Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(88,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.88");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.bl (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - x^{2} - 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 121.2 | ||
Root | \(-0.895644 - 1.09445i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.121 |
Dual form | 273.2.bl.b.88.2 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.89564 | − | 1.09445i | 1.34042 | − | 0.773893i | 0.353553 | − | 0.935414i | \(-0.384973\pi\) |
0.986869 | + | 0.161521i | \(0.0516399\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.39564 | − | 2.41733i | 0.697822 | − | 1.20866i | ||||
\(5\) | −1.50000 | − | 0.866025i | −0.670820 | − | 0.387298i | 0.125567 | − | 0.992085i | \(-0.459925\pi\) |
−0.796387 | + | 0.604787i | \(0.793258\pi\) | |||||||
\(6\) | 1.89564 | − | 1.09445i | 0.773893 | − | 0.446808i | ||||
\(7\) | − | 2.64575i | − | 1.00000i | ||||||
\(8\) | − | 1.73205i | − | 0.612372i | ||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.79129 | −1.19891 | ||||||||
\(11\) | 3.46410i | 1.04447i | 0.852803 | + | 0.522233i | \(0.174901\pi\) | ||||
−0.852803 | + | 0.522233i | \(0.825099\pi\) | |||||||
\(12\) | 1.39564 | − | 2.41733i | 0.402888 | − | 0.697822i | ||||
\(13\) | −1.00000 | + | 3.46410i | −0.277350 | + | 0.960769i | ||||
\(14\) | −2.89564 | − | 5.01540i | −0.773893 | − | 1.34042i | ||||
\(15\) | −1.50000 | − | 0.866025i | −0.387298 | − | 0.223607i | ||||
\(16\) | 0.895644 | + | 1.55130i | 0.223911 | + | 0.387825i | ||||
\(17\) | −0.500000 | + | 0.866025i | −0.121268 | + | 0.210042i | −0.920268 | − | 0.391289i | \(-0.872029\pi\) |
0.799000 | + | 0.601331i | \(0.205363\pi\) | |||||||
\(18\) | 1.89564 | − | 1.09445i | 0.446808 | − | 0.257964i | ||||
\(19\) | − | 5.29150i | − | 1.21395i | −0.794719 | − | 0.606977i | \(-0.792382\pi\) | ||
0.794719 | − | 0.606977i | \(-0.207618\pi\) | |||||||
\(20\) | −4.18693 | + | 2.41733i | −0.936226 | + | 0.540531i | ||||
\(21\) | − | 2.64575i | − | 0.577350i | ||||||
\(22\) | 3.79129 | + | 6.56670i | 0.808305 | + | 1.40003i | ||||
\(23\) | 4.29129 | + | 7.43273i | 0.894795 | + | 1.54983i | 0.834058 | + | 0.551677i | \(0.186012\pi\) |
0.0607377 | + | 0.998154i | \(0.480655\pi\) | |||||||
\(24\) | − | 1.73205i | − | 0.353553i | ||||||
\(25\) | −1.00000 | − | 1.73205i | −0.200000 | − | 0.346410i | ||||
\(26\) | 1.89564 | + | 7.66115i | 0.371766 | + | 1.50248i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −6.39564 | − | 3.69253i | −1.20866 | − | 0.697822i | ||||
\(29\) | 3.50000 | − | 6.06218i | 0.649934 | − | 1.12572i | −0.333205 | − | 0.942855i | \(-0.608130\pi\) |
0.983138 | − | 0.182864i | \(-0.0585367\pi\) | |||||||
\(30\) | −3.79129 | −0.692191 | ||||||||
\(31\) | −5.29129 | + | 3.05493i | −0.950343 | + | 0.548681i | −0.893188 | − | 0.449684i | \(-0.851537\pi\) |
−0.0571558 | + | 0.998365i | \(0.518203\pi\) | |||||||
\(32\) | 6.39564 | + | 3.69253i | 1.13060 | + | 0.652753i | ||||
\(33\) | 3.46410i | 0.603023i | ||||||||
\(34\) | 2.18890i | 0.375393i | ||||||||
\(35\) | −2.29129 | + | 3.96863i | −0.387298 | + | 0.670820i | ||||
\(36\) | 1.39564 | − | 2.41733i | 0.232607 | − | 0.402888i | ||||
\(37\) | −6.08258 | + | 3.51178i | −0.999969 | + | 0.577333i | −0.908239 | − | 0.418451i | \(-0.862573\pi\) |
−0.0917301 | + | 0.995784i | \(0.529240\pi\) | |||||||
\(38\) | −5.79129 | − | 10.0308i | −0.939471 | − | 1.62721i | ||||
\(39\) | −1.00000 | + | 3.46410i | −0.160128 | + | 0.554700i | ||||
\(40\) | −1.50000 | + | 2.59808i | −0.237171 | + | 0.410792i | ||||
\(41\) | −3.08258 | − | 1.77973i | −0.481417 | − | 0.277946i | 0.239590 | − | 0.970874i | \(-0.422987\pi\) |
−0.721007 | + | 0.692928i | \(0.756320\pi\) | |||||||
\(42\) | −2.89564 | − | 5.01540i | −0.446808 | − | 0.773893i | ||||
\(43\) | −2.29129 | − | 3.96863i | −0.349418 | − | 0.605210i | 0.636728 | − | 0.771088i | \(-0.280287\pi\) |
−0.986146 | + | 0.165878i | \(0.946954\pi\) | |||||||
\(44\) | 8.37386 | + | 4.83465i | 1.26241 | + | 0.728851i | ||||
\(45\) | −1.50000 | − | 0.866025i | −0.223607 | − | 0.129099i | ||||
\(46\) | 16.2695 | + | 9.39320i | 2.39881 | + | 1.38495i | ||||
\(47\) | 0.708712 | + | 0.409175i | 0.103376 | + | 0.0596843i | 0.550797 | − | 0.834639i | \(-0.314324\pi\) |
−0.447421 | + | 0.894324i | \(0.647657\pi\) | |||||||
\(48\) | 0.895644 | + | 1.55130i | 0.129275 | + | 0.223911i | ||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | −3.79129 | − | 2.18890i | −0.536169 | − | 0.309557i | ||||
\(51\) | −0.500000 | + | 0.866025i | −0.0700140 | + | 0.121268i | ||||
\(52\) | 6.97822 | + | 7.25198i | 0.967705 | + | 1.00567i | ||||
\(53\) | 3.08258 | + | 5.33918i | 0.423424 | + | 0.733392i | 0.996272 | − | 0.0862695i | \(-0.0274946\pi\) |
−0.572848 | + | 0.819662i | \(0.694161\pi\) | |||||||
\(54\) | 1.89564 | − | 1.09445i | 0.257964 | − | 0.148936i | ||||
\(55\) | 3.00000 | − | 5.19615i | 0.404520 | − | 0.700649i | ||||
\(56\) | −4.58258 | −0.612372 | ||||||||
\(57\) | − | 5.29150i | − | 0.700877i | ||||||
\(58\) | − | 15.3223i | − | 2.01192i | ||||||
\(59\) | −3.70871 | − | 2.14123i | −0.482833 | − | 0.278764i | 0.238763 | − | 0.971078i | \(-0.423258\pi\) |
−0.721596 | + | 0.692314i | \(0.756591\pi\) | |||||||
\(60\) | −4.18693 | + | 2.41733i | −0.540531 | + | 0.312075i | ||||
\(61\) | −5.16515 | −0.661330 | −0.330665 | − | 0.943748i | \(-0.607273\pi\) | ||||
−0.330665 | + | 0.943748i | \(0.607273\pi\) | |||||||
\(62\) | −6.68693 | + | 11.5821i | −0.849241 | + | 1.47093i | ||||
\(63\) | − | 2.64575i | − | 0.333333i | ||||||
\(64\) | 12.5826 | 1.57282 | ||||||||
\(65\) | 4.50000 | − | 4.33013i | 0.558156 | − | 0.537086i | ||||
\(66\) | 3.79129 | + | 6.56670i | 0.466675 | + | 0.808305i | ||||
\(67\) | − | 14.0471i | − | 1.71613i | −0.513543 | − | 0.858064i | \(-0.671667\pi\) | ||
0.513543 | − | 0.858064i | \(-0.328333\pi\) | |||||||
\(68\) | 1.39564 | + | 2.41733i | 0.169247 | + | 0.293144i | ||||
\(69\) | 4.29129 | + | 7.43273i | 0.516610 | + | 0.894795i | ||||
\(70\) | 10.0308i | 1.19891i | ||||||||
\(71\) | −3.87386 | + | 2.23658i | −0.459743 | + | 0.265433i | −0.711936 | − | 0.702244i | \(-0.752181\pi\) |
0.252193 | + | 0.967677i | \(0.418848\pi\) | |||||||
\(72\) | − | 1.73205i | − | 0.204124i | ||||||
\(73\) | 7.50000 | − | 4.33013i | 0.877809 | − | 0.506803i | 0.00787336 | − | 0.999969i | \(-0.497494\pi\) |
0.869935 | + | 0.493166i | \(0.164160\pi\) | |||||||
\(74\) | −7.68693 | + | 13.3142i | −0.893588 | + | 1.54774i | ||||
\(75\) | −1.00000 | − | 1.73205i | −0.115470 | − | 0.200000i | ||||
\(76\) | −12.7913 | − | 7.38505i | −1.46726 | − | 0.847124i | ||||
\(77\) | 9.16515 | 1.04447 | ||||||||
\(78\) | 1.89564 | + | 7.66115i | 0.214639 | + | 0.867455i | ||||
\(79\) | 0.708712 | − | 1.22753i | 0.0797363 | − | 0.138107i | −0.823400 | − | 0.567462i | \(-0.807925\pi\) |
0.903136 | + | 0.429354i | \(0.141259\pi\) | |||||||
\(80\) | − | 3.10260i | − | 0.346881i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.79129 | −0.860404 | ||||||||
\(83\) | − | 3.46410i | − | 0.380235i | −0.981761 | − | 0.190117i | \(-0.939113\pi\) | ||
0.981761 | − | 0.190117i | \(-0.0608868\pi\) | |||||||
\(84\) | −6.39564 | − | 3.69253i | −0.697822 | − | 0.402888i | ||||
\(85\) | 1.50000 | − | 0.866025i | 0.162698 | − | 0.0939336i | ||||
\(86\) | −8.68693 | − | 5.01540i | −0.936736 | − | 0.540825i | ||||
\(87\) | 3.50000 | − | 6.06218i | 0.375239 | − | 0.649934i | ||||
\(88\) | 6.00000 | 0.639602 | ||||||||
\(89\) | −13.5000 | + | 7.79423i | −1.43100 | + | 0.826187i | −0.997197 | − | 0.0748225i | \(-0.976161\pi\) |
−0.433800 | + | 0.901009i | \(0.642828\pi\) | |||||||
\(90\) | −3.79129 | −0.399637 | ||||||||
\(91\) | 9.16515 | + | 2.64575i | 0.960769 | + | 0.277350i | ||||
\(92\) | 23.9564 | 2.49763 | ||||||||
\(93\) | −5.29129 | + | 3.05493i | −0.548681 | + | 0.316781i | ||||
\(94\) | 1.79129 | 0.184757 | ||||||||
\(95\) | −4.58258 | + | 7.93725i | −0.470162 | + | 0.814345i | ||||
\(96\) | 6.39564 | + | 3.69253i | 0.652753 | + | 0.376867i | ||||
\(97\) | 9.08258 | − | 5.24383i | 0.922196 | − | 0.532430i | 0.0378609 | − | 0.999283i | \(-0.487946\pi\) |
0.884335 | + | 0.466853i | \(0.154612\pi\) | |||||||
\(98\) | −13.2695 | + | 7.66115i | −1.34042 | + | 0.773893i | ||||
\(99\) | 3.46410i | 0.348155i | ||||||||
\(100\) | −5.58258 | −0.558258 | ||||||||
\(101\) | 13.1652 | 1.30998 | 0.654991 | − | 0.755637i | \(-0.272673\pi\) | ||||
0.654991 | + | 0.755637i | \(0.272673\pi\) | |||||||
\(102\) | 2.18890i | 0.216734i | ||||||||
\(103\) | −1.70871 | + | 2.95958i | −0.168364 | + | 0.291616i | −0.937845 | − | 0.347055i | \(-0.887182\pi\) |
0.769481 | + | 0.638670i | \(0.220515\pi\) | |||||||
\(104\) | 6.00000 | + | 1.73205i | 0.588348 | + | 0.169842i | ||||
\(105\) | −2.29129 | + | 3.96863i | −0.223607 | + | 0.387298i | ||||
\(106\) | 11.6869 | + | 6.74745i | 1.13514 | + | 0.655371i | ||||
\(107\) | 0.708712 | + | 1.22753i | 0.0685138 | + | 0.118669i | 0.898247 | − | 0.439490i | \(-0.144841\pi\) |
−0.829733 | + | 0.558160i | \(0.811508\pi\) | |||||||
\(108\) | 1.39564 | − | 2.41733i | 0.134296 | − | 0.232607i | ||||
\(109\) | 16.6652 | − | 9.62163i | 1.59623 | − | 0.921585i | 0.604028 | − | 0.796963i | \(-0.293562\pi\) |
0.992204 | − | 0.124622i | \(-0.0397717\pi\) | |||||||
\(110\) | − | 13.1334i | − | 1.25222i | ||||||
\(111\) | −6.08258 | + | 3.51178i | −0.577333 | + | 0.333323i | ||||
\(112\) | 4.10436 | − | 2.36965i | 0.387825 | − | 0.223911i | ||||
\(113\) | −6.08258 | − | 10.5353i | −0.572201 | − | 0.991080i | −0.996340 | − | 0.0854834i | \(-0.972757\pi\) |
0.424139 | − | 0.905597i | \(-0.360577\pi\) | |||||||
