Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(451,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.451");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.i (of order \(3\), 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: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 5x^{2} + 4x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 451.1 | ||
Root | \(-0.780776 - 1.35234i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.451 |
Dual form | 1950.2.i.z.601.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | ||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | −0.280776 | − | 0.486319i | −0.106124 | − | 0.183811i | 0.808073 | − | 0.589082i | \(-0.200511\pi\) |
−0.914197 | + | 0.405271i | \(0.867177\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.78078 | + | 3.08440i | −0.536924 | + | 0.929980i | 0.462143 | + | 0.886805i | \(0.347081\pi\) |
−0.999068 | + | 0.0431749i | \(0.986253\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −3.34233 | − | 1.35234i | −0.926995 | − | 0.375073i | ||||
\(14\) | 0.561553 | 0.150081 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.56155 | − | 4.43674i | −0.621268 | − | 1.07607i | −0.989250 | − | 0.146235i | \(-0.953285\pi\) |
0.367982 | − | 0.929833i | \(-0.380049\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 3.28078 | + | 5.68247i | 0.752662 | + | 1.30365i | 0.946528 | + | 0.322620i | \(0.104564\pi\) |
−0.193867 | + | 0.981028i | \(0.562103\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.561553 | 0.122541 | ||||||||
\(22\) | −1.78078 | − | 3.08440i | −0.379663 | − | 0.657595i | ||||
\(23\) | −2.34233 | + | 4.05703i | −0.488409 | + | 0.845950i | −0.999911 | − | 0.0133324i | \(-0.995756\pi\) |
0.511502 | + | 0.859282i | \(0.329089\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.84233 | − | 2.21837i | 0.557427 | − | 0.435058i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.280776 | + | 0.486319i | −0.0530618 | + | 0.0919057i | ||||
\(29\) | 3.56155 | − | 6.16879i | 0.661364 | − | 1.14552i | −0.318894 | − | 0.947790i | \(-0.603311\pi\) |
0.980257 | − | 0.197725i | \(-0.0633554\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −1.78078 | − | 3.08440i | −0.309993 | − | 0.536924i | ||||
\(34\) | 5.12311 | 0.878605 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 1.78078 | − | 3.08440i | 0.292758 | − | 0.507071i | −0.681703 | − | 0.731629i | \(-0.738760\pi\) |
0.974461 | + | 0.224558i | \(0.0720937\pi\) | |||||||
\(38\) | −6.56155 | −1.06442 | ||||||||
\(39\) | 2.84233 | − | 2.21837i | 0.455137 | − | 0.355223i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.56155 | + | 4.43674i | −0.400047 | + | 0.692902i | −0.993731 | − | 0.111796i | \(-0.964340\pi\) |
0.593684 | + | 0.804698i | \(0.297673\pi\) | |||||||
\(42\) | −0.280776 | + | 0.486319i | −0.0433247 | + | 0.0750407i | ||||
\(43\) | −2.28078 | − | 3.95042i | −0.347815 | − | 0.602433i | 0.638046 | − | 0.769998i | \(-0.279743\pi\) |
−0.985861 | + | 0.167565i | \(0.946410\pi\) | |||||||
\(44\) | 3.56155 | 0.536924 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.34233 | − | 4.05703i | −0.345358 | − | 0.598177i | ||||
\(47\) | 4.00000 | 0.583460 | 0.291730 | − | 0.956501i | \(-0.405769\pi\) | ||||
0.291730 | + | 0.956501i | \(0.405769\pi\) | |||||||
\(48\) | −0.500000 | − | 0.866025i | −0.0721688 | − | 0.125000i | ||||
\(49\) | 3.34233 | − | 5.78908i | 0.477476 | − | 0.827012i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.12311 | 0.717378 | ||||||||
\(52\) | 0.500000 | + | 3.57071i | 0.0693375 | + | 0.495169i | ||||
\(53\) | −12.2462 | −1.68215 | −0.841073 | − | 0.540921i | \(-0.818076\pi\) | ||||
−0.841073 | + | 0.540921i | \(0.818076\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.280776 | − | 0.486319i | −0.0375203 | − | 0.0649871i | ||||
\(57\) | −6.56155 | −0.869099 | ||||||||
\(58\) | 3.56155 | + | 6.16879i | 0.467655 | + | 0.810002i | ||||
\(59\) | −3.12311 | − | 5.40938i | −0.406594 | − | 0.704241i | 0.587912 | − | 0.808925i | \(-0.299950\pi\) |
−0.994506 | + | 0.104684i | \(0.966617\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.34233 | − | 9.25319i | −0.684015 | − | 1.18475i | −0.973745 | − | 0.227641i | \(-0.926899\pi\) |
0.289730 | − | 0.957108i | \(-0.406434\pi\) | |||||||
\(62\) | −2.00000 | + | 3.46410i | −0.254000 | + | 0.439941i | ||||
\(63\) | −0.280776 | + | 0.486319i | −0.0353745 | + | 0.0612704i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.56155 | 0.438397 | ||||||||
\(67\) | 4.40388 | − | 7.62775i | 0.538020 | − | 0.931878i | −0.460991 | − | 0.887405i | \(-0.652506\pi\) |
0.999011 | − | 0.0444727i | \(-0.0141608\pi\) | |||||||
\(68\) | −2.56155 | + | 4.43674i | −0.310634 | + | 0.538034i | ||||
\(69\) | −2.34233 | − | 4.05703i | −0.281983 | − | 0.488409i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.21922 | − | 7.30791i | −0.500730 | − | 0.867289i | −1.00000 | 0.000842810i | \(-0.999732\pi\) | |
0.499270 | − | 0.866447i | \(-0.333602\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 9.00000 | 1.05337 | 0.526685 | − | 0.850060i | \(-0.323435\pi\) | ||||
0.526685 | + | 0.850060i | \(0.323435\pi\) | |||||||
\(74\) | 1.78078 | + | 3.08440i | 0.207011 | + | 0.358554i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.28078 | − | 5.68247i | 0.376331 | − | 0.651824i | ||||
\(77\) | 2.00000 | 0.227921 | ||||||||
\(78\) | 0.500000 | + | 3.57071i | 0.0566139 | + | 0.404304i | ||||
\(79\) | 4.80776 | 0.540916 | 0.270458 | − | 0.962732i | \(-0.412825\pi\) | ||||
0.270458 | + | 0.962732i | \(0.412825\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −2.56155 | − | 4.43674i | −0.282876 | − | 0.489956i | ||||
\(83\) | 2.43845 | 0.267654 | 0.133827 | − | 0.991005i | \(-0.457273\pi\) | ||||
0.133827 | + | 0.991005i | \(0.457273\pi\) | |||||||
\(84\) | −0.280776 | − | 0.486319i | −0.0306352 | − | 0.0530618i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.56155 | 0.491885 | ||||||||
\(87\) | 3.56155 | + | 6.16879i | 0.381839 | + | 0.661364i | ||||
\(88\) | −1.78078 | + | 3.08440i | −0.189831 | + | 0.328798i | ||||
\(89\) | 3.12311 | − | 5.40938i | 0.331049 | − | 0.573393i | −0.651669 | − | 0.758503i | \(-0.725931\pi\) |
0.982718 | + | 0.185110i | \(0.0592643\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.280776 | + | 2.00514i | 0.0294334 | + | 0.210196i | ||||
\(92\) | 4.68466 | 0.488409 | ||||||||
\(93\) | −2.00000 | + | 3.46410i | −0.207390 | + | 0.359211i | ||||
\(94\) | −2.00000 | + | 3.46410i | −0.206284 | + | 0.357295i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −8.90388 | − | 15.4220i | −0.904052 | − | 1.56586i | −0.822184 | − | 0.569221i | \(-0.807245\pi\) |
−0.0818678 | − | 0.996643i | \(-0.526089\pi\) | |||||||
\(98\) | 3.34233 | + | 5.78908i | 0.337626 | + | 0.584786i | ||||
\(99\) | 3.56155 | 0.357950 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.12311 | + | 8.87348i | −0.509768 | + | 0.882944i | 0.490168 | + | 0.871628i | \(0.336935\pi\) |
−0.999936 | + | 0.0113162i | \(0.996398\pi\) | |||||||
\(102\) | −2.56155 | + | 4.43674i | −0.253632 | + | 0.439303i | ||||
\(103\) | −8.56155 | −0.843595 | −0.421797 | − | 0.906690i | \(-0.638601\pi\) | ||||
−0.421797 | + | 0.906690i | \(0.638601\pi\) | |||||||
\(104\) | −3.34233 | − | 1.35234i | −0.327742 | − | 0.132608i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.12311 | − | 10.6055i | 0.594729 | − | 1.03010i | ||||
\(107\) | 9.68466 | − | 16.7743i | 0.936251 | − | 1.62163i | 0.163864 | − | 0.986483i | \(-0.447604\pi\) |
0.772387 | − | 0.635152i | \(-0.219062\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | 17.8078 | 1.70567 | 0.852837 | − | 0.522177i | \(-0.174880\pi\) | ||||
0.852837 | + | 0.522177i | \(0.174880\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.78078 | + | 3.08440i | 0.169024 | + | 0.292758i | ||||
\(112\) | 0.561553 | 0.0530618 | ||||||||
\(113\) | −2.00000 | − | 3.46410i | −0.188144 | − | 0.325875i | 0.756487 | − | 0.654008i | \(-0.226914\pi\) |
−0.944632 | + | 0.328133i | \(0.893581\pi\) | |||||||
\(114\) | 3.28078 | − | 5.68247i | 0.307273 | − | 0.532212i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.12311 | −0.661364 | ||||||||
\(117\) | 0.500000 | + | 3.57071i | 0.0462250 | + | 0.330113i | ||||
\(118\) | 6.24621 | 0.575010 | ||||||||
\(119\) | −1.43845 | + | 2.49146i | −0.131862 | + | 0.228392i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.842329 | − | 1.45896i | −0.0765754 | − | 0.132632i | ||||
\(122\) | 10.6847 | 0.967344 | ||||||||
\(123\) | −2.56155 | − | 4.43674i | −0.230967 | − | 0.400047i | ||||
\(124\) | −2.00000 | − | 3.46410i | −0.179605 | − | 0.311086i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.280776 | − | 0.486319i | −0.0250136 | − | 0.0433247i | ||||
