | −0.0303004 | + | 0.773302i | ||||
\(835\) | −2.61081 | − | 4.52206i | −0.0903509 | − | 0.156492i | ||||
\(836\) | −3.14228 | + | 5.44259i | −0.108678 | + | 0.188236i | ||||
\(837\) | 10.3641 | − | 13.8885i | 0.358237 | − | 0.480058i | ||||
\(838\) | 5.98141 | + | 10.3601i | 0.206625 | + | 0.357884i | ||||
\(839\) | − | 6.33231i | − | 0.218616i | −0.994008 | − | 0.109308i | \(-0.965137\pi\) | ||
0.994008 | − | 0.109308i | \(-0.0348634\pi\) | |||||||
\(840\) | −16.9368 | + | 2.45630i | −0.584376 | + | 0.0847502i | ||||
\(841\) | −10.6726 | −0.368021 | ||||||||
\(842\) | −7.03591 | + | 4.06218i | −0.242473 | + | 0.139992i | ||||
\(843\) | −20.8097 | + | 32.9892i | −0.716724 | + | 1.13621i | ||||
\(844\) | 5.11771 | − | 8.86413i | 0.176159 | − | 0.305116i | ||||
\(845\) | 46.7669 | − | 13.0353i | 1.60883 | − | 0.448426i | ||||
\(846\) | −1.88444 | + | 24.0097i | −0.0647885 | + | 0.825470i | ||||
\(847\) | −18.5828 | + | 15.8689i | −0.638513 | + | 0.545260i | ||||
\(848\) | − | 1.57633i | − | 0.0541313i | ||||||
\(849\) | −11.4557 | + | 6.02869i | −0.393158 | + | 0.206904i | ||||
\(850\) | −22.2991 | + | 38.6232i | −0.764853 | + | 1.32476i | ||||
\(851\) | −5.26097 | + | 9.11227i | −0.180344 | + | 0.312365i | ||||
\(852\) | −8.03038 | − | 15.2593i | −0.275116 | − | 0.522775i | ||||
\(853\) | 56.4541 | 1.93295 | 0.966475 | − | 0.256760i | \(-0.0826551\pi\) | ||||
0.966475 | + | 0.256760i | \(0.0826551\pi\) | |||||||
\(854\) | −4.94812 | + | 13.9698i | −0.169321 | + | 0.478036i | ||||
\(855\) | −4.14828 | + | 52.8532i | −0.141868 | + | 1.80754i | ||||
\(856\) | 5.15442 | − | 2.97590i | 0.176174 | − | 0.101714i | ||||
\(857\) | −18.6366 | + | 32.2796i | −0.636615 | + | 1.10265i | 0.349556 | + | 0.936916i | \(0.386333\pi\) |
−0.986171 | + | 0.165734i | \(0.947001\pi\) | |||||||
\(858\) | 6.40389 | + | 5.27081i | 0.218625 | + | 0.179942i | ||||
\(859\) | 21.9122 | − | 12.6510i | 0.747634 | − | 0.431646i | −0.0772046 | − | 0.997015i | \(-0.524599\pi\) |
0.824838 | + | 0.565369i | \(0.191266\pi\) | |||||||
\(860\) | 35.6599i | 1.21599i | ||||||||
\(861\) | 7.43784 | − | 18.6449i | 0.253481 | − | 0.635416i | ||||
\(862\) | 9.88364 | 0.336638 | ||||||||
\(863\) | 18.1156 | + | 31.3771i | 0.616661 | + | 1.06809i | 0.990091 | + | 0.140429i | \(0.0448482\pi\) |
−0.373430 | + | 0.927658i | \(0.621818\pi\) | |||||||
\(864\) | 3.10765 | − | 4.16443i | 0.105724 | − | 0.141677i | ||||
\(865\) | −71.6494 | − | 41.3668i | −2.43615 | − | 1.40651i | ||||
\(866\) | −12.3501 | + | 7.13030i | −0.419672 | + | 0.242298i | ||||
\(867\) | 13.5803 | + | 0.532118i | 0.461210 | + | 0.0180717i | ||||
\(868\) | −6.71000 | + | 5.73002i | −0.227752 | + | 0.194490i | ||||
\(869\) | 19.1915 | 0.651026 | ||||||||
