Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(131,546)]
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, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.131");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.z (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: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 131.6 | ||
Character | \(\chi\) | \(=\) | 546.131 |
Dual form | 546.2.z.a.521.6 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0.587248 | + | 1.62946i | 0.339048 | + | 0.940769i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0.386271 | − | 0.669041i | 0.172746 | − | 0.299204i | −0.766633 | − | 0.642085i | \(-0.778069\pi\) |
0.939379 | + | 0.342881i | \(0.111403\pi\) | |||||||
\(6\) | 0.306158 | − | 1.70478i | 0.124989 | − | 0.695973i | ||||
\(7\) | 1.82832 | + | 1.91239i | 0.691041 | + | 0.722816i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −2.31028 | + | 1.91379i | −0.770093 | + | 0.637931i | ||||
\(10\) | −0.669041 | + | 0.386271i | −0.211569 | + | 0.122150i | ||||
\(11\) | 3.31419 | − | 1.91345i | 0.999267 | − | 0.576927i | 0.0912355 | − | 0.995829i | \(-0.470918\pi\) |
0.908031 | + | 0.418902i | \(0.137585\pi\) | |||||||
\(12\) | −1.11753 | + | 1.32330i | −0.322603 | + | 0.382004i | ||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | −0.627178 | − | 2.57034i | −0.167620 | − | 0.686952i | ||||
\(15\) | 1.31701 | + | 0.236520i | 0.340051 | + | 0.0610692i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0.460437 | + | 0.797500i | 0.111672 | + | 0.193422i | 0.916445 | − | 0.400161i | \(-0.131046\pi\) |
−0.804772 | + | 0.593584i | \(0.797713\pi\) | |||||||
\(18\) | 2.95766 | − | 0.502255i | 0.697127 | − | 0.118383i | ||||
\(19\) | 2.92280 | + | 1.68748i | 0.670537 | + | 0.387135i | 0.796280 | − | 0.604928i | \(-0.206798\pi\) |
−0.125743 | + | 0.992063i | \(0.540132\pi\) | |||||||
\(20\) | 0.772542 | 0.172746 | ||||||||
\(21\) | −2.04249 | + | 4.10223i | −0.445707 | + | 0.895179i | ||||
\(22\) | −3.82690 | −0.815898 | ||||||||
\(23\) | −3.80849 | − | 2.19883i | −0.794126 | − | 0.458489i | 0.0472874 | − | 0.998881i | \(-0.484942\pi\) |
−0.841413 | + | 0.540393i | \(0.818276\pi\) | |||||||
\(24\) | 1.62946 | − | 0.587248i | 0.332612 | − | 0.119872i | ||||
\(25\) | 2.20159 | + | 3.81326i | 0.440318 | + | 0.762653i | ||||
\(26\) | 0.500000 | − | 0.866025i | 0.0980581 | − | 0.169842i | ||||
\(27\) | −4.47516 | − | 2.64064i | −0.861245 | − | 0.508191i | ||||
\(28\) | −0.742018 | + | 2.53957i | −0.140228 | + | 0.479933i | ||||
\(29\) | − | 0.669555i | − | 0.124333i | −0.998066 | − | 0.0621666i | \(-0.980199\pi\) | ||
0.998066 | − | 0.0621666i | \(-0.0198010\pi\) | |||||||
\(30\) | −1.02231 | − | 0.863338i | −0.186647 | − | 0.157623i | ||||
\(31\) | 0.824139 | − | 0.475817i | 0.148020 | − | 0.0854592i | −0.424161 | − | 0.905587i | \(-0.639431\pi\) |
0.572181 | + | 0.820128i | \(0.306098\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 5.06414 | + | 4.27667i | 0.881554 | + | 0.744473i | ||||
\(34\) | − | 0.920873i | − | 0.157928i | ||||||
\(35\) | 1.98570 | − | 0.484521i | 0.335644 | − | 0.0818991i | ||||
\(36\) | −2.81253 | − | 1.04386i | −0.468756 | − | 0.173977i | ||||
\(37\) | −3.37565 | + | 5.84680i | −0.554954 | + | 0.961208i | 0.442954 | + | 0.896545i | \(0.353931\pi\) |
−0.997907 | + | 0.0646632i | \(0.979403\pi\) | |||||||
\(38\) | −1.68748 | − | 2.92280i | −0.273745 | − | 0.474141i | ||||
\(39\) | −1.62946 | + | 0.587248i | −0.260922 | + | 0.0940349i | ||||
\(40\) | −0.669041 | − | 0.386271i | −0.105785 | − | 0.0610748i | ||||
\(41\) | 1.36972 | 0.213914 | 0.106957 | − | 0.994264i | \(-0.465889\pi\) | ||||
0.106957 | + | 0.994264i | \(0.465889\pi\) | |||||||
\(42\) | 3.81996 | − | 2.53139i | 0.589432 | − | 0.390602i | ||||
\(43\) | 1.18934 | 0.181373 | 0.0906865 | − | 0.995879i | \(-0.471094\pi\) | ||||
0.0906865 | + | 0.995879i | \(0.471094\pi\) | |||||||
\(44\) | 3.31419 | + | 1.91345i | 0.499633 | + | 0.288463i | ||||
\(45\) | 0.388013 | + | 2.28491i | 0.0578415 | + | 0.340615i | ||||
\(46\) | 2.19883 | + | 3.80849i | 0.324200 | + | 0.561532i | ||||
\(47\) | −5.17037 | + | 8.95534i | −0.754176 | + | 1.30627i | 0.191608 | + | 0.981472i | \(0.438630\pi\) |
−0.945783 | + | 0.324799i | \(0.894703\pi\) | |||||||
\(48\) | −1.70478 | − | 0.306158i | −0.246063 | − | 0.0441901i | ||||
\(49\) | −0.314476 | + | 6.99293i | −0.0449251 | + | 0.998990i | ||||
\(50\) | − | 4.40318i | − | 0.622704i | ||||||
\(51\) | −1.02910 | + | 1.21859i | −0.144103 | + | 0.170637i | ||||
\(52\) | −0.866025 | + | 0.500000i | −0.120096 | + | 0.0693375i | ||||
\(53\) | 7.30193 | − | 4.21577i | 1.00300 | − | 0.579081i | 0.0938633 | − | 0.995585i | \(-0.470078\pi\) |
0.909134 | + | 0.416505i | \(0.136745\pi\) | |||||||
\(54\) | 2.55528 | + | 4.52444i | 0.347730 | + | 0.615698i | ||||
\(55\) | − | 2.95644i | − | 0.398646i | ||||||
\(56\) | 1.91239 | − | 1.82832i | 0.255554 | − | 0.244320i | ||||
\(57\) | −1.03327 | + | 5.75356i | −0.136860 | + | 0.762077i | ||||
\(58\) | −0.334777 | + | 0.579851i | −0.0439584 | + | 0.0761382i | ||||
\(59\) | 1.98058 | + | 3.43047i | 0.257850 | + | 0.446609i | 0.965666 | − | 0.259788i | \(-0.0836527\pi\) |
−0.707816 | + | 0.706397i | \(0.750319\pi\) | |||||||
\(60\) | 0.453674 | + | 1.25883i | 0.0585690 | + | 0.162514i | ||||
\(61\) | −0.358567 | − | 0.207019i | −0.0459099 | − | 0.0265061i | 0.476869 | − | 0.878974i | \(-0.341771\pi\) |
−0.522779 | + | 0.852468i | \(0.675105\pi\) | |||||||
\(62\) | −0.951633 | −0.120858 | ||||||||
\(63\) | −7.88386 | − | 0.919124i | −0.993273 | − | 0.115799i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.669041 | + | 0.386271i | 0.0829843 | + | 0.0479110i | ||||
\(66\) | −2.24734 | − | 6.23578i | −0.276628 | − | 0.767572i | ||||
\(67\) | −4.70367 | − | 8.14699i | −0.574644 | − | 0.995313i | −0.996080 | − | 0.0884552i | \(-0.971807\pi\) |
0.421436 | − | 0.906858i | \(-0.361526\pi\) | |||||||
\(68\) | −0.460437 | + | 0.797500i | −0.0558361 | + | 0.0967110i | ||||
\(69\) | 1.34638 | − | 7.49705i | 0.162085 | − | 0.902538i | ||||
\(70\) | −1.96192 | − | 0.573240i | −0.234495 | − | 0.0685153i | ||||
\(71\) | 6.24239i | 0.740835i | 0.928865 | + | 0.370418i | \(0.120785\pi\) | ||||
−0.928865 | + | 0.370418i | \(0.879215\pi\) | |||||||
\(72\) | 1.91379 | + | 2.31028i | 0.225543 | + | 0.272269i | ||||
\(73\) | 7.63416 | − | 4.40758i | 0.893511 | − | 0.515869i | 0.0184214 | − | 0.999830i | \(-0.494136\pi\) |
0.875089 | + | 0.483962i | \(0.160803\pi\) | |||||||
\(74\) | 5.84680 | − | 3.37565i | 0.679677 | − | 0.392411i | ||||
\(75\) | −4.92068 | + | 5.82673i | −0.568192 | + | 0.672813i | ||||
\(76\) | 3.37496i | 0.387135i | ||||||||
\(77\) | 9.71868 | + | 2.83963i | 1.10755 | + | 0.323606i | ||||
\(78\) | 1.70478 | + | 0.306158i | 0.193028 | + | 0.0346656i | ||||
\(79\) | 6.47880 | − | 11.2216i | 0.728922 | − | 1.26253i | −0.228417 | − | 0.973563i | \(-0.573355\pi\) |
0.957339 | − | 0.288967i | \(-0.0933118\pi\) | |||||||
\(80\) | 0.386271 | + | 0.669041i | 0.0431864 | + | 0.0748010i | ||||
\(81\) | 1.67478 | − | 8.84280i | 0.186087 | − | 0.982533i | ||||
\(82\) | −1.18621 | − | 0.684859i | −0.130995 | − | 0.0756300i | ||||
\(83\) | −2.22220 | −0.243918 | −0.121959 | − | 0.992535i | \(-0.538918\pi\) | ||||
−0.121959 | + | 0.992535i | \(0.538918\pi\) | |||||||
\(84\) | −4.57387 | + | 0.282269i | −0.499051 | + | 0.0307980i | ||||
\(85\) | 0.711413 | 0.0771636 | ||||||||
\(86\) | −1.03000 | − | 0.594671i | −0.111068 | − | 0.0641250i | ||||
\(87\) | 1.09101 | − | 0.393195i | 0.116969 | − | 0.0421549i | ||||
\(88\) | −1.91345 | − | 3.31419i | −0.203974 | − | 0.353294i | ||||
\(89\) | 2.00944 | − | 3.48046i | 0.213001 | − | 0.368928i | −0.739652 | − | 0.672990i | \(-0.765010\pi\) |
0.952652 | + | 0.304062i | \(0.0983430\pi\) | |||||||
\(90\) | 0.806428 | − | 2.17280i | 0.0850050 | − | 0.229033i | ||||
\(91\) | −1.91239 | + | 1.82832i | −0.200473 | + | 0.191660i | ||||
\(92\) | − | 4.39767i | − | 0.458489i | ||||||
\(93\) | 1.25930 | + | 1.06348i | 0.130583 | + | 0.110278i | ||||
\(94\) | 8.95534 | − | 5.17037i | 0.923673 | − | 0.533283i | ||||
\(95\) | 2.25799 | − | 1.30365i | 0.231665 | − | 0.133752i | ||||
\(96\) | 1.32330 | + | 1.11753i | 0.135059 | + | 0.114057i | ||||
\(97\) | − | 9.41494i | − | 0.955942i | −0.878376 | − | 0.477971i | \(-0.841372\pi\) | ||
0.878376 | − | 0.477971i | \(-0.158628\pi\) | |||||||
\(98\) | 3.76881 | − | 5.89882i | 0.380707 | − | 0.595871i | ||||
\(99\) | −3.99476 | + | 10.7633i | −0.401489 | + | 1.08175i | ||||
\(100\) | −2.20159 | + | 3.81326i | −0.220159 | + | 0.381326i | ||||
\(101\) | 3.54281 | + | 6.13632i | 0.352522 | + | 0.610587i | 0.986691 | − | 0.162608i | \(-0.0519907\pi\) |
−0.634168 | + | 0.773195i | \(0.718657\pi\) | |||||||
\(102\) | 1.50053 | − | 0.540781i | 0.148574 | − | 0.0535453i | ||||
\(103\) | 4.56989 | + | 2.63842i | 0.450284 | + | 0.259972i | 0.707950 | − | 0.706262i | \(-0.249620\pi\) |
−0.257666 | + | 0.966234i | \(0.582953\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 1.95560 | + | 2.95108i | 0.190847 | + | 0.287996i | ||||
\(106\) | −8.43154 | −0.818944 | ||||||||
\(107\) | −16.1078 | − | 9.29984i | −1.55720 | − | 0.899049i | −0.997523 | − | 0.0703370i | \(-0.977593\pi\) |
−0.559675 | − | 0.828712i | \(-0.689074\pi\) | |||||||
\(108\) | 0.0492786 | − | 5.19592i | 0.00474184 | − | 0.499978i | ||||
\(109\) | −5.36127 | − | 9.28600i | −0.513517 | − | 0.889437i | −0.999877 | − | 0.0156787i | \(-0.995009\pi\) |
0.486360 | − | 0.873758i | \(-0.338324\pi\) | |||||||
\(110\) | −1.47822 | + | 2.56035i | −0.140943 | + | 0.244120i | ||||
\(111\) | −11.5095 | − | 2.06697i | −1.09243 | − | 0.196188i | ||||
\(112\) | −2.57034 | + | 0.627178i | −0.242874 | + | 0.0592628i | ||||
\(113\) | − | 14.5031i | − | 1.36434i | −0.731194 | − | 0.682169i | \(-0.761037\pi\) | ||
0.731194 | − | 0.682169i | \(-0.238963\pi\) | |||||||
\(114\) | 3.77162 | − | 4.46609i | 0.353244 | − | 0.418288i | ||||
\(115\) | −2.94222 | + | 1.69869i | −0.274363 | + | 0.158404i | ||||