\(127\) | −0.596118 | + | 1.03251i | −0.0528969 | + | 0.0916201i | −0.891261 | − | 0.453490i | \(-0.850179\pi\) |
0.838364 | + | 0.545110i | \(0.183512\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 4.56155 | 0.401622 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.12311 | 0.797089 | 0.398545 | − | 0.917149i | \(-0.369515\pi\) | ||||
0.398545 | + | 0.917149i | \(0.369515\pi\) | |||||||
\(132\) | −1.78078 | + | 3.08440i | −0.154997 | + | 0.268462i | ||||
\(133\) | 1.84233 | − | 3.19101i | 0.159750 | − | 0.276695i | ||||
\(134\) | 4.40388 | + | 7.62775i | 0.380437 | + | 0.658937i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.56155 | − | 4.43674i | −0.219651 | − | 0.380447i | ||||
\(137\) | 8.24621 | + | 14.2829i | 0.704521 | + | 1.22027i | 0.966864 | + | 0.255292i | \(0.0821716\pi\) |
−0.262343 | + | 0.964975i | \(0.584495\pi\) | |||||||
\(138\) | 4.68466 | 0.398785 | ||||||||
\(139\) | −8.71922 | − | 15.1021i | −0.739555 | − | 1.28095i | −0.952696 | − | 0.303925i | \(-0.901703\pi\) |
0.213141 | − | 0.977021i | \(-0.431631\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00000 | + | 3.46410i | −0.168430 | + | 0.291730i | ||||
\(142\) | 8.43845 | 0.708139 | ||||||||
\(143\) | 10.1231 | − | 7.90084i | 0.846537 | − | 0.660702i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.50000 | + | 7.79423i | −0.372423 | + | 0.645055i | ||||
\(147\) | 3.34233 | + | 5.78908i | 0.275671 | + | 0.477476i | ||||
\(148\) | −3.56155 | −0.292758 | ||||||||
\(149\) | −3.12311 | − | 5.40938i | −0.255855 | − | 0.443153i | 0.709273 | − | 0.704934i | \(-0.249024\pi\) |
−0.965127 | + | 0.261781i | \(0.915690\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.31534 | −0.351178 | −0.175589 | − | 0.984464i | \(-0.556183\pi\) | ||||
−0.175589 | + | 0.984464i | \(0.556183\pi\) | |||||||
\(152\) | 3.28078 | + | 5.68247i | 0.266106 | + | 0.460909i | ||||
\(153\) | −2.56155 | + | 4.43674i | −0.207089 | + | 0.358689i | ||||
\(154\) | −1.00000 | + | 1.73205i | −0.0805823 | + | 0.139573i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.34233 | − | 1.35234i | −0.267601 | − | 0.108274i | ||||
\(157\) | 0.753789 | 0.0601589 | 0.0300794 | − | 0.999548i | \(-0.490424\pi\) | ||||
0.0300794 | + | 0.999548i | \(0.490424\pi\) | |||||||
\(158\) | −2.40388 | + | 4.16365i | −0.191243 | + | 0.331242i | ||||
\(159\) | 6.12311 | − | 10.6055i | 0.485594 | − | 0.841073i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.63068 | 0.207327 | ||||||||
\(162\) | −0.500000 | − | 0.866025i | −0.0392837 | − | 0.0680414i | ||||
\(163\) | −8.24621 | − | 14.2829i | −0.645893 | − | 1.11872i | −0.984094 | − | 0.177646i | \(-0.943152\pi\) |
0.338201 | − | 0.941074i | \(-0.390182\pi\) | |||||||
\(164\) | 5.12311 | 0.400047 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.21922 | + | 2.11176i | −0.0946301 | + | 0.163904i | ||||
\(167\) | −5.65767 | + | 9.79937i | −0.437804 | + | 0.758298i | −0.997520 | − | 0.0703862i | \(-0.977577\pi\) |
0.559716 | + | 0.828684i | \(0.310910\pi\) | |||||||
\(168\) | 0.561553 | 0.0433247 | ||||||||
\(169\) | 9.34233 | + | 9.03996i | 0.718641 | + | 0.695382i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.28078 | − | 5.68247i | 0.250887 | − | 0.434549i | ||||
\(172\) | −2.28078 | + | 3.95042i | −0.173908 | + | 0.301217i | ||||
\(173\) | 8.56155 | + | 14.8290i | 0.650923 | + | 1.12743i | 0.982899 | + | 0.184144i | \(0.0589512\pi\) |
−0.331977 | + | 0.943288i | \(0.607715\pi\) | |||||||
\(174\) | −7.12311 | −0.540001 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.78078 | − | 3.08440i | −0.134231 | − | 0.232495i | ||||
\(177\) | 6.24621 | 0.469494 | ||||||||
\(178\) | 3.12311 | + | 5.40938i | 0.234087 | + | 0.405450i | ||||
\(179\) | 1.65767 | − | 2.87117i | 0.123900 | − | 0.214601i | −0.797402 | − | 0.603448i | \(-0.793793\pi\) |
0.921302 | + | 0.388847i | \(0.127126\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.4924 | 1.30020 | 0.650101 | − | 0.759848i | \(-0.274727\pi\) | ||||
0.650101 | + | 0.759848i | \(0.274727\pi\) | |||||||
\(182\) | −1.87689 | − | 0.759413i | −0.139125 | − | 0.0562914i | ||||
\(183\) | 10.6847 | 0.789833 | ||||||||
\(184\) | −2.34233 | + | 4.05703i | −0.172679 | + | 0.299088i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.00000 | − | 3.46410i | −0.146647 | − | 0.254000i | ||||
\(187\) | 18.2462 | 1.33430 | ||||||||
\(188\) | −2.00000 | − | 3.46410i | −0.145865 | − | 0.252646i | ||||
\(189\) | −0.280776 | − | 0.486319i | −0.0204235 | − | 0.0353745i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.46543 | + | 11.1985i | 0.467822 | + | 0.810292i | 0.999324 | − | 0.0367651i | \(-0.0117053\pi\) |
−0.531501 | + | 0.847057i | \(0.678372\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | −1.50000 | + | 2.59808i | −0.107972 | + | 0.187014i | −0.914949 | − | 0.403570i | \(-0.867769\pi\) |
0.806976 | + | 0.590584i | \(0.201102\pi\) | |||||||
\(194\) | 17.8078 | 1.27852 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.68466 | −0.477476 | ||||||||
\(197\) | 1.56155 | − | 2.70469i | 0.111256 | − | 0.192701i | −0.805021 | − | 0.593246i | \(-0.797846\pi\) |
0.916277 | + | 0.400545i | \(0.131179\pi\) | |||||||
\(198\) | −1.78078 | + | 3.08440i | −0.126554 | + | 0.219198i | ||||
\(199\) | 4.28078 | + | 7.41452i | 0.303456 | + | 0.525602i | 0.976916 | − | 0.213622i | \(-0.0685261\pi\) |
−0.673460 | + | 0.739223i | \(0.735193\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.40388 | + | 7.62775i | 0.310626 | + | 0.538020i | ||||
\(202\) | −5.12311 | − | 8.87348i | −0.360460 | − | 0.624336i | ||||
\(203\) | −4.00000 | −0.280745 | ||||||||
\(204\) | −2.56155 | − | 4.43674i | −0.179345 | − | 0.310634i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.28078 | − | 7.41452i | 0.298256 | − | 0.516594i | ||||
\(207\) | 4.68466 | 0.325606 | ||||||||
\(208\) | 2.84233 | − | 2.21837i | 0.197080 | − | 0.153816i | ||||
\(209\) | −23.3693 | −1.61649 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.56155 | − | 6.16879i | 0.245187 | − | 0.424677i | −0.716997 | − | 0.697076i | \(-0.754484\pi\) |
0.962184 | + | 0.272399i | \(0.0878172\pi\) | |||||||
\(212\) | 6.12311 | + | 10.6055i | 0.420537 | + | 0.728391i | ||||
\(213\) | 8.43845 | 0.578193 | ||||||||
\(214\) | 9.68466 | + | 16.7743i | 0.662030 | + | 1.14667i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −1.12311 | − | 1.94528i | −0.0762414 | − | 0.132054i | ||||
\(218\) | −8.90388 | + | 15.4220i | −0.603047 | + | 1.04451i | ||||
\(219\) | −4.50000 | + | 7.79423i | −0.304082 | + | 0.526685i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.56155 | + | 18.2931i | 0.172309 | + | 1.23053i | ||||
\(222\) | −3.56155 | −0.239036 | ||||||||
\(223\) | 2.28078 | − | 3.95042i | 0.152732 | − | 0.264540i | −0.779499 | − | 0.626404i | \(-0.784526\pi\) |
0.932231 | + | 0.361864i | \(0.117860\pi\) | |||||||
\(224\) | −0.280776 | + | 0.486319i | −0.0187602 | + | 0.0324936i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.00000 | 0.266076 | ||||||||
\(227\) | −8.65767 | − | 14.9955i | −0.574630 | − | 0.995288i | −0.996082 | − | 0.0884373i | \(-0.971813\pi\) |
0.421452 | − | 0.906851i | \(-0.361521\pi\) | |||||||
\(228\) | 3.28078 | + | 5.68247i | 0.217275 | + | 0.376331i | ||||
\(229\) | −23.4924 | −1.55242 | −0.776211 | − | 0.630473i | \(-0.782861\pi\) | ||||
−0.776211 | + | 0.630473i | \(0.782861\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.00000 | + | 1.73205i | −0.0657952 | + | 0.113961i | ||||
\(232\) | 3.56155 | − | 6.16879i | 0.233827 | − | 0.405001i | ||||
\(233\) | −0.630683 | −0.0413174 | −0.0206587 | − | 0.999787i | \(-0.506576\pi\) | ||||
−0.0206587 | + | 0.999787i | \(0.506576\pi\) | |||||||
\(234\) | −3.34233 | − | 1.35234i | −0.218495 | − | 0.0884055i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.12311 | + | 5.40938i | −0.203297 | + | 0.352120i | ||||
\(237\) | −2.40388 | + | 4.16365i | −0.156149 | + | 0.270458i | ||||
\(238\) | −1.43845 | − | 2.49146i | −0.0932407 | − | 0.161498i | ||||
\(239\) | −10.0540 | −0.650338 | −0.325169 | − | 0.945656i | \(-0.605421\pi\) | ||||
−0.325169 | + | 0.945656i | \(0.605421\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.71922 | − | 9.90599i | −0.368408 | − | 0.638101i | 0.620909 | − | 0.783883i | \(-0.286764\pi\) |
−0.989317 | + | 0.145782i | \(0.953430\pi\) | |||||||
\(242\) | 1.68466 | 0.108294 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −5.34233 | + | 9.25319i | −0.342008 | + | 0.592375i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.12311 | 0.326637 | ||||||||
\(247\) | −3.28078 | − | 23.4294i | −0.208751 | − | 1.49078i | ||||
\(248\) | 4.00000 | 0.254000 | ||||||||