\(870\) | −18.9742 | − | 36.0547i | −0.643285 | − | 1.22237i | ||||
\(871\) | −8.85834 | + | 11.6651i | −0.300153 | + | 0.395256i | ||||
\(872\) | −10.3694 | − | 5.98679i | −0.351153 | − | 0.202738i | ||||
\(873\) | 12.6550 | + | 26.5172i | 0.428307 | + | 0.897470i | ||||
\(874\) | 5.47512i | 0.185199i | ||||||||
\(875\) | −38.3482 | + | 7.10450i | −1.29641 | + | 0.240176i | ||||
\(876\) | 24.9623 | + | 0.978104i | 0.843399 | + | 0.0330471i | ||||
\(877\) | −9.94338 | + | 5.74081i | −0.335764 | + | 0.193853i | −0.658397 | − | 0.752671i | \(-0.728765\pi\) |
0.322633 | + | 0.946524i | \(0.395432\pi\) | |||||||
\(878\) | −17.7811 | − | 10.2659i | −0.600083 | − | 0.346458i | ||||
\(879\) | −21.4012 | − | 13.4999i | −0.721843 | − | 0.455341i | ||||
\(880\) | 4.29544 | − | 2.47997i | 0.144799 | − | 0.0835998i | ||||
\(881\) | 5.83608 | 0.196622 | 0.0983112 | − | 0.995156i | \(-0.468656\pi\) | ||||
0.0983112 | + | 0.995156i | \(0.468656\pi\) | |||||||
\(882\) | −4.90100 | + | 20.4201i | −0.165025 | + | 0.687580i | ||||
\(883\) | −1.68447 | −0.0566871 | −0.0283435 | − | 0.999598i | \(-0.509023\pi\) | ||||
−0.0283435 | + | 0.999598i | \(0.509023\pi\) | |||||||
\(884\) | −16.5696 | + | 6.96090i | −0.557296 | + | 0.234121i | ||||
\(885\) | −37.1222 | + | 58.8491i | −1.24785 | + | 1.97819i | ||||
\(886\) | 0.915950 | + | 0.528824i | 0.0307719 | + | 0.0177662i | ||||
\(887\) | −27.8345 | − | 48.2107i | −0.934591 | − | 1.61876i | −0.775362 | − | 0.631517i | \(-0.782433\pi\) |
−0.159228 | − | 0.987242i | \(-0.550901\pi\) | |||||||
\(888\) | −0.616695 | + | 15.7388i | −0.0206949 | + | 0.528159i | ||||
\(889\) | 5.11071 | + | 27.5863i | 0.171408 | + | 0.925213i | ||||
\(890\) | −11.0311 | −0.369764 | ||||||||
\(891\) | 4.28833 | + | 11.1572i | 0.143665 | + | 0.373782i | ||||
\(892\) | 10.6864 | − | 18.5094i | 0.357808 | − | 0.619741i | ||||
\(893\) | −32.8981 | − | 18.9937i | −1.10089 | − | 0.635600i | ||||
\(894\) | 6.69924 | + | 12.7299i | 0.224056 | + | 0.425750i | ||||
\(895\) | 90.7624 | 3.03385 | ||||||||
\(896\) | −2.01197 | + | 1.71813i | −0.0672153 | + | 0.0573987i | ||||
\(897\) | 7.12759 | + | 1.18719i | 0.237983 | + | 0.0396393i | ||||
\(898\) | −3.80080 | − | 6.58318i | −0.126834 | − | 0.219684i | ||||
\(899\) | −18.1918 | − | 10.5031i | −0.606732 | − | 0.350297i | ||||
\(900\) | 15.1984 | − | 22.1239i | 0.506614 | − | 0.737465i | ||||
\(901\) | −6.80472 | + | 3.92871i | −0.226698 | + | 0.130884i | ||||
\(902\) | 5.81770i | 0.193708i | ||||||||
\(903\) | 40.6424 | + | 16.2131i | 1.35250 | + | 0.539539i | ||||
\(904\) | − | 1.47456i | − | 0.0490430i | ||||||
\(905\) | −26.9149 | − | 46.6180i | −0.894681 | − | 1.54963i | ||||
\(906\) | −1.89904 | − | 1.19792i | −0.0630915 | − | 0.0397983i | ||||