\(116\) | 0.579851 | − | 0.334777i | 0.0538379 | − | 0.0310833i | ||||
\(117\) | −1.91379 | − | 2.31028i | −0.176930 | − | 0.213585i | ||||
\(118\) | − | 3.96116i | − | 0.364655i | ||||||
\(119\) | −0.683304 | + | 2.33862i | −0.0626384 | + | 0.214381i | ||||
\(120\) | 0.236520 | − | 1.31701i | 0.0215912 | − | 0.120226i | ||||
\(121\) | 1.82258 | − | 3.15680i | 0.165689 | − | 0.286982i | ||||
\(122\) | 0.207019 | + | 0.358567i | 0.0187426 | + | 0.0324632i | ||||
\(123\) | 0.804364 | + | 2.23190i | 0.0725270 | + | 0.201244i | ||||
\(124\) | 0.824139 | + | 0.475817i | 0.0740098 | + | 0.0427296i | ||||
\(125\) | 7.26435 | 0.649743 | ||||||||
\(126\) | 6.36806 | + | 4.73791i | 0.567312 | + | 0.422087i | ||||
\(127\) | −21.3088 | −1.89085 | −0.945423 | − | 0.325844i | \(-0.894352\pi\) | ||||
−0.945423 | + | 0.325844i | \(0.894352\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0.698439 | + | 1.93799i | 0.0614941 | + | 0.170630i | ||||
\(130\) | −0.386271 | − | 0.669041i | −0.0338782 | − | 0.0586788i | ||||
\(131\) | 8.43583 | − | 14.6113i | 0.737042 | − | 1.27659i | −0.216780 | − | 0.976220i | \(-0.569555\pi\) |
0.953822 | − | 0.300373i | \(-0.0971113\pi\) | |||||||
\(132\) | −1.17164 | + | 6.52401i | −0.101978 | + | 0.567843i | ||||
\(133\) | 2.11670 | + | 8.67480i | 0.183541 | + | 0.752200i | ||||
\(134\) | 9.40734i | 0.812670i | ||||||||
\(135\) | −3.49532 | + | 1.97406i | −0.300829 | + | 0.169900i | ||||
\(136\) | 0.797500 | − | 0.460437i | 0.0683850 | − | 0.0394821i | ||||
\(137\) | −12.2984 | + | 7.10051i | −1.05073 | + | 0.606637i | −0.922853 | − | 0.385153i | \(-0.874149\pi\) |
−0.127874 | + | 0.991790i | \(0.540815\pi\) | |||||||
\(138\) | −4.91452 | + | 5.81944i | −0.418352 | + | 0.495384i | ||||
\(139\) | − | 8.87171i | − | 0.752489i | −0.926520 | − | 0.376244i | \(-0.877215\pi\) | ||
0.926520 | − | 0.376244i | \(-0.122785\pi\) | |||||||
\(140\) | 1.41246 | + | 1.47740i | 0.119374 | + | 0.124863i | ||||
\(141\) | −17.6287 | − | 3.16590i | −1.48460 | − | 0.266617i | ||||
\(142\) | 3.12119 | − | 5.40607i | 0.261925 | − | 0.453667i | ||||
\(143\) | 1.91345 | + | 3.31419i | 0.160011 | + | 0.277147i | ||||
\(144\) | −0.502255 | − | 2.95766i | −0.0418546 | − | 0.246471i | ||||
\(145\) | −0.447959 | − | 0.258630i | −0.0372010 | − | 0.0214780i | ||||
\(146\) | −8.81517 | −0.729548 | ||||||||
\(147\) | −11.5794 | + | 3.59416i | −0.955051 | + | 0.296441i | ||||
\(148\) | −6.75130 | −0.554954 | ||||||||
\(149\) | −2.03761 | − | 1.17642i | −0.166928 | − | 0.0963758i | 0.414209 | − | 0.910182i | \(-0.364058\pi\) |
−0.581136 | + | 0.813806i | \(0.697392\pi\) | |||||||
\(150\) | 7.17480 | − | 2.58576i | 0.585820 | − | 0.211126i | ||||
\(151\) | 4.92244 | + | 8.52591i | 0.400582 | + | 0.693829i | 0.993796 | − | 0.111216i | \(-0.0354745\pi\) |
−0.593214 | + | 0.805045i | \(0.702141\pi\) | |||||||
\(152\) | 1.68748 | − | 2.92280i | 0.136873 | − | 0.237071i | ||||
\(153\) | −2.58999 | − | 0.961266i | −0.209388 | − | 0.0777138i | ||||
\(154\) | −6.99681 | − | 7.31853i | −0.563819 | − | 0.589744i | ||||
\(155\) | − | 0.735177i | − | 0.0590508i | ||||||
\(156\) | −1.32330 | − | 1.11753i | −0.105949 | − | 0.0894740i | ||||
\(157\) | −4.33375 | + | 2.50209i | −0.345871 | + | 0.199689i | −0.662865 | − | 0.748739i | \(-0.730660\pi\) |
0.316994 | + | 0.948427i | \(0.397326\pi\) | |||||||
\(158\) | −11.2216 | + | 6.47880i | −0.892744 | + | 0.515426i | ||||
\(159\) | 11.1575 | + | 9.42250i | 0.884845 | + | 0.747253i | ||||
\(160\) | − | 0.772542i | − | 0.0610748i | ||||||
\(161\) | −2.75812 | − | 11.3035i | −0.217370 | − | 0.890841i | ||||
\(162\) | −5.87180 | + | 6.82070i | −0.461332 | + | 0.535885i | ||||
\(163\) | 12.2918 | − | 21.2901i | 0.962772 | − | 1.66757i | 0.247286 | − | 0.968943i | \(-0.420461\pi\) |
0.715486 | − | 0.698627i | \(-0.246205\pi\) | |||||||
\(164\) | 0.684859 | + | 1.18621i | 0.0534785 | + | 0.0926274i | ||||
\(165\) | 4.81740 | − | 1.73616i | 0.375034 | − | 0.135160i | ||||
\(166\) | 1.92448 | + | 1.11110i | 0.149369 | + | 0.0862382i | ||||
\(167\) | −6.67521 | −0.516543 | −0.258272 | − | 0.966072i | \(-0.583153\pi\) | ||||
−0.258272 | + | 0.966072i | \(0.583153\pi\) | |||||||
\(168\) | 4.10223 | + | 2.04249i | 0.316494 | + | 0.157581i | ||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | −0.616102 | − | 0.355707i | −0.0472529 | − | 0.0272815i | ||||
\(171\) | −9.98198 | + | 1.69509i | −0.763341 | + | 0.129627i | ||||
\(172\) | 0.594671 | + | 1.03000i | 0.0453432 | + | 0.0785368i | ||||
\(173\) | 7.73453 | − | 13.3966i | 0.588046 | − | 1.01852i | −0.406443 | − | 0.913676i | \(-0.633231\pi\) |
0.994488 | − | 0.104848i | \(-0.0334358\pi\) | |||||||
\(174\) | −1.14144 | − | 0.204990i | −0.0865325 | − | 0.0155402i | ||||
\(175\) | −3.26724 | + | 11.1822i | −0.246980 | + | 0.845293i | ||||
\(176\) | 3.82690i | 0.288463i | ||||||||
\(177\) | −4.42672 | + | 5.24182i | −0.332733 | + | 0.393999i | ||||
\(178\) | −3.48046 | + | 2.00944i | −0.260871 | + | 0.150614i | ||||
\(179\) | −10.4115 | + | 6.01106i | −0.778189 | + | 0.449288i | −0.835788 | − | 0.549052i | \(-0.814989\pi\) |
0.0575988 | + | 0.998340i | \(0.481656\pi\) | |||||||
\(180\) | −1.78479 | + | 1.47849i | −0.133030 | + | 0.110200i | ||||
\(181\) | − | 16.4089i | − | 1.21966i | −0.792531 | − | 0.609832i | \(-0.791237\pi\) | ||
0.792531 | − | 0.609832i | \(-0.208763\pi\) | |||||||
\(182\) | 2.57034 | − | 0.627178i | 0.190526 | − | 0.0464895i | ||||
\(183\) | 0.126761 | − | 0.705843i | 0.00937045 | − | 0.0521774i | ||||
\(184\) | −2.19883 | + | 3.80849i | −0.162100 | + | 0.280766i | ||||
\(185\) | 2.60783 | + | 4.51690i | 0.191732 | + | 0.332089i | ||||
\(186\) | −0.558845 | − | 1.55065i | −0.0409765 | − | 0.113699i | ||||
\(187\) | 3.05195 | + | 1.76205i | 0.223181 | + | 0.128854i | ||||
\(188\) | −10.3407 | −0.754176 | ||||||||
\(189\) | −3.13210 | − | 13.3862i | −0.227827 | − | 0.973702i | ||||
\(190\) | −2.60730 | −0.189153 | ||||||||
\(191\) | −22.0735 | − | 12.7441i | −1.59718 | − | 0.922133i | −0.992027 | − | 0.126025i | \(-0.959778\pi\) |
−0.605155 | − | 0.796108i | \(-0.706889\pi\) | |||||||
\(192\) | −0.587248 | − | 1.62946i | −0.0423810 | − | 0.117596i | ||||
\(193\) | 5.08419 | + | 8.80607i | 0.365968 | + | 0.633875i | 0.988931 | − | 0.148376i | \(-0.0474047\pi\) |
−0.622963 | + | 0.782251i | \(0.714071\pi\) | |||||||
\(194\) | −4.70747 | + | 8.15357i | −0.337977 | + | 0.585392i | ||||
\(195\) | −0.236520 | + | 1.31701i | −0.0169376 | + | 0.0943132i | ||||
\(196\) | −6.21330 | + | 3.22412i | −0.443807 | + | 0.230294i | ||||
\(197\) | − | 1.47277i | − | 0.104930i | −0.998623 | − | 0.0524652i | \(-0.983292\pi\) | ||
0.998623 | − | 0.0524652i | \(-0.0167079\pi\) | |||||||
\(198\) | 8.84121 | − | 7.32390i | 0.628317 | − | 0.520487i | ||||
\(199\) | 16.5057 | − | 9.52955i | 1.17006 | − | 0.675532i | 0.216363 | − | 0.976313i | \(-0.430581\pi\) |
0.953693 | + | 0.300781i | \(0.0972473\pi\) | |||||||
\(200\) | 3.81326 | − | 2.20159i | 0.269639 | − | 0.155676i | ||||
\(201\) | 10.5130 | − | 12.4487i | 0.741528 | − | 0.878067i | ||||
\(202\) | − | 7.08561i | − | 0.498542i | ||||||
\(203\) | 1.28045 | − | 1.22416i | 0.0898700 | − | 0.0859193i | ||||
\(204\) | −1.56988 | − | 0.281933i | −0.109914 | − | 0.0197393i | ||||
\(205\) | 0.529082 | − | 0.916397i | 0.0369527 | − | 0.0640039i | ||||
\(206\) | −2.63842 | − | 4.56989i | −0.183828 | − | 0.318399i | ||||
\(207\) | 13.0068 | − | 2.20875i | 0.904035 | − | 0.153519i | ||||
\(208\) | −0.866025 | − | 0.500000i | −0.0600481 | − | 0.0346688i | ||||
\(209\) | 12.9156 | 0.893393 | ||||||||
\(210\) | −0.218064 | − | 3.53351i | −0.0150479 | − | 0.243835i | ||||
\(211\) | 23.7454 | 1.63470 | 0.817349 | − | 0.576143i | \(-0.195443\pi\) | ||||
0.817349 | + | 0.576143i | \(0.195443\pi\) | |||||||
\(212\) | 7.30193 | + | 4.21577i | 0.501498 | + | 0.289540i | ||||
\(213\) | −10.1717 | + | 3.66583i | −0.696955 | + | 0.251179i | ||||
\(214\) | 9.29984 | + | 16.1078i | 0.635724 | + | 1.10111i | ||||
\(215\) | 0.459408 | − | 0.795719i | 0.0313314 | − | 0.0542676i | ||||
\(216\) | −2.64064 | + | 4.47516i | −0.179673 | + | 0.304496i | ||||
\(217\) | 2.41674 | + | 0.706129i | 0.164059 | + | 0.0479352i | ||||
\(218\) | 10.7225i | 0.726222i | ||||||||
\(219\) | 11.6651 | + | 9.85121i | 0.788256 | + | 0.665683i | ||||
\(220\) | 2.56035 | − | 1.47822i | 0.172619 | − | 0.0996616i | ||||
\(221\) | −0.797500 | + | 0.460437i | −0.0536456 | + | 0.0309723i | ||||
\(222\) | 8.93401 | + | 7.54478i | 0.599611 | + | 0.506372i | ||||
\(223\) | 5.23154i | 0.350330i | 0.984539 | + | 0.175165i | \(0.0560458\pi\) | ||||
−0.984539 | + | 0.175165i | \(0.943954\pi\) | |||||||
\(224\) | 2.53957 | + | 0.742018i | 0.169682 | + | 0.0495781i | ||||
\(225\) | −12.3841 | − | 4.59632i | −0.825606 | − | 0.306421i | ||||
\(226\) | −7.25156 | + | 12.5601i | −0.482366 | + | 0.835483i | ||||
\(227\) | 14.0718 | + | 24.3731i | 0.933981 | + | 1.61770i | 0.776441 | + | 0.630190i | \(0.217023\pi\) |
0.157540 | + | 0.987513i | \(0.449644\pi\) | |||||||
\(228\) | −5.49936 | + | 1.98194i | −0.364204 | + | 0.131257i | ||||
\(229\) | 8.26533 | + | 4.77199i | 0.546189 | + | 0.315342i | 0.747583 | − | 0.664168i | \(-0.231214\pi\) |
−0.201395 | + | 0.979510i | \(0.564547\pi\) | |||||||
\(230\) | 3.39738 | 0.224017 | ||||||||
\(231\) | 1.08021 | + | 17.5038i | 0.0710728 | + | 1.15166i | ||||
\(232\) | −0.669555 | −0.0439584 | ||||||||
\(233\) | 2.06956 | + | 1.19486i | 0.135581 | + | 0.0782778i | 0.566256 | − | 0.824229i | \(-0.308391\pi\) |
−0.430675 | + | 0.902507i | \(0.641725\pi\) | |||||||
\(234\) | 0.502255 | + | 2.95766i | 0.0328334 | + | 0.193348i | ||||
\(235\) | 3.99433 | + | 6.91837i | 0.260561 | + | 0.451305i | ||||
\(236\) | −1.98058 | + | 3.43047i | −0.128925 | + | 0.223304i | ||||
\(237\) | 22.0898 | + | 3.96708i | 1.43489 | + | 0.257689i | ||||
\(238\) | 1.76107 | − | 1.68365i | 0.114153 | − | 0.109135i | ||||
\(239\) | 1.83106i | 0.118442i | 0.998245 | + | 0.0592208i | \(0.0188616\pi\) | ||||
−0.998245 | + | 0.0592208i | \(0.981138\pi\) | |||||||
\(240\) | −0.863338 | + | 1.02231i | −0.0557283 | + | 0.0659896i | ||||