\(249\) | −1.21922 | + | 2.11176i | −0.0772652 | + | 0.133827i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.46543 | + | 4.27026i | 0.155617 | + | 0.269536i | 0.933283 | − | 0.359141i | \(-0.116930\pi\) |
−0.777667 | + | 0.628677i | \(0.783597\pi\) | |||||||
\(252\) | 0.561553 | 0.0353745 | ||||||||
\(253\) | −8.34233 | − | 14.4493i | −0.524478 | − | 0.908422i | ||||
\(254\) | −0.596118 | − | 1.03251i | −0.0374038 | − | 0.0647852i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −13.8078 | + | 23.9157i | −0.861305 | + | 1.49182i | 0.00936553 | + | 0.999956i | \(0.497019\pi\) |
−0.870670 | + | 0.491867i | \(0.836315\pi\) | |||||||
\(258\) | −2.28078 | + | 3.95042i | −0.141995 | + | 0.245942i | ||||
\(259\) | −2.00000 | −0.124274 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.12311 | −0.440909 | ||||||||
\(262\) | −4.56155 | + | 7.90084i | −0.281814 | + | 0.488116i | ||||
\(263\) | −9.34233 | + | 16.1814i | −0.576073 | + | 0.997787i | 0.419851 | + | 0.907593i | \(0.362082\pi\) |
−0.995924 | + | 0.0901944i | \(0.971251\pi\) | |||||||
\(264\) | −1.78078 | − | 3.08440i | −0.109599 | − | 0.189831i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.84233 | + | 3.19101i | 0.112960 | + | 0.195653i | ||||
\(267\) | 3.12311 | + | 5.40938i | 0.191131 | + | 0.331049i | ||||
\(268\) | −8.80776 | −0.538020 | ||||||||
\(269\) | −10.6847 | − | 18.5064i | −0.651455 | − | 1.12835i | −0.982770 | − | 0.184833i | \(-0.940826\pi\) |
0.331315 | − | 0.943520i | \(-0.392508\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.96543 | − | 17.2606i | 0.605357 | − | 1.04851i | −0.386638 | − | 0.922232i | \(-0.626364\pi\) |
0.991995 | − | 0.126278i | \(-0.0403030\pi\) | |||||||
\(272\) | 5.12311 | 0.310634 | ||||||||
\(273\) | −1.87689 | − | 0.759413i | −0.113595 | − | 0.0459618i | ||||
\(274\) | −16.4924 | −0.996344 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.34233 | + | 4.05703i | −0.140992 | + | 0.244205i | ||||
\(277\) | −2.50000 | − | 4.33013i | −0.150210 | − | 0.260172i | 0.781094 | − | 0.624413i | \(-0.214662\pi\) |
−0.931305 | + | 0.364241i | \(0.881328\pi\) | |||||||
\(278\) | 17.4384 | 1.04589 | ||||||||
\(279\) | −2.00000 | − | 3.46410i | −0.119737 | − | 0.207390i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.2462 | −1.08848 | −0.544239 | − | 0.838930i | \(-0.683181\pi\) | ||||
−0.544239 | + | 0.838930i | \(0.683181\pi\) | |||||||
\(282\) | −2.00000 | − | 3.46410i | −0.119098 | − | 0.206284i | ||||
\(283\) | 5.80776 | − | 10.0593i | 0.345236 | − | 0.597966i | −0.640161 | − | 0.768241i | \(-0.721132\pi\) |
0.985397 | + | 0.170275i | \(0.0544656\pi\) | |||||||
\(284\) | −4.21922 | + | 7.30791i | −0.250365 | + | 0.433645i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.78078 | + | 12.7173i | 0.105300 | + | 0.751989i | ||||
\(287\) | 2.87689 | 0.169818 | ||||||||
\(288\) | −0.500000 | + | 0.866025i | −0.0294628 | + | 0.0510310i | ||||
\(289\) | −4.62311 | + | 8.00745i | −0.271947 | + | 0.471027i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.8078 | 1.04391 | ||||||||
\(292\) | −4.50000 | − | 7.79423i | −0.263343 | − | 0.456123i | ||||
\(293\) | −1.87689 | − | 3.25088i | −0.109649 | − | 0.189918i | 0.805979 | − | 0.591944i | \(-0.201639\pi\) |
−0.915628 | + | 0.402026i | \(0.868306\pi\) | |||||||
\(294\) | −6.68466 | −0.389857 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.78078 | − | 3.08440i | 0.103506 | − | 0.179277i | ||||
\(297\) | −1.78078 | + | 3.08440i | −0.103331 | + | 0.178975i | ||||
\(298\) | 6.24621 | 0.361833 | ||||||||
\(299\) | 13.3153 | − | 10.3923i | 0.770046 | − | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.28078 | + | 2.21837i | −0.0738227 | + | 0.127865i | ||||
\(302\) | 2.15767 | − | 3.73720i | 0.124160 | − | 0.215051i | ||||
\(303\) | −5.12311 | − | 8.87348i | −0.294315 | − | 0.509768i | ||||
\(304\) | −6.56155 | −0.376331 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.56155 | − | 4.43674i | −0.146434 | − | 0.253632i | ||||
\(307\) | 5.75379 | 0.328386 | 0.164193 | − | 0.986428i | \(-0.447498\pi\) | ||||
0.164193 | + | 0.986428i | \(0.447498\pi\) | |||||||
\(308\) | −1.00000 | − | 1.73205i | −0.0569803 | − | 0.0986928i | ||||
\(309\) | 4.28078 | − | 7.41452i | 0.243525 | − | 0.421797i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.6847 | −1.28633 | −0.643164 | − | 0.765728i | \(-0.722379\pi\) | ||||
−0.643164 | + | 0.765728i | \(0.722379\pi\) | |||||||
\(312\) | 2.84233 | − | 2.21837i | 0.160915 | − | 0.125590i | ||||
\(313\) | 31.0000 | 1.75222 | 0.876112 | − | 0.482108i | \(-0.160129\pi\) | ||||
0.876112 | + | 0.482108i | \(0.160129\pi\) | |||||||
\(314\) | −0.376894 | + | 0.652800i | −0.0212694 | + | 0.0368396i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.40388 | − | 4.16365i | −0.135229 | − | 0.234223i | ||||
\(317\) | −0.246211 | −0.0138286 | −0.00691430 | − | 0.999976i | \(-0.502201\pi\) | ||||
−0.00691430 | + | 0.999976i | \(0.502201\pi\) | |||||||
\(318\) | 6.12311 | + | 10.6055i | 0.343367 | + | 0.594729i | ||||
\(319\) | 12.6847 | + | 21.9705i | 0.710205 | + | 1.23011i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.68466 | + | 16.7743i | 0.540545 | + | 0.936251i | ||||
\(322\) | −1.31534 | + | 2.27824i | −0.0733011 | + | 0.126961i | ||||
\(323\) | 16.8078 | − | 29.1119i | 0.935209 | − | 1.61983i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16.4924 | 0.913431 | ||||||||
\(327\) | −8.90388 | + | 15.4220i | −0.492386 | + | 0.852837i | ||||
\(328\) | −2.56155 | + | 4.43674i | −0.141438 | + | 0.244978i | ||||
\(329\) | −1.12311 | − | 1.94528i | −0.0619188 | − | 0.107247i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.15767 | + | 3.73720i | 0.118596 | + | 0.205415i | 0.919212 | − | 0.393764i | \(-0.128827\pi\) |
−0.800615 | + | 0.599179i | \(0.795494\pi\) | |||||||
\(332\) | −1.21922 | − | 2.11176i | −0.0669136 | − | 0.115898i | ||||
\(333\) | −3.56155 | −0.195172 | ||||||||
\(334\) | −5.65767 | − | 9.79937i | −0.309574 | − | 0.536198i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.280776 | + | 0.486319i | −0.0153176 | + | 0.0265309i | ||||
\(337\) | −29.0540 | −1.58267 | −0.791335 | − | 0.611382i | \(-0.790614\pi\) | ||||
−0.791335 | + | 0.611382i | \(0.790614\pi\) | |||||||
\(338\) | −12.5000 | + | 3.57071i | −0.679910 | + | 0.194221i | ||||
\(339\) | 4.00000 | 0.217250 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.12311 | + | 12.3376i | −0.385738 | + | 0.668117i | ||||
\(342\) | 3.28078 | + | 5.68247i | 0.177404 | + | 0.307273i | ||||
\(343\) | −7.68466 | −0.414933 | ||||||||
\(344\) | −2.28078 | − | 3.95042i | −0.122971 | − | 0.212992i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.1231 | −0.920544 | ||||||||
\(347\) | 2.09612 | + | 3.63058i | 0.112526 | + | 0.194900i | 0.916788 | − | 0.399374i | \(-0.130773\pi\) |
−0.804262 | + | 0.594274i | \(0.797439\pi\) | |||||||
\(348\) | 3.56155 | − | 6.16879i | 0.190919 | − | 0.330682i | ||||
\(349\) | 1.37689 | − | 2.38485i | 0.0737035 | − | 0.127658i | −0.826818 | − | 0.562469i | \(-0.809851\pi\) |
0.900522 | + | 0.434811i | \(0.143185\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.34233 | − | 1.35234i | −0.178400 | − | 0.0721828i | ||||
\(352\) | 3.56155 | 0.189831 | ||||||||
\(353\) | 7.12311 | − | 12.3376i | 0.379125 | − | 0.656663i | −0.611810 | − | 0.791004i | \(-0.709558\pi\) |
0.990935 | + | 0.134341i | \(0.0428918\pi\) | |||||||
\(354\) | −3.12311 | + | 5.40938i | −0.165991 | + | 0.287505i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.24621 | −0.331049 | ||||||||
\(357\) | −1.43845 | − | 2.49146i | −0.0761307 | − | 0.131862i | ||||
\(358\) | 1.65767 | + | 2.87117i | 0.0876106 | + | 0.151746i | ||||
\(359\) | −13.1231 | −0.692611 | −0.346306 | − | 0.938122i | \(-0.612564\pi\) | ||||
−0.346306 | + | 0.938122i | \(0.612564\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.0270 | + | 20.8314i | −0.632999 | + | 1.09639i | ||||
\(362\) | −8.74621 | + | 15.1489i | −0.459691 | + | 0.796208i | ||||
\(363\) | 1.68466 | 0.0884216 | ||||||||
\(364\) | 1.59612 | − | 1.24573i | 0.0836593 | − | 0.0652941i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.34233 | + | 9.25319i | −0.279248 | + | 0.483672i | ||||
\(367\) | 15.4039 | − | 26.6803i | 0.804076 | − | 1.39270i | −0.112837 | − | 0.993614i | \(-0.535994\pi\) |
0.916913 | − | 0.399087i | \(-0.130673\pi\) | |||||||
\(368\) | −2.34233 | − | 4.05703i | −0.122102 | − | 0.211487i | ||||
\(369\) | 5.12311 | 0.266698 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.43845 | + | 5.95557i | 0.178515 | + | 0.309198i | ||||
\(372\) | 4.00000 | 0.207390 | ||||||||
\(373\) | −11.7462 | − | 20.3450i | −0.608196 | − | 1.05343i | −0.991538 | − | 0.129819i | \(-0.958560\pi\) |
0.383342 | − | 0.923607i | \(-0.374773\pi\) | |||||||
