Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(1699,1950)]
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, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.1699");
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.z (of order \(6\), degree \(2\), not 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: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.1731891456.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1699.2 | ||
Root | \(1.35234 - 0.780776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.1699 |
Dual form | 1950.2.z.m.1849.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0.866025 | + | 0.500000i | 0.500000 | + | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | 0.486319 | − | 0.280776i | 0.183811 | − | 0.106124i | −0.405271 | − | 0.914197i | \(-0.632823\pi\) |
0.589082 | + | 0.808073i | \(0.299489\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 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 | \(0.986253\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | −1.35234 | + | 3.34233i | −0.375073 | + | 0.926995i | ||||
\(14\) | −0.561553 | −0.150081 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 4.43674 | − | 2.56155i | 1.07607 | − | 0.621268i | 0.146235 | − | 0.989250i | \(-0.453285\pi\) |
0.929833 | + | 0.367982i | \(0.119951\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −3.28078 | − | 5.68247i | −0.752662 | − | 1.30365i | −0.946528 | − | 0.322620i | \(-0.895436\pi\) |
0.193867 | − | 0.981028i | \(-0.437897\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.561553 | 0.122541 | ||||||||
\(22\) | 3.08440 | − | 1.78078i | 0.657595 | − | 0.379663i | ||||
\(23\) | 4.05703 | + | 2.34233i | 0.845950 | + | 0.488409i | 0.859282 | − | 0.511502i | \(-0.170911\pi\) |
−0.0133324 | + | 0.999911i | \(0.504244\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.84233 | − | 2.21837i | 0.557427 | − | 0.435058i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0.486319 | + | 0.280776i | 0.0919057 | + | 0.0530618i | ||||
\(29\) | −3.56155 | + | 6.16879i | −0.661364 | + | 1.14552i | 0.318894 | + | 0.947790i | \(0.396689\pi\) |
−0.980257 | + | 0.197725i | \(0.936645\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | −3.08440 | + | 1.78078i | −0.536924 | + | 0.309993i | ||||
\(34\) | −5.12311 | −0.878605 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 3.08440 | + | 1.78078i | 0.507071 | + | 0.292758i | 0.731629 | − | 0.681703i | \(-0.238760\pi\) |
−0.224558 | + | 0.974461i | \(0.572094\pi\) | |||||||
\(38\) | 6.56155i | 1.06442i | ||||||||
\(39\) | −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 | \(0.297673\pi\) | |||||||
\(42\) | −0.486319 | − | 0.280776i | −0.0750407 | − | 0.0433247i | ||||
\(43\) | −3.95042 | + | 2.28078i | −0.602433 | + | 0.347815i | −0.769998 | − | 0.638046i | \(-0.779743\pi\) |
0.167565 | + | 0.985861i | \(0.446410\pi\) | |||||||
\(44\) | −3.56155 | −0.536924 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.34233 | − | 4.05703i | −0.345358 | − | 0.598177i | ||||
\(47\) | 4.00000i | 0.583460i | 0.956501 | + | 0.291730i | \(0.0942309\pi\) | ||||
−0.956501 | + | 0.291730i | \(0.905769\pi\) | |||||||
\(48\) | −0.866025 | + | 0.500000i | −0.125000 | + | 0.0721688i | ||||
\(49\) | −3.34233 | + | 5.78908i | −0.477476 | + | 0.827012i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.12311 | 0.717378 | ||||||||
\(52\) | −3.57071 | + | 0.500000i | −0.495169 | + | 0.0693375i | ||||
\(53\) | 12.2462i | 1.68215i | 0.540921 | + | 0.841073i | \(0.318076\pi\) | ||||
−0.540921 | + | 0.841073i | \(0.681924\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.280776 | − | 0.486319i | −0.0375203 | − | 0.0649871i | ||||
\(57\) | − | 6.56155i | − | 0.869099i | ||||||
\(58\) | 6.16879 | − | 3.56155i | 0.810002 | − | 0.467655i | ||||
\(59\) | 3.12311 | + | 5.40938i | 0.406594 | + | 0.704241i | 0.994506 | − | 0.104684i | \(-0.0333831\pi\) |
−0.587912 | + | 0.808925i | \(0.700050\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.34233 | − | 9.25319i | −0.684015 | − | 1.18475i | −0.973745 | − | 0.227641i | \(-0.926899\pi\) |
0.289730 | − | 0.957108i | \(-0.406434\pi\) | |||||||
\(62\) | −3.46410 | − | 2.00000i | −0.439941 | − | 0.254000i | ||||
\(63\) | 0.486319 | + | 0.280776i | 0.0612704 | + | 0.0353745i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.56155 | 0.438397 | ||||||||
\(67\) | 7.62775 | + | 4.40388i | 0.931878 | + | 0.538020i | 0.887405 | − | 0.460991i | \(-0.152506\pi\) |
0.0444727 | + | 0.999011i | \(0.485839\pi\) | |||||||
\(68\) | 4.43674 | + | 2.56155i | 0.538034 | + | 0.310634i | ||||
\(69\) | 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 | \(-0.333602\pi\) | |||||||
\(72\) | 0.866025 | − | 0.500000i | 0.102062 | − | 0.0589256i | ||||
\(73\) | − | 9.00000i | − | 1.05337i | −0.850060 | − | 0.526685i | \(-0.823435\pi\) | ||
0.850060 | − | 0.526685i | \(-0.176565\pi\) | |||||||
\(74\) | −1.78078 | − | 3.08440i | −0.207011 | − | 0.358554i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.28078 | − | 5.68247i | 0.376331 | − | 0.651824i | ||||
\(77\) | 2.00000i | 0.227921i | ||||||||
\(78\) | 3.57071 | − | 0.500000i | 0.404304 | − | 0.0566139i | ||||
\(79\) | −4.80776 | −0.540916 | −0.270458 | − | 0.962732i | \(-0.587175\pi\) | ||||
−0.270458 | + | 0.962732i | \(0.587175\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 4.43674 | − | 2.56155i | 0.489956 | − | 0.282876i | ||||
\(83\) | − | 2.43845i | − | 0.267654i | −0.991005 | − | 0.133827i | \(-0.957273\pi\) | ||
0.991005 | − | 0.133827i | \(-0.0427267\pi\) | |||||||
\(84\) | 0.280776 | + | 0.486319i | 0.0306352 | + | 0.0530618i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.56155 | 0.491885 | ||||||||
\(87\) | −6.16879 | + | 3.56155i | −0.661364 | + | 0.381839i | ||||
\(88\) | 3.08440 | + | 1.78078i | 0.328798 | + | 0.189831i | ||||
\(89\) | −3.12311 | + | 5.40938i | −0.331049 | + | 0.573393i | −0.982718 | − | 0.185110i | \(-0.940736\pi\) |
0.651669 | + | 0.758503i | \(0.274069\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.280776 | + | 2.00514i | 0.0294334 | + | 0.210196i | ||||
\(92\) | 4.68466i | 0.488409i | ||||||||
\(93\) | 3.46410 | + | 2.00000i | 0.359211 | + | 0.207390i | ||||
\(94\) | 2.00000 | − | 3.46410i | 0.206284 | − | 0.357295i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 15.4220 | − | 8.90388i | 1.56586 | − | 0.904052i | 0.569221 | − | 0.822184i | \(-0.307245\pi\) |
0.996643 | − | 0.0818678i | \(-0.0260885\pi\) | |||||||
\(98\) | 5.78908 | − | 3.34233i | 0.584786 | − | 0.337626i | ||||
\(99\) | −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 | \(0.996398\pi\) | |||||||
\(102\) | −4.43674 | − | 2.56155i | −0.439303 | − | 0.253632i | ||||
\(103\) | 8.56155i | 0.843595i | 0.906690 | + | 0.421797i | \(0.138601\pi\) | ||||
−0.906690 | + | 0.421797i | \(0.861399\pi\) | |||||||
\(104\) | 3.34233 | + | 1.35234i | 0.327742 | + | 0.132608i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.12311 | − | 10.6055i | 0.594729 | − | 1.03010i | ||||
\(107\) | 16.7743 | + | 9.68466i | 1.62163 | + | 0.936251i | 0.986483 | + | 0.163864i | \(0.0523958\pi\) |
0.635152 | + | 0.772387i | \(0.280938\pi\) | |||||||
\(108\) | −0.866025 | + | 0.500000i | −0.0833333 | + | 0.0481125i | ||||
\(109\) | −17.8078 | −1.70567 | −0.852837 | − | 0.522177i | \(-0.825120\pi\) | ||||
−0.852837 | + | 0.522177i | \(0.825120\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.78078 | + | 3.08440i | 0.169024 | + | 0.292758i | ||||
\(112\) | 0.561553i | 0.0530618i | ||||||||
\(113\) | −3.46410 | + | 2.00000i | −0.325875 | + | 0.188144i | −0.654008 | − | 0.756487i | \(-0.726914\pi\) |
0.328133 | + | 0.944632i | \(0.393581\pi\) | |||||||
\(114\) | −3.28078 | + | 5.68247i | −0.307273 | + | 0.532212i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.12311 | −0.661364 | ||||||||
\(117\) | −3.57071 | + | 0.500000i | −0.330113 | + | 0.0462250i | ||||
\(118\) | − | 6.24621i | − | 0.575010i | ||||||
\(119\) | 1.43845 | − | 2.49146i | 0.131862 | − | 0.228392i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.842329 | − | 1.45896i | −0.0765754 | − | 0.132632i | ||||
\(122\) | 10.6847i | 0.967344i | ||||||||
\(123\) | −4.43674 | + | 2.56155i | −0.400047 | + | 0.230967i | ||||