\(114\) | −5.79129 | − | 10.0308i | −0.542404 | − | 0.939471i | ||||
\(115\) | − | 14.8655i | − | 1.38621i | ||||||
\(116\) | −9.76951 | − | 16.9213i | −0.907076 | − | 1.57110i | ||||
\(117\) | −1.00000 | + | 3.46410i | −0.0924500 | + | 0.320256i | ||||
\(118\) | −9.37386 | −0.862934 | ||||||||
\(119\) | 2.29129 | + | 1.32288i | 0.210042 | + | 0.121268i | ||||
\(120\) | −1.50000 | + | 2.59808i | −0.136931 | + | 0.237171i | ||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | −9.79129 | + | 5.65300i | −0.886462 | + | 0.511799i | ||||
\(123\) | −3.08258 | − | 1.77973i | −0.277946 | − | 0.160472i | ||||
\(124\) | 17.0544i | 1.53153i | ||||||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | −2.89564 | − | 5.01540i | −0.257964 | − | 0.446808i | ||||
\(127\) | −3.29129 | + | 5.70068i | −0.292055 | + | 0.505853i | −0.974295 | − | 0.225274i | \(-0.927672\pi\) |
0.682241 | + | 0.731128i | \(0.261006\pi\) | |||||||
\(128\) | 11.0608 | − | 6.38595i | 0.977645 | − | 0.564444i | ||||
\(129\) | −2.29129 | − | 3.96863i | −0.201737 | − | 0.349418i | ||||
\(130\) | 3.79129 | − | 13.1334i | 0.332518 | − | 1.15188i | ||||
\(131\) | −0.708712 | + | 1.22753i | −0.0619205 | + | 0.107249i | −0.895324 | − | 0.445416i | \(-0.853056\pi\) |
0.833403 | + | 0.552665i | \(0.186389\pi\) | |||||||
\(132\) | 8.37386 | + | 4.83465i | 0.728851 | + | 0.420802i | ||||
\(133\) | −14.0000 | −1.21395 | ||||||||
\(134\) | −15.3739 | − | 26.6283i | −1.32810 | − | 2.30034i | ||||
\(135\) | −1.50000 | − | 0.866025i | −0.129099 | − | 0.0745356i | ||||
\(136\) | 1.50000 | + | 0.866025i | 0.128624 | + | 0.0742611i | ||||
\(137\) | −7.50000 | − | 4.33013i | −0.640768 | − | 0.369948i | 0.144142 | − | 0.989557i | \(-0.453958\pi\) |
−0.784910 | + | 0.619609i | \(0.787291\pi\) | |||||||
\(138\) | 16.2695 | + | 9.39320i | 1.38495 | + | 0.799603i | ||||
\(139\) | 3.29129 | + | 5.70068i | 0.279163 | + | 0.483525i | 0.971177 | − | 0.238359i | \(-0.0766096\pi\) |
−0.692014 | + | 0.721884i | \(0.743276\pi\) | |||||||
\(140\) | 6.39564 | + | 11.0776i | 0.540531 | + | 0.936226i | ||||
\(141\) | 0.708712 | + | 0.409175i | 0.0596843 | + | 0.0344588i | ||||
\(142\) | −4.89564 | + | 8.47950i | −0.410833 | + | 0.711584i | ||||
\(143\) | −12.0000 | − | 3.46410i | −1.00349 | − | 0.289683i | ||||
\(144\) | 0.895644 | + | 1.55130i | 0.0746370 | + | 0.129275i | ||||
\(145\) | −10.5000 | + | 6.06218i | −0.871978 | + | 0.503436i | ||||
\(146\) | 9.47822 | − | 16.4168i | 0.784423 | − | 1.35866i | ||||
\(147\) | −7.00000 | −0.577350 | ||||||||
\(148\) | 19.6048i | 1.61150i | ||||||||
\(149\) | − | 3.65480i | − | 0.299413i | −0.988730 | − | 0.149707i | \(-0.952167\pi\) | ||
0.988730 | − | 0.149707i | \(-0.0478329\pi\) | |||||||
\(150\) | −3.79129 | − | 2.18890i | −0.309557 | − | 0.178723i | ||||
\(151\) | −14.4564 | + | 8.34643i | −1.17645 | + | 0.679223i | −0.955190 | − | 0.295993i | \(-0.904350\pi\) |
−0.221258 | + | 0.975215i | \(0.571016\pi\) | |||||||
\(152\) | −9.16515 | −0.743392 | ||||||||
\(153\) | −0.500000 | + | 0.866025i | −0.0404226 | + | 0.0700140i | ||||
\(154\) | 17.3739 | − | 10.0308i | 1.40003 | − | 0.808305i | ||||
\(155\) | 10.5826 | 0.850013 | ||||||||
\(156\) | 6.97822 | + | 7.25198i | 0.558705 | + | 0.580623i | ||||
\(157\) | −5.08258 | − | 8.80328i | −0.405634 | − | 0.702578i | 0.588761 | − | 0.808307i | \(-0.299616\pi\) |
−0.994395 | + | 0.105729i | \(0.966282\pi\) | |||||||
\(158\) | − | 3.10260i | − | 0.246830i | ||||||
\(159\) | 3.08258 | + | 5.33918i | 0.244464 | + | 0.423424i | ||||
\(160\) | −6.39564 | − | 11.0776i | −0.505620 | − | 0.875760i | ||||
\(161\) | 19.6652 | − | 11.3537i | 1.54983 | − | 0.894795i | ||||
\(162\) | 1.89564 | − | 1.09445i | 0.148936 | − | 0.0859882i | ||||
\(163\) | − | 3.46410i | − | 0.271329i | −0.990755 | − | 0.135665i | \(-0.956683\pi\) | ||
0.990755 | − | 0.135665i | \(-0.0433170\pi\) | |||||||
\(164\) | −8.60436 | + | 4.96773i | −0.671887 | + | 0.387914i | ||||
\(165\) | 3.00000 | − | 5.19615i | 0.233550 | − | 0.404520i | ||||
\(166\) | −3.79129 | − | 6.56670i | −0.294261 | − | 0.509675i | ||||
\(167\) | 3.87386 | + | 2.23658i | 0.299769 | + | 0.173071i | 0.642339 | − | 0.766421i | \(-0.277964\pi\) |
−0.342570 | + | 0.939492i | \(0.611298\pi\) | |||||||
\(168\) | −4.58258 | −0.353553 | ||||||||
\(169\) | −11.0000 | − | 6.92820i | −0.846154 | − | 0.532939i | ||||
\(170\) | 1.89564 | − | 3.28335i | 0.145389 | − | 0.251822i | ||||
\(171\) | − | 5.29150i | − | 0.404651i | ||||||
\(172\) | −12.7913 | −0.975327 | ||||||||
\(173\) | 24.3303 | 1.84980 | 0.924899 | − | 0.380212i | \(-0.124149\pi\) | ||||
0.924899 | + | 0.380212i | \(0.124149\pi\) | |||||||
\(174\) | − | 15.3223i | − | 1.16158i | ||||||
\(175\) | −4.58258 | + | 2.64575i | −0.346410 | + | 0.200000i | ||||
\(176\) | −5.37386 | + | 3.10260i | −0.405070 | + | 0.233867i | ||||
\(177\) | −3.70871 | − | 2.14123i | −0.278764 | − | 0.160944i | ||||
\(178\) | −17.0608 | + | 29.5502i | −1.27876 | + | 2.21488i | ||||
\(179\) | 0.834849 | 0.0623995 | 0.0311998 | − | 0.999513i | \(-0.490067\pi\) | ||||
0.0311998 | + | 0.999513i | \(0.490067\pi\) | |||||||
\(180\) | −4.18693 | + | 2.41733i | −0.312075 | + | 0.180177i | ||||
\(181\) | 22.0000 | 1.63525 | 0.817624 | − | 0.575753i | \(-0.195291\pi\) | ||||
0.817624 | + | 0.575753i | \(0.195291\pi\) | |||||||
\(182\) | 20.2695 | − | 5.01540i | 1.50248 | − | 0.371766i | ||||
\(183\) | −5.16515 | −0.381819 | ||||||||
\(184\) | 12.8739 | − | 7.43273i | 0.949074 | − | 0.547948i | ||||
\(185\) | 12.1652 | 0.894400 | ||||||||
\(186\) | −6.68693 | + | 11.5821i | −0.490310 | + | 0.849241i | ||||
\(187\) | −3.00000 | − | 1.73205i | −0.219382 | − | 0.126660i | ||||
\(188\) | 1.97822 | − | 1.14213i | 0.144276 | − | 0.0832981i | ||||
\(189\) | − | 2.64575i | − | 0.192450i | ||||||
\(190\) | 20.0616i | 1.45542i | ||||||||
\(191\) | −14.3303 | −1.03690 | −0.518452 | − | 0.855107i | \(-0.673492\pi\) | ||||
−0.518452 | + | 0.855107i | \(0.673492\pi\) | |||||||
\(192\) | 12.5826 | 0.908069 | ||||||||
\(193\) | − | 3.65480i | − | 0.263078i | −0.991311 | − | 0.131539i | \(-0.958008\pi\) | ||
0.991311 | − | 0.131539i | \(-0.0419919\pi\) | |||||||
\(194\) | 11.4782 | − | 19.8809i | 0.824088 | − | 1.42736i | ||||
\(195\) | 4.50000 | − | 4.33013i | 0.322252 | − | 0.310087i | ||||
\(196\) | −9.76951 | + | 16.9213i | −0.697822 | + | 1.20866i | ||||
\(197\) | 15.2477 | + | 8.80328i | 1.08636 | + | 0.627208i | 0.932604 | − | 0.360902i | \(-0.117531\pi\) |
0.153752 | + | 0.988110i | \(0.450864\pi\) | |||||||
\(198\) | 3.79129 | + | 6.56670i | 0.269435 | + | 0.466675i | ||||
\(199\) | −1.29129 | + | 2.23658i | −0.0915370 | + | 0.158547i | −0.908158 | − | 0.418627i | \(-0.862511\pi\) |
0.816621 | + | 0.577174i | \(0.195845\pi\) | |||||||
\(200\) | −3.00000 | + | 1.73205i | −0.212132 | + | 0.122474i | ||||
\(201\) | − | 14.0471i | − | 0.990807i | ||||||
\(202\) | 24.9564 | − | 14.4086i | 1.75593 | − | 1.01379i | ||||
\(203\) | −16.0390 | − | 9.26013i | −1.12572 | − | 0.649934i | ||||
\(204\) | 1.39564 | + | 2.41733i | 0.0977146 | + | 0.169247i | ||||
\(205\) | 3.08258 | + | 5.33918i | 0.215296 | + | 0.372904i | ||||
\(206\) | 7.48040i | 0.521184i | ||||||||
\(207\) | 4.29129 | + | 7.43273i | 0.298265 | + | 0.516610i | ||||
\(208\) | −6.26951 | + | 1.55130i | −0.434712 | + | 0.107563i | ||||
\(209\) | 18.3303 | 1.26793 | ||||||||
\(210\) | 10.0308i | 0.692191i | ||||||||
\(211\) | −3.29129 | + | 5.70068i | −0.226582 | + | 0.392451i | −0.956793 | − | 0.290771i | \(-0.906088\pi\) |
0.730211 | + | 0.683222i | \(0.239422\pi\) | |||||||
\(212\) | 17.2087 | 1.18190 | ||||||||
\(213\) | −3.87386 | + | 2.23658i | −0.265433 | + | 0.153248i | ||||
\(214\) | 2.68693 | + | 1.55130i | 0.183675 | + | 0.106045i | ||||
\(215\) | 7.93725i | 0.541316i | ||||||||
\(216\) | − | 1.73205i | − | 0.117851i | ||||||
\(217\) | 8.08258 | + | 13.9994i | 0.548681 | + | 0.950343i | ||||
\(218\) | 21.0608 | − | 36.4784i | 1.42642 | − | 2.47063i | ||||
\(219\) | 7.50000 | − | 4.33013i | 0.506803 | − | 0.292603i | ||||
\(220\) | −8.37386 | − | 14.5040i | −0.564566 | − | 0.977857i | ||||
\(221\) | −2.50000 | − | 2.59808i | −0.168168 | − | 0.174766i | ||||
\(222\) | −7.68693 | + | 13.3142i | −0.515913 | + | 0.893588i | ||||
\(223\) | −2.29129 | − | 1.32288i | −0.153436 | − | 0.0885863i | 0.421316 | − | 0.906914i | \(-0.361568\pi\) |
−0.574752 | + | 0.818327i | \(0.694902\pi\) | |||||||
\(224\) | 9.76951 | − | 16.9213i | 0.652753 | − | 1.13060i | ||||
\(225\) | −1.00000 | − | 1.73205i | −0.0666667 | − | 0.115470i | ||||
\(226\) | −23.0608 | − | 13.3142i | −1.53398 | − | 0.885645i | ||||
\(227\) | −23.6216 | − | 13.6379i | −1.56782 | − | 0.905181i | −0.996423 | − | 0.0845077i | \(-0.973068\pi\) |
−0.571397 | − | 0.820674i | \(-0.693598\pi\) | |||||||
\(228\) | −12.7913 | − | 7.38505i | −0.847124 | − | 0.489087i | ||||
\(229\) | 9.08258 | + | 5.24383i | 0.600193 | + | 0.346522i | 0.769118 | − | 0.639107i | \(-0.220696\pi\) |
−0.168924 | + | 0.985629i | \(0.554029\pi\) | |||||||
\(230\) | −16.2695 | − | 28.1796i | −1.07278 | − | 1.85811i | ||||
\(231\) | 9.16515 | 0.603023 | ||||||||
\(232\) | −10.5000 | − | 6.06218i | −0.689359 | − | 0.398001i | ||||
\(233\) | −10.0826 | + | 17.4635i | −0.660531 | + | 1.14407i | 0.319945 | + | 0.947436i | \(0.396336\pi\) |
−0.980476 | + | 0.196638i | \(0.936998\pi\) | |||||||
\(234\) | 1.89564 | + | 7.66115i | 0.123922 | + | 0.500825i | ||||
\(235\) | −0.708712 | − | 1.22753i | −0.0462313 | − | 0.0800749i | ||||
\(236\) | −10.3521 | + | 5.97678i | −0.673863 | + | 0.389055i | ||||
\(237\) | 0.708712 | − | 1.22753i | 0.0460358 | − | 0.0797363i | ||||
\(238\) | 5.79129 | 0.375393 | ||||||||