\(907\) | 2.07089 | − | 3.58688i | 0.0687627 | − | 0.119100i | −0.829594 | − | 0.558367i | \(-0.811428\pi\) |
0.898357 | + | 0.439266i | \(0.144762\pi\) | |||||||
\(908\) | 13.1596 | − | 7.59771i | 0.436717 | − | 0.252139i | ||||
\(909\) | 28.0249 | + | 2.19959i | 0.929527 | + | 0.0729557i | ||||
\(910\) | −31.8222 | − | 16.0167i | −1.05490 | − | 0.530948i | ||||
\(911\) | − | 1.50513i | − | 0.0498672i | −0.999689 | − | 0.0249336i | \(-0.992063\pi\) | ||
0.999689 | − | 0.0249336i | \(-0.00793743\pi\) | |||||||
\(912\) | 3.81695 | + | 7.25294i | 0.126392 | + | 0.240169i | ||||
\(913\) | −7.75958 | − | 4.48000i | −0.256805 | − | 0.148266i | ||||
\(914\) | 9.27260 | + | 5.35354i | 0.306710 | + | 0.177079i | ||||
\(915\) | −16.8742 | − | 32.0642i | −0.557843 | − | 1.06001i | ||||
\(916\) | 21.5625 | 0.712445 | ||||||||
\(917\) | −1.04025 | + | 0.888324i | −0.0343520 | + | 0.0293350i | ||||
\(918\) | −25.7224 | − | 3.03609i | −0.848965 | − | 0.100206i | ||||
\(919\) | −18.6222 | − | 32.2546i | −0.614289 | − | 1.06398i | −0.990509 | − | 0.137450i | \(-0.956109\pi\) |
0.376220 | − | 0.926531i | \(-0.377224\pi\) | |||||||
\(920\) | 2.16055 | − | 3.74219i | 0.0712313 | − | 0.123376i | ||||
\(921\) | 5.10920 | − | 8.09951i | 0.168354 | − | 0.266888i | ||||
\(922\) | −8.24337 | + | 4.75931i | −0.271481 | + | 0.156740i | ||||
\(923\) | 4.50670 | − | 35.6109i | 0.148340 | − | 1.17215i | ||||
\(924\) | −0.873519 | − | 6.02315i | −0.0287367 | − | 0.198147i | ||||
\(925\) | 81.3631i | 2.67520i | ||||||||
\(926\) | −15.3688 | + | 8.87316i | −0.505049 | + | 0.291590i | ||||
\(927\) | 0.445420 | + | 0.305989i | 0.0146295 | + | 0.0100500i | ||||
\(928\) | −5.45477 | − | 3.14931i | −0.179061 | − | 0.103381i | ||||
\(929\) | 34.7114 | − | 20.0407i | 1.13885 | − | 0.657513i | 0.192701 | − | 0.981257i | \(-0.438275\pi\) |
0.946145 | + | 0.323745i | \(0.104942\pi\) | |||||||
\(930\) | 0.844637 | − | 21.5561i | 0.0276967 | − | 0.706853i | ||||
\(931\) | −25.7389 | − | 20.8492i | −0.843558 | − | 0.683306i | ||||
\(932\) | − | 27.5547i | − | 0.902586i | ||||||
\(933\) | 20.1782 | + | 38.3426i | 0.660605 | + | 1.25528i | ||||
\(934\) | 2.60380 | − | 4.50991i | 0.0851988 | − | 0.147569i | ||||
\(935\) | −21.4112 | − | 12.3618i | −0.700221 | − | 0.404273i | ||||
\(936\) | 10.2696 | − | 3.39627i | 0.335673 | − | 0.111010i | ||||
\(937\) | 26.4374i | 0.863673i | 0.901952 | + | 0.431836i | \(0.142134\pi\) | ||||
−0.901952 | + | 0.431836i | \(0.857866\pi\) | |||||||
\(938\) | 10.5684 | − | 1.95792i | 0.345069 | − | 0.0639285i | ||||
\(939\) | −0.972896 | + | 24.8294i | −0.0317493 | + | 0.810278i | ||||
\(940\) | 14.9903 | + | 25.9640i | 0.488931 | + | 0.846853i | ||||
\(941\) | −16.8380 | − | 9.72143i | −0.548903 | − | 0.316909i | 0.199776 | − | 0.979842i | \(-0.435978\pi\) |