\(124\) | 2.00000 | + | 3.46410i | 0.179605 | + | 0.311086i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.280776 | − | 0.486319i | −0.0250136 | − | 0.0433247i | ||||
\(127\) | −1.03251 | − | 0.596118i | −0.0916201 | − | 0.0528969i | 0.453490 | − | 0.891261i | \(-0.350179\pi\) |
−0.545110 | + | 0.838364i | \(0.683512\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | −4.56155 | −0.401622 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.12311 | 0.797089 | 0.398545 | − | 0.917149i | \(-0.369515\pi\) | ||||
0.398545 | + | 0.917149i | \(0.369515\pi\) | |||||||
\(132\) | −3.08440 | − | 1.78078i | −0.268462 | − | 0.154997i | ||||
\(133\) | −3.19101 | − | 1.84233i | −0.276695 | − | 0.159750i | ||||
\(134\) | −4.40388 | − | 7.62775i | −0.380437 | − | 0.658937i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.56155 | − | 4.43674i | −0.219651 | − | 0.380447i | ||||
\(137\) | −14.2829 | + | 8.24621i | −1.22027 | + | 0.704521i | −0.964975 | − | 0.262343i | \(-0.915505\pi\) |
−0.255292 | + | 0.966864i | \(0.582172\pi\) | |||||||
\(138\) | − | 4.68466i | − | 0.398785i | ||||||
\(139\) | 8.71922 | + | 15.1021i | 0.739555 | + | 1.28095i | 0.952696 | + | 0.303925i | \(0.0982973\pi\) |
−0.213141 | + | 0.977021i | \(0.568369\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00000 | + | 3.46410i | −0.168430 | + | 0.291730i | ||||
\(142\) | 8.43845i | 0.708139i | ||||||||
\(143\) | −7.90084 | − | 10.1231i | −0.660702 | − | 0.846537i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.50000 | + | 7.79423i | −0.372423 | + | 0.645055i | ||||
\(147\) | −5.78908 | + | 3.34233i | −0.477476 | + | 0.275671i | ||||
\(148\) | 3.56155i | 0.292758i | ||||||||
\(149\) | 3.12311 | + | 5.40938i | 0.255855 | + | 0.443153i | 0.965127 | − | 0.261781i | \(-0.0843098\pi\) |
−0.709273 | + | 0.704934i | \(0.750976\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.31534 | −0.351178 | −0.175589 | − | 0.984464i | \(-0.556183\pi\) | ||||
−0.175589 | + | 0.984464i | \(0.556183\pi\) | |||||||
\(152\) | −5.68247 | + | 3.28078i | −0.460909 | + | 0.266106i | ||||
\(153\) | 4.43674 | + | 2.56155i | 0.358689 | + | 0.207089i | ||||
\(154\) | 1.00000 | − | 1.73205i | 0.0805823 | − | 0.139573i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.34233 | − | 1.35234i | −0.267601 | − | 0.108274i | ||||
\(157\) | 0.753789i | 0.0601589i | 0.999548 | + | 0.0300794i | \(0.00957603\pi\) | ||||
−0.999548 | + | 0.0300794i | \(0.990424\pi\) | |||||||
\(158\) | 4.16365 | + | 2.40388i | 0.331242 | + | 0.191243i | ||||
\(159\) | −6.12311 | + | 10.6055i | −0.485594 | + | 0.841073i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.63068 | 0.207327 | ||||||||
\(162\) | 0.866025 | − | 0.500000i | 0.0680414 | − | 0.0392837i | ||||
\(163\) | −14.2829 | + | 8.24621i | −1.11872 | + | 0.645893i | −0.941074 | − | 0.338201i | \(-0.890182\pi\) |
−0.177646 | + | 0.984094i | \(0.556848\pi\) | |||||||
\(164\) | −5.12311 | −0.400047 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.21922 | + | 2.11176i | −0.0946301 | + | 0.163904i | ||||
\(167\) | −9.79937 | − | 5.65767i | −0.758298 | − | 0.437804i | 0.0703862 | − | 0.997520i | \(-0.477577\pi\) |
−0.828684 | + | 0.559716i | \(0.810910\pi\) | |||||||
\(168\) | − | 0.561553i | − | 0.0433247i | ||||||
\(169\) | −9.34233 | − | 9.03996i | −0.718641 | − | 0.695382i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.28078 | − | 5.68247i | 0.250887 | − | 0.434549i | ||||
\(172\) | −3.95042 | − | 2.28078i | −0.301217 | − | 0.173908i | ||||
\(173\) | 14.8290 | − | 8.56155i | 1.12743 | − | 0.650923i | 0.184144 | − | 0.982899i | \(-0.441049\pi\) |
0.943288 | + | 0.331977i | \(0.107715\pi\) | |||||||
\(174\) | 7.12311 | 0.540001 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.78078 | − | 3.08440i | −0.134231 | − | 0.232495i | ||||
\(177\) | 6.24621i | 0.469494i | ||||||||
\(178\) | 5.40938 | − | 3.12311i | 0.405450 | − | 0.234087i | ||||
\(179\) | −1.65767 | + | 2.87117i | −0.123900 | + | 0.214601i | −0.921302 | − | 0.388847i | \(-0.872874\pi\) |
0.797402 | + | 0.603448i | \(0.206207\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.4924 | 1.30020 | 0.650101 | − | 0.759848i | \(-0.274727\pi\) | ||||
0.650101 | + | 0.759848i | \(0.274727\pi\) | |||||||
\(182\) | 0.759413 | − | 1.87689i | 0.0562914 | − | 0.139125i | ||||
\(183\) | − | 10.6847i | − | 0.789833i | ||||||
\(184\) | 2.34233 | − | 4.05703i | 0.172679 | − | 0.299088i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.00000 | − | 3.46410i | −0.146647 | − | 0.254000i | ||||
\(187\) | 18.2462i | 1.33430i | ||||||||
\(188\) | −3.46410 | + | 2.00000i | −0.252646 | + | 0.145865i | ||||
\(189\) | 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 | \(0.678372\pi\) | |||||||
\(192\) | −0.866025 | − | 0.500000i | −0.0625000 | − | 0.0360844i | ||||
\(193\) | 2.59808 | + | 1.50000i | 0.187014 | + | 0.107972i | 0.590584 | − | 0.806976i | \(-0.298898\pi\) |
−0.403570 | + | 0.914949i | \(0.632231\pi\) | |||||||
\(194\) | −17.8078 | −1.27852 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.68466 | −0.477476 | ||||||||
\(197\) | 2.70469 | + | 1.56155i | 0.192701 | + | 0.111256i | 0.593246 | − | 0.805021i | \(-0.297846\pi\) |
−0.400545 | + | 0.916277i | \(0.631179\pi\) | |||||||
\(198\) | 3.08440 | + | 1.78078i | 0.219198 | + | 0.126554i | ||||
\(199\) | −4.28078 | − | 7.41452i | −0.303456 | − | 0.525602i | 0.673460 | − | 0.739223i | \(-0.264807\pi\) |
−0.976916 | + | 0.213622i | \(0.931474\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.40388 | + | 7.62775i | 0.310626 | + | 0.538020i | ||||
\(202\) | 8.87348 | − | 5.12311i | 0.624336 | − | 0.360460i | ||||
\(203\) | 4.00000i | 0.280745i | ||||||||
\(204\) | 2.56155 | + | 4.43674i | 0.179345 | + | 0.310634i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.28078 | − | 7.41452i | 0.298256 | − | 0.516594i | ||||
\(207\) | 4.68466i | 0.325606i | ||||||||
\(208\) | −2.21837 | − | 2.84233i | −0.153816 | − | 0.197080i | ||||
\(209\) | 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 | \(0.0878172\pi\) | |||||||
\(212\) | −10.6055 | + | 6.12311i | −0.728391 | + | 0.420537i | ||||
\(213\) | − | 8.43845i | − | 0.578193i | ||||||
\(214\) | −9.68466 | − | 16.7743i | −0.662030 | − | 1.14667i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 1.94528 | − | 1.12311i | 0.132054 | − | 0.0762414i | ||||
\(218\) | 15.4220 | + | 8.90388i | 1.04451 | + | 0.603047i | ||||
\(219\) | 4.50000 | − | 7.79423i | 0.304082 | − | 0.526685i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.56155 | + | 18.2931i | 0.172309 | + | 1.23053i | ||||
\(222\) | − | 3.56155i | − | 0.239036i | ||||||
\(223\) | −3.95042 | − | 2.28078i | −0.264540 | − | 0.152732i | 0.361864 | − | 0.932231i | \(-0.382140\pi\) |
−0.626404 | + | 0.779499i | \(0.715474\pi\) | |||||||
\(224\) | 0.280776 | − | 0.486319i | 0.0187602 | − | 0.0324936i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.00000 | 0.266076 | ||||||||
\(227\) | 14.9955 | − | 8.65767i | 0.995288 | − | 0.574630i | 0.0884373 | − | 0.996082i | \(-0.471813\pi\) |
0.906851 | + | 0.421452i | \(0.138479\pi\) | |||||||
\(228\) | 5.68247 | − | 3.28078i | 0.376331 | − | 0.217275i | ||||
\(229\) | 23.4924 | 1.55242 | 0.776211 | − | 0.630473i | \(-0.217139\pi\) | ||||
0.776211 | + | 0.630473i | \(0.217139\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.00000 | + | 1.73205i | −0.0657952 | + | 0.113961i | ||||
\(232\) | 6.16879 | + | 3.56155i | 0.405001 | + | 0.233827i | ||||
\(233\) | 0.630683i | 0.0413174i | 0.999787 | + | 0.0206587i | \(0.00657634\pi\) | ||||
−0.999787 | + | 0.0206587i | \(0.993424\pi\) | |||||||
\(234\) | 3.34233 | + | 1.35234i | 0.218495 | + | 0.0884055i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.12311 | + | 5.40938i | −0.203297 | + | 0.352120i | ||||
\(237\) | −4.16365 | − | 2.40388i | −0.270458 | − | 0.156149i | ||||
\(238\) | −2.49146 | + | 1.43845i | −0.161498 | + | 0.0932407i | ||||
\(239\) | 10.0540 | 0.650338 | 0.325169 | − | 0.945656i | \(-0.394579\pi\) | ||||
0.325169 | + | 0.945656i | \(0.394579\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.71922 | − | 9.90599i | −0.368408 | − | 0.638101i | 0.620909 | − | 0.783883i | \(-0.286764\pi\) |
−0.989317 | + | 0.145782i | \(0.953430\pi\) | |||||||
\(242\) | 1.68466i | 0.108294i | ||||||||