\(239\) | 2.01810i | 0.130540i | 0.997868 | + | 0.0652701i | \(0.0207909\pi\) | ||||
−0.997868 | + | 0.0652701i | \(0.979209\pi\) | |||||||
\(240\) | − | 3.10260i | − | 0.200272i | ||||||
\(241\) | 12.2477 | + | 7.07123i | 0.788945 | + | 0.455498i | 0.839591 | − | 0.543219i | \(-0.182795\pi\) |
−0.0506457 | + | 0.998717i | \(0.516128\pi\) | |||||||
\(242\) | −1.89564 | + | 1.09445i | −0.121857 | + | 0.0703539i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −7.20871 | + | 12.4859i | −0.461491 | + | 0.799325i | ||||
\(245\) | 10.5000 | + | 6.06218i | 0.670820 | + | 0.387298i | ||||
\(246\) | −7.79129 | −0.496754 | ||||||||
\(247\) | 18.3303 | + | 5.29150i | 1.16633 | + | 0.336690i | ||||
\(248\) | 5.29129 | + | 9.16478i | 0.335997 | + | 0.581964i | ||||
\(249\) | − | 3.46410i | − | 0.219529i | ||||||
\(250\) | 13.2695 | + | 22.9835i | 0.839237 | + | 1.45360i | ||||
\(251\) | 10.2913 | + | 17.8250i | 0.649580 | + | 1.12511i | 0.983223 | + | 0.182407i | \(0.0583887\pi\) |
−0.333643 | + | 0.942700i | \(0.608278\pi\) | |||||||
\(252\) | −6.39564 | − | 3.69253i | −0.402888 | − | 0.232607i | ||||
\(253\) | −25.7477 | + | 14.8655i | −1.61875 | + | 0.934583i | ||||
\(254\) | 14.4086i | 0.904076i | ||||||||
\(255\) | 1.50000 | − | 0.866025i | 0.0939336 | − | 0.0542326i | ||||
\(256\) | 1.39564 | − | 2.41733i | 0.0872277 | − | 0.151083i | ||||
\(257\) | 4.66515 | + | 8.08028i | 0.291004 | + | 0.504034i | 0.974047 | − | 0.226344i | \(-0.0726773\pi\) |
−0.683043 | + | 0.730378i | \(0.739344\pi\) | |||||||
\(258\) | −8.68693 | − | 5.01540i | −0.540825 | − | 0.312245i | ||||
\(259\) | 9.29129 | + | 16.0930i | 0.577333 | + | 0.999969i | ||||
\(260\) | −4.18693 | − | 16.9213i | −0.259662 | − | 1.04941i | ||||
\(261\) | 3.50000 | − | 6.06218i | 0.216645 | − | 0.375239i | ||||
\(262\) | 3.10260i | 0.191679i | ||||||||
\(263\) | −4.83485 | −0.298130 | −0.149065 | − | 0.988827i | \(-0.547626\pi\) | ||||
−0.149065 | + | 0.988827i | \(0.547626\pi\) | |||||||
\(264\) | 6.00000 | 0.369274 | ||||||||
\(265\) | − | 10.6784i | − | 0.655966i | ||||||
\(266\) | −26.5390 | + | 15.3223i | −1.62721 | + | 0.939471i | ||||
\(267\) | −13.5000 | + | 7.79423i | −0.826187 | + | 0.476999i | ||||
\(268\) | −33.9564 | − | 19.6048i | −2.07422 | − | 1.19755i | ||||
\(269\) | −8.08258 | + | 13.9994i | −0.492803 | + | 0.853560i | −0.999966 | − | 0.00829015i | \(-0.997361\pi\) |
0.507162 | + | 0.861851i | \(0.330694\pi\) | |||||||
\(270\) | −3.79129 | −0.230730 | ||||||||
\(271\) | −10.0390 | + | 5.79603i | −0.609827 | + | 0.352084i | −0.772898 | − | 0.634531i | \(-0.781193\pi\) |
0.163071 | + | 0.986614i | \(0.447860\pi\) | |||||||
\(272\) | −1.79129 | −0.108613 | ||||||||
\(273\) | 9.16515 | + | 2.64575i | 0.554700 | + | 0.160128i | ||||
\(274\) | −18.9564 | −1.14520 | ||||||||
\(275\) | 6.00000 | − | 3.46410i | 0.361814 | − | 0.208893i | ||||
\(276\) | 23.9564 | 1.44201 | ||||||||
\(277\) | −4.66515 | + | 8.08028i | −0.280302 | + | 0.485497i | −0.971459 | − | 0.237208i | \(-0.923768\pi\) |
0.691157 | + | 0.722704i | \(0.257101\pi\) | |||||||
\(278\) | 12.4782 | + | 7.20430i | 0.748394 | + | 0.432085i | ||||
\(279\) | −5.29129 | + | 3.05493i | −0.316781 | + | 0.182894i | ||||
\(280\) | 6.87386 | + | 3.96863i | 0.410792 | + | 0.237171i | ||||
\(281\) | 3.65480i | 0.218027i | 0.994040 | + | 0.109014i | \(0.0347692\pi\) | ||||
−0.994040 | + | 0.109014i | \(0.965231\pi\) | |||||||
\(282\) | 1.79129 | 0.106670 | ||||||||
\(283\) | −30.3303 | −1.80295 | −0.901475 | − | 0.432832i | \(-0.857514\pi\) | ||||
−0.901475 | + | 0.432832i | \(0.857514\pi\) | |||||||
\(284\) | 12.4859i | 0.740899i | ||||||||
\(285\) | −4.58258 | + | 7.93725i | −0.271448 | + | 0.470162i | ||||
\(286\) | −26.5390 | + | 6.56670i | −1.56928 | + | 0.388297i | ||||
\(287\) | −4.70871 | + | 8.15573i | −0.277946 | + | 0.481417i | ||||
\(288\) | 6.39564 | + | 3.69253i | 0.376867 | + | 0.217584i | ||||
\(289\) | 8.00000 | + | 13.8564i | 0.470588 | + | 0.815083i | ||||
\(290\) | −13.2695 | + | 22.9835i | −0.779212 | + | 1.34964i | ||||
\(291\) | 9.08258 | − | 5.24383i | 0.532430 | − | 0.307399i | ||||
\(292\) | − | 24.1733i | − | 1.41463i | ||||||
\(293\) | 16.8303 | − | 9.71698i | 0.983237 | − | 0.567672i | 0.0799910 | − | 0.996796i | \(-0.474511\pi\) |
0.903246 | + | 0.429124i | \(0.141178\pi\) | |||||||
\(294\) | −13.2695 | + | 7.66115i | −0.773893 | + | 0.446808i | ||||
\(295\) | 3.70871 | + | 6.42368i | 0.215930 | + | 0.374001i | ||||
\(296\) | 6.08258 | + | 10.5353i | 0.353543 | + | 0.612354i | ||||
\(297\) | 3.46410i | 0.201008i | ||||||||
\(298\) | −4.00000 | − | 6.92820i | −0.231714 | − | 0.401340i | ||||
\(299\) | −30.0390 | + | 7.43273i | −1.73720 | + | 0.429846i | ||||
\(300\) | −5.58258 | −0.322310 | ||||||||
\(301\) | −10.5000 | + | 6.06218i | −0.605210 | + | 0.349418i | ||||
\(302\) | −18.2695 | + | 31.6437i | −1.05129 | + | 1.82089i | ||||
\(303\) | 13.1652 | 0.756318 | ||||||||
\(304\) | 8.20871 | − | 4.73930i | 0.470802 | − | 0.271818i | ||||
\(305\) | 7.74773 | + | 4.47315i | 0.443634 | + | 0.256132i | ||||
\(306\) | 2.18890i | 0.125131i | ||||||||
\(307\) | − | 20.9753i | − | 1.19712i | −0.801076 | − | 0.598562i | \(-0.795739\pi\) | ||
0.801076 | − | 0.598562i | \(-0.204261\pi\) | |||||||
\(308\) | 12.7913 | − | 22.1552i | 0.728851 | − | 1.26241i | ||||
\(309\) | −1.70871 | + | 2.95958i | −0.0972052 | + | 0.168364i | ||||
\(310\) | 20.0608 | − | 11.5821i | 1.13938 | − | 0.657819i | ||||
\(311\) | 4.29129 | + | 7.43273i | 0.243337 | + | 0.421471i | 0.961663 | − | 0.274235i | \(-0.0884247\pi\) |
−0.718326 | + | 0.695707i | \(0.755091\pi\) | |||||||
\(312\) | 6.00000 | + | 1.73205i | 0.339683 | + | 0.0980581i | ||||
\(313\) | 6.91742 | − | 11.9813i | 0.390996 | − | 0.677225i | −0.601585 | − | 0.798809i | \(-0.705464\pi\) |
0.992581 | + | 0.121584i | \(0.0387973\pi\) | |||||||
\(314\) | −19.2695 | − | 11.1253i | −1.08744 | − | 0.627834i | ||||
\(315\) | −2.29129 | + | 3.96863i | −0.129099 | + | 0.223607i | ||||
\(316\) | −1.97822 | − | 3.42638i | −0.111284 | − | 0.192749i | ||||
\(317\) | 1.66515 | + | 0.961376i | 0.0935242 | + | 0.0539962i | 0.546033 | − | 0.837764i | \(-0.316137\pi\) |
−0.452508 | + | 0.891760i | \(0.649471\pi\) | |||||||
\(318\) | 11.6869 | + | 6.74745i | 0.655371 | + | 0.378378i | ||||
\(319\) | 21.0000 | + | 12.1244i | 1.17577 | + | 0.678834i | ||||
\(320\) | −18.8739 | − | 10.8968i | −1.05508 | − | 0.609151i | ||||
\(321\) | 0.708712 | + | 1.22753i | 0.0395565 | + | 0.0685138i | ||||
\(322\) | 24.8521 | − | 43.0451i | 1.38495 | − | 2.39881i | ||||
\(323\) | 4.58258 | + | 2.64575i | 0.254981 | + | 0.147214i | ||||
\(324\) | 1.39564 | − | 2.41733i | 0.0775358 | − | 0.134296i | ||||
\(325\) | 7.00000 | − | 1.73205i | 0.388290 | − | 0.0960769i | ||||
\(326\) | −3.79129 | − | 6.56670i | −0.209980 | − | 0.363696i | ||||
\(327\) | 16.6652 | − | 9.62163i | 0.921585 | − | 0.532077i | ||||
\(328\) | −3.08258 | + | 5.33918i | −0.170207 | + | 0.294807i | ||||
\(329\) | 1.08258 | − | 1.87508i | 0.0596843 | − | 0.103376i | ||||
\(330\) | − | 13.1334i | − | 0.722970i | ||||||
\(331\) | 26.0761i | 1.43327i | 0.697447 | + | 0.716636i | \(0.254319\pi\) | ||||
−0.697447 | + | 0.716636i | \(0.745681\pi\) | |||||||
\(332\) | −8.37386 | − | 4.83465i | −0.459575 | − | 0.265336i | ||||
\(333\) | −6.08258 | + | 3.51178i | −0.333323 | + | 0.192444i | ||||
\(334\) | 9.79129 | 0.535755 | ||||||||
\(335\) | −12.1652 | + | 21.0707i | −0.664653 | + | 1.15121i | ||||
\(336\) | 4.10436 | − | 2.36965i | 0.223911 | − | 0.129275i | ||||
\(337\) | 23.4955 | 1.27988 | 0.639939 | − | 0.768425i | \(-0.278959\pi\) | ||||
0.639939 | + | 0.768425i | \(0.278959\pi\) | |||||||
\(338\) | −28.4347 | − | 1.09445i | −1.54664 | − | 0.0595303i | ||||
\(339\) | −6.08258 | − | 10.5353i | −0.330360 | − | 0.572201i | ||||
\(340\) | − | 4.83465i | − | 0.262196i | ||||||
\(341\) | −10.5826 | − | 18.3296i | −0.573079 | − | 0.992601i | ||||
\(342\) | −5.79129 | − | 10.0308i | −0.313157 | − | 0.542404i | ||||
\(343\) | 18.5203i | 1.00000i | ||||||||
\(344\) | −6.87386 | + | 3.96863i | −0.370614 | + | 0.213974i | ||||
\(345\) | − | 14.8655i | − | 0.800329i | ||||||
\(346\) | 46.1216 | − | 26.6283i | 2.47951 | − | 1.43155i | ||||
\(347\) | 12.8739 | − | 22.2982i | 0.691105 | − | 1.19703i | −0.280371 | − | 0.959892i | \(-0.590457\pi\) |
0.971476 | − | 0.237138i | \(-0.0762092\pi\) | |||||||
\(348\) | −9.76951 | − | 16.9213i | −0.523701 | − | 0.907076i | ||||
\(349\) | 9.08258 | + | 5.24383i | 0.486179 | + | 0.280696i | 0.722988 | − | 0.690861i | \(-0.242768\pi\) |
−0.236809 | + | 0.971556i | \(0.576102\pi\) | |||||||
\(350\) | −5.79129 | + | 10.0308i | −0.309557 | + | 0.536169i | ||||
\(351\) | −1.00000 | + | 3.46410i | −0.0533761 | + | 0.184900i | ||||
\(352\) | −12.7913 | + | 22.1552i | −0.681778 | + | 1.18087i | ||||
\(353\) | − | 19.3386i | − | 1.02929i | −0.857403 | − | 0.514645i | \(-0.827924\pi\) | ||
0.857403 | − | 0.514645i | \(-0.172076\pi\) | |||||||
\(354\) | −9.37386 | −0.498215 | ||||||||
\(355\) | 7.74773 | 0.411207 | ||||||||
\(356\) | 43.5119i | 2.30612i | ||||||||
\(357\) | 2.29129 | + | 1.32288i | 0.121268 | + | 0.0700140i | ||||
\(358\) | 1.58258 | − | 0.913701i | 0.0836417 | − | 0.0482906i | ||||
\(359\) | −16.0390 | − | 9.26013i | −0.846507 | − | 0.488731i | 0.0129639 | − | 0.999916i | \(-0.495873\pi\) |
−0.859471 | + | 0.511185i | \(0.829207\pi\) | |||||||
\(360\) | −1.50000 | + | 2.59808i | −0.0790569 | + | 0.136931i | ||||
\(361\) | −9.00000 | −0.473684 | ||||||||
\(362\) | 41.7042 | − | 24.0779i | 2.19192 | − | 1.26551i | ||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 19.1869 | − | 18.4626i | 1.00567 | − | 0.967705i | ||||
\(365\) | −15.0000 | −0.785136 | ||||||||