\(374\) | −9.12311 | + | 15.8017i | −0.471745 | + | 0.817086i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.00000 | 0.206284 | ||||||||
\(377\) | −20.2462 | + | 15.8017i | −1.04273 | + | 0.813828i | ||||
\(378\) | 0.561553 | 0.0288832 | ||||||||
\(379\) | −6.52699 | + | 11.3051i | −0.335269 | + | 0.580703i | −0.983536 | − | 0.180710i | \(-0.942160\pi\) |
0.648268 | + | 0.761413i | \(0.275494\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.596118 | − | 1.03251i | −0.0305400 | − | 0.0528969i | ||||
\(382\) | −12.9309 | −0.661601 | ||||||||
\(383\) | 4.78078 | + | 8.28055i | 0.244286 | + | 0.423116i | 0.961931 | − | 0.273293i | \(-0.0881130\pi\) |
−0.717644 | + | 0.696410i | \(0.754780\pi\) | |||||||
\(384\) | −0.500000 | − | 0.866025i | −0.0255155 | − | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.50000 | − | 2.59808i | −0.0763480 | − | 0.132239i | ||||
\(387\) | −2.28078 | + | 3.95042i | −0.115938 | + | 0.200811i | ||||
\(388\) | −8.90388 | + | 15.4220i | −0.452026 | + | 0.782932i | ||||
\(389\) | −13.3693 | −0.677851 | −0.338926 | − | 0.940813i | \(-0.610064\pi\) | ||||
−0.338926 | + | 0.940813i | \(0.610064\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000 | 1.21373 | ||||||||
\(392\) | 3.34233 | − | 5.78908i | 0.168813 | − | 0.292393i | ||||
\(393\) | −4.56155 | + | 7.90084i | −0.230100 | + | 0.398545i | ||||
\(394\) | 1.56155 | + | 2.70469i | 0.0786699 | + | 0.136260i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.78078 | − | 3.08440i | −0.0894874 | − | 0.154997i | ||||
\(397\) | −5.40388 | − | 9.35980i | −0.271213 | − | 0.469755i | 0.697960 | − | 0.716137i | \(-0.254091\pi\) |
−0.969173 | + | 0.246382i | \(0.920758\pi\) | |||||||
\(398\) | −8.56155 | −0.429152 | ||||||||
\(399\) | 1.84233 | + | 3.19101i | 0.0922318 | + | 0.159750i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.6847 | − | 32.3628i | 0.933067 | − | 1.61612i | 0.155023 | − | 0.987911i | \(-0.450455\pi\) |
0.778045 | − | 0.628209i | \(-0.216212\pi\) | |||||||
\(402\) | −8.80776 | −0.439291 | ||||||||
\(403\) | −13.3693 | − | 5.40938i | −0.665973 | − | 0.269460i | ||||
\(404\) | 10.2462 | 0.509768 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.00000 | − | 3.46410i | 0.0992583 | − | 0.171920i | ||||
\(407\) | 6.34233 | + | 10.9852i | 0.314378 | + | 0.544518i | ||||
\(408\) | 5.12311 | 0.253632 | ||||||||
\(409\) | 0.123106 | + | 0.213225i | 0.00608718 | + | 0.0105433i | 0.869053 | − | 0.494719i | \(-0.164729\pi\) |
−0.862966 | + | 0.505262i | \(0.831396\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.4924 | −0.813511 | ||||||||
\(412\) | 4.28078 | + | 7.41452i | 0.210899 | + | 0.365287i | ||||
\(413\) | −1.75379 | + | 3.03765i | −0.0862983 | + | 0.149473i | ||||
\(414\) | −2.34233 | + | 4.05703i | −0.115119 | + | 0.199392i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.500000 | + | 3.57071i | 0.0245145 | + | 0.175069i | ||||
\(417\) | 17.4384 | 0.853964 | ||||||||
\(418\) | 11.6847 | − | 20.2384i | 0.571515 | − | 0.989894i | ||||
\(419\) | −8.46543 | + | 14.6626i | −0.413564 | + | 0.716313i | −0.995276 | − | 0.0970811i | \(-0.969049\pi\) |
0.581713 | + | 0.813394i | \(0.302383\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.7538 | 0.719056 | 0.359528 | − | 0.933134i | \(-0.382938\pi\) | ||||
0.359528 | + | 0.933134i | \(0.382938\pi\) | |||||||
\(422\) | 3.56155 | + | 6.16879i | 0.173374 | + | 0.300292i | ||||
\(423\) | −2.00000 | − | 3.46410i | −0.0972433 | − | 0.168430i | ||||
\(424\) | −12.2462 | −0.594729 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.21922 | + | 7.30791i | −0.204422 | + | 0.354069i | ||||
\(427\) | −3.00000 | + | 5.19615i | −0.145180 | + | 0.251459i | ||||
\(428\) | −19.3693 | −0.936251 | ||||||||
\(429\) | 1.78078 | + | 12.7173i | 0.0859767 | + | 0.613996i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.3423 | + | 26.5737i | −0.739014 | + | 1.28001i | 0.213926 | + | 0.976850i | \(0.431375\pi\) |
−0.952940 | + | 0.303160i | \(0.901958\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 0.657671 | + | 1.13912i | 0.0316056 | + | 0.0547426i | 0.881396 | − | 0.472379i | \(-0.156605\pi\) |
−0.849790 | + | 0.527121i | \(0.823271\pi\) | |||||||
\(434\) | 2.24621 | 0.107822 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.90388 | − | 15.4220i | −0.426419 | − | 0.738579i | ||||
\(437\) | −30.7386 | −1.47043 | ||||||||
\(438\) | −4.50000 | − | 7.79423i | −0.215018 | − | 0.372423i | ||||
\(439\) | −10.9654 | + | 18.9927i | −0.523352 | + | 0.906472i | 0.476279 | + | 0.879294i | \(0.341985\pi\) |
−0.999631 | + | 0.0271774i | \(0.991348\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.68466 | −0.318317 | ||||||||
\(442\) | −17.1231 | − | 6.92820i | −0.814463 | − | 0.329541i | ||||
\(443\) | 17.8078 | 0.846072 | 0.423036 | − | 0.906113i | \(-0.360964\pi\) | ||||
0.423036 | + | 0.906113i | \(0.360964\pi\) | |||||||
\(444\) | 1.78078 | − | 3.08440i | 0.0845119 | − | 0.146379i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.28078 | + | 3.95042i | 0.107998 | + | 0.187058i | ||||
\(447\) | 6.24621 | 0.295436 | ||||||||
\(448\) | −0.280776 | − | 0.486319i | −0.0132654 | − | 0.0229764i | ||||
\(449\) | −2.56155 | − | 4.43674i | −0.120887 | − | 0.209383i | 0.799231 | − | 0.601024i | \(-0.205241\pi\) |
−0.920118 | + | 0.391642i | \(0.871907\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.12311 | − | 15.8017i | −0.429590 | − | 0.744072i | ||||
\(452\) | −2.00000 | + | 3.46410i | −0.0940721 | + | 0.162938i | ||||
\(453\) | 2.15767 | − | 3.73720i | 0.101376 | − | 0.175589i | ||||
\(454\) | 17.3153 | 0.812649 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.56155 | −0.307273 | ||||||||
\(457\) | −18.7462 | + | 32.4694i | −0.876911 | + | 1.51885i | −0.0221975 | + | 0.999754i | \(0.507066\pi\) |
−0.854713 | + | 0.519100i | \(0.826267\pi\) | |||||||
\(458\) | 11.7462 | − | 20.3450i | 0.548864 | − | 0.950661i | ||||
\(459\) | −2.56155 | − | 4.43674i | −0.119563 | − | 0.207089i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.6847 | − | 30.6307i | −0.823657 | − | 1.42662i | −0.902942 | − | 0.429763i | \(-0.858597\pi\) |
0.0792850 | − | 0.996852i | \(-0.474736\pi\) | |||||||
\(462\) | −1.00000 | − | 1.73205i | −0.0465242 | − | 0.0805823i | ||||
\(463\) | 7.19224 | 0.334252 | 0.167126 | − | 0.985936i | \(-0.446551\pi\) | ||||
0.167126 | + | 0.985936i | \(0.446551\pi\) | |||||||
\(464\) | 3.56155 | + | 6.16879i | 0.165341 | + | 0.286379i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.315342 | − | 0.546188i | 0.0146079 | − | 0.0253017i | ||||
\(467\) | −7.56155 | −0.349907 | −0.174953 | − | 0.984577i | \(-0.555978\pi\) | ||||
−0.174953 | + | 0.984577i | \(0.555978\pi\) | |||||||
\(468\) | 2.84233 | − | 2.21837i | 0.131387 | − | 0.102544i | ||||
\(469\) | −4.94602 | −0.228386 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.376894 | + | 0.652800i | −0.0173664 | + | 0.0300794i | ||||
\(472\) | −3.12311 | − | 5.40938i | −0.143753 | − | 0.248987i | ||||
\(473\) | 16.2462 | 0.747002 | ||||||||
\(474\) | −2.40388 | − | 4.16365i | −0.110414 | − | 0.191243i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.87689 | 0.131862 | ||||||||
\(477\) | 6.12311 | + | 10.6055i | 0.280358 | + | 0.485594i | ||||
\(478\) | 5.02699 | − | 8.70700i | 0.229929 | − | 0.398249i | ||||
\(479\) | −14.8078 | + | 25.6478i | −0.676584 | + | 1.17188i | 0.299419 | + | 0.954122i | \(0.403207\pi\) |
−0.976003 | + | 0.217756i | \(0.930126\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.1231 | + | 7.90084i | −0.461574 | + | 0.360247i | ||||
\(482\) | 11.4384 | 0.521007 | ||||||||
\(483\) | −1.31534 | + | 2.27824i | −0.0598501 | + | 0.103663i | ||||
\(484\) | −0.842329 | + | 1.45896i | −0.0382877 | + | 0.0663162i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −15.1577 | − | 26.2539i | −0.686860 | − | 1.18968i | −0.972849 | − | 0.231443i | \(-0.925655\pi\) |
0.285989 | − | 0.958233i | \(-0.407678\pi\) | |||||||
\(488\) | −5.34233 | − | 9.25319i | −0.241836 | − | 0.418872i | ||||
\(489\) | 16.4924 | 0.745813 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.1501 | − | 19.3125i | 0.503197 | − | 0.871562i | −0.496797 | − | 0.867867i | \(-0.665490\pi\) |
0.999993 | − | 0.00369513i | \(-0.00117620\pi\) | |||||||
\(492\) | −2.56155 | + | 4.43674i | −0.115484 | + | 0.200024i | ||||
\(493\) | −36.4924 | −1.64354 | ||||||||
\(494\) | 21.9309 | + | 8.87348i | 0.986716 | + | 0.399237i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.00000 | + | 3.46410i | −0.0898027 | + | 0.155543i | ||||
\(497\) | −2.36932 | + | 4.10378i | −0.106278 | + | 0.184080i | ||||
\(498\) | −1.21922 | − | 2.11176i | −0.0546347 | − | 0.0946301i | ||||
\(499\) | −31.0540 | −1.39017 | −0.695083 | − | 0.718929i | \(-0.744633\pi\) | ||||