\(241\) | 23.6939 | − | 13.6797i | 1.52626 | − | 0.881187i | 0.526746 | − | 0.850023i | \(-0.323412\pi\) |
0.999514 | − | 0.0311640i | \(-0.00992142\pi\) | |||||||
\(242\) | −3.15680 | + | 1.82258i | −0.202927 | + | 0.117160i | ||||
\(243\) | 15.3925 | − | 2.46393i | 0.987429 | − | 0.158061i | ||||
\(244\) | − | 0.414038i | − | 0.0265061i | ||||||
\(245\) | 4.55708 | + | 2.91156i | 0.291141 | + | 0.186013i | ||||
\(246\) | 0.419350 | − | 2.33506i | 0.0267368 | − | 0.148878i | ||||
\(247\) | −1.68748 | + | 2.92280i | −0.107372 | + | 0.185973i | ||||
\(248\) | −0.475817 | − | 0.824139i | −0.0302144 | − | 0.0523329i | ||||
\(249\) | −1.30498 | − | 3.62099i | −0.0827000 | − | 0.229471i | ||||
\(250\) | −6.29111 | − | 3.63217i | −0.397885 | − | 0.229719i | ||||
\(251\) | 1.71927 | 0.108519 | 0.0542597 | − | 0.998527i | \(-0.482720\pi\) | ||||
0.0542597 | + | 0.998527i | \(0.482720\pi\) | |||||||
\(252\) | −3.14594 | − | 7.28718i | −0.198176 | − | 0.459049i | ||||
\(253\) | −16.8294 | −1.05806 | ||||||||
\(254\) | 18.4539 | + | 10.6544i | 1.15790 | + | 0.668515i | ||||
\(255\) | 0.417776 | + | 1.15922i | 0.0261621 | + | 0.0725931i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 5.01277 | − | 8.68237i | 0.312688 | − | 0.541591i | −0.666255 | − | 0.745724i | \(-0.732104\pi\) |
0.978943 | + | 0.204132i | \(0.0654373\pi\) | |||||||
\(258\) | 0.364127 | − | 2.02756i | 0.0226696 | − | 0.126231i | ||||
\(259\) | −17.3531 | + | 4.23427i | −1.07827 | + | 0.263105i | ||||
\(260\) | 0.772542i | 0.0479110i | ||||||||
\(261\) | 1.28139 | + | 1.54686i | 0.0793161 | + | 0.0957481i | ||||
\(262\) | −14.6113 | + | 8.43583i | −0.902688 | + | 0.521167i | ||||
\(263\) | −0.658897 | + | 0.380414i | −0.0406293 | + | 0.0234573i | −0.520177 | − | 0.854058i | \(-0.674134\pi\) |
0.479548 | + | 0.877516i | \(0.340801\pi\) | |||||||
\(264\) | 4.27667 | − | 5.06414i | 0.263211 | − | 0.311676i | ||||
\(265\) | − | 6.51372i | − | 0.400134i | ||||||
\(266\) | 2.50428 | − | 8.57094i | 0.153547 | − | 0.525518i | ||||
\(267\) | 6.85131 | + | 1.23042i | 0.419293 | + | 0.0753002i | ||||
\(268\) | 4.70367 | − | 8.14699i | 0.287322 | − | 0.497657i | ||||
\(269\) | 2.79727 | + | 4.84501i | 0.170552 | + | 0.295406i | 0.938613 | − | 0.344972i | \(-0.112111\pi\) |
−0.768061 | + | 0.640377i | \(0.778778\pi\) | |||||||
\(270\) | 4.01406 | + | 0.0380698i | 0.244288 | + | 0.00231685i | ||||
\(271\) | −21.7749 | − | 12.5717i | −1.32273 | − | 0.763679i | −0.338567 | − | 0.940942i | \(-0.609942\pi\) |
−0.984163 | + | 0.177263i | \(0.943276\pi\) | |||||||
\(272\) | −0.920873 | −0.0558361 | ||||||||
\(273\) | −4.10223 | − | 2.04249i | −0.248278 | − | 0.123617i | ||||
\(274\) | 14.2010 | 0.857915 | ||||||||
\(275\) | 14.5930 | + | 8.42526i | 0.879990 | + | 0.508062i | ||||
\(276\) | 7.16582 | − | 2.58252i | 0.431332 | − | 0.155450i | ||||
\(277\) | 12.9452 | + | 22.4217i | 0.777802 | + | 1.34719i | 0.933206 | + | 0.359341i | \(0.116998\pi\) |
−0.155405 | + | 0.987851i | \(0.549668\pi\) | |||||||
\(278\) | −4.43586 | + | 7.68313i | −0.266045 | + | 0.460803i | ||||
\(279\) | −0.993375 | + | 2.67650i | −0.0594718 | + | 0.160238i | ||||
\(280\) | −0.484521 | − | 1.98570i | −0.0289557 | − | 0.118668i | ||||
\(281\) | 2.03189i | 0.121212i | 0.998162 | + | 0.0606062i | \(0.0193034\pi\) | ||||
−0.998162 | + | 0.0606062i | \(0.980697\pi\) | |||||||
\(282\) | 13.6839 | + | 11.5561i | 0.814865 | + | 0.688154i | ||||
\(283\) | −23.6297 | + | 13.6426i | −1.40464 | + | 0.810968i | −0.994864 | − | 0.101219i | \(-0.967726\pi\) |
−0.409774 | + | 0.912187i | \(0.634392\pi\) | |||||||
\(284\) | −5.40607 | + | 3.12119i | −0.320791 | + | 0.185209i | ||||
\(285\) | 3.45024 | + | 2.91373i | 0.204375 | + | 0.172595i | ||||
\(286\) | − | 3.82690i | − | 0.226289i | ||||||
\(287\) | 2.50428 | + | 2.61943i | 0.147823 | + | 0.154620i | ||||
\(288\) | −1.04386 | + | 2.81253i | −0.0615102 | + | 0.165730i | ||||
\(289\) | 8.07600 | − | 13.9880i | 0.475059 | − | 0.822826i | ||||
\(290\) | 0.258630 | + | 0.447959i | 0.0151872 | + | 0.0263051i | ||||
\(291\) | 15.3413 | − | 5.52890i | 0.899321 | − | 0.324110i | ||||
\(292\) | 7.63416 | + | 4.40758i | 0.446755 | + | 0.257934i | ||||
\(293\) | −13.0574 | −0.762819 | −0.381410 | − | 0.924406i | \(-0.624561\pi\) | ||||
−0.381410 | + | 0.924406i | \(0.624561\pi\) | |||||||
\(294\) | 11.8251 | + | 2.67706i | 0.689655 | + | 0.156129i | ||||
\(295\) | 3.06017 | 0.178170 | ||||||||
\(296\) | 5.84680 | + | 3.37565i | 0.339838 | + | 0.196206i | ||||
\(297\) | −19.8843 | − | 0.188584i | −1.15380 | − | 0.0109428i | ||||
\(298\) | 1.17642 | + | 2.03761i | 0.0681480 | + | 0.118036i | ||||
\(299\) | 2.19883 | − | 3.80849i | 0.127162 | − | 0.220251i | ||||
\(300\) | −7.50644 | − | 1.34807i | −0.433385 | − | 0.0778308i | ||||
\(301\) | 2.17450 | + | 2.27449i | 0.125336 | + | 0.131099i | ||||
\(302\) | − | 9.84487i | − | 0.566509i | ||||||
\(303\) | −7.91838 | + | 9.37640i | −0.454899 | + | 0.538660i | ||||
\(304\) | −2.92280 | + | 1.68748i | −0.167634 | + | 0.0967836i | ||||
\(305\) | −0.277008 | + | 0.159931i | −0.0158615 | + | 0.00915761i | ||||
\(306\) | 1.76236 | + | 2.12747i | 0.100748 | + | 0.121620i | ||||
\(307\) | 17.1766i | 0.980319i | 0.871633 | + | 0.490159i | \(0.163061\pi\) | ||||
−0.871633 | + | 0.490159i | \(0.836939\pi\) | |||||||
\(308\) | 2.40015 | + | 9.83643i | 0.136761 | + | 0.560483i | ||||
\(309\) | −1.61555 | + | 8.99586i | −0.0919055 | + | 0.511756i | ||||
\(310\) | −0.367588 | + | 0.636682i | −0.0208776 | + | 0.0361611i | ||||
\(311\) | −15.5708 | − | 26.9693i | −0.882936 | − | 1.52929i | −0.848061 | − | 0.529899i | \(-0.822230\pi\) |
−0.0348756 | − | 0.999392i | \(-0.511104\pi\) | |||||||
\(312\) | 0.587248 | + | 1.62946i | 0.0332464 | + | 0.0922500i | ||||
\(313\) | 6.59778 | + | 3.80923i | 0.372929 | + | 0.215311i | 0.674737 | − | 0.738058i | \(-0.264257\pi\) |
−0.301808 | + | 0.953369i | \(0.597590\pi\) | |||||||
\(314\) | 5.00418 | 0.282402 | ||||||||
\(315\) | −3.66024 | + | 4.91959i | −0.206231 | + | 0.277188i | ||||
\(316\) | 12.9576 | 0.728922 | ||||||||
\(317\) | 18.6264 | + | 10.7540i | 1.04616 | + | 0.604003i | 0.921573 | − | 0.388205i | \(-0.126905\pi\) |
0.124591 | + | 0.992208i | \(0.460238\pi\) | |||||||
\(318\) | −4.95141 | − | 13.7389i | −0.277661 | − | 0.770437i | ||||
\(319\) | −1.28116 | − | 2.21903i | −0.0717312 | − | 0.124242i | ||||
\(320\) | −0.386271 | + | 0.669041i | −0.0215932 | + | 0.0374005i | ||||
\(321\) | 5.69444 | − | 31.7083i | 0.317833 | − | 1.76978i | ||||
\(322\) | −3.26315 | + | 11.1682i | −0.181848 | + | 0.622378i | ||||
\(323\) | 3.10791i | 0.172929i | ||||||||
\(324\) | 8.49548 | − | 2.97100i | 0.471971 | − | 0.165055i | ||||
\(325\) | −3.81326 | + | 2.20159i | −0.211522 | + | 0.122122i | ||||
\(326\) | −21.2901 | + | 12.2918i | −1.17915 | + | 0.680783i | ||||
\(327\) | 11.9828 | − | 14.1892i | 0.662648 | − | 0.784662i | ||||
\(328\) | − | 1.36972i | − | 0.0756300i | ||||||
\(329\) | −26.5792 | + | 6.48548i | −1.46536 | + | 0.357556i | ||||
\(330\) | −5.04007 | − | 0.905139i | −0.277447 | − | 0.0498262i | ||||
\(331\) | 0.786513 | − | 1.36228i | 0.0432306 | − | 0.0748777i | −0.843600 | − | 0.536971i | \(-0.819568\pi\) |
0.886831 | + | 0.462094i | \(0.152902\pi\) | |||||||
\(332\) | −1.11110 | − | 1.92448i | −0.0609796 | − | 0.105620i | ||||
\(333\) | −3.39087 | − | 19.9680i | −0.185819 | − | 1.09424i | ||||
\(334\) | 5.78090 | + | 3.33760i | 0.316317 | + | 0.182626i | ||||
\(335\) | −7.26756 | −0.397069 | ||||||||
\(336\) | −2.53139 | − | 3.81996i | −0.138099 | − | 0.208396i | ||||
\(337\) | −9.70044 | −0.528416 | −0.264208 | − | 0.964466i | \(-0.585111\pi\) | ||||
−0.264208 | + | 0.964466i | \(0.585111\pi\) | |||||||
\(338\) | 0.866025 | + | 0.500000i | 0.0471056 | + | 0.0271964i | ||||
\(339\) | 23.6322 | − | 8.51693i | 1.28353 | − | 0.462576i | ||||
\(340\) | 0.355707 | + | 0.616102i | 0.0192909 | + | 0.0334128i | ||||
\(341\) | 1.82090 | − | 3.15390i | 0.0986074 | − | 0.170793i | ||||
\(342\) | 9.49219 | + | 3.52300i | 0.513279 | + | 0.190502i | ||||
\(343\) | −13.9482 | + | 12.1839i | −0.753131 | + | 0.657871i | ||||
\(344\) | − | 1.18934i | − | 0.0641250i | ||||||
\(345\) | −4.49576 | − | 3.79668i | −0.242044 | − | 0.204406i | ||||
\(346\) | −13.3966 | + | 7.73453i | −0.720206 | + | 0.415811i | ||||
\(347\) | −19.9014 | + | 11.4901i | −1.06836 | + | 0.616818i | −0.927733 | − | 0.373244i | \(-0.878245\pi\) |
−0.140627 | + | 0.990063i | \(0.544912\pi\) | |||||||
\(348\) | 0.886023 | + | 0.748247i | 0.0474958 | + | 0.0401103i | ||||
\(349\) | 16.2489i | 0.869786i | 0.900482 | + | 0.434893i | \(0.143214\pi\) | ||||
−0.900482 | + | 0.434893i | \(0.856786\pi\) | |||||||
\(350\) | 8.42060 | − | 8.05043i | 0.450100 | − | 0.430314i | ||||
\(351\) | 2.64064 | − | 4.47516i | 0.140947 | − | 0.238866i | ||||
\(352\) | 1.91345 | − | 3.31419i | 0.101987 | − | 0.176647i | ||||
\(353\) | 10.8201 | + | 18.7410i | 0.575897 | + | 0.997482i | 0.995944 | + | 0.0899798i | \(0.0286802\pi\) |
−0.420047 | + | 0.907502i | \(0.637986\pi\) | |||||||
\(354\) | 6.45456 | − | 2.32619i | 0.343056 | − | 0.123635i | ||||
\(355\) | 4.17641 | + | 2.41125i | 0.221661 | + | 0.127976i | ||||
\(356\) | 4.01889 | 0.213001 | ||||||||
\(357\) | −4.21196 | + | 0.259934i | −0.222921 | + | 0.0137571i | ||||
\(358\) | 12.0221 | 0.635389 | ||||||||
\(359\) | −30.5776 | − | 17.6540i | −1.61383 | − | 0.931742i | −0.988473 | − | 0.151400i | \(-0.951622\pi\) |
−0.625353 | − | 0.780342i | \(-0.715045\pi\) | |||||||
\(360\) | 2.28491 | − | 0.388013i | 0.120426 | − | 0.0204501i | ||||
\(361\) | −3.80482 | − | 6.59014i | −0.200254 | − | 0.346850i | ||||
\(362\) | −8.20445 | + | 14.2105i | −0.431216 | + | 0.746889i | ||||
\(363\) | 6.21419 | + | 1.11600i | 0.326161 | + | 0.0585747i | ||||
\(364\) | −2.53957 | − | 0.742018i | −0.133110 | − | 0.0388923i | ||||
\(365\) | − | 6.81009i | − | 0.356456i | ||||||
\(366\) | −0.462700 | + | 0.547897i | −0.0241857 | + | 0.0286390i | ||||
\(367\) | 1.52944 | − | 0.883022i | 0.0798360 | − | 0.0460934i | −0.459551 | − | 0.888152i | \(-0.651989\pi\) |