\(366\) | −9.79129 | + | 5.65300i | −0.511799 | + | 0.295487i | ||||
\(367\) | 15.1652 | 0.791614 | 0.395807 | − | 0.918334i | \(-0.370465\pi\) | ||||
0.395807 | + | 0.918334i | \(0.370465\pi\) | |||||||
\(368\) | −7.68693 | + | 13.3142i | −0.400709 | + | 0.694048i | ||||
\(369\) | −3.08258 | − | 1.77973i | −0.160472 | − | 0.0926488i | ||||
\(370\) | 23.0608 | − | 13.3142i | 1.19887 | − | 0.692170i | ||||
\(371\) | 14.1261 | − | 8.15573i | 0.733392 | − | 0.423424i | ||||
\(372\) | 17.0544i | 0.884227i | ||||||||
\(373\) | −26.0000 | −1.34623 | −0.673114 | − | 0.739538i | \(-0.735044\pi\) | ||||
−0.673114 | + | 0.739538i | \(0.735044\pi\) | |||||||
\(374\) | −7.58258 | −0.392086 | ||||||||
\(375\) | 12.1244i | 0.626099i | ||||||||
\(376\) | 0.708712 | − | 1.22753i | 0.0365490 | − | 0.0633048i | ||||
\(377\) | 17.5000 | + | 18.1865i | 0.901296 | + | 0.936654i | ||||
\(378\) | −2.89564 | − | 5.01540i | −0.148936 | − | 0.257964i | ||||
\(379\) | 16.0390 | + | 9.26013i | 0.823869 | + | 0.475661i | 0.851749 | − | 0.523950i | \(-0.175542\pi\) |
−0.0278799 | + | 0.999611i | \(0.508876\pi\) | |||||||
\(380\) | 12.7913 | + | 22.1552i | 0.656179 | + | 1.13654i | ||||
\(381\) | −3.29129 | + | 5.70068i | −0.168618 | + | 0.292055i | ||||
\(382\) | −27.1652 | + | 15.6838i | −1.38989 | + | 0.802453i | ||||
\(383\) | 17.7019i | 0.904525i | 0.891885 | + | 0.452263i | \(0.149383\pi\) | ||||
−0.891885 | + | 0.452263i | \(0.850617\pi\) | |||||||
\(384\) | 11.0608 | − | 6.38595i | 0.564444 | − | 0.325882i | ||||
\(385\) | −13.7477 | − | 7.93725i | −0.700649 | − | 0.404520i | ||||
\(386\) | −4.00000 | − | 6.92820i | −0.203595 | − | 0.352636i | ||||
\(387\) | −2.29129 | − | 3.96863i | −0.116473 | − | 0.201737i | ||||
\(388\) | − | 29.2741i | − | 1.48617i | ||||||
\(389\) | −13.6652 | − | 23.6687i | −0.692851 | − | 1.20005i | −0.970900 | − | 0.239486i | \(-0.923021\pi\) |
0.278049 | − | 0.960567i | \(-0.410312\pi\) | |||||||
\(390\) | 3.79129 | − | 13.1334i | 0.191979 | − | 0.665036i | ||||
\(391\) | −8.58258 | −0.434040 | ||||||||
\(392\) | 12.1244i | 0.612372i | ||||||||
\(393\) | −0.708712 | + | 1.22753i | −0.0357498 | + | 0.0619205i | ||||
\(394\) | 38.5390 | 1.94157 | ||||||||
\(395\) | −2.12614 | + | 1.22753i | −0.106978 | + | 0.0617635i | ||||
\(396\) | 8.37386 | + | 4.83465i | 0.420802 | + | 0.242950i | ||||
\(397\) | − | 36.8498i | − | 1.84944i | −0.380649 | − | 0.924720i | \(-0.624299\pi\) | ||
0.380649 | − | 0.924720i | \(-0.375701\pi\) | |||||||
\(398\) | 5.65300i | 0.283359i | ||||||||
\(399\) | −14.0000 | −0.700877 | ||||||||
\(400\) | 1.79129 | − | 3.10260i | 0.0895644 | − | 0.155130i | ||||
\(401\) | 30.0826 | − | 17.3682i | 1.50225 | − | 0.867326i | 0.502256 | − | 0.864719i | \(-0.332504\pi\) |
0.999997 | − | 0.00260643i | \(-0.000829654\pi\) | |||||||
\(402\) | −15.3739 | − | 26.6283i | −0.766779 | − | 1.32810i | ||||
\(403\) | −5.29129 | − | 21.3845i | −0.263578 | − | 1.06524i | ||||
\(404\) | 18.3739 | − | 31.8245i | 0.914134 | − | 1.58333i | ||||
\(405\) | −1.50000 | − | 0.866025i | −0.0745356 | − | 0.0430331i | ||||
\(406\) | −40.5390 | −2.01192 | ||||||||
\(407\) | −12.1652 | − | 21.0707i | −0.603004 | − | 1.04443i | ||||
\(408\) | 1.50000 | + | 0.866025i | 0.0742611 | + | 0.0428746i | ||||
\(409\) | 27.0826 | + | 15.6361i | 1.33915 | + | 0.773157i | 0.986681 | − | 0.162668i | \(-0.0520098\pi\) |
0.352466 | + | 0.935825i | \(0.385343\pi\) | |||||||
\(410\) | 11.6869 | + | 6.74745i | 0.577176 | + | 0.333233i | ||||
\(411\) | −7.50000 | − | 4.33013i | −0.369948 | − | 0.213589i | ||||
\(412\) | 4.76951 | + | 8.26103i | 0.234977 | + | 0.406992i | ||||
\(413\) | −5.66515 | + | 9.81233i | −0.278764 | + | 0.482833i | ||||
\(414\) | 16.2695 | + | 9.39320i | 0.799603 | + | 0.461651i | ||||
\(415\) | −3.00000 | + | 5.19615i | −0.147264 | + | 0.255069i | ||||
\(416\) | −19.1869 | + | 18.4626i | −0.940717 | + | 0.905205i | ||||
\(417\) | 3.29129 | + | 5.70068i | 0.161175 | + | 0.279163i | ||||
\(418\) | 34.7477 | − | 20.0616i | 1.69957 | − | 0.981245i | ||||
\(419\) | −5.87386 | + | 10.1738i | −0.286957 | + | 0.497024i | −0.973082 | − | 0.230460i | \(-0.925977\pi\) |
0.686125 | + | 0.727484i | \(0.259310\pi\) | |||||||
\(420\) | 6.39564 | + | 11.0776i | 0.312075 | + | 0.540531i | ||||
\(421\) | − | 40.5046i | − | 1.97407i | −0.160492 | − | 0.987037i | \(-0.551308\pi\) | ||
0.160492 | − | 0.987037i | \(-0.448692\pi\) | |||||||
\(422\) | 14.4086i | 0.701400i | ||||||||
\(423\) | 0.708712 | + | 0.409175i | 0.0344588 | + | 0.0198948i | ||||
\(424\) | 9.24773 | − | 5.33918i | 0.449109 | − | 0.259293i | ||||
\(425\) | 2.00000 | 0.0970143 | ||||||||
\(426\) | −4.89564 | + | 8.47950i | −0.237195 | + | 0.410833i | ||||
\(427\) | 13.6657i | 0.661330i | ||||||||
\(428\) | 3.95644 | 0.191242 | ||||||||
\(429\) | −12.0000 | − | 3.46410i | −0.579365 | − | 0.167248i | ||||
\(430\) | 8.68693 | + | 15.0462i | 0.418921 | + | 0.725593i | ||||
\(431\) | − | 8.56490i | − | 0.412557i | −0.978493 | − | 0.206278i | \(-0.933865\pi\) | ||
0.978493 | − | 0.206278i | \(-0.0661353\pi\) | |||||||
\(432\) | 0.895644 | + | 1.55130i | 0.0430917 | + | 0.0746370i | ||||
\(433\) | 7.66515 | + | 13.2764i | 0.368364 | + | 0.638025i | 0.989310 | − | 0.145829i | \(-0.0465848\pi\) |
−0.620946 | + | 0.783853i | \(0.713251\pi\) | |||||||
\(434\) | 30.6434 | + | 17.6920i | 1.47093 | + | 0.849241i | ||||
\(435\) | −10.5000 | + | 6.06218i | −0.503436 | + | 0.290659i | ||||
\(436\) | − | 53.7135i | − | 2.57241i | ||||||
\(437\) | 39.3303 | − | 22.7074i | 1.88142 | − | 1.08624i | ||||
\(438\) | 9.47822 | − | 16.4168i | 0.452887 | − | 0.784423i | ||||
\(439\) | 5.29129 | + | 9.16478i | 0.252539 | + | 0.437411i | 0.964224 | − | 0.265088i | \(-0.0854009\pi\) |
−0.711685 | + | 0.702499i | \(0.752068\pi\) | |||||||
\(440\) | −9.00000 | − | 5.19615i | −0.429058 | − | 0.247717i | ||||
\(441\) | −7.00000 | −0.333333 | ||||||||
\(442\) | −7.58258 | − | 2.18890i | −0.360666 | − | 0.104115i | ||||
\(443\) | 2.87386 | − | 4.97768i | 0.136541 | − | 0.236497i | −0.789644 | − | 0.613565i | \(-0.789735\pi\) |
0.926185 | + | 0.377069i | \(0.123068\pi\) | |||||||
\(444\) | 19.6048i | 0.930401i | ||||||||
\(445\) | 27.0000 | 1.27992 | ||||||||
\(446\) | −5.79129 | −0.274225 | ||||||||
\(447\) | − | 3.65480i | − | 0.172866i | ||||||
\(448\) | − | 33.2904i | − | 1.57282i | ||||||
\(449\) | −10.6652 | + | 6.15753i | −0.503320 | + | 0.290592i | −0.730083 | − | 0.683358i | \(-0.760519\pi\) |
0.226764 | + | 0.973950i | \(0.427185\pi\) | |||||||
\(450\) | −3.79129 | − | 2.18890i | −0.178723 | − | 0.103186i | ||||
\(451\) | 6.16515 | − | 10.6784i | 0.290306 | − | 0.502824i | ||||
\(452\) | −33.9564 | −1.59718 | ||||||||
\(453\) | −14.4564 | + | 8.34643i | −0.679223 | + | 0.392149i | ||||
\(454\) | −59.7042 | −2.80206 | ||||||||
\(455\) | −11.4564 | − | 11.9059i | −0.537086 | − | 0.558156i | ||||
\(456\) | −9.16515 | −0.429198 | ||||||||
\(457\) | −3.24773 | + | 1.87508i | −0.151922 | + | 0.0877124i | −0.574034 | − | 0.818831i | \(-0.694622\pi\) |
0.422112 | + | 0.906544i | \(0.361289\pi\) | |||||||
\(458\) | 22.9564 | 1.07268 | ||||||||
\(459\) | −0.500000 | + | 0.866025i | −0.0233380 | + | 0.0404226i | ||||
\(460\) | −35.9347 | − | 20.7469i | −1.67546 | − | 0.967328i | ||||
\(461\) | −27.4129 | + | 15.8268i | −1.27675 | + | 0.737129i | −0.976248 | − | 0.216654i | \(-0.930486\pi\) |
−0.300497 | + | 0.953783i | \(0.597152\pi\) | |||||||
\(462\) | 17.3739 | − | 10.0308i | 0.808305 | − | 0.466675i | ||||
\(463\) | − | 38.4865i | − | 1.78862i | −0.447448 | − | 0.894310i | \(-0.647667\pi\) | ||
0.447448 | − | 0.894310i | \(-0.352333\pi\) | |||||||
\(464\) | 12.5390 | 0.582109 | ||||||||
\(465\) | 10.5826 | 0.490755 | ||||||||
\(466\) | 44.1395i | 2.04472i | ||||||||
\(467\) | 14.4564 | − | 25.0393i | 0.668964 | − | 1.15868i | −0.309230 | − | 0.950987i | \(-0.600071\pi\) |
0.978194 | − | 0.207693i | \(-0.0665954\pi\) | |||||||
\(468\) | 6.97822 | + | 7.25198i | 0.322568 | + | 0.335223i | ||||
\(469\) | −37.1652 | −1.71613 | ||||||||
\(470\) | −2.68693 | − | 1.55130i | −0.123939 | − | 0.0715562i | ||||
\(471\) | −5.08258 | − | 8.80328i | −0.234193 | − | 0.405634i | ||||
\(472\) | −3.70871 | + | 6.42368i | −0.170707 | + | 0.295674i | ||||
\(473\) | 13.7477 | − | 7.93725i | 0.632121 | − | 0.364955i | ||||
\(474\) | − | 3.10260i | − | 0.142507i | ||||||
\(475\) | −9.16515 | + | 5.29150i | −0.420526 | + | 0.242791i | ||||
\(476\) | 6.39564 | − | 3.69253i | 0.293144 | − | 0.169247i | ||||
\(477\) | 3.08258 | + | 5.33918i | 0.141141 | + | 0.244464i | ||||
\(478\) | 2.20871 | + | 3.82560i | 0.101024 | + | 0.174979i | ||||
\(479\) | 28.2849i | 1.29237i | 0.763181 | + | 0.646185i | \(0.223637\pi\) | ||||
−0.763181 | + | 0.646185i | \(0.776363\pi\) | |||||||
\(480\) | −6.39564 | − | 11.0776i | −0.291920 | − | 0.505620i | ||||
\(481\) | −6.08258 | − | 24.5824i | −0.277342 | − | 1.12086i | ||||
\(482\) | 30.9564 | 1.41003 | ||||||||
\(483\) | 19.6652 | − | 11.3537i | 0.894795 | − | 0.516610i | ||||
\(484\) | −1.39564 | + | 2.41733i | −0.0634384 | + | 0.109878i | ||||
\(485\) | −18.1652 | −0.824837 | ||||||||
\(486\) | 1.89564 | − | 1.09445i | 0.0859882 | − | 0.0496453i | ||||
\(487\) | −9.54356 | − | 5.50998i | −0.432460 | − | 0.249681i | 0.267934 | − | 0.963437i | \(-0.413659\pi\) |
−0.700394 | + | 0.713756i | \(0.746992\pi\) | |||||||
\(488\) | 8.94630i | 0.404980i | ||||||||
\(489\) | − | 3.46410i | − | 0.156652i | ||||||
\(490\) | 26.5390 | 1.19891 | ||||||||
\(491\) | −1.87386 | + | 3.24563i | −0.0845663 | + | 0.146473i | −0.905206 | − | 0.424972i | \(-0.860284\pi\) |
0.820640 | + | 0.571445i | \(0.193617\pi\) | |||||||
\(492\) | −8.60436 | + | 4.96773i | −0.387914 | + | 0.223962i | ||||