−0.695083 | + | 0.718929i | \(0.744633\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.65767 | − | 9.79937i | −0.252766 | − | 0.437804i | ||||
\(502\) | −4.93087 | −0.220075 | ||||||||
\(503\) | 18.3423 | + | 31.7698i | 0.817844 | + | 1.41655i | 0.907268 | + | 0.420554i | \(0.138164\pi\) |
−0.0894236 | + | 0.995994i | \(0.528502\pi\) | |||||||
\(504\) | −0.280776 | + | 0.486319i | −0.0125068 | + | 0.0216624i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 16.6847 | 0.741724 | ||||||||
\(507\) | −12.5000 | + | 3.57071i | −0.555144 | + | 0.158581i | ||||
\(508\) | 1.19224 | 0.0528969 | ||||||||
\(509\) | −0.123106 | + | 0.213225i | −0.00545656 | + | 0.00945104i | −0.868741 | − | 0.495267i | \(-0.835070\pi\) |
0.863284 | + | 0.504718i | \(0.168404\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.52699 | − | 4.37687i | −0.111787 | − | 0.193621i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 3.28078 | + | 5.68247i | 0.144850 | + | 0.250887i | ||||
\(514\) | −13.8078 | − | 23.9157i | −0.609034 | − | 1.05488i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.28078 | − | 3.95042i | −0.100406 | − | 0.173908i | ||||
\(517\) | −7.12311 | + | 12.3376i | −0.313274 | + | 0.542606i | ||||
\(518\) | 1.00000 | − | 1.73205i | 0.0439375 | − | 0.0761019i | ||||
\(519\) | −17.1231 | −0.751621 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.7386 | −0.645711 | −0.322856 | − | 0.946448i | \(-0.604643\pi\) | ||||
−0.322856 | + | 0.946448i | \(0.604643\pi\) | |||||||
\(522\) | 3.56155 | − | 6.16879i | 0.155885 | − | 0.270001i | ||||
\(523\) | 1.96543 | − | 3.40423i | 0.0859425 | − | 0.148857i | −0.819850 | − | 0.572578i | \(-0.805943\pi\) |
0.905792 | + | 0.423722i | \(0.139277\pi\) | |||||||
\(524\) | −4.56155 | − | 7.90084i | −0.199272 | − | 0.345150i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.34233 | − | 16.1814i | −0.407345 | − | 0.705542i | ||||
\(527\) | −10.2462 | − | 17.7470i | −0.446332 | − | 0.773070i | ||||
\(528\) | 3.56155 | 0.154997 | ||||||||
\(529\) | 0.526988 | + | 0.912769i | 0.0229125 | + | 0.0396856i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.12311 | + | 5.40938i | −0.135531 | + | 0.234747i | ||||
\(532\) | −3.68466 | −0.159750 | ||||||||
\(533\) | 14.5616 | − | 11.3649i | 0.630731 | − | 0.492270i | ||||
\(534\) | −6.24621 | −0.270300 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.40388 | − | 7.62775i | 0.190219 | − | 0.329469i | ||||
\(537\) | 1.65767 | + | 2.87117i | 0.0715338 | + | 0.123900i | ||||
\(538\) | 21.3693 | 0.921297 | ||||||||
\(539\) | 11.9039 | + | 20.6181i | 0.512736 | + | 0.888086i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.6847 | −1.49121 | −0.745605 | − | 0.666388i | \(-0.767839\pi\) | ||||
−0.745605 | + | 0.666388i | \(0.767839\pi\) | |||||||
\(542\) | 9.96543 | + | 17.2606i | 0.428052 | + | 0.741408i | ||||
\(543\) | −8.74621 | + | 15.1489i | −0.375336 | + | 0.650101i | ||||
\(544\) | −2.56155 | + | 4.43674i | −0.109826 | + | 0.190224i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.59612 | − | 1.24573i | 0.0683075 | − | 0.0533124i | ||||
\(547\) | −2.06913 | −0.0884696 | −0.0442348 | − | 0.999021i | \(-0.514085\pi\) | ||||
−0.0442348 | + | 0.999021i | \(0.514085\pi\) | |||||||
\(548\) | 8.24621 | − | 14.2829i | 0.352261 | − | 0.610133i | ||||
\(549\) | −5.34233 | + | 9.25319i | −0.228005 | + | 0.394916i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 46.7386 | 1.99113 | ||||||||
\(552\) | −2.34233 | − | 4.05703i | −0.0996962 | − | 0.172679i | ||||
\(553\) | −1.34991 | − | 2.33811i | −0.0574039 | − | 0.0994264i | ||||
\(554\) | 5.00000 | 0.212430 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.71922 | + | 15.1021i | −0.369777 | + | 0.640473i | ||||
\(557\) | −4.80776 | + | 8.32729i | −0.203712 | + | 0.352839i | −0.949721 | − | 0.313096i | \(-0.898634\pi\) |
0.746010 | + | 0.665935i | \(0.231967\pi\) | |||||||
\(558\) | 4.00000 | 0.169334 | ||||||||
\(559\) | 2.28078 | + | 16.2880i | 0.0964666 | + | 0.688909i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.12311 | + | 15.8017i | −0.385178 | + | 0.667148i | ||||
\(562\) | 9.12311 | − | 15.8017i | 0.384835 | − | 0.666554i | ||||
\(563\) | −0.0961180 | − | 0.166481i | −0.00405089 | − | 0.00701635i | 0.863993 | − | 0.503504i | \(-0.167956\pi\) |
−0.868044 | + | 0.496488i | \(0.834623\pi\) | |||||||
\(564\) | 4.00000 | 0.168430 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 5.80776 | + | 10.0593i | 0.244119 | + | 0.422826i | ||||
\(567\) | 0.561553 | 0.0235830 | ||||||||
\(568\) | −4.21922 | − | 7.30791i | −0.177035 | − | 0.306633i | ||||
\(569\) | 22.2462 | − | 38.5316i | 0.932610 | − | 1.61533i | 0.153768 | − | 0.988107i | \(-0.450859\pi\) |
0.778842 | − | 0.627220i | \(-0.215807\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.4233 | −1.69166 | −0.845831 | − | 0.533451i | \(-0.820895\pi\) | ||||
−0.845831 | + | 0.533451i | \(0.820895\pi\) | |||||||
\(572\) | −11.9039 | − | 4.81645i | −0.497726 | − | 0.201386i | ||||
\(573\) | −12.9309 | −0.540195 | ||||||||
\(574\) | −1.43845 | + | 2.49146i | −0.0600396 | + | 0.103992i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 23.0000 | 0.957503 | 0.478751 | − | 0.877951i | \(-0.341090\pi\) | ||||
0.478751 | + | 0.877951i | \(0.341090\pi\) | |||||||
\(578\) | −4.62311 | − | 8.00745i | −0.192296 | − | 0.333066i | ||||
\(579\) | −1.50000 | − | 2.59808i | −0.0623379 | − | 0.107972i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.684658 | − | 1.18586i | −0.0284044 | − | 0.0491979i | ||||
\(582\) | −8.90388 | + | 15.4220i | −0.369078 | + | 0.639261i | ||||
\(583\) | 21.8078 | − | 37.7722i | 0.903185 | − | 1.56436i | ||||
\(584\) | 9.00000 | 0.372423 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.75379 | 0.155068 | ||||||||
\(587\) | −5.46543 | + | 9.46641i | −0.225583 | + | 0.390721i | −0.956494 | − | 0.291752i | \(-0.905762\pi\) |
0.730911 | + | 0.682472i | \(0.239095\pi\) | |||||||
\(588\) | 3.34233 | − | 5.78908i | 0.137835 | − | 0.238738i | ||||
\(589\) | 13.1231 | + | 22.7299i | 0.540728 | + | 0.936569i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.56155 | + | 2.70469i | 0.0642337 | + | 0.111256i | ||||
\(592\) | 1.78078 | + | 3.08440i | 0.0731895 | + | 0.126768i | ||||
\(593\) | 26.9848 | 1.10813 | 0.554067 | − | 0.832472i | \(-0.313075\pi\) | ||||
0.554067 | + | 0.832472i | \(0.313075\pi\) | |||||||
\(594\) | −1.78078 | − | 3.08440i | −0.0730661 | − | 0.126554i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.12311 | + | 5.40938i | −0.127927 | + | 0.221577i | ||||
\(597\) | −8.56155 | −0.350401 | ||||||||
\(598\) | 2.34233 | + | 16.7276i | 0.0957850 | + | 0.684041i | ||||
\(599\) | −30.6847 | −1.25374 | −0.626871 | − | 0.779123i | \(-0.715665\pi\) | ||||
−0.626871 | + | 0.779123i | \(0.715665\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.40388 | + | 12.8239i | −0.302011 | + | 0.523098i | −0.976591 | − | 0.215103i | \(-0.930991\pi\) |
0.674581 | + | 0.738201i | \(0.264324\pi\) | |||||||
\(602\) | −1.28078 | − | 2.21837i | −0.0522005 | − | 0.0904140i | ||||
\(603\) | −8.80776 | −0.358680 | ||||||||
\(604\) | 2.15767 | + | 3.73720i | 0.0877944 | + | 0.152064i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.2462 | 0.416224 | ||||||||
\(607\) | 7.31534 | + | 12.6705i | 0.296921 | + | 0.514281i | 0.975430 | − | 0.220310i | \(-0.0707070\pi\) |
−0.678509 | + | 0.734592i | \(0.737374\pi\) | |||||||
\(608\) | 3.28078 | − | 5.68247i | 0.133053 | − | 0.230455i | ||||
\(609\) | 2.00000 | − | 3.46410i | 0.0810441 | − | 0.140372i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.3693 | − | 5.40938i | −0.540865 | − | 0.218840i | ||||
\(612\) | 5.12311 | 0.207089 | ||||||||
\(613\) | −16.7732 | + | 29.0520i | −0.677463 | + | 1.17340i | 0.298279 | + | 0.954479i | \(0.403587\pi\) |
−0.975742 | + | 0.218922i | \(0.929746\pi\) | |||||||
\(614\) | −2.87689 | + | 4.98293i | −0.116102 | + | 0.201095i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.00000 | 0.0805823 | ||||||||
\(617\) | −11.3153 | − | 19.5987i | −0.455538 | − | 0.789016i | 0.543180 | − | 0.839616i | \(-0.317220\pi\) |
−0.998719 | + | 0.0506001i | \(0.983887\pi\) | |||||||
\(618\) | 4.28078 | + | 7.41452i | 0.172198 | + | 0.298256i | ||||
\(619\) | 41.3002 | 1.65999 | 0.829997 | − | 0.557767i | \(-0.188342\pi\) | ||||
0.829997 | + | 0.557767i | \(0.188342\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.34233 | + | 4.05703i | −0.0939944 | + | 0.162803i | ||||
\(622\) | 11.3423 | − | 19.6455i | 0.454786 | − | 0.787712i | ||||
\(623\) | −3.50758 | −0.140528 | ||||||||
\(624\) | 0.500000 | + | 3.57071i | 0.0200160 | + | 0.142943i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −15.5000 | + | 26.8468i | −0.619505 | + | 1.07301i | ||||