−0.748680 | + | 0.662932i | \(0.769312\pi\) | |||||||
\(942\) | −25.8303 | − | 16.2939i | −0.841598 | − | 0.530883i | ||||
\(943\) | 2.53420 | + | 4.38935i | 0.0825247 | + | 0.142937i | ||||
\(944\) | 10.7566i | 0.350099i | ||||||||
\(945\) | −28.5346 | − | 42.6823i | −0.928232 | − | 1.38846i | ||||
\(946\) | −12.6815 | −0.412312 | ||||||||
\(947\) | −21.6374 | − | 37.4771i | −0.703122 | − | 1.21784i | −0.967365 | − | 0.253386i | \(-0.918456\pi\) |
0.264244 | − | 0.964456i | \(-0.414878\pi\) | |||||||
\(948\) | 13.3533 | − | 21.1687i | 0.433695 | − | 0.687528i | ||||
\(949\) | 41.4151 | + | 31.4502i | 1.34439 | + | 1.02092i | ||||
\(950\) | 21.1687 | + | 36.6653i | 0.686804 | + | 1.18958i | ||||
\(951\) | −26.2617 | − | 1.02902i | −0.851594 | − | 0.0333682i | ||||
\(952\) | 12.4313 | + | 4.40320i | 0.402902 | + | 0.142708i | ||||
\(953\) | − | 61.0356i | − | 1.97714i | −0.150767 | − | 0.988569i | \(-0.548174\pi\) | ||
0.150767 | − | 0.988569i | \(-0.451826\pi\) | |||||||
\(954\) | 4.26787 | − | 2.03679i | 0.138177 | − | 0.0659435i | ||||
\(955\) | −0.772483 | + | 1.33798i | −0.0249970 | + | 0.0432960i | ||||
\(956\) | −6.04907 | + | 10.4773i | −0.195641 | + | 0.338860i | ||||
\(957\) | 12.8219 | − | 6.74769i | 0.414474 | − | 0.218122i | ||||
\(958\) | 17.7430i | 0.573251i | ||||||||
\(959\) | 3.46174 | + | 1.22615i | 0.111785 | + | 0.0395946i | ||||
\(960\) | 0.253262 | − | 6.46353i | 0.00817399 | − | 0.208610i | ||||
\(961\) | 9.93877 | + | 17.2145i | 0.320605 | + | 0.555305i | ||||
\(962\) | −19.8294 | + | 26.1123i | −0.639325 | + | 0.841893i | ||||
\(963\) | 14.7173 | + | 10.1103i | 0.474258 | + | 0.325799i | ||||
\(964\) | −1.76152 | − | 3.05105i | −0.0567348 | − | 0.0982676i | ||||
\(965\) | −28.3882 | −0.913849 | ||||||||
\(966\) | −3.28274 | − | 4.16386i | −0.105621 | − | 0.133970i | ||||
\(967\) | 31.0756i | 0.999325i | 0.866220 | + | 0.499662i | \(0.166543\pi\) | ||||
−0.866220 | + | 0.499662i | \(0.833457\pi\) | |||||||
\(968\) | −4.61806 | − | 7.99872i | −0.148430 | − | 0.257089i | ||||
\(969\) | 21.7966 | − | 34.5537i | 0.700208 | − | 1.11003i | ||||
\(970\) | 31.6763 | + | 18.2883i | 1.01707 | + | 0.587203i | ||||
\(971\) | −25.3208 | − | 43.8569i | −0.812583 | − | 1.40743i | −0.911051 | − | 0.412294i | \(-0.864728\pi\) |
0.0984680 | − | 0.995140i | \(-0.468606\pi\) | |||||||
\(972\) | 15.2906 | + | 3.03300i | 0.490445 | + | 0.0972834i | ||||
\(973\) | 33.5680 | − | 6.21890i | 1.07614 | − | 0.199369i | ||||
\(974\) | 21.9047i | 0.701873i | ||||||||
\(975\) | 52.3215 | − | 19.6074i | 1.67563 | − | 0.627941i | ||||
\(976\) | −4.85105 | − | 2.80076i | −0.155278 | − | 0.0896500i | ||||
\(977\) | 11.7338 | − | 20.3235i | 0.375396 | − | 0.650206i | −0.614990 | − | 0.788535i | \(-0.710840\pi\) |