\(493\) | 3.50000 | + | 6.06218i | 0.157632 | + | 0.273027i | ||||
\(494\) | 40.5390 | − | 10.0308i | 1.82394 | − | 0.451307i | ||||
\(495\) | 3.00000 | − | 5.19615i | 0.134840 | − | 0.233550i | ||||
\(496\) | −9.47822 | − | 5.47225i | −0.425585 | − | 0.245711i | ||||
\(497\) | 5.91742 | + | 10.2493i | 0.265433 | + | 0.459743i | ||||
\(498\) | −3.79129 | − | 6.56670i | −0.169892 | − | 0.294261i | ||||
\(499\) | 21.7087 | + | 12.5335i | 0.971815 | + | 0.561078i | 0.899789 | − | 0.436325i | \(-0.143720\pi\) |
0.0720262 | + | 0.997403i | \(0.477053\pi\) | |||||||
\(500\) | 29.3085 | + | 16.9213i | 1.31072 | + | 0.756743i | ||||
\(501\) | 3.87386 | + | 2.23658i | 0.173071 | + | 0.0999229i | ||||
\(502\) | 39.0172 | + | 22.5266i | 1.74142 | + | 1.00541i | ||||
\(503\) | −0.873864 | − | 1.51358i | −0.0389636 | − | 0.0674870i | 0.845886 | − | 0.533364i | \(-0.179072\pi\) |
−0.884850 | + | 0.465877i | \(0.845739\pi\) | |||||||
\(504\) | −4.58258 | −0.204124 | ||||||||
\(505\) | −19.7477 | − | 11.4014i | −0.878762 | − | 0.507354i | ||||
\(506\) | −32.5390 | + | 56.3592i | −1.44654 | + | 2.50547i | ||||
\(507\) | −11.0000 | − | 6.92820i | −0.488527 | − | 0.307692i | ||||
\(508\) | 9.18693 | + | 15.9122i | 0.407604 | + | 0.705991i | ||||
\(509\) | −24.2477 | + | 13.9994i | −1.07476 | + | 0.620514i | −0.929479 | − | 0.368876i | \(-0.879743\pi\) |
−0.145283 | + | 0.989390i | \(0.546409\pi\) | |||||||
\(510\) | 1.89564 | − | 3.28335i | 0.0839405 | − | 0.145389i | ||||
\(511\) | −11.4564 | − | 19.8431i | −0.506803 | − | 0.877809i | ||||
\(512\) | 19.4340i | 0.858868i | ||||||||
\(513\) | − | 5.29150i | − | 0.233626i | ||||||
\(514\) | 17.6869 | + | 10.2116i | 0.780137 | + | 0.450412i | ||||
\(515\) | 5.12614 | − | 2.95958i | 0.225885 | − | 0.130415i | ||||
\(516\) | −12.7913 | −0.563105 | ||||||||
\(517\) | −1.41742 | + | 2.45505i | −0.0623382 | + | 0.107973i | ||||
\(518\) | 35.2259 | + | 20.3377i | 1.54774 | + | 0.893588i | ||||
\(519\) | 24.3303 | 1.06798 | ||||||||
\(520\) | −7.50000 | − | 7.79423i | −0.328897 | − | 0.341800i | ||||
\(521\) | −1.66515 | − | 2.88413i | −0.0729516 | − | 0.126356i | 0.827242 | − | 0.561846i | \(-0.189909\pi\) |
−0.900194 | + | 0.435490i | \(0.856575\pi\) | |||||||
\(522\) | − | 15.3223i | − | 0.670639i | ||||||
\(523\) | 4.87386 | + | 8.44178i | 0.213119 | + | 0.369133i | 0.952689 | − | 0.303946i | \(-0.0983044\pi\) |
−0.739570 | + | 0.673080i | \(0.764971\pi\) | |||||||
\(524\) | 1.97822 | + | 3.42638i | 0.0864189 | + | 0.149682i | ||||
\(525\) | −4.58258 | + | 2.64575i | −0.200000 | + | 0.115470i | ||||
\(526\) | −9.16515 | + | 5.29150i | −0.399620 | + | 0.230720i | ||||
\(527\) | − | 6.10985i | − | 0.266149i | ||||||
\(528\) | −5.37386 | + | 3.10260i | −0.233867 | + | 0.135023i | ||||
\(529\) | −25.3303 | + | 43.8734i | −1.10132 | + | 1.90754i | ||||
\(530\) | −11.6869 | − | 20.2424i | −0.507648 | − | 0.879272i | ||||
\(531\) | −3.70871 | − | 2.14123i | −0.160944 | − | 0.0929213i | ||||
\(532\) | −19.5390 | + | 33.8426i | −0.847124 | + | 1.46726i | ||||
\(533\) | 9.24773 | − | 8.89863i | 0.400564 | − | 0.385442i | ||||
\(534\) | −17.0608 | + | 29.5502i | −0.738293 | + | 1.27876i | ||||
\(535\) | − | 2.45505i | − | 0.106141i | ||||||
\(536\) | −24.3303 | −1.05091 | ||||||||
\(537\) | 0.834849 | 0.0360264 | ||||||||
\(538\) | 35.3839i | 1.52551i | ||||||||
\(539\) | − | 24.2487i | − | 1.04447i | ||||||
\(540\) | −4.18693 | + | 2.41733i | −0.180177 | + | 0.104025i | ||||
\(541\) | −7.33485 | − | 4.23478i | −0.315350 | − | 0.182067i | 0.333968 | − | 0.942584i | \(-0.391612\pi\) |
−0.649318 | + | 0.760517i | \(0.724946\pi\) | |||||||
\(542\) | −12.6869 | + | 21.9744i | −0.544950 | + | 0.943882i | ||||
\(543\) | 22.0000 | 0.944110 | ||||||||
\(544\) | −6.39564 | + | 3.69253i | −0.274211 | + | 0.158316i | ||||
\(545\) | −33.3303 | −1.42771 | ||||||||
\(546\) | 20.2695 | − | 5.01540i | 0.867455 | − | 0.214639i | ||||
\(547\) | −8.00000 | −0.342055 | −0.171028 | − | 0.985266i | \(-0.554709\pi\) | ||||
−0.171028 | + | 0.985266i | \(0.554709\pi\) | |||||||
\(548\) | −20.9347 | + | 12.0866i | −0.894284 | + | 0.516315i | ||||
\(549\) | −5.16515 | −0.220443 | ||||||||
\(550\) | 7.58258 | − | 13.1334i | 0.323322 | − | 0.560010i | ||||
\(551\) | −32.0780 | − | 18.5203i | −1.36657 | − | 0.788990i | ||||
\(552\) | 12.8739 | − | 7.43273i | 0.547948 | − | 0.316358i | ||||
\(553\) | −3.24773 | − | 1.87508i | −0.138107 | − | 0.0797363i | ||||
\(554\) | 20.4231i | 0.867695i | ||||||||
\(555\) | 12.1652 | 0.516382 | ||||||||
\(556\) | 18.3739 | 0.779225 | ||||||||
\(557\) | − | 24.4394i | − | 1.03553i | −0.855523 | − | 0.517766i | \(-0.826764\pi\) | ||
0.855523 | − | 0.517766i | \(-0.173236\pi\) | |||||||
\(558\) | −6.68693 | + | 11.5821i | −0.283080 | + | 0.490310i | ||||
\(559\) | 16.0390 | − | 3.96863i | 0.678378 | − | 0.167855i | ||||
\(560\) | −8.20871 | −0.346881 | ||||||||
\(561\) | −3.00000 | − | 1.73205i | −0.126660 | − | 0.0731272i | ||||
\(562\) | 4.00000 | + | 6.92820i | 0.168730 | + | 0.292249i | ||||
\(563\) | −2.70871 | + | 4.69163i | −0.114159 | + | 0.197729i | −0.917443 | − | 0.397867i | \(-0.869751\pi\) |
0.803284 | + | 0.595596i | \(0.203084\pi\) | |||||||
\(564\) | 1.97822 | − | 1.14213i | 0.0832981 | − | 0.0480922i | ||||
\(565\) | 21.0707i | 0.886449i | ||||||||
\(566\) | −57.4955 | + | 33.1950i | −2.41671 | + | 1.39529i | ||||
\(567\) | − | 2.64575i | − | 0.111111i | ||||||
\(568\) | 3.87386 | + | 6.70973i | 0.162544 | + | 0.281534i | ||||
\(569\) | 2.66515 | + | 4.61618i | 0.111729 | + | 0.193520i | 0.916467 | − | 0.400109i | \(-0.131028\pi\) |
−0.804738 | + | 0.593629i | \(0.797694\pi\) | |||||||
\(570\) | 20.0616i | 0.840288i | ||||||||
\(571\) | −23.8739 | − | 41.3507i | −0.999090 | − | 1.73047i | −0.536481 | − | 0.843913i | \(-0.680247\pi\) |
−0.462609 | − | 0.886562i | \(-0.653087\pi\) | |||||||
\(572\) | −25.1216 | + | 24.1733i | −1.05039 | + | 1.01073i | ||||
\(573\) | −14.3303 | −0.598657 | ||||||||
\(574\) | 20.6138i | 0.860404i | ||||||||
\(575\) | 8.58258 | − | 14.8655i | 0.357918 | − | 0.619932i | ||||
\(576\) | 12.5826 | 0.524274 | ||||||||
\(577\) | −12.0826 | + | 6.97588i | −0.503004 | + | 0.290410i | −0.729953 | − | 0.683497i | \(-0.760458\pi\) |
0.226949 | + | 0.973907i | \(0.427125\pi\) | |||||||
\(578\) | 30.3303 | + | 17.5112i | 1.26157 | + | 0.728370i | ||||
\(579\) | − | 3.65480i | − | 0.151888i | ||||||
\(580\) | 33.8426i | 1.40524i | ||||||||
\(581\) | −9.16515 | −0.380235 | ||||||||
\(582\) | 11.4782 | − | 19.8809i | 0.475788 | − | 0.824088i | ||||
\(583\) | −18.4955 | + | 10.6784i | −0.766003 | + | 0.442252i | ||||
\(584\) | −7.50000 | − | 12.9904i | −0.310352 | − | 0.537546i | ||||
\(585\) | 4.50000 | − | 4.33013i | 0.186052 | − | 0.179029i | ||||
\(586\) | 21.2695 | − | 36.8399i | 0.878635 | − | 1.52184i | ||||
\(587\) | −18.8739 | − | 10.8968i | −0.779008 | − | 0.449760i | 0.0570708 | − | 0.998370i | \(-0.481824\pi\) |
−0.836079 | + | 0.548610i | \(0.815157\pi\) | |||||||
\(588\) | −9.76951 | + | 16.9213i | −0.402888 | + | 0.697822i | ||||
\(589\) | 16.1652 | + | 27.9989i | 0.666073 | + | 1.15367i | ||||
\(590\) | 14.0608 | + | 8.11800i | 0.578874 | + | 0.334213i | ||||
\(591\) | 15.2477 | + | 8.80328i | 0.627208 | + | 0.362119i | ||||
\(592\) | −10.8956 | − | 6.29060i | −0.447808 | − | 0.258542i | ||||
\(593\) | 15.2477 | + | 8.80328i | 0.626149 | + | 0.361507i | 0.779259 | − | 0.626702i | \(-0.215596\pi\) |
−0.153110 | + | 0.988209i | \(0.548929\pi\) | |||||||
\(594\) | 3.79129 | + | 6.56670i | 0.155558 | + | 0.269435i | ||||
\(595\) | −2.29129 | − | 3.96863i | −0.0939336 | − | 0.162698i | ||||
\(596\) | −8.83485 | − | 5.10080i | −0.361889 | − | 0.208937i | ||||
\(597\) | −1.29129 | + | 2.23658i | −0.0528489 | + | 0.0915370i | ||||
\(598\) | −48.8085 | + | 46.9660i | −1.99593 | + | 1.92058i | ||||
\(599\) | −4.12614 | − | 7.14668i | −0.168589 | − | 0.292005i | 0.769335 | − | 0.638846i | \(-0.220588\pi\) |
−0.937924 | + | 0.346841i | \(0.887255\pi\) | |||||||
\(600\) | −3.00000 | + | 1.73205i | −0.122474 | + | 0.0707107i | ||||
\(601\) | −13.0826 | + | 22.6597i | −0.533649 | + | 0.924308i | 0.465578 | + | 0.885007i | \(0.345846\pi\) |
−0.999227 | + | 0.0393010i | \(0.987487\pi\) | |||||||
\(602\) | −13.2695 | + | 22.9835i | −0.540825 | + | 0.936736i | ||||
\(603\) | − | 14.0471i | − | 0.572042i | ||||||
\(604\) | 46.5946i | 1.89591i | ||||||||
\(605\) | 1.50000 | + | 0.866025i | 0.0609837 | + | 0.0352089i | ||||
\(606\) | 24.9564 | − | 14.4086i | 1.01379 | − | 0.585310i | ||||
\(607\) | −8.00000 | −0.324710 | −0.162355 | − | 0.986732i | \(-0.551909\pi\) | ||||
−0.162355 | + | 0.986732i | \(0.551909\pi\) | |||||||
\(608\) | 19.5390 | − | 33.8426i | 0.792412 | − | 1.37250i | ||||
\(609\) | −16.0390 | − | 9.26013i | −0.649934 | − | 0.375239i | ||||
\(610\) | 19.5826 | 0.792875 | ||||||||
\(611\) | −2.12614 | + | 2.04588i | −0.0860143 | + | 0.0827673i | ||||
\(612\) | 1.39564 | + | 2.41733i | 0.0564156 | + | 0.0977146i | ||||
\(613\) | 24.4394i | 0.987099i | 0.869718 | + | 0.493549i | \(0.164301\pi\) | ||||
−0.869718 | + | 0.493549i | \(0.835699\pi\) | |||||||
\(614\) | −22.9564 | − | 39.7617i | −0.926446 | − | 1.60465i | ||||
\(615\) | 3.08258 | + | 5.33918i | 0.124301 | + | 0.215296i | ||||
\(616\) | − | 15.8745i | − | 0.639602i | ||||||
\(617\) | −18.2477 | + | 10.5353i | −0.734626 | + | 0.424136i | −0.820112 | − | 0.572203i | \(-0.806089\pi\) |
0.0854862 | + | 0.996339i | \(0.472756\pi\) | |||||||
\(618\) | 7.48040i | 0.300906i | ||||||||
\(619\) | 1.03901 | − | 0.599876i | 0.0417615 | − | 0.0241110i | −0.478974 | − | 0.877829i | \(-0.658991\pi\) |
0.520735 | + | 0.853718i | \(0.325658\pi\) | |||||||