\(243\) | −0.866025 | + | 0.500000i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | 5.34233 | − | 9.25319i | 0.342008 | − | 0.592375i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.12311 | 0.326637 | ||||||||
\(247\) | 23.4294 | − | 3.28078i | 1.49078 | − | 0.208751i | ||||
\(248\) | − | 4.00000i | − | 0.254000i | ||||||
\(249\) | 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 | \(0.783597\pi\) | |||||||
\(252\) | 0.561553i | 0.0353745i | ||||||||
\(253\) | −14.4493 | + | 8.34233i | −0.908422 | + | 0.524478i | ||||
\(254\) | 0.596118 | + | 1.03251i | 0.0374038 | + | 0.0647852i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −23.9157 | − | 13.8078i | −1.49182 | − | 0.861305i | −0.491867 | − | 0.870670i | \(-0.663685\pi\) |
−0.999956 | + | 0.00936553i | \(0.997019\pi\) | |||||||
\(258\) | 3.95042 | + | 2.28078i | 0.245942 | + | 0.141995i | ||||
\(259\) | 2.00000 | 0.124274 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.12311 | −0.440909 | ||||||||
\(262\) | −7.90084 | − | 4.56155i | −0.488116 | − | 0.281814i | ||||
\(263\) | 16.1814 | + | 9.34233i | 0.997787 | + | 0.576073i | 0.907593 | − | 0.419851i | \(-0.137918\pi\) |
0.0901944 | + | 0.995924i | \(0.471251\pi\) | |||||||
\(264\) | 1.78078 | + | 3.08440i | 0.109599 | + | 0.189831i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.84233 | + | 3.19101i | 0.112960 | + | 0.195653i | ||||
\(267\) | −5.40938 | + | 3.12311i | −0.331049 | + | 0.191131i | ||||
\(268\) | 8.80776i | 0.538020i | ||||||||
\(269\) | 10.6847 | + | 18.5064i | 0.651455 | + | 1.12835i | 0.982770 | + | 0.184833i | \(0.0591745\pi\) |
−0.331315 | + | 0.943520i | \(0.607492\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.96543 | − | 17.2606i | 0.605357 | − | 1.04851i | −0.386638 | − | 0.922232i | \(-0.626364\pi\) |
0.991995 | − | 0.126278i | \(-0.0403030\pi\) | |||||||
\(272\) | 5.12311i | 0.310634i | ||||||||
\(273\) | −0.759413 | + | 1.87689i | −0.0459618 | + | 0.113595i | ||||
\(274\) | 16.4924 | 0.996344 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.34233 | + | 4.05703i | −0.140992 | + | 0.244205i | ||||
\(277\) | 4.33013 | − | 2.50000i | 0.260172 | − | 0.150210i | −0.364241 | − | 0.931305i | \(-0.618672\pi\) |
0.624413 | + | 0.781094i | \(0.285338\pi\) | |||||||
\(278\) | − | 17.4384i | − | 1.04589i | ||||||
\(279\) | 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 | \(0.683181\pi\) | |||||||
\(282\) | 3.46410 | − | 2.00000i | 0.206284 | − | 0.119098i | ||||
\(283\) | −10.0593 | − | 5.80776i | −0.597966 | − | 0.345236i | 0.170275 | − | 0.985397i | \(-0.445534\pi\) |
−0.768241 | + | 0.640161i | \(0.778868\pi\) | |||||||
\(284\) | 4.21922 | − | 7.30791i | 0.250365 | − | 0.433645i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.78078 | + | 12.7173i | 0.105300 | + | 0.751989i | ||||
\(287\) | 2.87689i | 0.169818i | ||||||||
\(288\) | 0.866025 | + | 0.500000i | 0.0510310 | + | 0.0294628i | ||||
\(289\) | 4.62311 | − | 8.00745i | 0.271947 | − | 0.471027i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.8078 | 1.04391 | ||||||||
\(292\) | 7.79423 | − | 4.50000i | 0.456123 | − | 0.263343i | ||||
\(293\) | −3.25088 | + | 1.87689i | −0.189918 | + | 0.109649i | −0.591944 | − | 0.805979i | \(-0.701639\pi\) |
0.402026 | + | 0.915628i | \(0.368306\pi\) | |||||||
\(294\) | 6.68466 | 0.389857 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.78078 | − | 3.08440i | 0.103506 | − | 0.179277i | ||||
\(297\) | −3.08440 | − | 1.78078i | −0.178975 | − | 0.103331i | ||||
\(298\) | − | 6.24621i | − | 0.361833i | ||||||
\(299\) | −13.3153 | + | 10.3923i | −0.770046 | + | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.28078 | + | 2.21837i | −0.0738227 | + | 0.127865i | ||||
\(302\) | 3.73720 | + | 2.15767i | 0.215051 | + | 0.124160i | ||||
\(303\) | −8.87348 | + | 5.12311i | −0.509768 | + | 0.294315i | ||||
\(304\) | 6.56155 | 0.376331 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.56155 | − | 4.43674i | −0.146434 | − | 0.253632i | ||||
\(307\) | 5.75379i | 0.328386i | 0.986428 | + | 0.164193i | \(0.0525020\pi\) | ||||
−0.986428 | + | 0.164193i | \(0.947498\pi\) | |||||||
\(308\) | −1.73205 | + | 1.00000i | −0.0986928 | + | 0.0569803i | ||||
\(309\) | −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 | \(0.722379\pi\) | |||||||
\(312\) | 2.21837 | + | 2.84233i | 0.125590 | + | 0.160915i | ||||
\(313\) | − | 31.0000i | − | 1.75222i | −0.482108 | − | 0.876112i | \(-0.660129\pi\) | ||
0.482108 | − | 0.876112i | \(-0.339871\pi\) | |||||||
\(314\) | 0.376894 | − | 0.652800i | 0.0212694 | − | 0.0368396i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.40388 | − | 4.16365i | −0.135229 | − | 0.234223i | ||||
\(317\) | − | 0.246211i | − | 0.0138286i | −0.999976 | − | 0.00691430i | \(-0.997799\pi\) | ||
0.999976 | − | 0.00691430i | \(-0.00220091\pi\) | |||||||
\(318\) | 10.6055 | − | 6.12311i | 0.594729 | − | 0.343367i | ||||
\(319\) | −12.6847 | − | 21.9705i | −0.710205 | − | 1.23011i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.68466 | + | 16.7743i | 0.540545 | + | 0.936251i | ||||
\(322\) | −2.27824 | − | 1.31534i | −0.126961 | − | 0.0733011i | ||||
\(323\) | −29.1119 | − | 16.8078i | −1.61983 | − | 0.935209i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16.4924 | 0.913431 | ||||||||
\(327\) | −15.4220 | − | 8.90388i | −0.852837 | − | 0.492386i | ||||
\(328\) | 4.43674 | + | 2.56155i | 0.244978 | + | 0.141438i | ||||
\(329\) | 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 | \(0.795494\pi\) | |||||||
\(332\) | 2.11176 | − | 1.21922i | 0.115898 | − | 0.0669136i | ||||
\(333\) | 3.56155i | 0.195172i | ||||||||
\(334\) | 5.65767 | + | 9.79937i | 0.309574 | + | 0.536198i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.280776 | + | 0.486319i | −0.0153176 | + | 0.0265309i | ||||
\(337\) | − | 29.0540i | − | 1.58267i | −0.611382 | − | 0.791335i | \(-0.709386\pi\) | ||
0.611382 | − | 0.791335i | \(-0.290614\pi\) | |||||||
\(338\) | 3.57071 | + | 12.5000i | 0.194221 | + | 0.679910i | ||||
\(339\) | −4.00000 | −0.217250 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.12311 | + | 12.3376i | −0.385738 | + | 0.668117i | ||||
\(342\) | −5.68247 | + | 3.28078i | −0.307273 | + | 0.177404i | ||||
\(343\) | 7.68466i | 0.414933i | ||||||||
\(344\) | 2.28078 | + | 3.95042i | 0.122971 | + | 0.212992i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.1231 | −0.920544 | ||||||||
\(347\) | −3.63058 | + | 2.09612i | −0.194900 | + | 0.112526i | −0.594274 | − | 0.804262i | \(-0.702561\pi\) |
0.399374 | + | 0.916788i | \(0.369227\pi\) | |||||||
\(348\) | −6.16879 | − | 3.56155i | −0.330682 | − | 0.190919i | ||||
\(349\) | −1.37689 | + | 2.38485i | −0.0737035 | + | 0.127658i | −0.900522 | − | 0.434811i | \(-0.856815\pi\) |
0.826818 | + | 0.562469i | \(0.190149\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.34233 | − | 1.35234i | −0.178400 | − | 0.0721828i | ||||
\(352\) | 3.56155i | 0.189831i | ||||||||
\(353\) | −12.3376 | − | 7.12311i | −0.656663 | − | 0.379125i | 0.134341 | − | 0.990935i | \(-0.457108\pi\) |
−0.791004 | + | 0.611810i | \(0.790442\pi\) | |||||||
\(354\) | 3.12311 | − | 5.40938i | 0.165991 | − | 0.287505i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.24621 | −0.331049 | ||||||||
\(357\) | 2.49146 | − | 1.43845i | 0.131862 | − | 0.0761307i | ||||
\(358\) | 2.87117 | − | 1.65767i | 0.151746 | − | 0.0876106i | ||||
\(359\) | 13.1231 | 0.692611 | 0.346306 | − | 0.938122i | \(-0.387436\pi\) | ||||
0.346306 | + | 0.938122i | \(0.387436\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.0270 | + | 20.8314i | −0.632999 | + | 1.09639i | ||||
\(362\) | −15.1489 | − | 8.74621i | −0.796208 | − | 0.459691i | ||||
\(363\) | − | 1.68466i | − | 0.0884216i | ||||||
\(364\) | −1.59612 | + | 1.24573i | −0.0836593 | + | 0.0652941i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.34233 | + | 9.25319i | −0.279248 | + | 0.483672i | ||||
\(367\) | 26.6803 | + | 15.4039i | 1.39270 | + | 0.804076i | 0.993614 | − | 0.112837i | \(-0.0359938\pi\) |
0.399087 | + | 0.916913i | \(0.369327\pi\) | |||||||
\(368\) | −4.05703 | + | 2.34233i | −0.211487 | + | 0.122102i | ||||
\(369\) | −5.12311 | −0.266698 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.43845 | + | 5.95557i | 0.178515 | + | 0.309198i | ||||
\(372\) | 4.00000i | 0.207390i | ||||||||
\(373\) | −20.3450 | + | 11.7462i | −1.05343 | + | 0.608196i | −0.923607 | − | 0.383342i | \(-0.874773\pi\) |