0.990386 | + | 0.138329i | \(0.0441732\pi\) | |||||||
\(978\) | −10.3105 | + | 5.42601i | −0.329693 | + | 0.173505i | ||||
\(979\) | − | 3.92294i | − | 0.125378i | ||||||
\(980\) | 9.36489 | + | 24.4071i | 0.299150 | + | 0.779657i | ||||
\(981\) | 2.81066 | − | 35.8106i | 0.0897376 | − | 1.14334i | ||||
\(982\) | 3.11811 | − | 1.80024i | 0.0995030 | − | 0.0574481i | ||||
\(983\) | 42.6658 | + | 24.6331i | 1.36083 | + | 0.785675i | 0.989734 | − | 0.142920i | \(-0.0456492\pi\) |
0.371095 | + | 0.928595i | \(0.378983\pi\) | |||||||
\(984\) | 6.41709 | + | 4.04792i | 0.204569 | + | 0.129043i | ||||
\(985\) | 21.5136 | − | 12.4209i | 0.685481 | − | 0.395763i | ||||
\(986\) | 31.3963i | 0.999863i | ||||||||
\(987\) | 36.4073 | − | 5.28003i | 1.15886 | − | 0.168065i | ||||
\(988\) | −2.14210 | + | 16.9263i | −0.0681491 | + | 0.538498i | ||||
\(989\) | −9.56799 | + | 5.52408i | −0.304245 | + | 0.175656i | ||||
\(990\) | 12.2647 | + | 8.42541i | 0.389796 | + | 0.267777i | ||||
\(991\) | 2.66048 | − | 4.60809i | 0.0845131 | − | 0.146381i | −0.820671 | − | 0.571402i | \(-0.806400\pi\) |
0.905184 | + | 0.425021i | \(0.139733\pi\) | |||||||
\(992\) | −1.66752 | − | 2.88823i | −0.0529437 | − | 0.0917013i | ||||
\(993\) | 1.97891 | − | 50.5040i | 0.0627987 | − | 1.60270i | ||||
\(994\) | −20.0301 | + | 17.1048i | −0.635316 | + | 0.542530i | ||||
\(995\) | 56.4904 | 1.79087 | ||||||||
\(996\) | −10.3406 | + | 5.44188i | −0.327655 | + | 0.172433i | ||||
\(997\) | 20.5432 | + | 11.8606i | 0.650608 | + | 0.375629i | 0.788689 | − | 0.614792i | \(-0.210760\pi\) |
−0.138081 | + | 0.990421i | \(0.544093\pi\) | |||||||
\(998\) | 6.88661 | + | 3.97599i | 0.217992 | + | 0.125858i | ||||
\(999\) | −43.4093 | + | 18.6666i | −1.37341 | + | 0.590584i |
(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 | 546.2.bg.b.311.7 | yes | 36 | |
3.2 | odd | 2 | 546.2.bg.a.311.12 | yes | 36 | ||
7.5 | odd | 6 | inner | 546.2.bg.b.467.12 | yes | 36 | |
13.12 | even | 2 | 546.2.bg.a.311.7 | ✓ | 36 | ||
21.5 | even | 6 | 546.2.bg.a.467.7 | yes | 36 | ||
39.38 | odd | 2 | inner | 546.2.bg.b.311.12 | yes | 36 | |
91.12 | odd | 6 | 546.2.bg.a.467.12 | yes | 36 | ||
273.194 | even | 6 | inner | 546.2.bg.b.467.7 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.bg.a.311.7 | ✓ | 36 | 13.12 | even | 2 | ||
546.2.bg.a.311.12 | yes | 36 | 3.2 | odd | 2 | ||
546.2.bg.a.467.7 | yes | 36 | 21.5 | even | 6 | ||
546.2.bg.a.467.12 | yes | 36 | 91.12 | odd | 6 | ||
546.2.bg.b.311.7 | yes | 36 | 1.1 | even | 1 | trivial | |
546.2.bg.b.311.12 | yes | 36 | 39.38 | odd | 2 | inner | |
546.2.bg.b.467.7 | yes | 36 | 273.194 | even | 6 | inner | |
546.2.bg.b.467.12 | yes | 36 | 7.5 | odd | 6 | inner |