\(620\) | 14.7695 | − | 25.5815i | 0.593158 | − | 1.02738i | ||||
\(621\) | 4.29129 | + | 7.43273i | 0.172203 | + | 0.298265i | ||||
\(622\) | 16.2695 | + | 9.39320i | 0.652348 | + | 0.376633i | ||||
\(623\) | 20.6216 | + | 35.7176i | 0.826187 | + | 1.43100i | ||||
\(624\) | −6.26951 | + | 1.55130i | −0.250981 | + | 0.0621017i | ||||
\(625\) | 5.50000 | − | 9.52628i | 0.220000 | − | 0.381051i | ||||
\(626\) | − | 30.2831i | − | 1.21036i | ||||||
\(627\) | 18.3303 | 0.732042 | ||||||||
\(628\) | −28.3739 | −1.13224 | ||||||||
\(629\) | − | 7.02355i | − | 0.280047i | ||||||
\(630\) | 10.0308i | 0.399637i | ||||||||
\(631\) | −30.8739 | + | 17.8250i | −1.22907 | + | 0.709603i | −0.966835 | − | 0.255401i | \(-0.917793\pi\) |
−0.262234 | + | 0.965004i | \(0.584459\pi\) | |||||||
\(632\) | −2.12614 | − | 1.22753i | −0.0845732 | − | 0.0488283i | ||||
\(633\) | −3.29129 | + | 5.70068i | −0.130817 | + | 0.226582i | ||||
\(634\) | 4.20871 | 0.167149 | ||||||||
\(635\) | 9.87386 | − | 5.70068i | 0.391832 | − | 0.226224i | ||||
\(636\) | 17.2087 | 0.682370 | ||||||||
\(637\) | 7.00000 | − | 24.2487i | 0.277350 | − | 0.960769i | ||||
\(638\) | 53.0780 | 2.10138 | ||||||||
\(639\) | −3.87386 | + | 2.23658i | −0.153248 | + | 0.0884776i | ||||
\(640\) | −22.1216 | −0.874433 | ||||||||
\(641\) | 8.24773 | − | 14.2855i | 0.325766 | − | 0.564243i | −0.655901 | − | 0.754847i | \(-0.727711\pi\) |
0.981667 | + | 0.190604i | \(0.0610446\pi\) | |||||||
\(642\) | 2.68693 | + | 1.55130i | 0.106045 | + | 0.0612250i | ||||
\(643\) | 29.4564 | − | 17.0067i | 1.16165 | − | 0.670678i | 0.209950 | − | 0.977712i | \(-0.432670\pi\) |
0.951699 | + | 0.307034i | \(0.0993365\pi\) | |||||||
\(644\) | − | 63.3828i | − | 2.49763i | ||||||
\(645\) | 7.93725i | 0.312529i | ||||||||
\(646\) | 11.5826 | 0.455710 | ||||||||
\(647\) | −38.3303 | −1.50692 | −0.753460 | − | 0.657494i | \(-0.771617\pi\) | ||||
−0.753460 | + | 0.657494i | \(0.771617\pi\) | |||||||
\(648\) | − | 1.73205i | − | 0.0680414i | ||||||
\(649\) | 7.41742 | − | 12.8474i | 0.291159 | − | 0.504303i | ||||
\(650\) | 11.3739 | − | 10.9445i | 0.446120 | − | 0.429279i | ||||
\(651\) | 8.08258 | + | 13.9994i | 0.316781 | + | 0.548681i | ||||
\(652\) | −8.37386 | − | 4.83465i | −0.327946 | − | 0.189340i | ||||
\(653\) | −13.2477 | − | 22.9457i | −0.518424 | − | 0.897936i | −0.999771 | − | 0.0214061i | \(-0.993186\pi\) |
0.481347 | − | 0.876530i | \(-0.340148\pi\) | |||||||
\(654\) | 21.0608 | − | 36.4784i | 0.823542 | − | 1.42642i | ||||
\(655\) | 2.12614 | − | 1.22753i | 0.0830750 | − | 0.0479634i | ||||
\(656\) | − | 6.37600i | − | 0.248941i | ||||||
\(657\) | 7.50000 | − | 4.33013i | 0.292603 | − | 0.168934i | ||||
\(658\) | − | 4.73930i | − | 0.184757i | ||||||
\(659\) | −10.0390 | − | 17.3881i | −0.391064 | − | 0.677344i | 0.601526 | − | 0.798853i | \(-0.294560\pi\) |
−0.992590 | + | 0.121510i | \(0.961226\pi\) | |||||||
\(660\) | −8.37386 | − | 14.5040i | −0.325952 | − | 0.564566i | ||||
\(661\) | 5.48220i | 0.213233i | 0.994300 | + | 0.106616i | \(0.0340017\pi\) | ||||
−0.994300 | + | 0.106616i | \(0.965998\pi\) | |||||||
\(662\) | 28.5390 | + | 49.4310i | 1.10920 | + | 1.92119i | ||||
\(663\) | −2.50000 | − | 2.59808i | −0.0970920 | − | 0.100901i | ||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | 21.0000 | + | 12.1244i | 0.814345 | + | 0.470162i | ||||
\(666\) | −7.68693 | + | 13.3142i | −0.297863 | + | 0.515913i | ||||
\(667\) | 60.0780 | 2.32623 | ||||||||
\(668\) | 10.8131 | − | 6.24293i | 0.418370 | − | 0.241546i | ||||
\(669\) | −2.29129 | − | 1.32288i | −0.0885863 | − | 0.0511453i | ||||
\(670\) | 53.2566i | 2.05748i | ||||||||
\(671\) | − | 17.8926i | − | 0.690737i | ||||||
\(672\) | 9.76951 | − | 16.9213i | 0.376867 | − | 0.652753i | ||||
\(673\) | 17.6652 | − | 30.5969i | 0.680942 | − | 1.17943i | −0.293752 | − | 0.955882i | \(-0.594904\pi\) |
0.974694 | − | 0.223544i | \(-0.0717626\pi\) | |||||||
\(674\) | 44.5390 | − | 25.7146i | 1.71558 | − | 0.990490i | ||||
\(675\) | −1.00000 | − | 1.73205i | −0.0384900 | − | 0.0666667i | ||||
\(676\) | −32.0998 | + | 16.9213i | −1.23461 | + | 0.650819i | ||||
\(677\) | −14.9174 | + | 25.8377i | −0.573323 | + | 0.993025i | 0.422898 | + | 0.906177i | \(0.361013\pi\) |
−0.996222 | + | 0.0868478i | \(0.972321\pi\) | |||||||
\(678\) | −23.0608 | − | 13.3142i | −0.885645 | − | 0.511327i | ||||
\(679\) | −13.8739 | − | 24.0302i | −0.532430 | − | 0.922196i | ||||
\(680\) | −1.50000 | − | 2.59808i | −0.0575224 | − | 0.0996317i | ||||
\(681\) | −23.6216 | − | 13.6379i | −0.905181 | − | 0.522607i | ||||
\(682\) | −40.1216 | − | 23.1642i | −1.53634 | − | 0.887003i | ||||
\(683\) | 33.8739 | + | 19.5571i | 1.29615 | + | 0.748331i | 0.979736 | − | 0.200291i | \(-0.0641888\pi\) |
0.316411 | + | 0.948622i | \(0.397522\pi\) | |||||||
\(684\) | −12.7913 | − | 7.38505i | −0.489087 | − | 0.282375i | ||||
\(685\) | 7.50000 | + | 12.9904i | 0.286560 | + | 0.496337i | ||||
\(686\) | 20.2695 | + | 35.1078i | 0.773893 | + | 1.34042i | ||||
\(687\) | 9.08258 | + | 5.24383i | 0.346522 | + | 0.200064i | ||||
\(688\) | 4.10436 | − | 7.10895i | 0.156477 | − | 0.271026i | ||||
\(689\) | −21.5780 | + | 5.33918i | −0.822057 | + | 0.203406i | ||||
\(690\) | −16.2695 | − | 28.1796i | −0.619370 | − | 1.07278i | ||||
\(691\) | −6.54356 | + | 3.77793i | −0.248929 | + | 0.143719i | −0.619274 | − | 0.785175i | \(-0.712573\pi\) |
0.370345 | + | 0.928894i | \(0.379240\pi\) | |||||||
\(692\) | 33.9564 | − | 58.8143i | 1.29083 | − | 2.23578i | ||||
\(693\) | 9.16515 | 0.348155 | ||||||||
\(694\) | − | 56.3592i | − | 2.13937i | ||||||
\(695\) | − | 11.4014i | − | 0.432478i | ||||||
\(696\) | −10.5000 | − | 6.06218i | −0.398001 | − | 0.229786i | ||||
\(697\) | 3.08258 | − | 1.77973i | 0.116761 | − | 0.0674119i | ||||
\(698\) | 22.9564 | 0.868914 | ||||||||
\(699\) | −10.0826 | + | 17.4635i | −0.381358 | + | 0.660531i | ||||
\(700\) | 14.7701i | 0.558258i | ||||||||
\(701\) | 34.0000 | 1.28416 | 0.642081 | − | 0.766637i | \(-0.278071\pi\) | ||||
0.642081 | + | 0.766637i | \(0.278071\pi\) | |||||||
\(702\) | 1.89564 | + | 7.66115i | 0.0715465 | + | 0.289152i | ||||
\(703\) | 18.5826 | + | 32.1860i | 0.700855 | + | 1.21392i | ||||
\(704\) | 43.5873i | 1.64276i | ||||||||
\(705\) | −0.708712 | − | 1.22753i | −0.0266916 | − | 0.0462313i | ||||
\(706\) | −21.1652 | − | 36.6591i | −0.796561 | − | 1.37968i | ||||
\(707\) | − | 34.8317i | − | 1.30998i | ||||||
\(708\) | −10.3521 | + | 5.97678i | −0.389055 | + | 0.224621i | ||||
\(709\) | − | 29.5402i | − | 1.10941i | −0.832048 | − | 0.554703i | \(-0.812832\pi\) | ||
0.832048 | − | 0.554703i | \(-0.187168\pi\) | |||||||
\(710\) | 14.6869 | − | 8.47950i | 0.551191 | − | 0.318230i | ||||
\(711\) | 0.708712 | − | 1.22753i | 0.0265788 | − | 0.0460358i | ||||
\(712\) | 13.5000 | + | 23.3827i | 0.505934 | + | 0.876303i | ||||
\(713\) | −45.4129 | − | 26.2191i | −1.70073 | − | 0.981914i | ||||
\(714\) | 5.79129 | 0.216734 | ||||||||
\(715\) | 15.0000 | + | 15.5885i | 0.560968 | + | 0.582975i | ||||
\(716\) | 1.16515 | − | 2.01810i | 0.0435438 | − | 0.0754200i | ||||
\(717\) | 2.01810i | 0.0753674i | ||||||||
\(718\) | −40.5390 | −1.51290 | ||||||||
\(719\) | −34.3303 | −1.28030 | −0.640152 | − | 0.768248i | \(-0.721129\pi\) | ||||
−0.640152 | + | 0.768248i | \(0.721129\pi\) | |||||||
\(720\) | − | 3.10260i | − | 0.115627i | ||||||
\(721\) | 7.83030 | + | 4.52083i | 0.291616 | + | 0.168364i | ||||
\(722\) | −17.0608 | + | 9.85005i | −0.634937 | + | 0.366581i | ||||
\(723\) | 12.2477 | + | 7.07123i | 0.455498 | + | 0.262982i | ||||
\(724\) | 30.7042 | − | 53.1812i | 1.14111 | − | 1.97646i | ||||
\(725\) | −14.0000 | −0.519947 | ||||||||
\(726\) | −1.89564 | + | 1.09445i | −0.0703539 | + | 0.0406189i | ||||
\(727\) | 28.0000 | 1.03846 | 0.519231 | − | 0.854634i | \(-0.326218\pi\) | ||||
0.519231 | + | 0.854634i | \(0.326218\pi\) | |||||||
\(728\) | 4.58258 | − | 15.8745i | 0.169842 | − | 0.588348i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −28.4347 | + | 16.4168i | −1.05241 | + | 0.607611i | ||||
\(731\) | 4.58258 | 0.169493 | ||||||||
\(732\) | −7.20871 | + | 12.4859i | −0.266442 | + | 0.461491i | ||||
\(733\) | 25.8303 | + | 14.9131i | 0.954064 | + | 0.550829i | 0.894341 | − | 0.447386i | \(-0.147645\pi\) |
0.0597230 | + | 0.998215i | \(0.480978\pi\) | |||||||
\(734\) | 28.7477 | − | 16.5975i | 1.06110 | − | 0.612625i | ||||
\(735\) | 10.5000 | + | 6.06218i | 0.387298 | + | 0.223607i | ||||
\(736\) | 63.3828i | 2.33632i | ||||||||
\(737\) | 48.6606 | 1.79244 | ||||||||
\(738\) | −7.79129 | −0.286801 | ||||||||
\(739\) | 19.1479i | 0.704367i | 0.935931 | + | 0.352184i | \(0.114561\pi\) | ||||
−0.935931 | + | 0.352184i | \(0.885439\pi\) | |||||||
\(740\) | 16.9782 | − | 29.4071i | 0.624132 | − | 1.08103i | ||||
\(741\) | 18.3303 | + | 5.29150i | 0.673380 | + | 0.194388i | ||||
\(742\) | 17.8521 | − | 30.9207i | 0.655371 | − | 1.13514i | ||||
\(743\) | 6.70871 | + | 3.87328i | 0.246119 | + | 0.142097i | 0.617986 | − | 0.786189i | \(-0.287949\pi\) |
−0.371867 | + | 0.928286i | \(0.621282\pi\) | |||||||
\(744\) | 5.29129 | + | 9.16478i | 0.193988 | + | 0.335997i | ||||
\(745\) | −3.16515 | + | 5.48220i | −0.115962 | + | 0.200852i | ||||
\(746\) | −49.2867 | + | 28.4557i | −1.80452 | + | 1.04184i | ||||
\(747\) | − | 3.46410i | − | 0.126745i | ||||||
\(748\) | −8.37386 | + | 4.83465i | −0.306179 | + | 0.176772i | ||||
\(749\) | 3.24773 | − | 1.87508i | 0.118669 | − | 0.0685138i | ||||
\(750\) | 13.2695 | + | 22.9835i | 0.484534 | + | 0.839237i | ||||
\(751\) | 6.45644 | + | 11.1829i | 0.235599 | + | 0.408069i | 0.959447 | − | 0.281891i | \(-0.0909615\pi\) |