0.539387 | + | 0.842058i | \(0.318656\pi\) | |||||||
\(368\) | 3.80849 | − | 2.19883i | 0.198531 | − | 0.114622i | ||||
\(369\) | −3.16443 | + | 2.62136i | −0.164734 | + | 0.136462i | ||||
\(370\) | − | 5.21566i | − | 0.271149i | ||||||
\(371\) | 21.4125 | + | 6.25635i | 1.11168 | + | 0.324814i | ||||
\(372\) | −0.291350 | + | 1.62232i | −0.0151058 | + | 0.0841135i | ||||
\(373\) | −10.0388 | + | 17.3877i | −0.519788 | + | 0.900299i | 0.479948 | + | 0.877297i | \(0.340656\pi\) |
−0.999735 | + | 0.0230017i | \(0.992678\pi\) | |||||||
\(374\) | −1.76205 | − | 3.05195i | −0.0911132 | − | 0.157813i | ||||
\(375\) | 4.26598 | + | 11.8370i | 0.220294 | + | 0.611258i | ||||
\(376\) | 8.95534 | + | 5.17037i | 0.461836 | + | 0.266641i | ||||
\(377\) | 0.669555 | 0.0344838 | ||||||||
\(378\) | −3.98061 | + | 13.1588i | −0.204741 | + | 0.676817i | ||||
\(379\) | −4.71985 | −0.242443 | −0.121221 | − | 0.992626i | \(-0.538681\pi\) | ||||
−0.121221 | + | 0.992626i | \(0.538681\pi\) | |||||||
\(380\) | 2.25799 | + | 1.30365i | 0.115832 | + | 0.0668758i | ||||
\(381\) | −12.5135 | − | 34.7218i | −0.641088 | − | 1.77885i | ||||
\(382\) | 12.7441 | + | 22.0735i | 0.652047 | + | 1.12938i | ||||
\(383\) | 12.7793 | − | 22.1343i | 0.652989 | − | 1.13101i | −0.329404 | − | 0.944189i | \(-0.606848\pi\) |
0.982394 | − | 0.186822i | \(-0.0598187\pi\) | |||||||
\(384\) | −0.306158 | + | 1.70478i | −0.0156236 | + | 0.0869966i | ||||
\(385\) | 5.65387 | − | 5.40533i | 0.288148 | − | 0.275481i | ||||
\(386\) | − | 10.1684i | − | 0.517556i | ||||||
\(387\) | −2.74771 | + | 2.27616i | −0.139674 | + | 0.115704i | ||||
\(388\) | 8.15357 | − | 4.70747i | 0.413935 | − | 0.238985i | ||||
\(389\) | −32.8464 | + | 18.9639i | −1.66538 | + | 0.961506i | −0.695297 | + | 0.718722i | \(0.744727\pi\) |
−0.970080 | + | 0.242784i | \(0.921939\pi\) | |||||||
\(390\) | 0.863338 | − | 1.02231i | 0.0437168 | − | 0.0517665i | ||||
\(391\) | − | 4.04970i | − | 0.204802i | ||||||
\(392\) | 6.99293 | + | 0.314476i | 0.353196 | + | 0.0158834i | ||||
\(393\) | 28.7624 | + | 5.16540i | 1.45087 | + | 0.260560i | ||||
\(394\) | −0.736384 | + | 1.27546i | −0.0370985 | + | 0.0642565i | ||||
\(395\) | −5.00515 | − | 8.66917i | −0.251836 | − | 0.436193i | ||||
\(396\) | −11.3187 | + | 1.92208i | −0.568784 | + | 0.0965881i | ||||
\(397\) | 18.8568 | + | 10.8870i | 0.946398 | + | 0.546403i | 0.891960 | − | 0.452114i | \(-0.149330\pi\) |
0.0544380 | + | 0.998517i | \(0.482663\pi\) | |||||||
\(398\) | −19.0591 | −0.955347 | ||||||||
\(399\) | −12.8922 | + | 8.54334i | −0.645418 | + | 0.427702i | ||||
\(400\) | −4.40318 | −0.220159 | ||||||||
\(401\) | 7.72906 | + | 4.46237i | 0.385971 | + | 0.222840i | 0.680413 | − | 0.732829i | \(-0.261800\pi\) |
−0.294442 | + | 0.955669i | \(0.595134\pi\) | |||||||
\(402\) | −15.3289 | + | 5.52444i | −0.764535 | + | 0.275534i | ||||
\(403\) | 0.475817 | + | 0.824139i | 0.0237021 | + | 0.0410533i | ||||
\(404\) | −3.54281 | + | 6.13632i | −0.176261 | + | 0.305293i | ||||
\(405\) | −5.26927 | − | 4.53621i | −0.261832 | − | 0.225406i | ||||
\(406\) | −1.72098 | + | 0.419930i | −0.0854110 | + | 0.0208408i | ||||
\(407\) | 25.8366i | 1.28067i | ||||||||
\(408\) | 1.21859 | + | 1.02910i | 0.0603294 | + | 0.0509482i | ||||
\(409\) | 29.4999 | − | 17.0317i | 1.45867 | − | 0.842166i | 0.459727 | − | 0.888060i | \(-0.347947\pi\) |
0.998946 | + | 0.0458943i | \(0.0146138\pi\) | |||||||
\(410\) | −0.916397 | + | 0.529082i | −0.0452576 | + | 0.0261295i | ||||
\(411\) | −18.7922 | − | 15.8701i | −0.926952 | − | 0.782812i | ||||
\(412\) | 5.27685i | 0.259972i | ||||||||
\(413\) | −2.93925 | + | 10.0596i | −0.144631 | + | 0.495003i | ||||
\(414\) | −12.3686 | − | 4.59057i | −0.607883 | − | 0.225614i | ||||
\(415\) | −0.858372 | + | 1.48674i | −0.0421358 | + | 0.0729814i | ||||
\(416\) | 0.500000 | + | 0.866025i | 0.0245145 | + | 0.0424604i | ||||
\(417\) | 14.4561 | − | 5.20990i | 0.707918 | − | 0.255130i | ||||
\(418\) | −11.1853 | − | 6.45782i | −0.547089 | − | 0.315862i | ||||
\(419\) | −4.85711 | −0.237285 | −0.118643 | − | 0.992937i | \(-0.537854\pi\) | ||||
−0.118643 | + | 0.992937i | \(0.537854\pi\) | |||||||
\(420\) | −1.57791 | + | 3.16914i | −0.0769939 | + | 0.154638i | ||||
\(421\) | −3.83457 | −0.186886 | −0.0934428 | − | 0.995625i | \(-0.529787\pi\) | ||||
−0.0934428 | + | 0.995625i | \(0.529787\pi\) | |||||||
\(422\) | −20.5641 | − | 11.8727i | −1.00104 | − | 0.577953i | ||||
\(423\) | −5.19368 | − | 30.5844i | −0.252526 | − | 1.48706i | ||||
\(424\) | −4.21577 | − | 7.30193i | −0.204736 | − | 0.354613i | ||||
\(425\) | −2.02739 | + | 3.51153i | −0.0983426 | + | 0.170334i | ||||
\(426\) | 10.6419 | + | 1.91116i | 0.515601 | + | 0.0925960i | ||||
\(427\) | −0.259676 | − | 1.06422i | −0.0125666 | − | 0.0515011i | ||||
\(428\) | − | 18.5997i | − | 0.899049i | ||||||
\(429\) | −4.27667 | + | 5.06414i | −0.206480 | + | 0.244499i | ||||
\(430\) | −0.795719 | + | 0.459408i | −0.0383730 | + | 0.0221546i | ||||
\(431\) | −24.5591 | + | 14.1792i | −1.18297 | + | 0.682987i | −0.956699 | − | 0.291078i | \(-0.905986\pi\) |
−0.226269 | + | 0.974065i | \(0.572653\pi\) | |||||||
\(432\) | 4.52444 | − | 2.55528i | 0.217682 | − | 0.122941i | ||||
\(433\) | 4.33579i | 0.208365i | 0.994558 | + | 0.104182i | \(0.0332226\pi\) | ||||
−0.994558 | + | 0.104182i | \(0.966777\pi\) | |||||||
\(434\) | −1.73989 | − | 1.81989i | −0.0835175 | − | 0.0873577i | ||||
\(435\) | 0.158363 | − | 0.881812i | 0.00759293 | − | 0.0422796i | ||||
\(436\) | 5.36127 | − | 9.28600i | 0.256758 | − | 0.444719i | ||||
\(437\) | −7.42098 | − | 12.8535i | −0.354994 | − | 0.614867i | ||||
\(438\) | −5.17669 | − | 14.3640i | −0.247352 | − | 0.686337i | ||||
\(439\) | −26.4597 | − | 15.2765i | −1.26285 | − | 0.729109i | −0.289228 | − | 0.957260i | \(-0.593399\pi\) |
−0.973626 | + | 0.228151i | \(0.926732\pi\) | |||||||
\(440\) | −2.95644 | −0.140943 | ||||||||
\(441\) | −12.6565 | − | 16.7575i | −0.602691 | − | 0.797975i | ||||
\(442\) | 0.920873 | 0.0438015 | ||||||||
\(443\) | 10.3560 | + | 5.97906i | 0.492030 | + | 0.284074i | 0.725416 | − | 0.688310i | \(-0.241647\pi\) |
−0.233386 | + | 0.972384i | \(0.574981\pi\) | |||||||
\(444\) | −3.96469 | − | 11.0010i | −0.188156 | − | 0.522083i | ||||
\(445\) | −1.55238 | − | 2.68880i | −0.0735898 | − | 0.127461i | ||||
\(446\) | 2.61577 | − | 4.53064i | 0.123860 | − | 0.214532i | ||||
\(447\) | 0.720340 | − | 4.01106i | 0.0340709 | − | 0.189717i | ||||
\(448\) | −1.82832 | − | 1.91239i | −0.0863801 | − | 0.0903520i | ||||
\(449\) | − | 19.0480i | − | 0.898929i | −0.893298 | − | 0.449465i | \(-0.851615\pi\) | ||
0.893298 | − | 0.449465i | \(-0.148385\pi\) | |||||||
\(450\) | 8.42678 | + | 10.1726i | 0.397242 | + | 0.479540i | ||||
\(451\) | 4.53951 | − | 2.62089i | 0.213757 | − | 0.123413i | ||||
\(452\) | 12.5601 | − | 7.25156i | 0.590776 | − | 0.341085i | ||||
\(453\) | −11.0019 | + | 13.0277i | −0.516916 | + | 0.612097i | ||||
\(454\) | − | 28.1437i | − | 1.32085i | ||||||
\(455\) | 0.484521 | + | 1.98570i | 0.0227147 | + | 0.0930908i | ||||
\(456\) | 5.75356 | + | 1.03327i | 0.269435 | + | 0.0483874i | ||||
\(457\) | −5.32789 | + | 9.22817i | −0.249228 | + | 0.431676i | −0.963312 | − | 0.268385i | \(-0.913510\pi\) |
0.714084 | + | 0.700060i | \(0.246844\pi\) | |||||||
\(458\) | −4.77199 | − | 8.26533i | −0.222981 | − | 0.386214i | ||||
\(459\) | 0.0453793 | − | 4.78478i | 0.00211813 | − | 0.223335i | ||||
\(460\) | −2.94222 | − | 1.69869i | −0.137182 | − | 0.0792019i | ||||
\(461\) | 28.5410 | 1.32929 | 0.664643 | − | 0.747161i | \(-0.268584\pi\) | ||||
0.664643 | + | 0.747161i | \(0.268584\pi\) | |||||||
\(462\) | 7.81639 | − | 15.6988i | 0.363651 | − | 0.730375i | ||||
\(463\) | −36.2254 | −1.68354 | −0.841769 | − | 0.539838i | \(-0.818486\pi\) | ||||
−0.841769 | + | 0.539838i | \(0.818486\pi\) | |||||||
\(464\) | 0.579851 | + | 0.334777i | 0.0269189 | + | 0.0155416i | ||||
\(465\) | 1.19794 | − | 0.431731i | 0.0555532 | − | 0.0200210i | ||||
\(466\) | −1.19486 | − | 2.06956i | −0.0553508 | − | 0.0958704i | ||||
\(467\) | −1.19484 | + | 2.06953i | −0.0552908 | + | 0.0957665i | −0.892346 | − | 0.451352i | \(-0.850942\pi\) |
0.837055 | + | 0.547118i | \(0.184275\pi\) | |||||||
\(468\) | 1.04386 | − | 2.81253i | 0.0482526 | − | 0.130009i | ||||
\(469\) | 6.98041 | − | 23.8906i | 0.322325 | − | 1.10316i | ||||
\(470\) | − | 7.98865i | − | 0.368489i | ||||||
\(471\) | −6.62205 | − | 5.59232i | −0.305128 | − | 0.257681i | ||||
\(472\) | 3.43047 | − | 1.98058i | 0.157900 | − | 0.0911637i | ||||
\(473\) | 3.94171 | − | 2.27575i | 0.181240 | − | 0.104639i | ||||
\(474\) | −17.1468 | − | 14.4805i | −0.787580 | − | 0.665112i | ||||
\(475\) | 14.8606i | 0.681849i | ||||||||
\(476\) | −2.36696 | + | 0.577552i | −0.108489 | + | 0.0264720i | ||||
\(477\) | −8.80138 | + | 23.7140i | −0.402987 | + | 1.08579i | ||||
\(478\) | 0.915531 | − | 1.58575i | 0.0418754 | − | 0.0725303i | ||||
\(479\) | 17.6332 | + | 30.5416i | 0.805681 | + | 1.39548i | 0.915830 | + | 0.401566i | \(0.131534\pi\) |
−0.110149 | + | 0.993915i | \(0.535133\pi\) | |||||||
\(480\) | 1.25883 | − | 0.453674i | 0.0574573 | − | 0.0207073i | ||||
\(481\) | −5.84680 | − | 3.37565i | −0.266591 | − | 0.153916i | ||||
\(482\) | −27.3594 | −1.24619 | ||||||||
\(483\) | 16.7989 | − | 11.1322i | 0.764377 | − | 0.506533i | ||||
\(484\) | 3.64516 | 0.165689 | ||||||||
\(485\) | −6.29898 | − | 3.63672i | −0.286022 | − | 0.165135i | ||||
\(486\) | −14.5623 | − | 5.56243i | −0.660557 | − | 0.252317i | ||||
\(487\) | −10.1938 | − | 17.6562i | −0.461927 | − | 0.800080i | 0.537130 | − | 0.843499i | \(-0.319508\pi\) |
−0.999057 | + | 0.0434188i | \(0.986175\pi\) | |||||||
\(488\) | −0.207019 | + | 0.358567i | −0.00937131 | + | 0.0162316i | ||||
\(489\) | 41.9097 | + | 7.52650i | 1.89522 | + | 0.340360i | ||||
\(490\) | −2.49077 | − | 4.80003i | −0.112521 | − | 0.216843i | ||||
\(491\) | 22.5720i | 1.01866i | 0.860571 | + | 0.509330i | \(0.170107\pi\) | ||||