\(627\) | 11.6847 | − | 20.2384i | 0.466640 | − | 0.808245i | ||||
\(628\) | −0.376894 | − | 0.652800i | −0.0150397 | − | 0.0260496i | ||||
\(629\) | −18.2462 | −0.727524 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.03457 | − | 3.52397i | −0.0809948 | − | 0.140287i | 0.822683 | − | 0.568501i | \(-0.192476\pi\) |
−0.903677 | + | 0.428214i | \(0.859143\pi\) | |||||||
\(632\) | 4.80776 | 0.191243 | ||||||||
\(633\) | 3.56155 | + | 6.16879i | 0.141559 | + | 0.245187i | ||||
\(634\) | 0.123106 | − | 0.213225i | 0.00488915 | − | 0.00846825i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −12.2462 | −0.485594 | ||||||||
\(637\) | −19.0000 | + | 14.8290i | −0.752807 | + | 0.587548i | ||||
\(638\) | −25.3693 | −1.00438 | ||||||||
\(639\) | −4.21922 | + | 7.30791i | −0.166910 | + | 0.289096i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.8769 | − | 18.8393i | −0.429611 | − | 0.744109i | 0.567227 | − | 0.823561i | \(-0.308016\pi\) |
−0.996839 | + | 0.0794524i | \(0.974683\pi\) | |||||||
\(642\) | −19.3693 | −0.764446 | ||||||||
\(643\) | 22.7732 | + | 39.4443i | 0.898087 | + | 1.55553i | 0.829937 | + | 0.557858i | \(0.188377\pi\) |
0.0681507 | + | 0.997675i | \(0.478290\pi\) | |||||||
\(644\) | −1.31534 | − | 2.27824i | −0.0518317 | − | 0.0897752i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.8078 | + | 29.1119i | 0.661293 | + | 1.14539i | ||||
\(647\) | 14.7116 | − | 25.4813i | 0.578374 | − | 1.00177i | −0.417291 | − | 0.908773i | \(-0.637021\pi\) |
0.995666 | − | 0.0930013i | \(-0.0296461\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | 22.2462 | 0.873240 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.24621 | 0.0880360 | ||||||||
\(652\) | −8.24621 | + | 14.2829i | −0.322947 | + | 0.559360i | ||||
\(653\) | −1.80776 | + | 3.13114i | −0.0707433 | + | 0.122531i | −0.899227 | − | 0.437482i | \(-0.855870\pi\) |
0.828484 | + | 0.560013i | \(0.189204\pi\) | |||||||
\(654\) | −8.90388 | − | 15.4220i | −0.348169 | − | 0.603047i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.56155 | − | 4.43674i | −0.100012 | − | 0.173226i | ||||
\(657\) | −4.50000 | − | 7.79423i | −0.175562 | − | 0.304082i | ||||
\(658\) | 2.24621 | 0.0875664 | ||||||||
\(659\) | −15.3423 | − | 26.5737i | −0.597652 | − | 1.03516i | −0.993167 | − | 0.116704i | \(-0.962767\pi\) |
0.395514 | − | 0.918460i | \(-0.370566\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.7732 | + | 18.6597i | −0.419029 | + | 0.725779i | −0.995842 | − | 0.0910968i | \(-0.970963\pi\) |
0.576813 | + | 0.816876i | \(0.304296\pi\) | |||||||
\(662\) | −4.31534 | −0.167721 | ||||||||
\(663\) | −17.1231 | − | 6.92820i | −0.665006 | − | 0.269069i | ||||
\(664\) | 2.43845 | 0.0946301 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.78078 | − | 3.08440i | 0.0690037 | − | 0.119518i | ||||
\(667\) | 16.6847 | + | 28.8987i | 0.646033 | + | 1.11896i | ||||
\(668\) | 11.3153 | 0.437804 | ||||||||
\(669\) | 2.28078 | + | 3.95042i | 0.0881799 | + | 0.152732i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38.0540 | 1.46906 | ||||||||
\(672\) | −0.280776 | − | 0.486319i | −0.0108312 | − | 0.0187602i | ||||
\(673\) | −22.6231 | + | 39.1844i | −0.872057 | + | 1.51045i | −0.0121912 | + | 0.999926i | \(0.503881\pi\) |
−0.859865 | + | 0.510521i | \(0.829453\pi\) | |||||||
\(674\) | 14.5270 | − | 25.1615i | 0.559559 | − | 0.969184i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.15767 | − | 12.6107i | 0.121449 | − | 0.485026i | ||||
\(677\) | −29.6155 | −1.13822 | −0.569109 | − | 0.822262i | \(-0.692712\pi\) | ||||
−0.569109 | + | 0.822262i | \(0.692712\pi\) | |||||||
\(678\) | −2.00000 | + | 3.46410i | −0.0768095 | + | 0.133038i | ||||
\(679\) | −5.00000 | + | 8.66025i | −0.191882 | + | 0.332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.3153 | 0.663525 | ||||||||
\(682\) | −7.12311 | − | 12.3376i | −0.272758 | − | 0.472430i | ||||
\(683\) | −9.78078 | − | 16.9408i | −0.374251 | − | 0.648222i | 0.615964 | − | 0.787775i | \(-0.288767\pi\) |
−0.990215 | + | 0.139553i | \(0.955433\pi\) | |||||||
\(684\) | −6.56155 | −0.250887 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.84233 | − | 6.65511i | 0.146701 | − | 0.254093i | ||||
\(687\) | 11.7462 | − | 20.3450i | 0.448146 | − | 0.776211i | ||||
\(688\) | 4.56155 | 0.173908 | ||||||||
\(689\) | 40.9309 | + | 16.5611i | 1.55934 | + | 0.630927i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.0885 | − | 43.4546i | 0.954413 | − | 1.65309i | 0.218707 | − | 0.975790i | \(-0.429816\pi\) |
0.735706 | − | 0.677301i | \(-0.236851\pi\) | |||||||
\(692\) | 8.56155 | − | 14.8290i | 0.325461 | − | 0.563716i | ||||
\(693\) | −1.00000 | − | 1.73205i | −0.0379869 | − | 0.0657952i | ||||
\(694\) | −4.19224 | −0.159135 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.56155 | + | 6.16879i | 0.135000 | + | 0.233827i | ||||
\(697\) | 26.2462 | 0.994146 | ||||||||
\(698\) | 1.37689 | + | 2.38485i | 0.0521162 | + | 0.0902679i | ||||
\(699\) | 0.315342 | − | 0.546188i | 0.0119273 | − | 0.0206587i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.12311 | −0.344575 | −0.172287 | − | 0.985047i | \(-0.555116\pi\) | ||||
−0.172287 | + | 0.985047i | \(0.555116\pi\) | |||||||
\(702\) | 2.84233 | − | 2.21837i | 0.107277 | − | 0.0837270i | ||||
\(703\) | 23.3693 | 0.881390 | ||||||||
\(704\) | −1.78078 | + | 3.08440i | −0.0671155 | + | 0.116248i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.12311 | + | 12.3376i | 0.268082 | + | 0.464331i | ||||
\(707\) | 5.75379 | 0.216393 | ||||||||
\(708\) | −3.12311 | − | 5.40938i | −0.117373 | − | 0.203297i | ||||
\(709\) | 22.6231 | + | 39.1844i | 0.849629 | + | 1.47160i | 0.881540 | + | 0.472109i | \(0.156507\pi\) |
−0.0319115 | + | 0.999491i | \(0.510159\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.40388 | − | 4.16365i | −0.0901526 | − | 0.156149i | ||||
\(712\) | 3.12311 | − | 5.40938i | 0.117043 | − | 0.202725i | ||||
\(713\) | −9.36932 | + | 16.2281i | −0.350884 | + | 0.607748i | ||||
\(714\) | 2.87689 | 0.107665 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.31534 | −0.123900 | ||||||||
\(717\) | 5.02699 | − | 8.70700i | 0.187736 | − | 0.325169i | ||||
\(718\) | 6.56155 | − | 11.3649i | 0.244875 | − | 0.424136i | ||||
\(719\) | 10.7808 | + | 18.6729i | 0.402055 | + | 0.696380i | 0.993974 | − | 0.109618i | \(-0.0349627\pi\) |
−0.591919 | + | 0.805998i | \(0.701629\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.40388 | + | 4.16365i | 0.0895252 | + | 0.155062i | ||||
\(722\) | −12.0270 | − | 20.8314i | −0.447598 | − | 0.775263i | ||||
\(723\) | 11.4384 | 0.425400 | ||||||||
\(724\) | −8.74621 | − | 15.1489i | −0.325050 | − | 0.563004i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.842329 | + | 1.45896i | −0.0312618 | + | 0.0541470i | ||||
\(727\) | 35.7926 | 1.32747 | 0.663737 | − | 0.747966i | \(-0.268969\pi\) | ||||
0.663737 | + | 0.747966i | \(0.268969\pi\) | |||||||
\(728\) | 0.280776 | + | 2.00514i | 0.0104063 | + | 0.0743156i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.6847 | + | 20.2384i | −0.432173 | + | 0.748545i | ||||
\(732\) | −5.34233 | − | 9.25319i | −0.197458 | − | 0.342008i | ||||
\(733\) | 17.9848 | 0.664285 | 0.332143 | − | 0.943229i | \(-0.392228\pi\) | ||||
0.332143 | + | 0.943229i | \(0.392228\pi\) | |||||||
\(734\) | 15.4039 | + | 26.6803i | 0.568568 | + | 0.984788i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.68466 | 0.172679 | ||||||||
\(737\) | 15.6847 | + | 27.1666i | 0.577752 | + | 1.00070i | ||||
\(738\) | −2.56155 | + | 4.43674i | −0.0942921 | + | 0.163319i | ||||
\(739\) | 2.43845 | − | 4.22351i | 0.0896997 | − | 0.155364i | −0.817684 | − | 0.575667i | \(-0.804743\pi\) |
0.907384 | + | 0.420302i | \(0.138076\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.9309 | + | 8.87348i | 0.805651 | + | 0.325975i | ||||
\(742\) | −6.87689 | −0.252459 | ||||||||
\(743\) | −1.43845 | + | 2.49146i | −0.0527715 | + | 0.0914029i | −0.891204 | − | 0.453602i | \(-0.850139\pi\) |
0.838433 | + | 0.545005i | \(0.183472\pi\) | |||||||
\(744\) | −2.00000 | + | 3.46410i | −0.0733236 | + | 0.127000i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 23.4924 | 0.860119 | ||||||||
\(747\) | −1.21922 | − | 2.11176i | −0.0446091 | − | 0.0772652i | ||||
\(748\) | −9.12311 | − | 15.8017i | −0.333574 | − | 0.577767i | ||||
\(749\) | −10.8769 | −0.397433 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.8769 | + | 29.2316i | −0.615847 | + | 1.06668i | 0.374389 | + | 0.927272i | \(0.377853\pi\) |
−0.990235 | + | 0.139406i | \(0.955481\pi\) | |||||||
\(752\) | −2.00000 | + | 3.46410i | −0.0729325 | + | 0.126323i | ||||
\(753\) | −4.93087 | −0.179691 | ||||||||
\(754\) | −3.56155 | − | 25.4346i | −0.129704 | − | 0.926273i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.280776 | + | 0.486319i | −0.0102117 | + | 0.0176873i | ||||