−0.723848 | + | 0.689960i | \(0.757628\pi\) | |||||||
\(752\) | 1.46590i | 0.0534559i | ||||||||
\(753\) | 10.2913 | + | 17.8250i | 0.375035 | + | 0.649580i | ||||
\(754\) | 53.0780 | + | 15.3223i | 1.93299 | + | 0.558006i | ||||
\(755\) | 28.9129 | 1.05225 | ||||||||
\(756\) | −6.39564 | − | 3.69253i | −0.232607 | − | 0.134296i | ||||
\(757\) | −2.24773 | + | 3.89318i | −0.0816950 | + | 0.141500i | −0.903978 | − | 0.427579i | \(-0.859367\pi\) |
0.822283 | + | 0.569079i | \(0.192700\pi\) | |||||||
\(758\) | 40.5390 | 1.47244 | ||||||||
\(759\) | −25.7477 | + | 14.8655i | −0.934583 | + | 0.539582i | ||||
\(760\) | 13.7477 | + | 7.93725i | 0.498682 | + | 0.287914i | ||||
\(761\) | 1.44600i | 0.0524175i | 0.999656 | + | 0.0262087i | \(0.00834345\pi\) | ||||
−0.999656 | + | 0.0262087i | \(0.991657\pi\) | |||||||
\(762\) | 14.4086i | 0.521969i | ||||||||
\(763\) | −25.4564 | − | 44.0918i | −0.921585 | − | 1.59623i | ||||
\(764\) | −20.0000 | + | 34.6410i | −0.723575 | + | 1.25327i | ||||
\(765\) | 1.50000 | − | 0.866025i | 0.0542326 | − | 0.0313112i | ||||
\(766\) | 19.3739 | + | 33.5565i | 0.700006 | + | 1.21245i | ||||
\(767\) | 11.1261 | − | 10.7061i | 0.401742 | − | 0.386576i | ||||
\(768\) | 1.39564 | − | 2.41733i | 0.0503610 | − | 0.0872277i | ||||
\(769\) | −2.91742 | − | 1.68438i | −0.105205 | − | 0.0607401i | 0.446474 | − | 0.894796i | \(-0.352679\pi\) |
−0.551679 | + | 0.834056i | \(0.686013\pi\) | |||||||
\(770\) | −34.7477 | −1.25222 | ||||||||
\(771\) | 4.66515 | + | 8.08028i | 0.168011 | + | 0.291004i | ||||
\(772\) | −8.83485 | − | 5.10080i | −0.317973 | − | 0.183582i | ||||
\(773\) | 21.2477 | + | 12.2674i | 0.764228 | + | 0.441227i | 0.830812 | − | 0.556554i | \(-0.187877\pi\) |
−0.0665839 | + | 0.997781i | \(0.521210\pi\) | |||||||
\(774\) | −8.68693 | − | 5.01540i | −0.312245 | − | 0.180275i | ||||
\(775\) | 10.5826 | + | 6.10985i | 0.380137 | + | 0.219472i | ||||
\(776\) | −9.08258 | − | 15.7315i | −0.326045 | − | 0.564727i | ||||
\(777\) | 9.29129 | + | 16.0930i | 0.333323 | + | 0.577333i | ||||
\(778\) | −51.8085 | − | 29.9117i | −1.85743 | − | 1.07239i | ||||
\(779\) | −9.41742 | + | 16.3115i | −0.337414 | + | 0.584419i | ||||
\(780\) | −4.18693 | − | 16.9213i | −0.149916 | − | 0.605879i | ||||
\(781\) | −7.74773 | − | 13.4195i | −0.277235 | − | 0.480186i | ||||
\(782\) | −16.2695 | + | 9.39320i | −0.581796 | + | 0.335900i | ||||
\(783\) | 3.50000 | − | 6.06218i | 0.125080 | − | 0.216645i | ||||
\(784\) | −6.26951 | − | 10.8591i | −0.223911 | − | 0.387825i | ||||
\(785\) | 17.6066i | 0.628405i | ||||||||
\(786\) | 3.10260i | 0.110666i | ||||||||
\(787\) | −26.2913 | − | 15.1793i | −0.937183 | − | 0.541083i | −0.0481070 | − | 0.998842i | \(-0.515319\pi\) |
−0.889076 | + | 0.457759i | \(0.848652\pi\) | |||||||
\(788\) | 42.5608 | − | 24.5725i | 1.51617 | − | 0.875359i | ||||
\(789\) | −4.83485 | −0.172125 | ||||||||
\(790\) | −2.68693 | + | 4.65390i | −0.0955967 | + | 0.165578i | ||||
\(791\) | −27.8739 | + | 16.0930i | −0.991080 | + | 0.572201i | ||||
\(792\) | 6.00000 | 0.213201 | ||||||||
\(793\) | 5.16515 | − | 17.8926i | 0.183420 | − | 0.635385i | ||||
\(794\) | −40.3303 | − | 69.8541i | −1.43127 | − | 2.47903i | ||||
\(795\) | − | 10.6784i | − | 0.378722i | ||||||
\(796\) | 3.60436 | + | 6.24293i | 0.127753 | + | 0.221275i | ||||
\(797\) | −12.0826 | − | 20.9276i | −0.427987 | − | 0.741295i | 0.568707 | − | 0.822540i | \(-0.307444\pi\) |
−0.996694 | + | 0.0812451i | \(0.974110\pi\) | |||||||
\(798\) | −26.5390 | + | 15.3223i | −0.939471 | + | 0.542404i | ||||
\(799\) | −0.708712 | + | 0.409175i | −0.0250724 | + | 0.0144756i | ||||
\(800\) | − | 14.7701i | − | 0.522202i | ||||||
\(801\) | −13.5000 | + | 7.79423i | −0.476999 | + | 0.275396i | ||||
\(802\) | 38.0172 | − | 65.8478i | 1.34244 | − | 2.32517i | ||||
\(803\) | 15.0000 | + | 25.9808i | 0.529339 | + | 0.916841i | ||||
\(804\) | −33.9564 | − | 19.6048i | −1.19755 | − | 0.691407i | ||||
\(805\) | −39.3303 | −1.38621 | ||||||||
\(806\) | −33.4347 | − | 34.7463i | −1.17769 | − | 1.22389i | ||||
\(807\) | −8.08258 | + | 13.9994i | −0.284520 | + | 0.492803i | ||||
\(808\) | − | 22.8027i | − | 0.802197i | ||||||
\(809\) | −33.1652 | −1.16602 | −0.583012 | − | 0.812463i | \(-0.698126\pi\) | ||||
−0.583012 | + | 0.812463i | \(0.698126\pi\) | |||||||
\(810\) | −3.79129 | −0.133212 | ||||||||
\(811\) | 0.190700i | 0.00669640i | 0.999994 | + | 0.00334820i | \(0.00106577\pi\) | ||||
−0.999994 | + | 0.00334820i | \(0.998934\pi\) | |||||||
\(812\) | −44.7695 | + | 25.8477i | −1.57110 | + | 0.907076i | ||||
\(813\) | −10.0390 | + | 5.79603i | −0.352084 | + | 0.203276i | ||||
\(814\) | −46.1216 | − | 26.6283i | −1.61656 | − | 0.933322i | ||||
\(815\) | −3.00000 | + | 5.19615i | −0.105085 | + | 0.182013i | ||||
\(816\) | −1.79129 | −0.0627076 | ||||||||
\(817\) | −21.0000 | + | 12.1244i | −0.734697 | + | 0.424178i | ||||
\(818\) | 68.4519 | 2.39336 | ||||||||
\(819\) | 9.16515 | + | 2.64575i | 0.320256 | + | 0.0924500i | ||||
\(820\) | 17.2087 | 0.600954 | ||||||||
\(821\) | 33.2477 | − | 19.1956i | 1.16035 | − | 0.669931i | 0.208965 | − | 0.977923i | \(-0.432991\pi\) |
0.951389 | + | 0.307993i | \(0.0996572\pi\) | |||||||
\(822\) | −18.9564 | −0.661182 | ||||||||
\(823\) | −15.2913 | + | 26.4853i | −0.533021 | + | 0.923219i | 0.466236 | + | 0.884661i | \(0.345610\pi\) |
−0.999256 | + | 0.0385585i | \(0.987723\pi\) | |||||||
\(824\) | 5.12614 | + | 2.95958i | 0.178577 | + | 0.103102i | ||||
\(825\) | 6.00000 | − | 3.46410i | 0.208893 | − | 0.120605i | ||||
\(826\) | 24.8009i | 0.862934i | ||||||||
\(827\) | 36.6591i | 1.27476i | 0.770549 | + | 0.637381i | \(0.219982\pi\) | ||||
−0.770549 | + | 0.637381i | \(0.780018\pi\) | |||||||
\(828\) | 23.9564 | 0.832544 | ||||||||
\(829\) | −46.6606 | −1.62059 | −0.810295 | − | 0.586022i | \(-0.800693\pi\) | ||||
−0.810295 | + | 0.586022i | \(0.800693\pi\) | |||||||
\(830\) | 13.1334i | 0.455867i | ||||||||
\(831\) | −4.66515 | + | 8.08028i | −0.161832 | + | 0.280302i | ||||
\(832\) | −12.5826 | + | 43.5873i | −0.436222 | + | 1.51112i | ||||
\(833\) | 3.50000 | − | 6.06218i | 0.121268 | − | 0.210042i | ||||
\(834\) | 12.4782 | + | 7.20430i | 0.432085 | + | 0.249465i | ||||
\(835\) | −3.87386 | − | 6.70973i | −0.134061 | − | 0.232200i | ||||
\(836\) | 25.5826 | − | 44.3103i | 0.884792 | − | 1.53250i | ||||
\(837\) | −5.29129 | + | 3.05493i | −0.182894 | + | 0.105594i | ||||
\(838\) | 25.7146i | 0.888297i | ||||||||
\(839\) | −23.1261 | + | 13.3519i | −0.798403 | + | 0.460958i | −0.842912 | − | 0.538051i | \(-0.819161\pi\) |
0.0445095 | + | 0.999009i | \(0.485828\pi\) | |||||||
\(840\) | 6.87386 | + | 3.96863i | 0.237171 | + | 0.136931i | ||||
\(841\) | −10.0000 | − | 17.3205i | −0.344828 | − | 0.597259i | ||||
\(842\) | −44.3303 | − | 76.7823i | −1.52772 | − | 2.64609i | ||||
\(843\) | 3.65480i | 0.125878i | ||||||||
\(844\) | 9.18693 | + | 15.9122i | 0.316227 | + | 0.547722i | ||||
\(845\) | 10.5000 | + | 19.9186i | 0.361211 | + | 0.685220i | ||||
\(846\) | 1.79129 | 0.0615857 | ||||||||
\(847\) | 2.64575i | 0.0909091i | ||||||||
\(848\) | −5.52178 | + | 9.56400i | −0.189619 | + | 0.328429i | ||||
\(849\) | −30.3303 | −1.04093 | ||||||||
\(850\) | 3.79129 | − | 2.18890i | 0.130040 | − | 0.0750787i | ||||
\(851\) | −52.2042 | − | 30.1401i | −1.78954 | − | 1.03319i | ||||
\(852\) | 12.4859i | 0.427758i | ||||||||
\(853\) | 30.9862i | 1.06095i | 0.847701 | + | 0.530474i | \(0.177986\pi\) | ||||
−0.847701 | + | 0.530474i | \(0.822014\pi\) | |||||||
\(854\) | 14.9564 | + | 25.9053i | 0.511799 | + | 0.886462i | ||||
\(855\) | −4.58258 | + | 7.93725i | −0.156721 | + | 0.271448i | ||||
\(856\) | 2.12614 | − | 1.22753i | 0.0726698 | − | 0.0419560i | ||||
\(857\) | −5.66515 | − | 9.81233i | −0.193518 | − | 0.335183i | 0.752896 | − | 0.658140i | \(-0.228656\pi\) |
−0.946414 | + | 0.322957i | \(0.895323\pi\) | |||||||
\(858\) | −26.5390 | + | 6.56670i | −0.906027 | + | 0.224184i | ||||
\(859\) | 23.4564 | − | 40.6277i | 0.800323 | − | 1.38620i | −0.119080 | − | 0.992885i | \(-0.537994\pi\) |
0.919403 | − | 0.393316i | \(-0.128672\pi\) | |||||||
\(860\) | 19.1869 | + | 11.0776i | 0.654269 | + | 0.377742i | ||||
\(861\) | −4.70871 | + | 8.15573i | −0.160472 | + | 0.277946i | ||||
\(862\) | −9.37386 | − | 16.2360i | −0.319275 | − | 0.553001i | ||||
\(863\) | 17.4564 | + | 10.0785i | 0.594224 | + | 0.343075i | 0.766766 | − | 0.641927i | \(-0.221865\pi\) |
−0.172542 | + | 0.985002i | \(0.555198\pi\) | |||||||
\(864\) | 6.39564 | + | 3.69253i | 0.217584 | + | 0.125622i | ||||
\(865\) | −36.4955 | − | 21.0707i | −1.24088 | − | 0.716424i | ||||
\(866\) | 29.0608 | + | 16.7783i | 0.987526 | + | 0.570148i | ||||
\(867\) | 8.00000 | + | 13.8564i | 0.271694 | + | 0.470588i | ||||
\(868\) | 45.1216 | 1.53153 | ||||||||
\(869\) | 4.25227 | + | 2.45505i | 0.144248 | + | 0.0832819i | ||||
\(870\) | −13.2695 | + | 22.9835i | −0.449878 | + | 0.779212i | ||||
\(871\) | 48.6606 | + | 14.0471i | 1.64880 | + | 0.475968i | ||||
\(872\) | −16.6652 | − | 28.8649i | −0.564353 | − | 0.977488i | ||||
\(873\) | 9.08258 | − | 5.24383i | 0.307399 | − | 0.177477i | ||||
\(874\) | 49.7042 | − | 86.0901i | 1.68127 | − | 2.91204i | ||||
\(875\) | 32.0780 | 1.08444 | ||||||||
\(876\) | − | 24.1733i | − | 0.816739i | ||||||
\(877\) | 16.0652i | 0.542484i | 0.962511 | + | 0.271242i | \(0.0874343\pi\) | ||||
−0.962511 | + | 0.271242i | \(0.912566\pi\) | |||||||
\(878\) | 20.0608 | + | 11.5821i | 0.677019 | + | 0.390877i | ||||
\(879\) | 16.8303 | − | 9.71698i | 0.567672 | − | 0.327746i | ||||
\(880\) | 10.7477 | 0.362306 | ||||||||
\(881\) | −9.24773 | + | 16.0175i | −0.311564 | + | 0.539644i | −0.978701 | − | 0.205290i | \(-0.934186\pi\) |