−0.129819 | + | 0.991538i | \(0.541440\pi\) | |||||||
\(374\) | 9.12311 | − | 15.8017i | 0.471745 | − | 0.817086i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.00000 | 0.206284 | ||||||||
\(377\) | −15.8017 | − | 20.2462i | −0.813828 | − | 1.04273i | ||||
\(378\) | − | 0.561553i | − | 0.0288832i | ||||||
\(379\) | 6.52699 | − | 11.3051i | 0.335269 | − | 0.580703i | −0.648268 | − | 0.761413i | \(-0.724506\pi\) |
0.983536 | + | 0.180710i | \(0.0578395\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.596118 | − | 1.03251i | −0.0305400 | − | 0.0528969i | ||||
\(382\) | − | 12.9309i | − | 0.661601i | ||||||
\(383\) | 8.28055 | − | 4.78078i | 0.423116 | − | 0.244286i | −0.273293 | − | 0.961931i | \(-0.588113\pi\) |
0.696410 | + | 0.717644i | \(0.254780\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.50000 | − | 2.59808i | −0.0763480 | − | 0.132239i | ||||
\(387\) | −3.95042 | − | 2.28078i | −0.200811 | − | 0.115938i | ||||
\(388\) | 15.4220 | + | 8.90388i | 0.782932 | + | 0.452026i | ||||
\(389\) | 13.3693 | 0.677851 | 0.338926 | − | 0.940813i | \(-0.389936\pi\) | ||||
0.338926 | + | 0.940813i | \(0.389936\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000 | 1.21373 | ||||||||
\(392\) | 5.78908 | + | 3.34233i | 0.292393 | + | 0.168813i | ||||
\(393\) | 7.90084 | + | 4.56155i | 0.398545 | + | 0.230100i | ||||
\(394\) | −1.56155 | − | 2.70469i | −0.0786699 | − | 0.136260i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.78078 | − | 3.08440i | −0.0894874 | − | 0.154997i | ||||
\(397\) | 9.35980 | − | 5.40388i | 0.469755 | − | 0.271213i | −0.246382 | − | 0.969173i | \(-0.579242\pi\) |
0.716137 | + | 0.697960i | \(0.245909\pi\) | |||||||
\(398\) | 8.56155i | 0.429152i | ||||||||
\(399\) | −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 | \(-0.216212\pi\) | |||||||
\(402\) | − | 8.80776i | − | 0.439291i | ||||||
\(403\) | −5.40938 | + | 13.3693i | −0.269460 | + | 0.665973i | ||||
\(404\) | −10.2462 | −0.509768 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.00000 | − | 3.46410i | 0.0992583 | − | 0.171920i | ||||
\(407\) | −10.9852 | + | 6.34233i | −0.544518 | + | 0.314378i | ||||
\(408\) | − | 5.12311i | − | 0.253632i | ||||||
\(409\) | −0.123106 | − | 0.213225i | −0.00608718 | − | 0.0105433i | 0.862966 | − | 0.505262i | \(-0.168604\pi\) |
−0.869053 | + | 0.494719i | \(0.835271\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.4924 | −0.813511 | ||||||||
\(412\) | −7.41452 | + | 4.28078i | −0.365287 | + | 0.210899i | ||||
\(413\) | 3.03765 | + | 1.75379i | 0.149473 | + | 0.0862983i | ||||
\(414\) | 2.34233 | − | 4.05703i | 0.115119 | − | 0.199392i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.500000 | + | 3.57071i | 0.0245145 | + | 0.175069i | ||||
\(417\) | 17.4384i | 0.853964i | ||||||||
\(418\) | −20.2384 | − | 11.6847i | −0.989894 | − | 0.571515i | ||||
\(419\) | 8.46543 | − | 14.6626i | 0.413564 | − | 0.716313i | −0.581713 | − | 0.813394i | \(-0.697617\pi\) |
0.995276 | + | 0.0970811i | \(0.0309506\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.7538 | 0.719056 | 0.359528 | − | 0.933134i | \(-0.382938\pi\) | ||||
0.359528 | + | 0.933134i | \(0.382938\pi\) | |||||||
\(422\) | −6.16879 | + | 3.56155i | −0.300292 | + | 0.173374i | ||||
\(423\) | −3.46410 | + | 2.00000i | −0.168430 | + | 0.0972433i | ||||
\(424\) | 12.2462 | 0.594729 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.21922 | + | 7.30791i | −0.204422 | + | 0.354069i | ||||
\(427\) | −5.19615 | − | 3.00000i | −0.251459 | − | 0.145180i | ||||
\(428\) | 19.3693i | 0.936251i | ||||||||
\(429\) | −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 | \(0.901958\pi\) | |||||||
\(432\) | −0.866025 | − | 0.500000i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | 1.13912 | − | 0.657671i | 0.0547426 | − | 0.0316056i | −0.472379 | − | 0.881396i | \(-0.656605\pi\) |
0.527121 | + | 0.849790i | \(0.323271\pi\) | |||||||
\(434\) | −2.24621 | −0.107822 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.90388 | − | 15.4220i | −0.426419 | − | 0.738579i | ||||
\(437\) | − | 30.7386i | − | 1.47043i | ||||||
\(438\) | −7.79423 | + | 4.50000i | −0.372423 | + | 0.215018i | ||||
\(439\) | 10.9654 | − | 18.9927i | 0.523352 | − | 0.906472i | −0.476279 | − | 0.879294i | \(-0.658015\pi\) |
0.999631 | − | 0.0271774i | \(-0.00865191\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.68466 | −0.318317 | ||||||||
\(442\) | 6.92820 | − | 17.1231i | 0.329541 | − | 0.814463i | ||||
\(443\) | − | 17.8078i | − | 0.846072i | −0.906113 | − | 0.423036i | \(-0.860964\pi\) | ||
0.906113 | − | 0.423036i | \(-0.139036\pi\) | |||||||
\(444\) | −1.78078 | + | 3.08440i | −0.0845119 | + | 0.146379i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.28078 | + | 3.95042i | 0.107998 | + | 0.187058i | ||||
\(447\) | 6.24621i | 0.295436i | ||||||||
\(448\) | −0.486319 | + | 0.280776i | −0.0229764 | + | 0.0132654i | ||||
\(449\) | 2.56155 | + | 4.43674i | 0.120887 | + | 0.209383i | 0.920118 | − | 0.391642i | \(-0.128093\pi\) |
−0.799231 | + | 0.601024i | \(0.794759\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.12311 | − | 15.8017i | −0.429590 | − | 0.744072i | ||||
\(452\) | −3.46410 | − | 2.00000i | −0.162938 | − | 0.0940721i | ||||
\(453\) | −3.73720 | − | 2.15767i | −0.175589 | − | 0.101376i | ||||
\(454\) | −17.3153 | −0.812649 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.56155 | −0.307273 | ||||||||
\(457\) | −32.4694 | − | 18.7462i | −1.51885 | − | 0.876911i | −0.999754 | − | 0.0221975i | \(-0.992934\pi\) |
−0.519100 | − | 0.854713i | \(-0.673733\pi\) | |||||||
\(458\) | −20.3450 | − | 11.7462i | −0.950661 | − | 0.548864i | ||||
\(459\) | 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 | \(-0.474736\pi\) | |||||||
\(462\) | 1.73205 | − | 1.00000i | 0.0805823 | − | 0.0465242i | ||||
\(463\) | − | 7.19224i | − | 0.334252i | −0.985936 | − | 0.167126i | \(-0.946551\pi\) | ||
0.985936 | − | 0.167126i | \(-0.0534486\pi\) | |||||||
\(464\) | −3.56155 | − | 6.16879i | −0.165341 | − | 0.286379i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.315342 | − | 0.546188i | 0.0146079 | − | 0.0253017i | ||||
\(467\) | − | 7.56155i | − | 0.349907i | −0.984577 | − | 0.174953i | \(-0.944022\pi\) | ||
0.984577 | − | 0.174953i | \(-0.0559775\pi\) | |||||||
\(468\) | −2.21837 | − | 2.84233i | −0.102544 | − | 0.131387i | ||||
\(469\) | 4.94602 | 0.228386 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.376894 | + | 0.652800i | −0.0173664 | + | 0.0300794i | ||||
\(472\) | 5.40938 | − | 3.12311i | 0.248987 | − | 0.143753i | ||||
\(473\) | − | 16.2462i | − | 0.747002i | ||||||
\(474\) | 2.40388 | + | 4.16365i | 0.110414 | + | 0.191243i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.87689 | 0.131862 | ||||||||
\(477\) | −10.6055 | + | 6.12311i | −0.485594 | + | 0.280358i | ||||
\(478\) | −8.70700 | − | 5.02699i | −0.398249 | − | 0.229929i | ||||
\(479\) | 14.8078 | − | 25.6478i | 0.676584 | − | 1.17188i | −0.299419 | − | 0.954122i | \(-0.596793\pi\) |
0.976003 | − | 0.217756i | \(-0.0698738\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.1231 | + | 7.90084i | −0.461574 | + | 0.360247i | ||||
\(482\) | 11.4384i | 0.521007i | ||||||||
\(483\) | 2.27824 | + | 1.31534i | 0.103663 | + | 0.0598501i | ||||
\(484\) | 0.842329 | − | 1.45896i | 0.0382877 | − | 0.0663162i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 26.2539 | − | 15.1577i | 1.18968 | − | 0.686860i | 0.231443 | − | 0.972849i | \(-0.425655\pi\) |
0.958233 | + | 0.285989i | \(0.0923220\pi\) | |||||||
\(488\) | −9.25319 | + | 5.34233i | −0.418872 | + | 0.241836i | ||||
\(489\) | −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 | \(-0.00117620\pi\) | |||||||
\(492\) | −4.43674 | − | 2.56155i | −0.200024 | − | 0.115484i | ||||
\(493\) | 36.4924i | 1.64354i | ||||||||
\(494\) | −21.9309 | − | 8.87348i | −0.986716 | − | 0.399237i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.00000 | + | 3.46410i | −0.0898027 | + | 0.155543i | ||||
\(497\) | −4.10378 | − | 2.36932i | −0.184080 | − | 0.106278i | ||||
\(498\) | −2.11176 | + | 1.21922i | −0.0946301 | + | 0.0546347i | ||||
\(499\) | 31.0540 | 1.39017 | 0.695083 | − | 0.718929i | \(-0.255367\pi\) | ||||