−0.860571 | + | 0.509330i | \(0.829893\pi\) | |||||||
\(492\) | −1.53070 | + | 1.81255i | −0.0690093 | + | 0.0817160i | ||||
\(493\) | 0.533970 | − | 0.308288i | 0.0240488 | − | 0.0138846i | ||||
\(494\) | 2.92280 | − | 1.68748i | 0.131503 | − | 0.0759233i | ||||
\(495\) | 5.65802 | + | 6.83020i | 0.254309 | + | 0.306995i | ||||
\(496\) | 0.951633i | 0.0427296i | ||||||||
\(497\) | −11.9379 | + | 11.4131i | −0.535487 | + | 0.511947i | ||||
\(498\) | −0.680345 | + | 3.78836i | −0.0304870 | + | 0.169760i | ||||
\(499\) | −2.26315 | + | 3.91989i | −0.101312 | + | 0.175478i | −0.912226 | − | 0.409688i | \(-0.865638\pi\) |
0.810913 | + | 0.585167i | \(0.198971\pi\) | |||||||
\(500\) | 3.63217 | + | 6.29111i | 0.162436 | + | 0.281347i | ||||
\(501\) | −3.92000 | − | 10.8770i | −0.175133 | − | 0.485948i | ||||
\(502\) | −1.48893 | − | 0.859635i | −0.0664543 | − | 0.0383674i | ||||
\(503\) | −27.1387 | −1.21005 | −0.605027 | − | 0.796205i | \(-0.706838\pi\) | ||||
−0.605027 | + | 0.796205i | \(0.706838\pi\) | |||||||
\(504\) | −0.919124 | + | 7.88386i | −0.0409410 | + | 0.351175i | ||||
\(505\) | 5.47393 | 0.243587 | ||||||||
\(506\) | 14.5747 | + | 8.41472i | 0.647925 | + | 0.374080i | ||||
\(507\) | −0.587248 | − | 1.62946i | −0.0260806 | − | 0.0723669i | ||||
\(508\) | −10.6544 | − | 18.4539i | −0.472712 | − | 0.818761i | ||||
\(509\) | 2.22767 | − | 3.85843i | 0.0987396 | − | 0.171022i | −0.812424 | − | 0.583068i | \(-0.801852\pi\) |
0.911163 | + | 0.412046i | \(0.135186\pi\) | |||||||
\(510\) | 0.217805 | − | 1.21280i | 0.00964457 | − | 0.0537038i | ||||
\(511\) | 22.3867 | + | 6.54101i | 0.990330 | + | 0.289357i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −8.62398 | − | 15.2698i | −0.380758 | − | 0.674178i | ||||
\(514\) | −8.68237 | + | 5.01277i | −0.382963 | + | 0.221104i | ||||
\(515\) | 3.53043 | − | 2.03829i | 0.155569 | − | 0.0898179i | ||||
\(516\) | −1.32913 | + | 1.57386i | −0.0585115 | + | 0.0692853i | ||||
\(517\) | 39.5730i | 1.74042i | ||||||||
\(518\) | 17.1454 | + | 5.00959i | 0.753325 | + | 0.220109i | ||||
\(519\) | 26.3713 | + | 4.73598i | 1.15757 | + | 0.207887i | ||||
\(520\) | 0.386271 | − | 0.669041i | 0.0169391 | − | 0.0293394i | ||||
\(521\) | 15.3496 | + | 26.5864i | 0.672480 | + | 1.16477i | 0.977199 | + | 0.212327i | \(0.0681043\pi\) |
−0.304719 | + | 0.952442i | \(0.598562\pi\) | |||||||
\(522\) | −0.336287 | − | 1.98031i | −0.0147189 | − | 0.0866760i | ||||
\(523\) | −36.4278 | − | 21.0316i | −1.59288 | − | 0.919648i | −0.992810 | − | 0.119699i | \(-0.961807\pi\) |
−0.600068 | − | 0.799949i | \(-0.704860\pi\) | |||||||
\(524\) | 16.8717 | 0.737042 | ||||||||
\(525\) | −20.1396 | + | 1.24288i | −0.878964 | + | 0.0542437i | ||||
\(526\) | 0.760829 | 0.0331737 | ||||||||
\(527\) | 0.758927 | + | 0.438167i | 0.0330594 | + | 0.0190869i | ||||
\(528\) | −6.23578 | + | 2.24734i | −0.271378 | + | 0.0978029i | ||||
\(529\) | −1.83026 | − | 3.17010i | −0.0795764 | − | 0.137830i | ||||
\(530\) | −3.25686 | + | 5.64104i | −0.141469 | + | 0.245031i | ||||
\(531\) | −11.1409 | − | 4.13491i | −0.483474 | − | 0.179440i | ||||
\(532\) | −6.45424 | + | 6.17052i | −0.279827 | + | 0.267526i | ||||
\(533\) | 1.36972i | 0.0593290i | ||||||||
\(534\) | −5.31820 | − | 4.49123i | −0.230141 | − | 0.194354i | ||||
\(535\) | −12.4439 | + | 7.18451i | −0.537998 | + | 0.310614i | ||||
\(536\) | −8.14699 | + | 4.70367i | −0.351896 | + | 0.203168i | ||||
\(537\) | −15.9089 | − | 13.4351i | −0.686520 | − | 0.579767i | ||||
\(538\) | − | 5.59454i | − | 0.241198i | ||||||
\(539\) | 12.3384 | + | 23.7777i | 0.531452 | + | 1.02418i | ||||
\(540\) | −3.45725 | − | 2.04000i | −0.148776 | − | 0.0877877i | ||||
\(541\) | 6.24183 | − | 10.8112i | 0.268357 | − | 0.464808i | −0.700081 | − | 0.714064i | \(-0.746853\pi\) |
0.968438 | + | 0.249256i | \(0.0801859\pi\) | |||||||
\(542\) | 12.5717 | + | 21.7749i | 0.540003 | + | 0.935312i | ||||
\(543\) | 26.7376 | − | 9.63609i | 1.14742 | − | 0.413524i | ||||
\(544\) | 0.797500 | + | 0.460437i | 0.0341925 | + | 0.0197411i | ||||
\(545\) | −8.28361 | −0.354831 | ||||||||
\(546\) | 2.53139 | + | 3.81996i | 0.108333 | + | 0.163479i | ||||
\(547\) | 27.7028 | 1.18449 | 0.592243 | − | 0.805759i | \(-0.298242\pi\) | ||||
0.592243 | + | 0.805759i | \(0.298242\pi\) | |||||||
\(548\) | −12.2984 | − | 7.10051i | −0.525363 | − | 0.303319i | ||||
\(549\) | 1.22458 | − | 0.207953i | 0.0522639 | − | 0.00887520i | ||||
\(550\) | −8.42526 | − | 14.5930i | −0.359254 | − | 0.622247i | ||||
\(551\) | 1.12986 | − | 1.95698i | 0.0481337 | − | 0.0833700i | ||||
\(552\) | −7.49705 | − | 1.34638i | −0.319095 | − | 0.0573058i | ||||
\(553\) | 33.3055 | − | 8.12673i | 1.41629 | − | 0.345584i | ||||
\(554\) | − | 25.8904i | − | 1.09998i | ||||||
\(555\) | −5.82866 | + | 6.90190i | −0.247413 | + | 0.292969i | ||||
\(556\) | 7.68313 | − | 4.43586i | 0.325837 | − | 0.188122i | ||||
\(557\) | −10.8733 | + | 6.27773i | −0.460718 | + | 0.265996i | −0.712346 | − | 0.701828i | \(-0.752367\pi\) |
0.251628 | + | 0.967824i | \(0.419034\pi\) | |||||||
\(558\) | 2.19854 | − | 1.82123i | 0.0930716 | − | 0.0770988i | ||||
\(559\) | 1.18934i | 0.0503038i | ||||||||
\(560\) | −0.573240 | + | 1.96192i | −0.0242238 | + | 0.0829064i | ||||
\(561\) | −1.07893 | + | 6.00779i | −0.0455524 | + | 0.253649i | ||||
\(562\) | 1.01595 | − | 1.75967i | 0.0428551 | − | 0.0742272i | ||||
\(563\) | 16.3961 | + | 28.3989i | 0.691015 | + | 1.19687i | 0.971506 | + | 0.237016i | \(0.0761694\pi\) |
−0.280491 | + | 0.959857i | \(0.590497\pi\) | |||||||
\(564\) | −6.07258 | − | 16.8498i | −0.255702 | − | 0.709505i | ||||
\(565\) | −9.70318 | − | 5.60213i | −0.408216 | − | 0.235683i | ||||
\(566\) | 27.2852 | 1.14688 | ||||||||
\(567\) | 19.9729 | − | 12.9646i | 0.838784 | − | 0.544464i | ||||
\(568\) | 6.24239 | 0.261925 | ||||||||
\(569\) | −8.48347 | − | 4.89793i | −0.355646 | − | 0.205332i | 0.311523 | − | 0.950238i | \(-0.399161\pi\) |
−0.667169 | + | 0.744906i | \(0.732494\pi\) | |||||||
\(570\) | −1.53113 | − | 4.24849i | −0.0641320 | − | 0.177950i | ||||
\(571\) | 5.46052 | + | 9.45789i | 0.228516 | + | 0.395801i | 0.957368 | − | 0.288870i | \(-0.0932795\pi\) |
−0.728853 | + | 0.684670i | \(0.759946\pi\) | |||||||
\(572\) | −1.91345 | + | 3.31419i | −0.0800054 | + | 0.138573i | ||||
\(573\) | 7.80344 | − | 43.4518i | 0.325994 | − | 1.81523i | ||||
\(574\) | −0.859057 | − | 3.52064i | −0.0358563 | − | 0.146949i | ||||
\(575\) | − | 19.3637i | − | 0.807523i | ||||||
\(576\) | 2.31028 | − | 1.91379i | 0.0962616 | − | 0.0797414i | ||||
\(577\) | −28.7040 | + | 16.5723i | −1.19496 | + | 0.689912i | −0.959428 | − | 0.281954i | \(-0.909017\pi\) |
−0.235534 | + | 0.971866i | \(0.575684\pi\) | |||||||
\(578\) | −13.9880 | + | 8.07600i | −0.581826 | + | 0.335917i | ||||
\(579\) | −11.3635 | + | 13.4558i | −0.472249 | + | 0.559205i | ||||
\(580\) | − | 0.517259i | − | 0.0214780i | ||||||
\(581\) | −4.06290 | − | 4.24972i | −0.168558 | − | 0.176308i | ||||
\(582\) | −16.0504 | − | 2.88246i | −0.665309 | − | 0.119482i | ||||
\(583\) | 16.1333 | − | 27.9437i | 0.668174 | − | 1.15731i | ||||
\(584\) | −4.40758 | − | 7.63416i | −0.182387 | − | 0.315904i | ||||
\(585\) | −2.28491 | + | 0.388013i | −0.0944696 | + | 0.0160424i | ||||
\(586\) | 11.3080 | + | 6.52868i | 0.467130 | + | 0.269697i | ||||
\(587\) | 36.3462 | 1.50017 | 0.750084 | − | 0.661342i | \(-0.230013\pi\) | ||||
0.750084 | + | 0.661342i | \(0.230013\pi\) | |||||||
\(588\) | −8.90232 | − | 8.23096i | −0.367126 | − | 0.339439i | ||||
\(589\) | 3.21173 | 0.132337 | ||||||||
\(590\) | −2.65018 | − | 1.53008i | −0.109106 | − | 0.0629925i | ||||
\(591\) | 2.39982 | − | 0.864880i | 0.0987153 | − | 0.0355764i | ||||
\(592\) | −3.37565 | − | 5.84680i | −0.138738 | − | 0.240302i | ||||
\(593\) | 11.5189 | − | 19.9513i | 0.473023 | − | 0.819300i | −0.526500 | − | 0.850175i | \(-0.676496\pi\) |
0.999523 | + | 0.0308749i | \(0.00982935\pi\) | |||||||
\(594\) | 17.1260 | + | 10.1054i | 0.702688 | + | 0.414632i | ||||
\(595\) | 1.30069 | + | 1.36050i | 0.0533232 | + | 0.0557751i | ||||
\(596\) | − | 2.35283i | − | 0.0963758i | ||||||
\(597\) | 25.2209 | + | 21.2991i | 1.03222 | + | 0.871715i | ||||
\(598\) | −3.80849 | + | 2.19883i | −0.155741 | + | 0.0899170i | ||||
\(599\) | 14.6236 | − | 8.44293i | 0.597503 | − | 0.344969i | −0.170556 | − | 0.985348i | \(-0.554556\pi\) |
0.768059 | + | 0.640379i | \(0.221223\pi\) | |||||||
\(600\) | 5.82673 | + | 4.92068i | 0.237875 | + | 0.200886i | ||||
\(601\) | − | 10.3410i | − | 0.421817i | −0.977506 | − | 0.210908i | \(-0.932358\pi\) | ||
0.977506 | − | 0.210908i | \(-0.0676421\pi\) | |||||||
\(602\) | −0.745929 | − | 3.05701i | −0.0304018 | − | 0.124595i | ||||
\(603\) | 26.4585 | + | 9.81997i | 1.07747 | + | 0.399900i | ||||
\(604\) | −4.92244 | + | 8.52591i | −0.200291 | + | 0.346914i | ||||
\(605\) | −1.40802 | − | 2.43876i | −0.0572442 | − | 0.0991499i | ||||
\(606\) | 11.5457 | − | 4.16101i | 0.469013 | − | 0.169030i | ||||
\(607\) | 2.02862 | + | 1.17123i | 0.0823393 | + | 0.0475386i | 0.540604 | − | 0.841277i | \(-0.318196\pi\) |
−0.458265 | + | 0.888816i | \(0.651529\pi\) | |||||||
\(608\) | 3.37496 | 0.136873 | ||||||||
\(609\) | 2.74666 | + | 1.36756i | 0.111300 | + | 0.0554162i | ||||
\(610\) | 0.319862 | 0.0129508 | ||||||||
\(611\) | −8.95534 | − | 5.17037i | −0.362294 | − | 0.209171i | ||||
\(612\) | −0.462513 | − | 2.72363i | −0.0186960 | − | 0.110096i | ||||
\(613\) | −5.05945 | − | 8.76322i | −0.204349 | − | 0.353943i | 0.745576 | − | 0.666421i | \(-0.232174\pi\) |
−0.949925 | + | 0.312478i | \(0.898841\pi\) | |||||||
\(614\) | 8.58829 | − | 14.8754i | 0.346595 | − | 0.600320i | ||||
\(615\) | 1.80393 | + | 0.323966i | 0.0727416 | + | 0.0130636i | ||||
\(616\) | 2.83963 | − | 9.71868i | 0.114412 | − | 0.391577i | ||||
\(617\) | − | 34.5810i | − | 1.39218i | −0.717956 | − | 0.696089i | \(-0.754922\pi\) | ||
0.717956 | − | 0.696089i | \(-0.245078\pi\) | |||||||
\(618\) | 5.89704 | − | 6.98286i | 0.237214 | − | 0.280892i | ||||