\(757\) | 9.15767 | − | 15.8616i | 0.332841 | − | 0.576498i | −0.650227 | − | 0.759740i | \(-0.725326\pi\) |
0.983068 | + | 0.183243i | \(0.0586594\pi\) | |||||||
\(758\) | −6.52699 | − | 11.3051i | −0.237071 | − | 0.410619i | ||||
\(759\) | 16.6847 | 0.605615 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.4924 | − | 37.2260i | −0.779100 | − | 1.34944i | −0.932461 | − | 0.361270i | \(-0.882343\pi\) |
0.153361 | − | 0.988170i | \(-0.450990\pi\) | |||||||
\(762\) | 1.19224 | 0.0431902 | ||||||||
\(763\) | −5.00000 | − | 8.66025i | −0.181012 | − | 0.313522i | ||||
\(764\) | 6.46543 | − | 11.1985i | 0.233911 | − | 0.405146i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.56155 | −0.345473 | ||||||||
\(767\) | 3.12311 | + | 22.3034i | 0.112769 | + | 0.805330i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 10.8423 | − | 18.7795i | 0.390984 | − | 0.677205i | −0.601595 | − | 0.798801i | \(-0.705468\pi\) |
0.992580 | + | 0.121596i | \(0.0388013\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.8078 | − | 23.9157i | −0.497274 | − | 0.861305i | ||||
\(772\) | 3.00000 | 0.107972 | ||||||||
\(773\) | −5.80776 | − | 10.0593i | −0.208891 | − | 0.361809i | 0.742475 | − | 0.669874i | \(-0.233652\pi\) |
−0.951365 | + | 0.308065i | \(0.900319\pi\) | |||||||
\(774\) | −2.28078 | − | 3.95042i | −0.0819808 | − | 0.141995i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.90388 | − | 15.4220i | −0.319631 | − | 0.553617i | ||||
\(777\) | 1.00000 | − | 1.73205i | 0.0358748 | − | 0.0621370i | ||||
\(778\) | 6.68466 | − | 11.5782i | 0.239657 | − | 0.415097i | ||||
\(779\) | −33.6155 | −1.20440 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.0540 | 1.07542 | ||||||||
\(782\) | −12.0000 | + | 20.7846i | −0.429119 | + | 0.743256i | ||||
\(783\) | 3.56155 | − | 6.16879i | 0.127280 | − | 0.220455i | ||||
\(784\) | 3.34233 | + | 5.78908i | 0.119369 | + | 0.206753i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.56155 | − | 7.90084i | −0.162705 | − | 0.281814i | ||||
\(787\) | 6.00000 | + | 10.3923i | 0.213877 | + | 0.370446i | 0.952925 | − | 0.303207i | \(-0.0980575\pi\) |
−0.739048 | + | 0.673653i | \(0.764724\pi\) | |||||||
\(788\) | −3.12311 | −0.111256 | ||||||||
\(789\) | −9.34233 | − | 16.1814i | −0.332596 | − | 0.576073i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.12311 | + | 1.94528i | −0.0399330 | + | 0.0691661i | ||||
\(792\) | 3.56155 | 0.126554 | ||||||||
\(793\) | 5.34233 | + | 38.1519i | 0.189712 | + | 1.35481i | ||||
\(794\) | 10.8078 | 0.383553 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.28078 | − | 7.41452i | 0.151728 | − | 0.262801i | ||||
\(797\) | 4.87689 | + | 8.44703i | 0.172748 | + | 0.299209i | 0.939380 | − | 0.342878i | \(-0.111402\pi\) |
−0.766631 | + | 0.642088i | \(0.778069\pi\) | |||||||
\(798\) | −3.68466 | −0.130435 | ||||||||
\(799\) | −10.2462 | − | 17.7470i | −0.362485 | − | 0.627842i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.24621 | −0.220699 | ||||||||
\(802\) | 18.6847 | + | 32.3628i | 0.659778 | + | 1.14277i | ||||
\(803\) | −16.0270 | + | 27.7596i | −0.565580 | + | 0.979613i | ||||
\(804\) | 4.40388 | − | 7.62775i | 0.155313 | − | 0.269010i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.3693 | − | 8.87348i | 0.400467 | − | 0.312555i | ||||
\(807\) | 21.3693 | 0.752236 | ||||||||
\(808\) | −5.12311 | + | 8.87348i | −0.180230 | + | 0.312168i | ||||
\(809\) | 4.80776 | − | 8.32729i | 0.169032 | − | 0.292772i | −0.769048 | − | 0.639191i | \(-0.779269\pi\) |
0.938080 | + | 0.346419i | \(0.112603\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.9309 | 0.418949 | 0.209475 | − | 0.977814i | \(-0.432825\pi\) | ||||
0.209475 | + | 0.977814i | \(0.432825\pi\) | |||||||
\(812\) | 2.00000 | + | 3.46410i | 0.0701862 | + | 0.121566i | ||||
\(813\) | 9.96543 | + | 17.2606i | 0.349503 | + | 0.605357i | ||||
\(814\) | −12.6847 | −0.444597 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.56155 | + | 4.43674i | −0.0896723 | + | 0.155317i | ||||
\(817\) | 14.9654 | − | 25.9209i | 0.523574 | − | 0.906857i | ||||
\(818\) | −0.246211 | −0.00860857 | ||||||||
\(819\) | 1.59612 | − | 1.24573i | 0.0557729 | − | 0.0435294i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.4924 | − | 23.3696i | 0.470889 | − | 0.815603i | −0.528557 | − | 0.848898i | \(-0.677267\pi\) |
0.999446 | + | 0.0332946i | \(0.0106000\pi\) | |||||||
\(822\) | 8.24621 | − | 14.2829i | 0.287620 | − | 0.498172i | ||||
\(823\) | 17.8963 | + | 30.9973i | 0.623826 | + | 1.08050i | 0.988767 | + | 0.149467i | \(0.0477559\pi\) |
−0.364941 | + | 0.931031i | \(0.618911\pi\) | |||||||
\(824\) | −8.56155 | −0.298256 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.75379 | − | 3.03765i | −0.0610221 | − | 0.105693i | ||||
\(827\) | 34.9309 | 1.21467 | 0.607333 | − | 0.794448i | \(-0.292240\pi\) | ||||
0.607333 | + | 0.794448i | \(0.292240\pi\) | |||||||
\(828\) | −2.34233 | − | 4.05703i | −0.0814016 | − | 0.140992i | ||||
\(829\) | 28.7732 | − | 49.8366i | 0.999335 | − | 1.73090i | 0.468078 | − | 0.883687i | \(-0.344947\pi\) |
0.531257 | − | 0.847211i | \(-0.321720\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.00000 | 0.173448 | ||||||||
\(832\) | −3.34233 | − | 1.35234i | −0.115874 | − | 0.0468841i | ||||
\(833\) | −34.2462 | −1.18656 | ||||||||
\(834\) | −8.71922 | + | 15.1021i | −0.301922 | + | 0.522944i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 11.6847 | + | 20.2384i | 0.404122 | + | 0.699960i | ||||
\(837\) | 4.00000 | 0.138260 | ||||||||
\(838\) | −8.46543 | − | 14.6626i | −0.292434 | − | 0.506510i | ||||
\(839\) | −0.657671 | − | 1.13912i | −0.0227053 | − | 0.0393268i | 0.854449 | − | 0.519534i | \(-0.173895\pi\) |
−0.877155 | + | 0.480208i | \(0.840561\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.8693 | − | 18.8262i | −0.374804 | − | 0.649180i | ||||
\(842\) | −7.37689 | + | 12.7772i | −0.254225 | + | 0.440330i | ||||
\(843\) | 9.12311 | − | 15.8017i | 0.314216 | − | 0.544239i | ||||
\(844\) | −7.12311 | −0.245187 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.00000 | 0.137523 | ||||||||
\(847\) | −0.473012 | + | 0.819281i | −0.0162529 | + | 0.0281508i | ||||
\(848\) | 6.12311 | − | 10.6055i | 0.210268 | − | 0.364195i | ||||
\(849\) | 5.80776 | + | 10.0593i | 0.199322 | + | 0.345236i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.34233 | + | 14.4493i | 0.285971 | + | 0.495317i | ||||
\(852\) | −4.21922 | − | 7.30791i | −0.144548 | − | 0.250365i | ||||
\(853\) | −46.9848 | −1.60873 | −0.804365 | − | 0.594135i | \(-0.797494\pi\) | ||||
−0.804365 | + | 0.594135i | \(0.797494\pi\) | |||||||
\(854\) | −3.00000 | − | 5.19615i | −0.102658 | − | 0.177809i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.68466 | − | 16.7743i | 0.331015 | − | 0.573334i | ||||
\(857\) | −39.7538 | −1.35796 | −0.678982 | − | 0.734155i | \(-0.737578\pi\) | ||||
−0.678982 | + | 0.734155i | \(0.737578\pi\) | |||||||
\(858\) | −11.9039 | − | 4.81645i | −0.406392 | − | 0.164431i | ||||
\(859\) | −34.4233 | −1.17451 | −0.587254 | − | 0.809403i | \(-0.699791\pi\) | ||||
−0.587254 | + | 0.809403i | \(0.699791\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.43845 | + | 2.49146i | −0.0490221 | + | 0.0849089i | ||||
\(862\) | −15.3423 | − | 26.5737i | −0.522562 | − | 0.905104i | ||||
\(863\) | 30.9309 | 1.05290 | 0.526450 | − | 0.850206i | \(-0.323523\pi\) | ||||
0.526450 | + | 0.850206i | \(0.323523\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.31534 | −0.0446971 | ||||||||
\(867\) | −4.62311 | − | 8.00745i | −0.157009 | − | 0.271947i | ||||
\(868\) | −1.12311 | + | 1.94528i | −0.0381207 | + | 0.0660270i | ||||
\(869\) | −8.56155 | + | 14.8290i | −0.290431 | + | 0.503041i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.0346 | + | 19.5389i | −0.848264 | + | 0.662050i | ||||
\(872\) | 17.8078 | 0.603047 | ||||||||
\(873\) | −8.90388 | + | 15.4220i | −0.301351 | + | 0.521955i | ||||
\(874\) | 15.3693 | − | 26.6204i | 0.519875 | − | 0.900450i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9.00000 | 0.304082 | ||||||||
\(877\) | −5.25379 | − | 9.09983i | −0.177408 | − | 0.307279i | 0.763584 | − | 0.645708i | \(-0.223438\pi\) |
−0.940992 | + | 0.338429i | \(0.890105\pi\) | |||||||
\(878\) | −10.9654 | − | 18.9927i | −0.370066 | − | 0.640972i | ||||
\(879\) | 3.75379 | 0.126612 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.4384 | + | 35.4004i | −0.688589 | + | 1.19267i | 0.283706 | + | 0.958911i | \(0.408436\pi\) |
−0.972294 | + | 0.233759i | \(0.924897\pi\) | |||||||
\(882\) | 3.34233 | − | 5.78908i | 0.112542 | − | 0.194929i | ||||
\(883\) | 17.7538 | 0.597463 | 0.298731 | − | 0.954337i | \(-0.403437\pi\) | ||||