0.695083 | + | 0.718929i | \(0.255367\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.65767 | − | 9.79937i | −0.252766 | − | 0.437804i | ||||
\(502\) | − | 4.93087i | − | 0.220075i | ||||||
\(503\) | 31.7698 | − | 18.3423i | 1.41655 | − | 0.817844i | 0.420554 | − | 0.907268i | \(-0.361836\pi\) |
0.995994 | + | 0.0894236i | \(0.0285025\pi\) | |||||||
\(504\) | 0.280776 | − | 0.486319i | 0.0125068 | − | 0.0216624i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 16.6847 | 0.741724 | ||||||||
\(507\) | −3.57071 | − | 12.5000i | −0.158581 | − | 0.555144i | ||||
\(508\) | − | 1.19224i | − | 0.0528969i | ||||||
\(509\) | 0.123106 | − | 0.213225i | 0.00545656 | − | 0.00945104i | −0.863284 | − | 0.504718i | \(-0.831596\pi\) |
0.868741 | + | 0.495267i | \(0.164930\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.52699 | − | 4.37687i | −0.111787 | − | 0.193621i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 5.68247 | − | 3.28078i | 0.250887 | − | 0.144850i | ||||
\(514\) | 13.8078 | + | 23.9157i | 0.609034 | + | 1.05488i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.28078 | − | 3.95042i | −0.100406 | − | 0.173908i | ||||
\(517\) | −12.3376 | − | 7.12311i | −0.542606 | − | 0.313274i | ||||
\(518\) | −1.73205 | − | 1.00000i | −0.0761019 | − | 0.0439375i | ||||
\(519\) | 17.1231 | 0.751621 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.7386 | −0.645711 | −0.322856 | − | 0.946448i | \(-0.604643\pi\) | ||||
−0.322856 | + | 0.946448i | \(0.604643\pi\) | |||||||
\(522\) | 6.16879 | + | 3.56155i | 0.270001 | + | 0.155885i | ||||
\(523\) | −3.40423 | − | 1.96543i | −0.148857 | − | 0.0859425i | 0.423722 | − | 0.905792i | \(-0.360723\pi\) |
−0.572578 | + | 0.819850i | \(0.694057\pi\) | |||||||
\(524\) | 4.56155 | + | 7.90084i | 0.199272 | + | 0.345150i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.34233 | − | 16.1814i | −0.407345 | − | 0.705542i | ||||
\(527\) | 17.7470 | − | 10.2462i | 0.773070 | − | 0.446332i | ||||
\(528\) | − | 3.56155i | − | 0.154997i | ||||||
\(529\) | −0.526988 | − | 0.912769i | −0.0229125 | − | 0.0396856i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.12311 | + | 5.40938i | −0.135531 | + | 0.234747i | ||||
\(532\) | − | 3.68466i | − | 0.159750i | ||||||
\(533\) | −11.3649 | − | 14.5616i | −0.492270 | − | 0.630731i | ||||
\(534\) | 6.24621 | 0.270300 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.40388 | − | 7.62775i | 0.190219 | − | 0.329469i | ||||
\(537\) | −2.87117 | + | 1.65767i | −0.123900 | + | 0.0715338i | ||||
\(538\) | − | 21.3693i | − | 0.921297i | ||||||
\(539\) | −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 | \(0.767839\pi\) | |||||||
\(542\) | −17.2606 | + | 9.96543i | −0.741408 | + | 0.428052i | ||||
\(543\) | 15.1489 | + | 8.74621i | 0.650101 | + | 0.375336i | ||||
\(544\) | 2.56155 | − | 4.43674i | 0.109826 | − | 0.190224i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.59612 | − | 1.24573i | 0.0683075 | − | 0.0533124i | ||||
\(547\) | − | 2.06913i | − | 0.0884696i | −0.999021 | − | 0.0442348i | \(-0.985915\pi\) | ||
0.999021 | − | 0.0442348i | \(-0.0140850\pi\) | |||||||
\(548\) | −14.2829 | − | 8.24621i | −0.610133 | − | 0.352261i | ||||
\(549\) | 5.34233 | − | 9.25319i | 0.228005 | − | 0.394916i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 46.7386 | 1.99113 | ||||||||
\(552\) | 4.05703 | − | 2.34233i | 0.172679 | − | 0.0996962i | ||||
\(553\) | −2.33811 | + | 1.34991i | −0.0994264 | + | 0.0574039i | ||||
\(554\) | −5.00000 | −0.212430 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.71922 | + | 15.1021i | −0.369777 | + | 0.640473i | ||||
\(557\) | −8.32729 | − | 4.80776i | −0.352839 | − | 0.203712i | 0.313096 | − | 0.949721i | \(-0.398634\pi\) |
−0.665935 | + | 0.746010i | \(0.731967\pi\) | |||||||
\(558\) | − | 4.00000i | − | 0.169334i | ||||||
\(559\) | −2.28078 | − | 16.2880i | −0.0964666 | − | 0.688909i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.12311 | + | 15.8017i | −0.385178 | + | 0.667148i | ||||
\(562\) | 15.8017 | + | 9.12311i | 0.666554 | + | 0.384835i | ||||
\(563\) | −0.166481 | + | 0.0961180i | −0.00701635 | + | 0.00405089i | −0.503504 | − | 0.863993i | \(-0.667956\pi\) |
0.496488 | + | 0.868044i | \(0.334623\pi\) | |||||||
\(564\) | −4.00000 | −0.168430 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 5.80776 | + | 10.0593i | 0.244119 | + | 0.422826i | ||||
\(567\) | 0.561553i | 0.0235830i | ||||||||
\(568\) | −7.30791 | + | 4.21922i | −0.306633 | + | 0.177035i | ||||
\(569\) | −22.2462 | + | 38.5316i | −0.932610 | + | 1.61533i | −0.153768 | + | 0.988107i | \(0.549141\pi\) |
−0.778842 | + | 0.627220i | \(0.784193\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.4233 | −1.69166 | −0.845831 | − | 0.533451i | \(-0.820895\pi\) | ||||
−0.845831 | + | 0.533451i | \(0.820895\pi\) | |||||||
\(572\) | 4.81645 | − | 11.9039i | 0.201386 | − | 0.497726i | ||||
\(573\) | 12.9309i | 0.540195i | ||||||||
\(574\) | 1.43845 | − | 2.49146i | 0.0600396 | − | 0.103992i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 23.0000i | 0.957503i | 0.877951 | + | 0.478751i | \(0.158910\pi\) | ||||
−0.877951 | + | 0.478751i | \(0.841090\pi\) | |||||||
\(578\) | −8.00745 | + | 4.62311i | −0.333066 | + | 0.192296i | ||||
\(579\) | 1.50000 | + | 2.59808i | 0.0623379 | + | 0.107972i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.684658 | − | 1.18586i | −0.0284044 | − | 0.0491979i | ||||
\(582\) | −15.4220 | − | 8.90388i | −0.639261 | − | 0.369078i | ||||
\(583\) | −37.7722 | − | 21.8078i | −1.56436 | − | 0.903185i | ||||
\(584\) | −9.00000 | −0.372423 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.75379 | 0.155068 | ||||||||
\(587\) | −9.46641 | − | 5.46543i | −0.390721 | − | 0.225583i | 0.291752 | − | 0.956494i | \(-0.405762\pi\) |
−0.682472 | + | 0.730911i | \(0.739095\pi\) | |||||||
\(588\) | −5.78908 | − | 3.34233i | −0.238738 | − | 0.137835i | ||||
\(589\) | −13.1231 | − | 22.7299i | −0.540728 | − | 0.936569i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.56155 | + | 2.70469i | 0.0642337 | + | 0.111256i | ||||
\(592\) | −3.08440 | + | 1.78078i | −0.126768 | + | 0.0731895i | ||||
\(593\) | − | 26.9848i | − | 1.10813i | −0.832472 | − | 0.554067i | \(-0.813075\pi\) | ||
0.832472 | − | 0.554067i | \(-0.186925\pi\) | |||||||
\(594\) | 1.78078 | + | 3.08440i | 0.0730661 | + | 0.126554i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.12311 | + | 5.40938i | −0.127927 | + | 0.221577i | ||||
\(597\) | − | 8.56155i | − | 0.350401i | ||||||
\(598\) | 16.7276 | − | 2.34233i | 0.684041 | − | 0.0957850i | ||||
\(599\) | 30.6847 | 1.25374 | 0.626871 | − | 0.779123i | \(-0.284335\pi\) | ||||
0.626871 | + | 0.779123i | \(0.284335\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.40388 | + | 12.8239i | −0.302011 | + | 0.523098i | −0.976591 | − | 0.215103i | \(-0.930991\pi\) |
0.674581 | + | 0.738201i | \(0.264324\pi\) | |||||||
\(602\) | 2.21837 | − | 1.28078i | 0.0904140 | − | 0.0522005i | ||||
\(603\) | 8.80776i | 0.358680i | ||||||||
\(604\) | −2.15767 | − | 3.73720i | −0.0877944 | − | 0.152064i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.2462 | 0.416224 | ||||||||
\(607\) | −12.6705 | + | 7.31534i | −0.514281 | + | 0.296921i | −0.734592 | − | 0.678509i | \(-0.762626\pi\) |
0.220310 | + | 0.975430i | \(0.429293\pi\) | |||||||
\(608\) | −5.68247 | − | 3.28078i | −0.230455 | − | 0.133053i | ||||
\(609\) | −2.00000 | + | 3.46410i | −0.0810441 | + | 0.140372i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.3693 | − | 5.40938i | −0.540865 | − | 0.218840i | ||||
\(612\) | 5.12311i | 0.207089i | ||||||||
\(613\) | 29.0520 | + | 16.7732i | 1.17340 | + | 0.677463i | 0.954479 | − | 0.298279i | \(-0.0964127\pi\) |
0.218922 | + | 0.975742i | \(0.429746\pi\) | |||||||
\(614\) | 2.87689 | − | 4.98293i | 0.116102 | − | 0.201095i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.00000 | 0.0805823 | ||||||||
\(617\) | 19.5987 | − | 11.3153i | 0.789016 | − | 0.455538i | −0.0506001 | − | 0.998719i | \(-0.516113\pi\) |
0.839616 | + | 0.543180i | \(0.182780\pi\) | |||||||
\(618\) | 7.41452 | − | 4.28078i | 0.298256 | − | 0.172198i | ||||
\(619\) | −41.3002 | −1.65999 | −0.829997 | − | 0.557767i | \(-0.811658\pi\) | ||||
−0.829997 | + | 0.557767i | \(0.811658\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.34233 | + | 4.05703i | −0.0939944 | + | 0.162803i | ||||