\(619\) | 26.2353 | − | 15.1469i | 1.05449 | − | 0.608807i | 0.130583 | − | 0.991437i | \(-0.458315\pi\) |
0.923902 | + | 0.382630i | \(0.124982\pi\) | |||||||
\(620\) | 0.636682 | − | 0.367588i | 0.0255697 | − | 0.0147627i | ||||
\(621\) | 11.2373 | + | 19.8970i | 0.450937 | + | 0.798438i | ||||
\(622\) | 31.1415i | 1.24866i | ||||||||
\(623\) | 10.3299 | − | 2.52056i | 0.413859 | − | 0.100984i | ||||
\(624\) | 0.306158 | − | 1.70478i | 0.0122561 | − | 0.0682457i | ||||
\(625\) | −8.20194 | + | 14.2062i | −0.328078 | + | 0.568247i | ||||
\(626\) | −3.80923 | − | 6.59778i | −0.152248 | − | 0.263700i | ||||
\(627\) | 7.58468 | + | 21.0455i | 0.302903 | + | 0.840477i | ||||
\(628\) | −4.33375 | − | 2.50209i | −0.172935 | − | 0.0998444i | ||||
\(629\) | −6.21709 | −0.247892 | ||||||||
\(630\) | 5.62965 | − | 2.43037i | 0.224291 | − | 0.0968284i | ||||
\(631\) | −27.2816 | −1.08606 | −0.543032 | − | 0.839712i | \(-0.682724\pi\) | ||||
−0.543032 | + | 0.839712i | \(0.682724\pi\) | |||||||
\(632\) | −11.2216 | − | 6.47880i | −0.446372 | − | 0.257713i | ||||
\(633\) | 13.9444 | + | 38.6921i | 0.554241 | + | 1.53787i | ||||
\(634\) | −10.7540 | − | 18.6264i | −0.427095 | − | 0.739750i | ||||
\(635\) | −8.23096 | + | 14.2564i | −0.326636 | + | 0.565749i | ||||
\(636\) | −2.58139 | + | 14.3739i | −0.102359 | + | 0.569962i | ||||
\(637\) | −6.99293 | − | 0.314476i | −0.277070 | − | 0.0124600i | ||||
\(638\) | 2.56232i | 0.101443i | ||||||||
\(639\) | −11.9466 | − | 14.4217i | −0.472602 | − | 0.570512i | ||||
\(640\) | 0.669041 | − | 0.386271i | 0.0264462 | − | 0.0152687i | ||||
\(641\) | 21.0288 | − | 12.1410i | 0.830588 | − | 0.479540i | −0.0234659 | − | 0.999725i | \(-0.507470\pi\) |
0.854054 | + | 0.520184i | \(0.174137\pi\) | |||||||
\(642\) | −20.7857 | + | 24.6130i | −0.820346 | + | 0.971397i | ||||
\(643\) | − | 7.83521i | − | 0.308991i | −0.987994 | − | 0.154495i | \(-0.950625\pi\) | ||
0.987994 | − | 0.154495i | \(-0.0493752\pi\) | |||||||
\(644\) | 8.41006 | − | 8.04035i | 0.331403 | − | 0.316834i | ||||
\(645\) | 1.56638 | + | 0.281303i | 0.0616761 | + | 0.0110763i | ||||
\(646\) | 1.55396 | − | 2.69153i | 0.0611396 | − | 0.105897i | ||||
\(647\) | −19.0438 | − | 32.9849i | −0.748691 | − | 1.29677i | −0.948450 | − | 0.316926i | \(-0.897349\pi\) |
0.199760 | − | 0.979845i | \(-0.435984\pi\) | |||||||
\(648\) | −8.84280 | − | 1.67478i | −0.347378 | − | 0.0657917i | ||||
\(649\) | 13.1281 | + | 7.57949i | 0.515321 | + | 0.297521i | ||||
\(650\) | 4.40318 | 0.172707 | ||||||||
\(651\) | 0.268616 | + | 4.35265i | 0.0105279 | + | 0.170594i | ||||
\(652\) | 24.5837 | 0.962772 | ||||||||
\(653\) | −26.2455 | − | 15.1528i | −1.02707 | − | 0.592976i | −0.110923 | − | 0.993829i | \(-0.535381\pi\) |
−0.916143 | + | 0.400853i | \(0.868714\pi\) | |||||||
\(654\) | −17.4720 | + | 6.29679i | −0.683208 | + | 0.246224i | ||||
\(655\) | −6.51703 | − | 11.2878i | −0.254641 | − | 0.441052i | ||||
\(656\) | −0.684859 | + | 1.18621i | −0.0267392 | + | 0.0463137i | ||||
\(657\) | −9.20183 | + | 24.7930i | −0.358998 | + | 0.967265i | ||||
\(658\) | 26.2610 | + | 7.67301i | 1.02376 | + | 0.299125i | ||||
\(659\) | 7.53008i | 0.293330i | 0.989186 | + | 0.146665i | \(0.0468539\pi\) | ||||
−0.989186 | + | 0.146665i | \(0.953146\pi\) | |||||||
\(660\) | 3.91226 | + | 3.30391i | 0.152285 | + | 0.128605i | ||||
\(661\) | −17.5516 | + | 10.1334i | −0.682679 | + | 0.394145i | −0.800864 | − | 0.598847i | \(-0.795626\pi\) |
0.118185 | + | 0.992992i | \(0.462293\pi\) | |||||||
\(662\) | −1.36228 | + | 0.786513i | −0.0529465 | + | 0.0305687i | ||||
\(663\) | −1.21859 | − | 1.02910i | −0.0473262 | − | 0.0399671i | ||||
\(664\) | 2.22220i | 0.0862382i | ||||||||
\(665\) | 6.62141 | + | 1.93466i | 0.256767 | + | 0.0750230i | ||||
\(666\) | −7.04744 | + | 18.9883i | −0.273083 | + | 0.735780i | ||||
\(667\) | −1.47224 | + | 2.54999i | −0.0570053 | + | 0.0987362i | ||||
\(668\) | −3.33760 | − | 5.78090i | −0.129136 | − | 0.223670i | ||||
\(669\) | −8.52458 | + | 3.07221i | −0.329579 | + | 0.118778i | ||||
\(670\) | 6.29389 | + | 3.63378i | 0.243154 | + | 0.140385i | ||||
\(671\) | −1.58448 | −0.0611683 | ||||||||
\(672\) | 0.282269 | + | 4.57387i | 0.0108887 | + | 0.176441i | ||||
\(673\) | −20.5105 | −0.790622 | −0.395311 | − | 0.918547i | \(-0.629363\pi\) | ||||
−0.395311 | + | 0.918547i | \(0.629363\pi\) | |||||||
\(674\) | 8.40082 | + | 4.85022i | 0.323588 | + | 0.186823i | ||||
\(675\) | 0.216982 | − | 22.8786i | 0.00835166 | − | 0.880596i | ||||
\(676\) | −0.500000 | − | 0.866025i | −0.0192308 | − | 0.0333087i | ||||
\(677\) | −24.9728 | + | 43.2541i | −0.959782 | + | 1.66239i | −0.236756 | + | 0.971569i | \(0.576084\pi\) |
−0.723026 | + | 0.690821i | \(0.757249\pi\) | |||||||
\(678\) | −24.7246 | − | 4.44025i | −0.949542 | − | 0.170527i | ||||
\(679\) | 18.0050 | − | 17.2135i | 0.690970 | − | 0.660595i | ||||
\(680\) | − | 0.711413i | − | 0.0272815i | ||||||
\(681\) | −31.4514 | + | 37.2426i | −1.20522 | + | 1.42714i | ||||
\(682\) | −3.15390 | + | 1.82090i | −0.120769 | + | 0.0697260i | ||||
\(683\) | 18.3255 | − | 10.5802i | 0.701206 | − | 0.404842i | −0.106590 | − | 0.994303i | \(-0.533993\pi\) |
0.807797 | + | 0.589461i | \(0.200660\pi\) | |||||||
\(684\) | −6.45898 | − | 7.79710i | −0.246965 | − | 0.298130i | ||||
\(685\) | 10.9709i | 0.419176i | ||||||||
\(686\) | 18.1714 | − | 3.57750i | 0.693789 | − | 0.136590i | ||||
\(687\) | −2.92197 | + | 16.2704i | −0.111480 | + | 0.620753i | ||||
\(688\) | −0.594671 | + | 1.03000i | −0.0226716 | + | 0.0392684i | ||||
\(689\) | 4.21577 | + | 7.30193i | 0.160608 | + | 0.278181i | ||||
\(690\) | 1.99511 | + | 5.53590i | 0.0759524 | + | 0.210748i | ||||
\(691\) | −36.8904 | − | 21.2987i | −1.40338 | − | 0.810239i | −0.408638 | − | 0.912697i | \(-0.633996\pi\) |
−0.994737 | + | 0.102457i | \(0.967329\pi\) | |||||||
\(692\) | 15.4691 | 0.588046 | ||||||||
\(693\) | −27.8873 | + | 12.0392i | −1.05935 | + | 0.457332i | ||||
\(694\) | 22.9801 | 0.872313 | ||||||||
\(695\) | −5.93554 | − | 3.42688i | −0.225148 | − | 0.129989i | ||||
\(696\) | −0.393195 | − | 1.09101i | −0.0149040 | − | 0.0413547i | ||||
\(697\) | 0.630668 | + | 1.09235i | 0.0238883 | + | 0.0413757i | ||||
\(698\) | 8.12447 | − | 14.0720i | 0.307516 | − | 0.532633i | ||||
\(699\) | −0.731632 | + | 4.07394i | −0.0276729 | + | 0.154091i | ||||
\(700\) | −11.3177 | + | 2.76158i | −0.427768 | + | 0.104378i | ||||
\(701\) | − | 20.9627i | − | 0.791752i | −0.918304 | − | 0.395876i | \(-0.870441\pi\) | ||
0.918304 | − | 0.395876i | \(-0.129559\pi\) | |||||||
\(702\) | −4.52444 | + | 2.55528i | −0.170764 | + | 0.0964429i | ||||
\(703\) | −19.7327 | + | 11.3927i | −0.744233 | + | 0.429683i | ||||
\(704\) | −3.31419 | + | 1.91345i | −0.124908 | + | 0.0721159i | ||||
\(705\) | −8.92755 | + | 10.5714i | −0.336231 | + | 0.398142i | ||||
\(706\) | − | 21.6402i | − | 0.814441i | ||||||
\(707\) | −5.25765 | + | 17.9944i | −0.197734 | + | 0.676749i | ||||
\(708\) | −6.75290 | − | 1.21274i | −0.253790 | − | 0.0455777i | ||||
\(709\) | −1.65400 | + | 2.86481i | −0.0621171 | + | 0.107590i | −0.895412 | − | 0.445239i | \(-0.853119\pi\) |
0.833294 | + | 0.552829i | \(0.186452\pi\) | |||||||
\(710\) | −2.41125 | − | 4.17641i | −0.0904927 | − | 0.156738i | ||||
\(711\) | 6.50802 | + | 38.3242i | 0.244070 | + | 1.43727i | ||||
\(712\) | −3.48046 | − | 2.00944i | −0.130436 | − | 0.0753071i | ||||
\(713\) | −4.18497 | −0.156728 | ||||||||
\(714\) | 3.77763 | + | 1.88087i | 0.141374 | + | 0.0703898i | ||||
\(715\) | 2.95644 | 0.110565 | ||||||||
\(716\) | −10.4115 | − | 6.01106i | −0.389095 | − | 0.224644i | ||||
\(717\) | −2.98364 | + | 1.07529i | −0.111426 | + | 0.0401573i | ||||
\(718\) | 17.6540 | + | 30.5776i | 0.658841 | + | 1.14115i | ||||
\(719\) | −5.95241 | + | 10.3099i | −0.221987 | + | 0.384493i | −0.955411 | − | 0.295278i | \(-0.904588\pi\) |
0.733424 | + | 0.679771i | \(0.237921\pi\) | |||||||
\(720\) | −2.17280 | − | 0.806428i | −0.0809755 | − | 0.0300538i | ||||
\(721\) | 3.30952 | + | 13.5633i | 0.123253 | + | 0.505124i | ||||
\(722\) | 7.60964i | 0.283201i | ||||||||
\(723\) | 36.2047 | + | 30.5749i | 1.34647 | + | 1.13709i | ||||
\(724\) | 14.2105 | − | 8.20445i | 0.528130 | − | 0.304916i | ||||
\(725\) | 2.55319 | − | 1.47408i | 0.0948231 | − | 0.0547461i | ||||
\(726\) | −4.82365 | − | 4.07358i | −0.179023 | − | 0.151185i | ||||
\(727\) | 13.6161i | 0.504993i | 0.967598 | + | 0.252496i | \(0.0812516\pi\) | ||||
−0.967598 | + | 0.252496i | \(0.918748\pi\) | |||||||
\(728\) | 1.82832 | + | 1.91239i | 0.0677621 | + | 0.0708779i | ||||
\(729\) | 13.0541 | + | 23.6345i | 0.483485 | + | 0.875353i | ||||
\(730\) | −3.40504 | + | 5.89771i | −0.126026 | + | 0.218284i | ||||
\(731\) | 0.547617 | + | 0.948500i | 0.0202543 | + | 0.0350815i | ||||
\(732\) | 0.674658 | − | 0.243143i | 0.0249361 | − | 0.00898682i | ||||
\(733\) | 25.9923 | + | 15.0067i | 0.960049 | + | 0.554285i | 0.896188 | − | 0.443674i | \(-0.146325\pi\) |
0.0638609 | + | 0.997959i | \(0.479659\pi\) | |||||||
\(734\) | −1.76604 | −0.0651859 | ||||||||
\(735\) | −2.06814 | + | 9.13540i | −0.0762844 | + | 0.336964i | ||||
\(736\) | −4.39767 | −0.162100 | ||||||||
\(737\) | −31.1777 | − | 18.0005i | −1.14845 | − | 0.663056i | ||||
\(738\) | 4.05115 | − | 0.687947i | 0.149125 | − | 0.0253237i | ||||
\(739\) | 7.04885 | + | 12.2090i | 0.259296 | + | 0.449114i | 0.966054 | − | 0.258342i | \(-0.0831760\pi\) |
−0.706757 | + | 0.707456i | \(0.749843\pi\) | |||||||
\(740\) | −2.60783 | + | 4.51690i | −0.0958658 | + | 0.166044i | ||||
\(741\) | −5.75356 | − | 1.03327i | −0.211362 | − | 0.0379582i | ||||
\(742\) | −15.4156 | − | 16.1244i | −0.565923 | − | 0.591945i | ||||
\(743\) | − | 29.9617i | − | 1.09919i | −0.835431 | − | 0.549595i | \(-0.814782\pi\) | ||
0.835431 | − | 0.549595i | \(-0.185218\pi\) | |||||||
\(744\) | 1.06348 | − | 1.25930i | 0.0389890 | − | 0.0461681i | ||||
\(745\) | −1.57414 | + | 0.908831i | −0.0576721 | + | 0.0332970i | ||||
\(746\) | 17.3877 | − | 10.0388i | 0.636607 | − | 0.367545i | ||||
\(747\) | 5.13391 | − | 4.25284i | 0.187840 | − | 0.155603i | ||||