0.298731 | + | 0.954337i | \(0.403437\pi\) | |||||||
\(884\) | 14.5616 | − | 11.3649i | 0.489758 | − | 0.382244i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.90388 | + | 15.4220i | −0.299132 | + | 0.518111i | ||||
\(887\) | 8.31534 | − | 14.4026i | 0.279202 | − | 0.483592i | −0.691985 | − | 0.721912i | \(-0.743263\pi\) |
0.971187 | + | 0.238320i | \(0.0765968\pi\) | |||||||
\(888\) | 1.78078 | + | 3.08440i | 0.0597589 | + | 0.103506i | ||||
\(889\) | 0.669503 | 0.0224544 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.78078 | − | 3.08440i | −0.0596583 | − | 0.103331i | ||||
\(892\) | −4.56155 | −0.152732 | ||||||||
\(893\) | 13.1231 | + | 22.7299i | 0.439148 | + | 0.760627i | ||||
\(894\) | −3.12311 | + | 5.40938i | −0.104452 | + | 0.180917i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.561553 | 0.0187602 | ||||||||
\(897\) | 2.34233 | + | 16.7276i | 0.0782081 | + | 0.558518i | ||||
\(898\) | 5.12311 | 0.170960 | ||||||||
\(899\) | 14.2462 | − | 24.6752i | 0.475138 | − | 0.822963i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.3693 | + | 54.3333i | 1.04506 | + | 1.81010i | ||||
\(902\) | 18.2462 | 0.607532 | ||||||||
\(903\) | −1.28078 | − | 2.21837i | −0.0426216 | − | 0.0738227i | ||||
\(904\) | −2.00000 | − | 3.46410i | −0.0665190 | − | 0.115214i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.15767 | + | 3.73720i | 0.0716838 | + | 0.124160i | ||||
\(907\) | −26.9309 | + | 46.6456i | −0.894225 | + | 1.54884i | −0.0594638 | + | 0.998230i | \(0.518939\pi\) |
−0.834761 | + | 0.550612i | \(0.814394\pi\) | |||||||
\(908\) | −8.65767 | + | 14.9955i | −0.287315 | + | 0.497644i | ||||
\(909\) | 10.2462 | 0.339845 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.3153 | 0.904998 | 0.452499 | − | 0.891765i | \(-0.350533\pi\) | ||||
0.452499 | + | 0.891765i | \(0.350533\pi\) | |||||||
\(912\) | 3.28078 | − | 5.68247i | 0.108637 | − | 0.188165i | ||||
\(913\) | −4.34233 | + | 7.52113i | −0.143710 | + | 0.248913i | ||||
\(914\) | −18.7462 | − | 32.4694i | −0.620070 | − | 1.07399i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.7462 | + | 20.3450i | 0.388106 | + | 0.672219i | ||||
\(917\) | −2.56155 | − | 4.43674i | −0.0845899 | − | 0.146514i | ||||
\(918\) | 5.12311 | 0.169088 | ||||||||
\(919\) | −19.8423 | − | 34.3679i | −0.654538 | − | 1.13369i | −0.982009 | − | 0.188832i | \(-0.939530\pi\) |
0.327471 | − | 0.944861i | \(-0.393804\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.87689 | + | 4.98293i | −0.0947969 | + | 0.164193i | ||||
\(922\) | 35.3693 | 1.16483 | ||||||||
\(923\) | 4.21922 | + | 30.1313i | 0.138877 | + | 0.991783i | ||||
\(924\) | 2.00000 | 0.0657952 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.59612 | + | 6.22866i | −0.118176 | + | 0.204686i | ||||
\(927\) | 4.28078 | + | 7.41452i | 0.140599 | + | 0.243525i | ||||
\(928\) | −7.12311 | −0.233827 | ||||||||
\(929\) | −3.93087 | − | 6.80847i | −0.128968 | − | 0.223379i | 0.794309 | − | 0.607514i | \(-0.207833\pi\) |
−0.923277 | + | 0.384135i | \(0.874500\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 43.8617 | 1.43751 | ||||||||
\(932\) | 0.315342 | + | 0.546188i | 0.0103294 | + | 0.0178910i | ||||
\(933\) | 11.3423 | − | 19.6455i | 0.371331 | − | 0.643164i | ||||
\(934\) | 3.78078 | − | 6.54850i | 0.123711 | − | 0.214273i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.500000 | + | 3.57071i | 0.0163430 | + | 0.116712i | ||||
\(937\) | 5.24621 | 0.171386 | 0.0856931 | − | 0.996322i | \(-0.472690\pi\) | ||||
0.0856931 | + | 0.996322i | \(0.472690\pi\) | |||||||
\(938\) | 2.47301 | − | 4.28338i | 0.0807467 | − | 0.139857i | ||||
\(939\) | −15.5000 | + | 26.8468i | −0.505823 | + | 0.876112i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 59.3693 | 1.93538 | 0.967692 | − | 0.252134i | \(-0.0811325\pi\) | ||||
0.967692 | + | 0.252134i | \(0.0811325\pi\) | |||||||
\(942\) | −0.376894 | − | 0.652800i | −0.0122799 | − | 0.0212694i | ||||
\(943\) | −12.0000 | − | 20.7846i | −0.390774 | − | 0.676840i | ||||
\(944\) | 6.24621 | 0.203297 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.12311 | + | 14.0696i | −0.264105 | + | 0.457443i | ||||
\(947\) | 15.8348 | − | 27.4266i | 0.514560 | − | 0.891245i | −0.485297 | − | 0.874349i | \(-0.661289\pi\) |
0.999857 | − | 0.0168952i | \(-0.00537816\pi\) | |||||||
\(948\) | 4.80776 | 0.156149 | ||||||||
\(949\) | −30.0810 | − | 12.1711i | −0.976469 | − | 0.395091i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.123106 | − | 0.213225i | 0.00399197 | − | 0.00691430i | ||||
\(952\) | −1.43845 | + | 2.49146i | −0.0466203 | + | 0.0807488i | ||||
\(953\) | −4.12311 | − | 7.14143i | −0.133560 | − | 0.231334i | 0.791486 | − | 0.611187i | \(-0.209308\pi\) |
−0.925047 | + | 0.379854i | \(0.875974\pi\) | |||||||
\(954\) | −12.2462 | −0.396486 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.02699 | + | 8.70700i | 0.162584 | + | 0.281604i | ||||
\(957\) | −25.3693 | −0.820074 | ||||||||
\(958\) | −14.8078 | − | 25.6478i | −0.478417 | − | 0.828643i | ||||
\(959\) | 4.63068 | − | 8.02058i | 0.149533 | − | 0.258998i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | −1.78078 | − | 12.7173i | −0.0574145 | − | 0.410022i | ||||
\(963\) | −19.3693 | −0.624168 | ||||||||
\(964\) | −5.71922 | + | 9.90599i | −0.184204 | + | 0.319050i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.31534 | − | 2.27824i | −0.0423204 | − | 0.0733011i | ||||
\(967\) | 41.3693 | 1.33035 | 0.665174 | − | 0.746689i | \(-0.268357\pi\) | ||||
0.665174 | + | 0.746689i | \(0.268357\pi\) | |||||||
\(968\) | −0.842329 | − | 1.45896i | −0.0270735 | − | 0.0468927i | ||||
\(969\) | 16.8078 | + | 29.1119i | 0.539943 | + | 0.935209i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.6847 | − | 34.0948i | −0.631711 | − | 1.09416i | −0.987202 | − | 0.159475i | \(-0.949020\pi\) |
0.355491 | − | 0.934680i | \(-0.384314\pi\) | |||||||
\(972\) | −0.500000 | + | 0.866025i | −0.0160375 | + | 0.0277778i | ||||
\(973\) | −4.89630 | + | 8.48065i | −0.156968 | + | 0.271877i | ||||
\(974\) | 30.3153 | 0.971366 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.6847 | 0.342008 | ||||||||
\(977\) | 14.8769 | − | 25.7675i | 0.475954 | − | 0.824377i | −0.523666 | − | 0.851923i | \(-0.675436\pi\) |
0.999621 | + | 0.0275468i | \(0.00876953\pi\) | |||||||
\(978\) | −8.24621 | + | 14.2829i | −0.263685 | + | 0.456715i | ||||
\(979\) | 11.1231 | + | 19.2658i | 0.355496 | + | 0.615737i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.90388 | − | 15.4220i | −0.284279 | − | 0.492386i | ||||
\(982\) | 11.1501 | + | 19.3125i | 0.355814 | + | 0.616288i | ||||
\(983\) | −5.75379 | −0.183517 | −0.0917587 | − | 0.995781i | \(-0.529249\pi\) | ||||
−0.0917587 | + | 0.995781i | \(0.529249\pi\) | |||||||
\(984\) | −2.56155 | − | 4.43674i | −0.0816593 | − | 0.141438i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 18.2462 | − | 31.6034i | 0.581078 | − | 1.00646i | ||||
\(987\) | 2.24621 | 0.0714977 | ||||||||
\(988\) | −18.6501 | + | 14.5560i | −0.593339 | + | 0.463086i | ||||
\(989\) | 21.3693 | 0.679505 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.5270 | − | 49.4102i | 0.906190 | − | 1.56957i | 0.0868773 | − | 0.996219i | \(-0.472311\pi\) |
0.819312 | − | 0.573347i | \(-0.194355\pi\) | |||||||
\(992\) | −2.00000 | − | 3.46410i | −0.0635001 | − | 0.109985i | ||||
\(993\) | −4.31534 | −0.136943 | ||||||||
\(994\) | −2.36932 | − | 4.10378i | −0.0751502 | − | 0.130164i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.43845 | 0.0772652 | ||||||||
\(997\) | 25.3348 | + | 43.8811i | 0.802360 | + | 1.38973i | 0.918059 | + | 0.396443i | \(0.129756\pi\) |
−0.115700 | + | 0.993284i | \(0.536911\pi\) | |||||||
\(998\) | 15.5270 | − | 26.8935i | 0.491498 | − | 0.851300i | ||||
\(999\) | 1.78078 | − | 3.08440i | 0.0563413 | − | 0.0975859i |
(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 | 1950.2.i.z.451.1 | ✓ | 4 | |
5.2 | odd | 4 | 1950.2.z.m.1699.2 | 8 | |||
5.3 | odd | 4 | 1950.2.z.m.1699.3 | 8 | |||
5.4 | even | 2 | 1950.2.i.bg.451.2 | yes | 4 | ||
13.3 | even | 3 | inner | 1950.2.i.z.601.1 | yes | 4 | |
65.3 | odd | 12 | 1950.2.z.m.1849.2 | 8 | |||
65.29 | even | 6 | 1950.2.i.bg.601.2 | yes | 4 | ||
65.42 | odd | 12 | 1950.2.z.m.1849.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.i.z.451.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1950.2.i.z.601.1 | yes | 4 | 13.3 | even | 3 | inner | |
1950.2.i.bg.451.2 | yes | 4 | 5.4 | even | 2 | ||
1950.2.i.bg.601.2 | yes | 4 | 65.29 | even | 6 | ||
1950.2.z.m.1699.2 | 8 | 5.2 | odd | 4 | |||
1950.2.z.m.1699.3 | 8 | 5.3 | odd | 4 | |||
1950.2.z.m.1849.2 | 8 | 65.3 | odd | 12 | |||
1950.2.z.m.1849.3 | 8 | 65.42 | odd | 12 |