\(622\) | 19.6455 | + | 11.3423i | 0.787712 | + | 0.454786i | ||||
\(623\) | 3.50758i | 0.140528i | ||||||||
\(624\) | −0.500000 | − | 3.57071i | −0.0200160 | − | 0.142943i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −15.5000 | + | 26.8468i | −0.619505 | + | 1.07301i | ||||
\(627\) | 20.2384 | + | 11.6847i | 0.808245 | + | 0.466640i | ||||
\(628\) | −0.652800 | + | 0.376894i | −0.0260496 | + | 0.0150397i | ||||
\(629\) | 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 | \(0.859143\pi\) | |||||||
\(632\) | 4.80776i | 0.191243i | ||||||||
\(633\) | 6.16879 | − | 3.56155i | 0.245187 | − | 0.141559i | ||||
\(634\) | −0.123106 | + | 0.213225i | −0.00488915 | + | 0.00846825i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −12.2462 | −0.485594 | ||||||||
\(637\) | −14.8290 | − | 19.0000i | −0.587548 | − | 0.752807i | ||||
\(638\) | 25.3693i | 1.00438i | ||||||||
\(639\) | 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 | \(0.974683\pi\) | |||||||
\(642\) | − | 19.3693i | − | 0.764446i | ||||||
\(643\) | 39.4443 | − | 22.7732i | 1.55553 | − | 0.898087i | 0.557858 | − | 0.829937i | \(-0.311623\pi\) |
0.997675 | − | 0.0681507i | \(-0.0217099\pi\) | |||||||
\(644\) | 1.31534 | + | 2.27824i | 0.0518317 | + | 0.0897752i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.8078 | + | 29.1119i | 0.661293 | + | 1.14539i | ||||
\(647\) | 25.4813 | + | 14.7116i | 1.00177 | + | 0.578374i | 0.908773 | − | 0.417291i | \(-0.137021\pi\) |
0.0930013 | + | 0.995666i | \(0.470354\pi\) | |||||||
\(648\) | 0.866025 | + | 0.500000i | 0.0340207 | + | 0.0196419i | ||||
\(649\) | −22.2462 | −0.873240 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.24621 | 0.0880360 | ||||||||
\(652\) | −14.2829 | − | 8.24621i | −0.559360 | − | 0.322947i | ||||
\(653\) | 3.13114 | + | 1.80776i | 0.122531 | + | 0.0707433i | 0.560013 | − | 0.828484i | \(-0.310796\pi\) |
−0.437482 | + | 0.899227i | \(0.644130\pi\) | |||||||
\(654\) | 8.90388 | + | 15.4220i | 0.348169 | + | 0.603047i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.56155 | − | 4.43674i | −0.100012 | − | 0.173226i | ||||
\(657\) | 7.79423 | − | 4.50000i | 0.304082 | − | 0.175562i | ||||
\(658\) | − | 2.24621i | − | 0.0875664i | ||||||
\(659\) | 15.3423 | + | 26.5737i | 0.597652 | + | 1.03516i | 0.993167 | + | 0.116704i | \(0.0372330\pi\) |
−0.395514 | + | 0.918460i | \(0.629434\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.7732 | + | 18.6597i | −0.419029 | + | 0.725779i | −0.995842 | − | 0.0910968i | \(-0.970963\pi\) |
0.576813 | + | 0.816876i | \(0.304296\pi\) | |||||||
\(662\) | − | 4.31534i | − | 0.167721i | ||||||
\(663\) | −6.92820 | + | 17.1231i | −0.269069 | + | 0.665006i | ||||
\(664\) | −2.43845 | −0.0946301 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.78078 | − | 3.08440i | 0.0690037 | − | 0.119518i | ||||
\(667\) | −28.8987 | + | 16.6847i | −1.11896 | + | 0.646033i | ||||
\(668\) | − | 11.3153i | − | 0.437804i | ||||||
\(669\) | −2.28078 | − | 3.95042i | −0.0881799 | − | 0.152732i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38.0540 | 1.46906 | ||||||||
\(672\) | 0.486319 | − | 0.280776i | 0.0187602 | − | 0.0108312i | ||||
\(673\) | 39.1844 | + | 22.6231i | 1.51045 | + | 0.872057i | 0.999926 | + | 0.0121912i | \(0.00388067\pi\) |
0.510521 | + | 0.859865i | \(0.329453\pi\) | |||||||
\(674\) | −14.5270 | + | 25.1615i | −0.559559 | + | 0.969184i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.15767 | − | 12.6107i | 0.121449 | − | 0.485026i | ||||
\(677\) | − | 29.6155i | − | 1.13822i | −0.822262 | − | 0.569109i | \(-0.807288\pi\) | ||
0.822262 | − | 0.569109i | \(-0.192712\pi\) | |||||||
\(678\) | 3.46410 | + | 2.00000i | 0.133038 | + | 0.0768095i | ||||
\(679\) | 5.00000 | − | 8.66025i | 0.191882 | − | 0.332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.3153 | 0.663525 | ||||||||
\(682\) | 12.3376 | − | 7.12311i | 0.472430 | − | 0.272758i | ||||
\(683\) | −16.9408 | + | 9.78078i | −0.648222 | + | 0.374251i | −0.787775 | − | 0.615964i | \(-0.788767\pi\) |
0.139553 | + | 0.990215i | \(0.455433\pi\) | |||||||
\(684\) | 6.56155 | 0.250887 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.84233 | − | 6.65511i | 0.146701 | − | 0.254093i | ||||
\(687\) | 20.3450 | + | 11.7462i | 0.776211 | + | 0.448146i | ||||
\(688\) | − | 4.56155i | − | 0.173908i | ||||||
\(689\) | −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 | \(-0.236851\pi\) | |||||||
\(692\) | 14.8290 | + | 8.56155i | 0.563716 | + | 0.325461i | ||||
\(693\) | −1.73205 | + | 1.00000i | −0.0657952 | + | 0.0379869i | ||||
\(694\) | 4.19224 | 0.159135 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.56155 | + | 6.16879i | 0.135000 | + | 0.233827i | ||||
\(697\) | 26.2462i | 0.994146i | ||||||||
\(698\) | 2.38485 | − | 1.37689i | 0.0902679 | − | 0.0521162i | ||||
\(699\) | −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 | \(0.555116\pi\) | |||||||
\(702\) | 2.21837 | + | 2.84233i | 0.0837270 | + | 0.107277i | ||||
\(703\) | − | 23.3693i | − | 0.881390i | ||||||
\(704\) | 1.78078 | − | 3.08440i | 0.0671155 | − | 0.116248i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.12311 | + | 12.3376i | 0.268082 | + | 0.464331i | ||||
\(707\) | 5.75379i | 0.216393i | ||||||||
\(708\) | −5.40938 | + | 3.12311i | −0.203297 | + | 0.117373i | ||||
\(709\) | −22.6231 | − | 39.1844i | −0.849629 | − | 1.47160i | −0.881540 | − | 0.472109i | \(-0.843493\pi\) |
0.0319115 | − | 0.999491i | \(-0.489841\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.40388 | − | 4.16365i | −0.0901526 | − | 0.156149i | ||||
\(712\) | 5.40938 | + | 3.12311i | 0.202725 | + | 0.117043i | ||||
\(713\) | 16.2281 | + | 9.36932i | 0.607748 | + | 0.350884i | ||||
\(714\) | −2.87689 | −0.107665 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.31534 | −0.123900 | ||||||||
\(717\) | 8.70700 | + | 5.02699i | 0.325169 | + | 0.187736i | ||||
\(718\) | −11.3649 | − | 6.56155i | −0.424136 | − | 0.244875i | ||||
\(719\) | −10.7808 | − | 18.6729i | −0.402055 | − | 0.696380i | 0.591919 | − | 0.805998i | \(-0.298371\pi\) |
−0.993974 | + | 0.109618i | \(0.965037\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.40388 | + | 4.16365i | 0.0895252 | + | 0.155062i | ||||
\(722\) | 20.8314 | − | 12.0270i | 0.775263 | − | 0.447598i | ||||
\(723\) | − | 11.4384i | − | 0.425400i | ||||||
\(724\) | 8.74621 | + | 15.1489i | 0.325050 | + | 0.563004i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.842329 | + | 1.45896i | −0.0312618 | + | 0.0541470i | ||||
\(727\) | 35.7926i | 1.32747i | 0.747966 | + | 0.663737i | \(0.231031\pi\) | ||||
−0.747966 | + | 0.663737i | \(0.768969\pi\) | |||||||
\(728\) | 2.00514 | − | 0.280776i | 0.0743156 | − | 0.0104063i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.6847 | + | 20.2384i | −0.432173 | + | 0.748545i | ||||
\(732\) | 9.25319 | − | 5.34233i | 0.342008 | − | 0.197458i | ||||
\(733\) | − | 17.9848i | − | 0.664285i | −0.943229 | − | 0.332143i | \(-0.892228\pi\) | ||
0.943229 | − | 0.332143i | \(-0.107772\pi\) | |||||||
\(734\) | −15.4039 | − | 26.6803i | −0.568568 | − | 0.984788i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.68466 | 0.172679 | ||||||||
\(737\) | −27.1666 | + | 15.6847i | −1.00070 | + | 0.577752i | ||||
\(738\) | 4.43674 | + | 2.56155i | 0.163319 | + | 0.0942921i | ||||
\(739\) | −2.43845 | + | 4.22351i | −0.0896997 | + | 0.155364i | −0.907384 | − | 0.420302i | \(-0.861924\pi\) |
0.817684 | + | 0.575667i | \(0.195257\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.9309 | + | 8.87348i | 0.805651 | + | 0.325975i | ||||
\(742\) | − | 6.87689i | − | 0.252459i | ||||||
\(743\) | 2.49146 | + | 1.43845i | 0.0914029 | + | 0.0527715i | 0.545005 | − | 0.838433i | \(-0.316528\pi\) |
−0.453602 | + | 0.891204i | \(0.649861\pi\) | |||||||
\(744\) | 2.00000 | − | 3.46410i | 0.0733236 | − | 0.127000i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 23.4924 | 0.860119 | ||||||||
\(747\) | 2.11176 | − | 1.21922i | 0.0772652 | − | 0.0446091i | ||||
\(748\) | −15.8017 | + | 9.12311i | −0.577767 | + | 0.333574i | ||||
\(749\) | 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 | \(0.955481\pi\) | |||||||
\(752\) | −3.46410 | − | 2.00000i | −0.126323 | − | 0.0729325i | ||||
\(753\) | 4.93087i | 0.179691i | ||||||||