\(748\) | 3.52409i | 0.128854i | ||||||||
\(749\) | −11.6653 | − | 47.8075i | −0.426241 | − | 1.74685i | ||||
\(750\) | 2.22404 | − | 12.3841i | 0.0812105 | − | 0.452203i | ||||
\(751\) | 9.00356 | − | 15.5946i | 0.328545 | − | 0.569056i | −0.653679 | − | 0.756772i | \(-0.726775\pi\) |
0.982223 | + | 0.187716i | \(0.0601085\pi\) | |||||||
\(752\) | −5.17037 | − | 8.95534i | −0.188544 | − | 0.326568i | ||||
\(753\) | 1.00964 | + | 2.80148i | 0.0367932 | + | 0.102092i | ||||
\(754\) | −0.579851 | − | 0.334777i | −0.0211169 | − | 0.0121919i | ||||
\(755\) | 7.60558 | 0.276795 | ||||||||
\(756\) | 10.0267 | − | 9.40557i | 0.364668 | − | 0.342077i | ||||
\(757\) | 3.82722 | 0.139103 | 0.0695513 | − | 0.997578i | \(-0.477843\pi\) | ||||
0.0695513 | + | 0.997578i | \(0.477843\pi\) | |||||||
\(758\) | 4.08751 | + | 2.35993i | 0.148465 | + | 0.0857164i | ||||
\(759\) | −9.88305 | − | 27.4229i | −0.358732 | − | 0.995388i | ||||
\(760\) | −1.30365 | − | 2.25799i | −0.0472883 | − | 0.0819058i | ||||
\(761\) | −22.7050 | + | 39.3261i | −0.823054 | + | 1.42557i | 0.0803432 | + | 0.996767i | \(0.474398\pi\) |
−0.903397 | + | 0.428804i | \(0.858935\pi\) | |||||||
\(762\) | −6.52385 | + | 36.3267i | −0.236334 | + | 1.31598i | ||||
\(763\) | 7.95632 | − | 27.2306i | 0.288038 | − | 0.985815i | ||||
\(764\) | − | 25.4883i | − | 0.922133i | ||||||
\(765\) | −1.64356 | + | 1.36150i | −0.0594232 | + | 0.0492251i | ||||
\(766\) | −22.1343 | + | 12.7793i | −0.799745 | + | 0.461733i | ||||
\(767\) | −3.43047 | + | 1.98058i | −0.123867 | + | 0.0715147i | ||||
\(768\) | 1.11753 | − | 1.32330i | 0.0403254 | − | 0.0477505i | ||||
\(769\) | 35.9405i | 1.29605i | 0.761621 | + | 0.648023i | \(0.224404\pi\) | ||||
−0.761621 | + | 0.648023i | \(0.775596\pi\) | |||||||
\(770\) | −7.59906 | + | 1.85421i | −0.273851 | + | 0.0668213i | ||||
\(771\) | 17.0913 | + | 3.06940i | 0.615529 | + | 0.110542i | ||||
\(772\) | −5.08419 | + | 8.80607i | −0.182984 | + | 0.316937i | ||||
\(773\) | 21.2282 | + | 36.7683i | 0.763525 | + | 1.32246i | 0.941023 | + | 0.338343i | \(0.109866\pi\) |
−0.177498 | + | 0.984121i | \(0.556800\pi\) | |||||||
\(774\) | 3.51767 | − | 0.597353i | 0.126440 | − | 0.0214714i | ||||
\(775\) | 3.62883 | + | 2.09511i | 0.130351 | + | 0.0752584i | ||||
\(776\) | −9.41494 | −0.337977 | ||||||||
\(777\) | −17.0902 | − | 25.7897i | −0.613106 | − | 0.925200i | ||||
\(778\) | 37.9277 | 1.35978 | ||||||||
\(779\) | 4.00341 | + | 2.31137i | 0.143437 | + | 0.0828135i | ||||
\(780\) | −1.25883 | + | 0.453674i | −0.0450732 | + | 0.0162441i | ||||
\(781\) | 11.9445 | + | 20.6885i | 0.427408 | + | 0.740292i | ||||
\(782\) | −2.02485 | + | 3.50714i | −0.0724084 | + | 0.125415i | ||||
\(783\) | −1.76805 | + | 2.99636i | −0.0631850 | + | 0.107081i | ||||
\(784\) | −5.89882 | − | 3.76881i | −0.210672 | − | 0.134600i | ||||
\(785\) | 3.86594i | 0.137981i | ||||||||
\(786\) | −22.3263 | − | 18.8546i | −0.796352 | − | 0.672521i | ||||
\(787\) | −37.9202 | + | 21.8933i | −1.35171 | + | 0.780411i | −0.988489 | − | 0.151292i | \(-0.951657\pi\) |
−0.363222 | + | 0.931703i | \(0.618323\pi\) | |||||||
\(788\) | 1.27546 | − | 0.736384i | 0.0454362 | − | 0.0262326i | ||||
\(789\) | −1.00681 | − | 0.850248i | −0.0358432 | − | 0.0302696i | ||||
\(790\) | 10.0103i | 0.356150i | ||||||||
\(791\) | 27.7356 | − | 26.5164i | 0.986165 | − | 0.942813i | ||||
\(792\) | 10.7633 | + | 3.99476i | 0.382457 | + | 0.141948i | ||||
\(793\) | 0.207019 | − | 0.358567i | 0.00735146 | − | 0.0127331i | ||||
\(794\) | −10.8870 | − | 18.8568i | −0.386365 | − | 0.669205i | ||||
\(795\) | 10.6138 | − | 3.82517i | 0.376434 | − | 0.135665i | ||||
\(796\) | 16.5057 | + | 9.52955i | 0.585028 | + | 0.337766i | ||||
\(797\) | −8.03088 | −0.284469 | −0.142234 | − | 0.989833i | \(-0.545429\pi\) | ||||
−0.142234 | + | 0.989833i | \(0.545429\pi\) | |||||||
\(798\) | 15.4366 | − | 0.952645i | 0.546451 | − | 0.0337233i | ||||
\(799\) | −9.52251 | −0.336882 | ||||||||
\(800\) | 3.81326 | + | 2.20159i | 0.134819 | + | 0.0778379i | ||||
\(801\) | 2.01851 | + | 11.8865i | 0.0713204 | + | 0.419989i | ||||
\(802\) | −4.46237 | − | 7.72906i | −0.157572 | − | 0.272923i | ||||
\(803\) | 16.8674 | − | 29.2152i | 0.595237 | − | 1.03098i | ||||
\(804\) | 16.0374 | + | 2.88013i | 0.565596 | + | 0.101574i | ||||
\(805\) | −8.62789 | − | 2.52092i | −0.304093 | − | 0.0888507i | ||||
\(806\) | − | 0.951633i | − | 0.0335199i | ||||||
\(807\) | −6.25206 | + | 7.40326i | −0.220083 | + | 0.260607i | ||||
\(808\) | 6.13632 | − | 3.54281i | 0.215875 | − | 0.124636i | ||||
\(809\) | −1.79744 | + | 1.03775i | −0.0631947 | + | 0.0364855i | −0.531264 | − | 0.847206i | \(-0.678283\pi\) |
0.468070 | + | 0.883692i | \(0.344950\pi\) | |||||||
\(810\) | 2.29522 | + | 6.56311i | 0.0806458 | + | 0.230604i | ||||
\(811\) | − | 19.8306i | − | 0.696346i | −0.937430 | − | 0.348173i | \(-0.886802\pi\) | ||
0.937430 | − | 0.348173i | \(-0.113198\pi\) | |||||||
\(812\) | 1.70038 | + | 0.496822i | 0.0596716 | + | 0.0174350i | ||||
\(813\) | 7.69788 | − | 42.8640i | 0.269977 | − | 1.50331i | ||||
\(814\) | 12.9183 | − | 22.3751i | 0.452785 | − | 0.784247i | ||||
\(815\) | −9.49597 | − | 16.4475i | −0.332629 | − | 0.576131i | ||||
\(816\) | −0.540781 | − | 1.50053i | −0.0189311 | − | 0.0525289i | ||||
\(817\) | 3.47621 | + | 2.00699i | 0.121617 | + | 0.0702157i | ||||
\(818\) | −34.0635 | −1.19100 | ||||||||
\(819\) | 0.919124 | − | 7.88386i | 0.0321168 | − | 0.275484i | ||||
\(820\) | 1.05816 | 0.0369527 | ||||||||
\(821\) | 39.1424 | + | 22.5989i | 1.36608 | + | 0.788706i | 0.990425 | − | 0.138053i | \(-0.0440845\pi\) |
0.375655 | + | 0.926760i | \(0.377418\pi\) | |||||||
\(822\) | 8.33952 | + | 23.1400i | 0.290874 | + | 0.807100i | ||||
\(823\) | −11.9409 | − | 20.6822i | −0.416233 | − | 0.720937i | 0.579324 | − | 0.815097i | \(-0.303317\pi\) |
−0.995557 | + | 0.0941605i | \(0.969983\pi\) | |||||||
\(824\) | 2.63842 | − | 4.56989i | 0.0919139 | − | 0.159200i | ||||
\(825\) | −5.15893 | + | 28.7264i | −0.179611 | + | 1.00012i | ||||
\(826\) | 7.57529 | − | 7.24228i | 0.263578 | − | 0.251991i | ||||
\(827\) | − | 0.667718i | − | 0.0232188i | −0.999933 | − | 0.0116094i | \(-0.996305\pi\) | ||
0.999933 | − | 0.0116094i | \(-0.00369548\pi\) | |||||||
\(828\) | 8.41623 | + | 10.1598i | 0.292484 | + | 0.353079i | ||||
\(829\) | 38.2467 | − | 22.0818i | 1.32836 | − | 0.766931i | 0.343317 | − | 0.939220i | \(-0.388450\pi\) |
0.985047 | + | 0.172289i | \(0.0551162\pi\) | |||||||
\(830\) | 1.48674 | − | 0.858372i | 0.0516056 | − | 0.0297945i | ||||
\(831\) | −28.9333 | + | 34.2608i | −1.00368 | + | 1.18849i | ||||
\(832\) | − | 1.00000i | − | 0.0346688i | ||||||
\(833\) | −5.72166 | + | 2.96901i | −0.198244 | + | 0.102870i | ||||
\(834\) | −15.1243 | − | 2.71615i | −0.523712 | − | 0.0940525i | ||||
\(835\) | −2.57844 | + | 4.46599i | −0.0892306 | + | 0.154552i | ||||
\(836\) | 6.45782 | + | 11.1853i | 0.223348 | + | 0.386851i | ||||
\(837\) | −4.94461 | − | 0.0468952i | −0.170911 | − | 0.00162093i | ||||
\(838\) | 4.20638 | + | 2.42855i | 0.145307 | + | 0.0838930i | ||||
\(839\) | −4.38156 | −0.151268 | −0.0756342 | − | 0.997136i | \(-0.524098\pi\) | ||||
−0.0756342 | + | 0.997136i | \(0.524098\pi\) | |||||||
\(840\) | 2.95108 | − | 1.95560i | 0.101822 | − | 0.0674747i | ||||
\(841\) | 28.5517 | 0.984541 | ||||||||
\(842\) | 3.32084 | + | 1.91729i | 0.114444 | + | 0.0660740i | ||||
\(843\) | −3.31089 | + | 1.19322i | −0.114033 | + | 0.0410968i | ||||
\(844\) | 11.8727 | + | 20.5641i | 0.408675 | + | 0.707845i | ||||
\(845\) | −0.386271 | + | 0.669041i | −0.0132881 | + | 0.0230157i | ||||
\(846\) | −10.7943 | + | 29.0837i | −0.371116 | + | 0.999917i | ||||
\(847\) | 9.36931 | − | 2.28617i | 0.321933 | − | 0.0785536i | ||||
\(848\) | 8.43154i | 0.289540i | ||||||||
\(849\) | −36.1065 | − | 30.4920i | −1.23917 | − | 1.04648i | ||||
\(850\) | 3.51153 | − | 2.02739i | 0.120445 | − | 0.0695387i | ||||
\(851\) | 25.7123 | − | 14.8450i | 0.881406 | − | 0.508880i | ||||
\(852\) | −8.26056 | − | 6.97606i | −0.283002 | − | 0.238996i | ||||
\(853\) | 40.6558i | 1.39203i | 0.718027 | + | 0.696015i | \(0.245045\pi\) | ||||
−0.718027 | + | 0.696015i | \(0.754955\pi\) | |||||||
\(854\) | −0.307224 | + | 1.05148i | −0.0105130 | + | 0.0359808i | ||||
\(855\) | −2.72166 | + | 7.33312i | −0.0930789 | + | 0.250787i | ||||
\(856\) | −9.29984 | + | 16.1078i | −0.317862 | + | 0.550553i | ||||
\(857\) | 4.68975 | + | 8.12288i | 0.160199 | + | 0.277472i | 0.934940 | − | 0.354806i | \(-0.115453\pi\) |
−0.774741 | + | 0.632279i | \(0.782120\pi\) | |||||||
\(858\) | 6.23578 | − | 2.24734i | 0.212886 | − | 0.0767229i | ||||
\(859\) | −19.3168 | − | 11.1526i | −0.659081 | − | 0.380520i | 0.132846 | − | 0.991137i | \(-0.457588\pi\) |
−0.791927 | + | 0.610616i | \(0.790922\pi\) | |||||||
\(860\) | 0.918817 | 0.0313314 | ||||||||
\(861\) | −2.79763 | + | 5.61889i | −0.0953429 | + | 0.191491i | ||||
\(862\) | 28.3584 | 0.965890 | ||||||||
\(863\) | 19.6995 | + | 11.3735i | 0.670577 | + | 0.387158i | 0.796295 | − | 0.604908i | \(-0.206790\pi\) |
−0.125718 | + | 0.992066i | \(0.540123\pi\) | |||||||
\(864\) | −5.19592 | − | 0.0492786i | −0.176769 | − | 0.00167649i | ||||
\(865\) | −5.97525 | − | 10.3494i | −0.203165 | − | 0.351891i | ||||
\(866\) | 2.16790 | − | 3.75491i | 0.0736681 | − | 0.127597i | ||||
\(867\) | 27.5356 | + | 4.94507i | 0.935157 | + | 0.167943i | ||||
\(868\) | 0.596844 | + | 2.44602i | 0.0202582 | + | 0.0830234i | ||||
\(869\) | − | 49.5875i | − | 1.68214i | ||||||
\(870\) | −0.578052 | + | 0.684490i | −0.0195978 | + | 0.0232064i | ||||
\(871\) | 8.14699 | − | 4.70367i | 0.276050 | − | 0.159378i | ||||
\(872\) | −9.28600 | + | 5.36127i | −0.314463 | + | 0.181556i | ||||
\(873\) | 18.0183 | + | 21.7511i | 0.609825 | + | 0.736164i | ||||
\(874\) | 14.8420i | 0.502037i | ||||||||
\(875\) | 13.2816 | + | 13.8923i | 0.448999 | + | 0.469645i | ||||
\(876\) | −2.69884 | + | 15.0279i | −0.0911852 | + | 0.507746i | ||||