0.667137 | + | 0.744935i | \(0.267519\pi\) | |||||||
\(882\) | −13.2695 | + | 7.66115i | −0.446808 | + | 0.257964i | ||||
\(883\) | 50.3303 | 1.69375 | 0.846875 | − | 0.531792i | \(-0.178481\pi\) | ||||
0.846875 | + | 0.531792i | \(0.178481\pi\) | |||||||
\(884\) | −9.76951 | + | 2.41733i | −0.328584 | + | 0.0813035i | ||||
\(885\) | 3.70871 | + | 6.42368i | 0.124667 | + | 0.215930i | ||||
\(886\) | − | 12.5812i | − | 0.422674i | ||||||
\(887\) | 18.7087 | + | 32.4044i | 0.628177 | + | 1.08803i | 0.987917 | + | 0.154982i | \(0.0495320\pi\) |
−0.359740 | + | 0.933053i | \(0.617135\pi\) | |||||||
\(888\) | 6.08258 | + | 10.5353i | 0.204118 | + | 0.353543i | ||||
\(889\) | 15.0826 | + | 8.70793i | 0.505853 | + | 0.292055i | ||||
\(890\) | 51.1824 | − | 29.5502i | 1.71564 | − | 0.990524i | ||||
\(891\) | 3.46410i | 0.116052i | ||||||||
\(892\) | −6.39564 | + | 3.69253i | −0.214142 | + | 0.123635i | ||||
\(893\) | 2.16515 | − | 3.75015i | 0.0724540 | − | 0.125494i | ||||
\(894\) | −4.00000 | − | 6.92820i | −0.133780 | − | 0.231714i | ||||
\(895\) | −1.25227 | − | 0.723000i | −0.0418589 | − | 0.0241672i | ||||
\(896\) | −16.8956 | − | 29.2641i | −0.564444 | − | 0.977645i | ||||
\(897\) | −30.0390 | + | 7.43273i | −1.00297 | + | 0.248172i | ||||
\(898\) | −13.4782 | + | 23.3450i | −0.449774 | + | 0.779031i | ||||
\(899\) | 42.7690i | 1.42643i | ||||||||
\(900\) | −5.58258 | −0.186086 | ||||||||
\(901\) | −6.16515 | −0.205391 | ||||||||
\(902\) | − | 26.9898i | − | 0.898662i | ||||||
\(903\) | −10.5000 | + | 6.06218i | −0.349418 | + | 0.201737i | ||||
\(904\) | −18.2477 | + | 10.5353i | −0.606910 | + | 0.350400i | ||||
\(905\) | −33.0000 | − | 19.0526i | −1.09696 | − | 0.633328i | ||||
\(906\) | −18.2695 | + | 31.6437i | −0.606964 | + | 1.05129i | ||||
\(907\) | 8.83485 | 0.293356 | 0.146678 | − | 0.989184i | \(-0.453142\pi\) | ||||
0.146678 | + | 0.989184i | \(0.453142\pi\) | |||||||
\(908\) | −65.9347 | + | 38.0674i | −2.18812 | + | 1.26331i | ||||
\(909\) | 13.1652 | 0.436661 | ||||||||
\(910\) | −34.7477 | − | 10.0308i | −1.15188 | − | 0.332518i | ||||
\(911\) | 48.6606 | 1.61220 | 0.806099 | − | 0.591781i | \(-0.201575\pi\) | ||||
0.806099 | + | 0.591781i | \(0.201575\pi\) | |||||||
\(912\) | 8.20871 | − | 4.73930i | 0.271818 | − | 0.156934i | ||||
\(913\) | 12.0000 | 0.397142 | ||||||||
\(914\) | −4.10436 | + | 7.10895i | −0.135760 | + | 0.235143i | ||||
\(915\) | 7.74773 | + | 4.47315i | 0.256132 | + | 0.147878i | ||||
\(916\) | 25.3521 | − | 14.6370i | 0.837656 | − | 0.483621i | ||||
\(917\) | 3.24773 | + | 1.87508i | 0.107249 | + | 0.0619205i | ||||
\(918\) | 2.18890i | 0.0722445i | ||||||||
\(919\) | −4.83485 | −0.159487 | −0.0797435 | − | 0.996815i | \(-0.525410\pi\) | ||||
−0.0797435 | + | 0.996815i | \(0.525410\pi\) | |||||||
\(920\) | −25.7477 | −0.848877 | ||||||||
\(921\) | − | 20.9753i | − | 0.691160i | ||||||
\(922\) | −34.6434 | + | 60.0041i | −1.14092 | + | 1.97613i | ||||
\(923\) | −3.87386 | − | 15.6560i | −0.127510 | − | 0.515325i | ||||
\(924\) | 12.7913 | − | 22.1552i | 0.420802 | − | 0.728851i | ||||
\(925\) | 12.1652 | + | 7.02355i | 0.399988 | + | 0.230933i | ||||
\(926\) | −42.1216 | − | 72.9567i | −1.38420 | − | 2.39751i | ||||
\(927\) | −1.70871 | + | 2.95958i | −0.0561215 | + | 0.0972052i | ||||
\(928\) | 44.7695 | − | 25.8477i | 1.46963 | − | 0.848492i | ||||
\(929\) | 42.3320i | 1.38887i | 0.719556 | + | 0.694434i | \(0.244345\pi\) | ||||
−0.719556 | + | 0.694434i | \(0.755655\pi\) | |||||||
\(930\) | 20.0608 | − | 11.5821i | 0.657819 | − | 0.379792i | ||||
\(931\) | 37.0405i | 1.21395i | ||||||||
\(932\) | 28.1434 | + | 48.7457i | 0.921867 | + | 1.59672i | ||||
\(933\) | 4.29129 | + | 7.43273i | 0.140490 | + | 0.243337i | ||||
\(934\) | − | 63.2874i | − | 2.07083i | ||||||
\(935\) | 3.00000 | + | 5.19615i | 0.0981105 | + | 0.169932i | ||||
\(936\) | 6.00000 | + | 1.73205i | 0.196116 | + | 0.0566139i | ||||
\(937\) | 0.504546 | 0.0164828 | 0.00824140 | − | 0.999966i | \(-0.497377\pi\) | ||||
0.00824140 | + | 0.999966i | \(0.497377\pi\) | |||||||
\(938\) | −70.4519 | + | 40.6754i | −2.30034 | + | 1.32810i | ||||
\(939\) | 6.91742 | − | 11.9813i | 0.225742 | − | 0.390996i | ||||
\(940\) | −3.95644 | −0.129045 | ||||||||
\(941\) | 28.8303 | − | 16.6452i | 0.939841 | − | 0.542617i | 0.0499305 | − | 0.998753i | \(-0.484100\pi\) |
0.889910 | + | 0.456135i | \(0.150767\pi\) | |||||||
\(942\) | −19.2695 | − | 11.1253i | −0.627834 | − | 0.362480i | ||||
\(943\) | − | 30.5493i | − | 0.994821i | ||||||
\(944\) | − | 7.67110i | − | 0.249673i | ||||||
\(945\) | −2.29129 | + | 3.96863i | −0.0745356 | + | 0.129099i | ||||
\(946\) | 17.3739 | − | 30.0924i | 0.564873 | − | 0.978389i | ||||
\(947\) | −13.0390 | + | 7.52808i | −0.423711 | + | 0.244630i | −0.696664 | − | 0.717398i | \(-0.745333\pi\) |
0.272953 | + | 0.962027i | \(0.412000\pi\) | |||||||
\(948\) | −1.97822 | − | 3.42638i | −0.0642496 | − | 0.111284i | ||||
\(949\) | 7.50000 | + | 30.3109i | 0.243460 | + | 0.983933i | ||||
\(950\) | −11.5826 | + | 20.0616i | −0.375788 | + | 0.650885i | ||||
\(951\) | 1.66515 | + | 0.961376i | 0.0539962 | + | 0.0311747i | ||||
\(952\) | 2.29129 | − | 3.96863i | 0.0742611 | − | 0.128624i | ||||
\(953\) | −23.6652 | − | 40.9892i | −0.766589 | − | 1.32777i | −0.939402 | − | 0.342817i | \(-0.888619\pi\) |
0.172813 | − | 0.984955i | \(-0.444714\pi\) | |||||||
\(954\) | 11.6869 | + | 6.74745i | 0.378378 | + | 0.218457i | ||||
\(955\) | 21.4955 | + | 12.4104i | 0.695577 | + | 0.401591i | ||||
\(956\) | 4.87841 | + | 2.81655i | 0.157779 | + | 0.0910938i | ||||
\(957\) | 21.0000 | + | 12.1244i | 0.678834 | + | 0.391925i | ||||
\(958\) | 30.9564 | + | 53.6181i | 1.00016 | + | 1.73232i | ||||
\(959\) | −11.4564 | + | 19.8431i | −0.369948 | + | 0.640768i | ||||
\(960\) | −18.8739 | − | 10.8968i | −0.609151 | − | 0.351694i | ||||
\(961\) | 3.16515 | − | 5.48220i | 0.102102 | − | 0.176845i | ||||
\(962\) | −38.4347 | − | 39.9425i | −1.23918 | − | 1.28780i | ||||
\(963\) | 0.708712 | + | 1.22753i | 0.0228379 | + | 0.0395565i | ||||
\(964\) | 34.1869 | − | 19.7378i | 1.10109 | − | 0.635713i | ||||
\(965\) | −3.16515 | + | 5.48220i | −0.101890 | + | 0.176478i | ||||
\(966\) | 24.8521 | − | 43.0451i | 0.799603 | − | 1.38495i | ||||
\(967\) | − | 5.29150i | − | 0.170163i | −0.996374 | − | 0.0850816i | \(-0.972885\pi\) | ||
0.996374 | − | 0.0850816i | \(-0.0271151\pi\) | |||||||
\(968\) | 1.73205i | 0.0556702i | ||||||||
\(969\) | 4.58258 | + | 2.64575i | 0.147214 | + | 0.0849938i | ||||
\(970\) | −34.4347 | + | 19.8809i | −1.10563 | + | 0.638336i | ||||
\(971\) | 50.3303 | 1.61518 | 0.807588 | − | 0.589747i | \(-0.200772\pi\) | ||||
0.807588 | + | 0.589747i | \(0.200772\pi\) | |||||||
\(972\) | 1.39564 | − | 2.41733i | 0.0447653 | − | 0.0775358i | ||||
\(973\) | 15.0826 | − | 8.70793i | 0.483525 | − | 0.279163i | ||||
\(974\) | −24.1216 | −0.772906 | ||||||||
\(975\) | 7.00000 | − | 1.73205i | 0.224179 | − | 0.0554700i | ||||
\(976\) | −4.62614 | − | 8.01270i | −0.148079 | − | 0.256480i | ||||
\(977\) | 3.65480i | 0.116927i | 0.998290 | + | 0.0584637i | \(0.0186202\pi\) | ||||
−0.998290 | + | 0.0584637i | \(0.981380\pi\) | |||||||
\(978\) | −3.79129 | − | 6.56670i | −0.121232 | − | 0.209980i | ||||
\(979\) | −27.0000 | − | 46.7654i | −0.862924 | − | 1.49463i | ||||
\(980\) | 29.3085 | − | 16.9213i | 0.936226 | − | 0.540531i | ||||
\(981\) | 16.6652 | − | 9.62163i | 0.532077 | − | 0.307195i | ||||
\(982\) | 8.20340i | 0.261781i | ||||||||
\(983\) | −20.2913 | + | 11.7152i | −0.647192 | + | 0.373656i | −0.787379 | − | 0.616469i | \(-0.788563\pi\) |
0.140188 | + | 0.990125i | \(0.455229\pi\) | |||||||
\(984\) | −3.08258 | + | 5.33918i | −0.0982689 | + | 0.170207i | ||||
\(985\) | −15.2477 | − | 26.4098i | −0.485833 | − | 0.841487i | ||||
\(986\) | 13.2695 | + | 7.66115i | 0.422587 | + | 0.243981i | ||||
\(987\) | 1.08258 | − | 1.87508i | 0.0344588 | − | 0.0596843i | ||||
\(988\) | 38.3739 | − | 36.9253i | 1.22084 | − | 1.17475i | ||||
\(989\) | 19.6652 | − | 34.0610i | 0.625315 | − | 1.08308i | ||||
\(990\) | − | 13.1334i | − | 0.417407i | ||||||
\(991\) | 32.6606 | 1.03750 | 0.518749 | − | 0.854926i | \(-0.326398\pi\) | ||||
0.518749 | + | 0.854926i | \(0.326398\pi\) | |||||||
\(992\) | −45.1216 | −1.43261 | ||||||||
\(993\) | 26.0761i | 0.827500i | ||||||||
\(994\) | 22.4347 | + | 12.9527i | 0.711584 | + | 0.410833i | ||||
\(995\) | 3.87386 | − | 2.23658i | 0.122810 | − | 0.0709042i | ||||
\(996\) | −8.37386 | − | 4.83465i | −0.265336 | − | 0.153192i | ||||
\(997\) | 23.6652 | − | 40.9892i | 0.749483 | − | 1.29814i | −0.198588 | − | 0.980083i | \(-0.563636\pi\) |
0.948071 | − | 0.318059i | \(-0.103031\pi\) | |||||||
\(998\) | 54.8693 | 1.73686 | ||||||||
\(999\) | −6.08258 | + | 3.51178i | −0.192444 | + | 0.111108i |
(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 | 273.2.bl.b.121.2 | yes | 4 | |
3.2 | odd | 2 | 819.2.do.d.667.1 | 4 | |||
7.4 | even | 3 | 273.2.t.b.4.2 | ✓ | 4 | ||
13.10 | even | 6 | 273.2.t.b.205.1 | yes | 4 | ||
21.11 | odd | 6 | 819.2.bm.d.550.1 | 4 | |||
39.23 | odd | 6 | 819.2.bm.d.478.2 | 4 | |||
91.88 | even | 6 | inner | 273.2.bl.b.88.2 | yes | 4 | |
273.179 | odd | 6 | 819.2.do.d.361.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.t.b.4.2 | ✓ | 4 | 7.4 | even | 3 | ||
273.2.t.b.205.1 | yes | 4 | 13.10 | even | 6 | ||
273.2.bl.b.88.2 | yes | 4 | 91.88 | even | 6 | inner | |
273.2.bl.b.121.2 | yes | 4 | 1.1 | even | 1 | trivial | |
819.2.bm.d.478.2 | 4 | 39.23 | odd | 6 | |||
819.2.bm.d.550.1 | 4 | 21.11 | odd | 6 | |||
819.2.do.d.361.1 | 4 | 273.179 | odd | 6 | |||
819.2.do.d.667.1 | 4 | 3.2 | odd | 2 |