\(754\) | 3.56155 | + | 25.4346i | 0.129704 | + | 0.926273i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.280776 | + | 0.486319i | −0.0102117 | + | 0.0176873i | ||||
\(757\) | 15.8616 | + | 9.15767i | 0.576498 | + | 0.332841i | 0.759740 | − | 0.650227i | \(-0.225326\pi\) |
−0.183243 | + | 0.983068i | \(0.558659\pi\) | |||||||
\(758\) | −11.3051 | + | 6.52699i | −0.410619 | + | 0.237071i | ||||
\(759\) | −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 | \(-0.450990\pi\) | |||||||
\(762\) | 1.19224i | 0.0431902i | ||||||||
\(763\) | −8.66025 | + | 5.00000i | −0.313522 | + | 0.181012i | ||||
\(764\) | −6.46543 | + | 11.1985i | −0.233911 | + | 0.405146i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.56155 | −0.345473 | ||||||||
\(767\) | −22.3034 | + | 3.12311i | −0.805330 | + | 0.112769i | ||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | −10.8423 | + | 18.7795i | −0.390984 | + | 0.677205i | −0.992580 | − | 0.121596i | \(-0.961199\pi\) |
0.601595 | + | 0.798801i | \(0.294532\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.8078 | − | 23.9157i | −0.497274 | − | 0.861305i | ||||
\(772\) | 3.00000i | 0.107972i | ||||||||
\(773\) | −10.0593 | + | 5.80776i | −0.361809 | + | 0.208891i | −0.669874 | − | 0.742475i | \(-0.733652\pi\) |
0.308065 | + | 0.951365i | \(0.400319\pi\) | |||||||
\(774\) | 2.28078 | + | 3.95042i | 0.0819808 | + | 0.141995i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.90388 | − | 15.4220i | −0.319631 | − | 0.553617i | ||||
\(777\) | 1.73205 | + | 1.00000i | 0.0621370 | + | 0.0358748i | ||||
\(778\) | −11.5782 | − | 6.68466i | −0.415097 | − | 0.239657i | ||||
\(779\) | 33.6155 | 1.20440 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.0540 | 1.07542 | ||||||||
\(782\) | −20.7846 | − | 12.0000i | −0.743256 | − | 0.429119i | ||||
\(783\) | −6.16879 | − | 3.56155i | −0.220455 | − | 0.127280i | ||||
\(784\) | −3.34233 | − | 5.78908i | −0.119369 | − | 0.206753i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.56155 | − | 7.90084i | −0.162705 | − | 0.281814i | ||||
\(787\) | −10.3923 | + | 6.00000i | −0.370446 | + | 0.213877i | −0.673653 | − | 0.739048i | \(-0.735276\pi\) |
0.303207 | + | 0.952925i | \(0.401942\pi\) | |||||||
\(788\) | 3.12311i | 0.111256i | ||||||||
\(789\) | 9.34233 | + | 16.1814i | 0.332596 | + | 0.576073i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.12311 | + | 1.94528i | −0.0399330 | + | 0.0691661i | ||||
\(792\) | 3.56155i | 0.126554i | ||||||||
\(793\) | 38.1519 | − | 5.34233i | 1.35481 | − | 0.189712i | ||||
\(794\) | −10.8078 | −0.383553 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.28078 | − | 7.41452i | 0.151728 | − | 0.262801i | ||||
\(797\) | −8.44703 | + | 4.87689i | −0.299209 | + | 0.172748i | −0.642088 | − | 0.766631i | \(-0.721931\pi\) |
0.342878 | + | 0.939380i | \(0.388598\pi\) | |||||||
\(798\) | 3.68466i | 0.130435i | ||||||||
\(799\) | 10.2462 | + | 17.7470i | 0.362485 | + | 0.627842i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.24621 | −0.220699 | ||||||||
\(802\) | −32.3628 | + | 18.6847i | −1.14277 | + | 0.659778i | ||||
\(803\) | 27.7596 | + | 16.0270i | 0.979613 | + | 0.565580i | ||||
\(804\) | −4.40388 | + | 7.62775i | −0.155313 | + | 0.269010i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.3693 | − | 8.87348i | 0.400467 | − | 0.312555i | ||||
\(807\) | 21.3693i | 0.752236i | ||||||||
\(808\) | 8.87348 | + | 5.12311i | 0.312168 | + | 0.180230i | ||||
\(809\) | −4.80776 | + | 8.32729i | −0.169032 | + | 0.292772i | −0.938080 | − | 0.346419i | \(-0.887397\pi\) |
0.769048 | + | 0.639191i | \(0.220731\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.9309 | 0.418949 | 0.209475 | − | 0.977814i | \(-0.432825\pi\) | ||||
0.209475 | + | 0.977814i | \(0.432825\pi\) | |||||||
\(812\) | −3.46410 | + | 2.00000i | −0.121566 | + | 0.0701862i | ||||
\(813\) | 17.2606 | − | 9.96543i | 0.605357 | − | 0.349503i | ||||
\(814\) | 12.6847 | 0.444597 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.56155 | + | 4.43674i | −0.0896723 | + | 0.155317i | ||||
\(817\) | 25.9209 | + | 14.9654i | 0.906857 | + | 0.523574i | ||||
\(818\) | 0.246211i | 0.00860857i | ||||||||
\(819\) | −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 | \(0.0106000\pi\) | |||||||
\(822\) | 14.2829 | + | 8.24621i | 0.498172 | + | 0.287620i | ||||
\(823\) | 30.9973 | − | 17.8963i | 1.08050 | − | 0.623826i | 0.149467 | − | 0.988767i | \(-0.452244\pi\) |
0.931031 | + | 0.364941i | \(0.118911\pi\) | |||||||
\(824\) | 8.56155 | 0.298256 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.75379 | − | 3.03765i | −0.0610221 | − | 0.105693i | ||||
\(827\) | 34.9309i | 1.21467i | 0.794448 | + | 0.607333i | \(0.207760\pi\) | ||||
−0.794448 | + | 0.607333i | \(0.792240\pi\) | |||||||
\(828\) | −4.05703 | + | 2.34233i | −0.140992 | + | 0.0814016i | ||||
\(829\) | −28.7732 | + | 49.8366i | −0.999335 | + | 1.73090i | −0.468078 | + | 0.883687i | \(0.655053\pi\) |
−0.531257 | + | 0.847211i | \(0.678280\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.00000 | 0.173448 | ||||||||
\(832\) | 1.35234 | − | 3.34233i | 0.0468841 | − | 0.115874i | ||||
\(833\) | 34.2462i | 1.18656i | ||||||||
\(834\) | 8.71922 | − | 15.1021i | 0.301922 | − | 0.522944i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 11.6847 | + | 20.2384i | 0.404122 | + | 0.699960i | ||||
\(837\) | 4.00000i | 0.138260i | ||||||||
\(838\) | −14.6626 | + | 8.46543i | −0.506510 | + | 0.292434i | ||||
\(839\) | 0.657671 | + | 1.13912i | 0.0227053 | + | 0.0393268i | 0.877155 | − | 0.480208i | \(-0.159439\pi\) |
−0.854449 | + | 0.519534i | \(0.826105\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.8693 | − | 18.8262i | −0.374804 | − | 0.649180i | ||||
\(842\) | −12.7772 | − | 7.37689i | −0.440330 | − | 0.254225i | ||||
\(843\) | −15.8017 | − | 9.12311i | −0.544239 | − | 0.314216i | ||||
\(844\) | 7.12311 | 0.245187 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.00000 | 0.137523 | ||||||||
\(847\) | −0.819281 | − | 0.473012i | −0.0281508 | − | 0.0162529i | ||||
\(848\) | −10.6055 | − | 6.12311i | −0.364195 | − | 0.210268i | ||||
\(849\) | −5.80776 | − | 10.0593i | −0.199322 | − | 0.345236i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.34233 | + | 14.4493i | 0.285971 | + | 0.495317i | ||||
\(852\) | 7.30791 | − | 4.21922i | 0.250365 | − | 0.144548i | ||||
\(853\) | 46.9848i | 1.60873i | 0.594135 | + | 0.804365i | \(0.297494\pi\) | ||||
−0.594135 | + | 0.804365i | \(0.702506\pi\) | |||||||
\(854\) | 3.00000 | + | 5.19615i | 0.102658 | + | 0.177809i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.68466 | − | 16.7743i | 0.331015 | − | 0.573334i | ||||
\(857\) | − | 39.7538i | − | 1.35796i | −0.734155 | − | 0.678982i | \(-0.762422\pi\) | ||
0.734155 | − | 0.678982i | \(-0.237578\pi\) | |||||||
\(858\) | −4.81645 | + | 11.9039i | −0.164431 | + | 0.406392i | ||||
\(859\) | 34.4233 | 1.17451 | 0.587254 | − | 0.809403i | \(-0.300209\pi\) | ||||
0.587254 | + | 0.809403i | \(0.300209\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.43845 | + | 2.49146i | −0.0490221 | + | 0.0849089i | ||||
\(862\) | 26.5737 | − | 15.3423i | 0.905104 | − | 0.522562i | ||||
\(863\) | − | 30.9309i | − | 1.05290i | −0.850206 | − | 0.526450i | \(-0.823523\pi\) | ||
0.850206 | − | 0.526450i | \(-0.176477\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.31534 | −0.0446971 | ||||||||
\(867\) | 8.00745 | − | 4.62311i | 0.271947 | − | 0.157009i | ||||
\(868\) | 1.94528 | + | 1.12311i | 0.0660270 | + | 0.0381207i | ||||
\(869\) | 8.56155 | − | 14.8290i | 0.290431 | − | 0.503041i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.0346 | + | 19.5389i | −0.848264 | + | 0.662050i | ||||
\(872\) | 17.8078i | 0.603047i | ||||||||
\(873\) | 15.4220 | + | 8.90388i | 0.521955 | + | 0.301351i | ||||
\(874\) | −15.3693 | + | 26.6204i | −0.519875 | + | 0.900450i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9.00000 | 0.304082 | ||||||||
\(877\) | 9.09983 | − | 5.25379i | 0.307279 | − | 0.177408i | −0.338429 | − | 0.940992i | \(-0.609895\pi\) |
0.645708 | + | 0.763584i | \(0.276562\pi\) | |||||||
\(878\) | −18.9927 | + | 10.9654i | −0.640972 | + | 0.370066i | ||||
\(879\) | −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 | \(0.924897\pi\) | |||||||
\(882\) | 5.78908 | + | 3.34233i | 0.194929 | + | 0.112542i | ||||