\(877\) | −8.52661 | + | 14.7685i | −0.287923 | + | 0.498697i | −0.973314 | − | 0.229478i | \(-0.926298\pi\) |
0.685391 | + | 0.728175i | \(0.259631\pi\) | |||||||
\(878\) | 15.2765 | + | 26.4597i | 0.515558 | + | 0.892972i | ||||
\(879\) | −7.66791 | − | 21.2765i | −0.258632 | − | 0.717637i | ||||
\(880\) | 2.56035 | + | 1.47822i | 0.0863095 | + | 0.0498308i | ||||
\(881\) | 28.2955 | 0.953298 | 0.476649 | − | 0.879094i | \(-0.341851\pi\) | ||||
0.476649 | + | 0.879094i | \(0.341851\pi\) | |||||||
\(882\) | 2.58212 | + | 20.8406i | 0.0869445 | + | 0.701741i | ||||
\(883\) | 47.9719 | 1.61438 | 0.807192 | − | 0.590289i | \(-0.200986\pi\) | ||||
0.807192 | + | 0.590289i | \(0.200986\pi\) | |||||||
\(884\) | −0.797500 | − | 0.460437i | −0.0268228 | − | 0.0154862i | ||||
\(885\) | 1.79708 | + | 4.98642i | 0.0604080 | + | 0.167617i | ||||
\(886\) | −5.97906 | − | 10.3560i | −0.200870 | − | 0.347918i | ||||
\(887\) | 21.6994 | − | 37.5844i | 0.728593 | − | 1.26196i | −0.228885 | − | 0.973454i | \(-0.573508\pi\) |
0.957478 | − | 0.288507i | \(-0.0931588\pi\) | |||||||
\(888\) | −2.06697 | + | 11.5095i | −0.0693629 | + | 0.386232i | ||||
\(889\) | −38.9593 | − | 40.7507i | −1.30665 | − | 1.36673i | ||||
\(890\) | 3.10476i | 0.104072i | ||||||||
\(891\) | −11.3697 | − | 32.5114i | −0.380899 | − | 1.08917i | ||||
\(892\) | −4.53064 | + | 2.61577i | −0.151697 | + | 0.0875824i | ||||
\(893\) | −30.2239 | + | 17.4498i | −1.01140 | + | 0.583935i | ||||
\(894\) | −2.62936 | + | 3.11351i | −0.0879390 | + | 0.104131i | ||||
\(895\) | 9.28760i | 0.310450i | ||||||||
\(896\) | 0.627178 | + | 2.57034i | 0.0209526 | + | 0.0858690i | ||||
\(897\) | 7.49705 | + | 1.34638i | 0.250319 | + | 0.0449544i | ||||
\(898\) | −9.52398 | + | 16.4960i | −0.317819 | + | 0.550479i | ||||
\(899\) | −0.318585 | − | 0.551806i | −0.0106254 | − | 0.0184038i | ||||
\(900\) | −2.21152 | − | 13.0231i | −0.0737173 | − | 0.434103i | ||||
\(901\) | 6.72415 | + | 3.88219i | 0.224014 | + | 0.129335i | ||||
\(902\) | −5.24177 | −0.174532 | ||||||||
\(903\) | −2.42921 | + | 4.87895i | −0.0808392 | + | 0.162361i | ||||
\(904\) | −14.5031 | −0.482366 | ||||||||
\(905\) | −10.9782 | − | 6.33828i | −0.364929 | − | 0.210692i | ||||
\(906\) | 16.0418 | − | 5.78138i | 0.532954 | − | 0.192074i | ||||
\(907\) | −13.9186 | − | 24.1077i | −0.462160 | − | 0.800484i | 0.536909 | − | 0.843640i | \(-0.319592\pi\) |
−0.999068 | + | 0.0431565i | \(0.986259\pi\) | |||||||
\(908\) | −14.0718 | + | 24.3731i | −0.466990 | + | 0.808851i | ||||
\(909\) | −19.9285 | − | 7.39641i | −0.660988 | − | 0.245324i | ||||
\(910\) | 0.573240 | − | 1.96192i | 0.0190027 | − | 0.0650371i | ||||
\(911\) | − | 5.08227i | − | 0.168383i | −0.996450 | − | 0.0841915i | \(-0.973169\pi\) | ||
0.996450 | − | 0.0841915i | \(-0.0268308\pi\) | |||||||
\(912\) | −4.46609 | − | 3.77162i | −0.147887 | − | 0.124891i | ||||
\(913\) | −7.36481 | + | 4.25207i | −0.243739 | + | 0.140723i | ||||
\(914\) | 9.22817 | − | 5.32789i | 0.305241 | − | 0.176231i | ||||
\(915\) | −0.423274 | − | 0.357455i | −0.0139930 | − | 0.0118171i | ||||
\(916\) | 9.54398i | 0.315342i | ||||||||
\(917\) | 43.3659 | − | 10.5815i | 1.43207 | − | 0.349433i | ||||
\(918\) | −2.43169 | + | 4.12105i | −0.0802578 | + | 0.136015i | ||||
\(919\) | −23.0372 | + | 39.9016i | −0.759927 | + | 1.31623i | 0.182961 | + | 0.983120i | \(0.441432\pi\) |
−0.942887 | + | 0.333111i | \(0.891901\pi\) | |||||||
\(920\) | 1.69869 | + | 2.94222i | 0.0560042 | + | 0.0970021i | ||||
\(921\) | −27.9885 | + | 10.0869i | −0.922254 | + | 0.332375i | ||||
\(922\) | −24.7172 | − | 14.2705i | −0.814018 | − | 0.469973i | ||||
\(923\) | −6.24239 | −0.205471 | ||||||||
\(924\) | −14.6186 | + | 9.68737i | −0.480916 | + | 0.318691i | ||||
\(925\) | −29.7272 | −0.977424 | ||||||||
\(926\) | 31.3721 | + | 18.1127i | 1.03095 | + | 0.595221i | ||||
\(927\) | −15.6071 | + | 2.65032i | −0.512605 | + | 0.0870480i | ||||
\(928\) | −0.334777 | − | 0.579851i | −0.0109896 | − | 0.0190346i | ||||
\(929\) | 6.38850 | − | 11.0652i | 0.209600 | − | 0.363038i | −0.741989 | − | 0.670413i | \(-0.766117\pi\) |
0.951589 | + | 0.307375i | \(0.0994505\pi\) | |||||||
\(930\) | −1.25331 | − | 0.225080i | −0.0410977 | − | 0.00738068i | ||||
\(931\) | −12.7196 | + | 19.9083i | −0.416868 | + | 0.652468i | ||||
\(932\) | 2.38972i | 0.0782778i | ||||||||
\(933\) | 34.8016 | − | 41.2096i | 1.13935 | − | 1.34914i | ||||
\(934\) | 2.06953 | − | 1.19484i | 0.0677171 | − | 0.0390965i | ||||
\(935\) | 2.35776 | − | 1.36125i | 0.0771070 | − | 0.0445178i | ||||
\(936\) | −2.31028 | + | 1.91379i | −0.0755138 | + | 0.0625543i | ||||
\(937\) | 8.53335i | 0.278772i | 0.990238 | + | 0.139386i | \(0.0445130\pi\) | ||||
−0.990238 | + | 0.139386i | \(0.955487\pi\) | |||||||
\(938\) | −17.9905 | + | 17.1996i | −0.587411 | + | 0.561588i | ||||
\(939\) | −2.33246 | + | 12.9878i | −0.0761168 | + | 0.423840i | ||||
\(940\) | −3.99433 | + | 6.91837i | −0.130281 | + | 0.225652i | ||||
\(941\) | −0.0600360 | − | 0.103985i | −0.00195712 | − | 0.00338983i | 0.865045 | − | 0.501694i | \(-0.167290\pi\) |
−0.867002 | + | 0.498304i | \(0.833956\pi\) | |||||||
\(942\) | 2.93870 | + | 8.15412i | 0.0957479 | + | 0.265676i | ||||
\(943\) | −5.21656 | − | 3.01178i | −0.169874 | − | 0.0980771i | ||||
\(944\) | −3.96116 | −0.128925 | ||||||||
\(945\) | −10.1657 | − | 3.07519i | −0.330692 | − | 0.100036i | ||||
\(946\) | −4.55149 | −0.147982 | ||||||||
\(947\) | 12.7440 | + | 7.35774i | 0.414124 | + | 0.239094i | 0.692560 | − | 0.721360i | \(-0.256483\pi\) |
−0.278436 | + | 0.960455i | \(0.589816\pi\) | |||||||
\(948\) | 7.60933 | + | 21.1139i | 0.247140 | + | 0.685748i | ||||
\(949\) | 4.40758 | + | 7.63416i | 0.143076 | + | 0.247815i | ||||
\(950\) | 7.43028 | − | 12.8696i | 0.241070 | − | 0.417546i | ||||
\(951\) | −6.58483 | + | 36.6663i | −0.213528 | + | 1.18898i | ||||
\(952\) | 2.33862 | + | 0.683304i | 0.0757951 | + | 0.0221460i | ||||
\(953\) | 6.79346i | 0.220062i | 0.993928 | + | 0.110031i | \(0.0350950\pi\) | ||||
−0.993928 | + | 0.110031i | \(0.964905\pi\) | |||||||
\(954\) | 19.4792 | − | 16.1362i | 0.630663 | − | 0.522430i | ||||
\(955\) | −17.0527 | + | 9.84538i | −0.551812 | + | 0.318589i | ||||
\(956\) | −1.58575 | + | 0.915531i | −0.0512867 | + | 0.0296104i | ||||
\(957\) | 2.86347 | − | 3.39072i | 0.0925628 | − | 0.109606i | ||||
\(958\) | − | 35.2664i | − | 1.13941i | ||||||
\(959\) | −36.0644 | − | 10.5374i | −1.16458 | − | 0.340271i | ||||
\(960\) | −1.31701 | − | 0.236520i | −0.0425064 | − | 0.00763365i | ||||
\(961\) | −15.0472 | + | 26.0625i | −0.485393 | + | 0.840726i | ||||
\(962\) | 3.37565 | + | 5.84680i | 0.108835 | + | 0.188508i | ||||
\(963\) | 55.0115 | − | 9.34177i | 1.77272 | − | 0.301034i | ||||
\(964\) | 23.6939 | + | 13.6797i | 0.763130 | + | 0.440593i | ||||
\(965\) | 7.85549 | 0.252877 | ||||||||
\(966\) | −20.1144 | + | 1.24132i | −0.647170 | + | 0.0399389i | ||||
\(967\) | 44.6854 | 1.43699 | 0.718493 | − | 0.695534i | \(-0.244832\pi\) | ||||
0.718493 | + | 0.695534i | \(0.244832\pi\) | |||||||
\(968\) | −3.15680 | − | 1.82258i | −0.101464 | − | 0.0585800i | ||||
\(969\) | −5.06422 | + | 1.82511i | −0.162686 | + | 0.0586311i | ||||
\(970\) | 3.63672 | + | 6.29898i | 0.116768 | + | 0.202248i | ||||
\(971\) | 26.1343 | − | 45.2659i | 0.838689 | − | 1.45265i | −0.0523020 | − | 0.998631i | \(-0.516656\pi\) |
0.890991 | − | 0.454021i | \(-0.150011\pi\) | |||||||
\(972\) | 9.83007 | + | 12.0983i | 0.315300 | + | 0.388054i | ||||
\(973\) | 16.9662 | − | 16.2203i | 0.543911 | − | 0.520000i | ||||
\(974\) | 20.3877i | 0.653263i | ||||||||
\(975\) | −5.82673 | − | 4.92068i | −0.186605 | − | 0.157588i | ||||
\(976\) | 0.358567 | − | 0.207019i | 0.0114775 | − | 0.00662652i | ||||
\(977\) | 36.1257 | − | 20.8572i | 1.15576 | − | 0.667280i | 0.205479 | − | 0.978662i | \(-0.434125\pi\) |
0.950285 | + | 0.311381i | \(0.100792\pi\) | |||||||
\(978\) | −32.5316 | − | 27.4730i | −1.04025 | − | 0.878490i | ||||
\(979\) | − | 15.3799i | − | 0.491543i | ||||||
\(980\) | −0.242946 | + | 5.40233i | −0.00776062 | + | 0.172571i | ||||
\(981\) | 30.1575 | + | 11.1929i | 0.962856 | + | 0.357361i | ||||
\(982\) | 11.2860 | − | 19.5479i | 0.360151 | − | 0.623800i | ||||
\(983\) | 18.6067 | + | 32.2278i | 0.593462 | + | 1.02791i | 0.993762 | + | 0.111522i | \(0.0355724\pi\) |
−0.400300 | + | 0.916384i | \(0.631094\pi\) | |||||||
\(984\) | 2.23190 | − | 0.804364i | 0.0711503 | − | 0.0256422i | ||||
\(985\) | −0.985342 | − | 0.568888i | −0.0313956 | − | 0.0181263i | ||||
\(986\) | −0.616575 | −0.0196358 | ||||||||
\(987\) | −26.1764 | − | 39.5012i | −0.833205 | − | 1.25734i | ||||
\(988\) | −3.37496 | −0.107372 | ||||||||
\(989\) | −4.52960 | − | 2.61517i | −0.144033 | − | 0.0831574i | ||||
\(990\) | −1.48489 | − | 8.74414i | −0.0471928 | − | 0.277907i | ||||
\(991\) | −13.6848 | − | 23.7027i | −0.434711 | − | 0.752942i | 0.562561 | − | 0.826756i | \(-0.309816\pi\) |
−0.997272 | + | 0.0738138i | \(0.976483\pi\) | |||||||
\(992\) | 0.475817 | − | 0.824139i | 0.0151072 | − | 0.0261664i | ||||
\(993\) | 2.68166 | + | 0.481595i | 0.0850998 | + | 0.0152829i | ||||
\(994\) | 16.0451 | − | 3.91509i | 0.508919 | − | 0.124179i | ||||
\(995\) | − | 14.7240i | − | 0.466781i | ||||||
\(996\) | 2.48338 | − | 2.94064i | 0.0786888 | − | 0.0931779i | ||||
\(997\) | −32.7195 | + | 18.8906i | −1.03624 | + | 0.598272i | −0.918765 | − | 0.394804i | \(-0.870812\pi\) |
−0.117472 | + | 0.993076i | \(0.537479\pi\) | |||||||
\(998\) | 3.91989 | − | 2.26315i | 0.124082 | − | 0.0716387i | ||||
\(999\) | 30.5458 | − | 17.2515i | 0.966428 | − | 0.545813i |
(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.z.a.131.6 | ✓ | 32 | |
3.2 | odd | 2 | 546.2.z.b.131.11 | yes | 32 | ||
7.3 | odd | 6 | 546.2.z.b.521.11 | yes | 32 | ||
21.17 | even | 6 | inner | 546.2.z.a.521.6 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.z.a.131.6 | ✓ | 32 | 1.1 | even | 1 | trivial | |
546.2.z.a.521.6 | yes | 32 | 21.17 | even | 6 | inner | |
546.2.z.b.131.11 | yes | 32 | 3.2 | odd | 2 | ||
546.2.z.b.521.11 | yes | 32 | 7.3 | odd | 6 |