\(883\) | − | 17.7538i | − | 0.597463i | −0.954337 | − | 0.298731i | \(-0.903437\pi\) | ||
0.954337 | − | 0.298731i | \(-0.0965634\pi\) | |||||||
\(884\) | −14.5616 | + | 11.3649i | −0.489758 | + | 0.382244i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.90388 | + | 15.4220i | −0.299132 | + | 0.518111i | ||||
\(887\) | 14.4026 | + | 8.31534i | 0.483592 | + | 0.279202i | 0.721912 | − | 0.691985i | \(-0.243263\pi\) |
−0.238320 | + | 0.971187i | \(0.576597\pi\) | |||||||
\(888\) | 3.08440 | − | 1.78078i | 0.103506 | − | 0.0597589i | ||||
\(889\) | −0.669503 | −0.0224544 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.78078 | − | 3.08440i | −0.0596583 | − | 0.103331i | ||||
\(892\) | − | 4.56155i | − | 0.152732i | ||||||
\(893\) | 22.7299 | − | 13.1231i | 0.760627 | − | 0.439148i | ||||
\(894\) | 3.12311 | − | 5.40938i | 0.104452 | − | 0.180917i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.561553 | 0.0187602 | ||||||||
\(897\) | −16.7276 | + | 2.34233i | −0.558518 | + | 0.0782081i | ||||
\(898\) | − | 5.12311i | − | 0.170960i | ||||||
\(899\) | −14.2462 | + | 24.6752i | −0.475138 | + | 0.822963i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.3693 | + | 54.3333i | 1.04506 | + | 1.81010i | ||||
\(902\) | 18.2462i | 0.607532i | ||||||||
\(903\) | −2.21837 | + | 1.28078i | −0.0738227 | + | 0.0426216i | ||||
\(904\) | 2.00000 | + | 3.46410i | 0.0665190 | + | 0.115214i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.15767 | + | 3.73720i | 0.0716838 | + | 0.124160i | ||||
\(907\) | −46.6456 | − | 26.9309i | −1.54884 | − | 0.894225i | −0.998230 | − | 0.0594638i | \(-0.981061\pi\) |
−0.550612 | − | 0.834761i | \(-0.685606\pi\) | |||||||
\(908\) | 14.9955 | + | 8.65767i | 0.497644 | + | 0.287315i | ||||
\(909\) | −10.2462 | −0.339845 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.3153 | 0.904998 | 0.452499 | − | 0.891765i | \(-0.350533\pi\) | ||||
0.452499 | + | 0.891765i | \(0.350533\pi\) | |||||||
\(912\) | 5.68247 | + | 3.28078i | 0.188165 | + | 0.108637i | ||||
\(913\) | 7.52113 | + | 4.34233i | 0.248913 | + | 0.143710i | ||||
\(914\) | 18.7462 | + | 32.4694i | 0.620070 | + | 1.07399i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.7462 | + | 20.3450i | 0.388106 | + | 0.672219i | ||||
\(917\) | 4.43674 | − | 2.56155i | 0.146514 | − | 0.0845899i | ||||
\(918\) | − | 5.12311i | − | 0.169088i | ||||||
\(919\) | 19.8423 | + | 34.3679i | 0.654538 | + | 1.13369i | 0.982009 | + | 0.188832i | \(0.0604702\pi\) |
−0.327471 | + | 0.944861i | \(0.606196\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.87689 | + | 4.98293i | −0.0947969 | + | 0.164193i | ||||
\(922\) | 35.3693i | 1.16483i | ||||||||
\(923\) | 30.1313 | − | 4.21922i | 0.991783 | − | 0.138877i | ||||
\(924\) | −2.00000 | −0.0657952 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.59612 | + | 6.22866i | −0.118176 | + | 0.204686i | ||||
\(927\) | −7.41452 | + | 4.28078i | −0.243525 | + | 0.140599i | ||||
\(928\) | 7.12311i | 0.233827i | ||||||||
\(929\) | 3.93087 | + | 6.80847i | 0.128968 | + | 0.223379i | 0.923277 | − | 0.384135i | \(-0.125500\pi\) |
−0.794309 | + | 0.607514i | \(0.792167\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 43.8617 | 1.43751 | ||||||||
\(932\) | −0.546188 | + | 0.315342i | −0.0178910 | + | 0.0103294i | ||||
\(933\) | −19.6455 | − | 11.3423i | −0.643164 | − | 0.371331i | ||||
\(934\) | −3.78078 | + | 6.54850i | −0.123711 | + | 0.214273i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.500000 | + | 3.57071i | 0.0163430 | + | 0.116712i | ||||
\(937\) | 5.24621i | 0.171386i | 0.996322 | + | 0.0856931i | \(0.0273105\pi\) | ||||
−0.996322 | + | 0.0856931i | \(0.972690\pi\) | |||||||
\(938\) | −4.28338 | − | 2.47301i | −0.139857 | − | 0.0807467i | ||||
\(939\) | 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 | \(0.0811325\pi\) | |||||||
\(942\) | 0.652800 | − | 0.376894i | 0.0212694 | − | 0.0122799i | ||||
\(943\) | −20.7846 | + | 12.0000i | −0.676840 | + | 0.390774i | ||||
\(944\) | −6.24621 | −0.203297 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.12311 | + | 14.0696i | −0.264105 | + | 0.457443i | ||||
\(947\) | 27.4266 | + | 15.8348i | 0.891245 | + | 0.514560i | 0.874349 | − | 0.485297i | \(-0.161289\pi\) |
0.0168952 | + | 0.999857i | \(0.494622\pi\) | |||||||
\(948\) | − | 4.80776i | − | 0.156149i | ||||||
\(949\) | 30.0810 | + | 12.1711i | 0.976469 | + | 0.395091i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.123106 | − | 0.213225i | 0.00399197 | − | 0.00691430i | ||||
\(952\) | −2.49146 | − | 1.43845i | −0.0807488 | − | 0.0466203i | ||||
\(953\) | −7.14143 | + | 4.12311i | −0.231334 | + | 0.133560i | −0.611187 | − | 0.791486i | \(-0.709308\pi\) |
0.379854 | + | 0.925047i | \(0.375974\pi\) | |||||||
\(954\) | 12.2462 | 0.396486 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.02699 | + | 8.70700i | 0.162584 | + | 0.281604i | ||||
\(957\) | − | 25.3693i | − | 0.820074i | ||||||
\(958\) | −25.6478 | + | 14.8078i | −0.828643 | + | 0.478417i | ||||
\(959\) | −4.63068 | + | 8.02058i | −0.149533 | + | 0.258998i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 12.7173 | − | 1.78078i | 0.410022 | − | 0.0574145i | ||||
\(963\) | 19.3693i | 0.624168i | ||||||||
\(964\) | 5.71922 | − | 9.90599i | 0.184204 | − | 0.319050i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.31534 | − | 2.27824i | −0.0423204 | − | 0.0733011i | ||||
\(967\) | 41.3693i | 1.33035i | 0.746689 | + | 0.665174i | \(0.231643\pi\) | ||||
−0.746689 | + | 0.665174i | \(0.768357\pi\) | |||||||
\(968\) | −1.45896 | + | 0.842329i | −0.0468927 | + | 0.0270735i | ||||
\(969\) | −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 | \(-0.384314\pi\) | |||||||
\(972\) | −0.866025 | − | 0.500000i | −0.0277778 | − | 0.0160375i | ||||
\(973\) | 8.48065 | + | 4.89630i | 0.271877 | + | 0.156968i | ||||
\(974\) | −30.3153 | −0.971366 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.6847 | 0.342008 | ||||||||
\(977\) | 25.7675 | + | 14.8769i | 0.824377 | + | 0.475954i | 0.851923 | − | 0.523666i | \(-0.175436\pi\) |
−0.0275468 | + | 0.999621i | \(0.508770\pi\) | |||||||
\(978\) | 14.2829 | + | 8.24621i | 0.456715 | + | 0.263685i | ||||
\(979\) | −11.1231 | − | 19.2658i | −0.355496 | − | 0.615737i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.90388 | − | 15.4220i | −0.284279 | − | 0.492386i | ||||
\(982\) | −19.3125 | + | 11.1501i | −0.616288 | + | 0.355814i | ||||
\(983\) | 5.75379i | 0.183517i | 0.995781 | + | 0.0917587i | \(0.0292488\pi\) | ||||
−0.995781 | + | 0.0917587i | \(0.970751\pi\) | |||||||
\(984\) | 2.56155 | + | 4.43674i | 0.0816593 | + | 0.141438i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 18.2462 | − | 31.6034i | 0.581078 | − | 1.00646i | ||||
\(987\) | 2.24621i | 0.0714977i | ||||||||
\(988\) | 14.5560 | + | 18.6501i | 0.463086 | + | 0.593339i | ||||
\(989\) | −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 | \(-0.194355\pi\) | |||||||
\(992\) | 3.46410 | − | 2.00000i | 0.109985 | − | 0.0635001i | ||||
\(993\) | 4.31534i | 0.136943i | ||||||||
\(994\) | 2.36932 | + | 4.10378i | 0.0751502 | + | 0.130164i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.43845 | 0.0772652 | ||||||||
\(997\) | −43.8811 | + | 25.3348i | −1.38973 | + | 0.802360i | −0.993284 | − | 0.115700i | \(-0.963089\pi\) |
−0.396443 | + | 0.918059i | \(0.629756\pi\) | |||||||
\(998\) | −26.8935 | − | 15.5270i | −0.851300 | − | 0.491498i | ||||
\(999\) | −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.z.m.1699.2 | 8 | ||
5.2 | odd | 4 | 1950.2.i.bg.451.2 | yes | 4 | ||
5.3 | odd | 4 | 1950.2.i.z.451.1 | ✓ | 4 | ||
5.4 | even | 2 | inner | 1950.2.z.m.1699.3 | 8 | ||
13.3 | even | 3 | inner | 1950.2.z.m.1849.3 | 8 | ||
65.3 | odd | 12 | 1950.2.i.z.601.1 | yes | 4 | ||
65.29 | even | 6 | inner | 1950.2.z.m.1849.2 | 8 | ||
65.42 | odd | 12 | 1950.2.i.bg.601.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.i.z.451.1 | ✓ | 4 | 5.3 | odd | 4 | ||
1950.2.i.z.601.1 | yes | 4 | 65.3 | odd | 12 | ||
1950.2.i.bg.451.2 | yes | 4 | 5.2 | odd | 4 | ||
1950.2.i.bg.601.2 | yes | 4 | 65.42 | odd | 12 | ||
1950.2.z.m.1699.2 | 8 | 1.1 | even | 1 | trivial | ||
1950.2.z.m.1699.3 | 8 | 5.4 | even | 2 | inner | ||
1950.2.z.m.1849.2 | 8 | 65.29 | even | 6 | inner | ||
1950.2.z.m.1849.3 | 8 | 13.3 | even | 3 | inner |