Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [154,2,Mod(23,154)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(154, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("154.23");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 154 = 2 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 154.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.22969619113\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 154.67 |
Dual form | 154.2.e.d.23.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/154\mathbb{Z}\right)^\times\).
\(n\) | \(45\) | \(57\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 1.50000 | − | 2.59808i | 0.866025 | − | 1.50000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 2.00000 | + | 3.46410i | 0.894427 | + | 1.54919i | 0.834512 | + | 0.550990i | \(0.185750\pi\) |
0.0599153 | + | 0.998203i | \(0.480917\pi\) | |||||||
\(6\) | 3.00000 | 1.22474 | ||||||||
\(7\) | −2.50000 | − | 0.866025i | −0.944911 | − | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −3.00000 | − | 5.19615i | −1.00000 | − | 1.73205i | ||||
\(10\) | −2.00000 | + | 3.46410i | −0.632456 | + | 1.09545i | ||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | 1.50000 | + | 2.59808i | 0.433013 | + | 0.750000i | ||||
\(13\) | −1.00000 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | −0.500000 | − | 2.59808i | −0.133631 | − | 0.694365i | ||||
\(15\) | 12.0000 | 3.09839 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.00000 | + | 1.73205i | −0.242536 | + | 0.420084i | −0.961436 | − | 0.275029i | \(-0.911312\pi\) |
0.718900 | + | 0.695113i | \(0.244646\pi\) | |||||||
\(18\) | 3.00000 | − | 5.19615i | 0.707107 | − | 1.22474i | ||||
\(19\) | −3.00000 | − | 5.19615i | −0.688247 | − | 1.19208i | −0.972404 | − | 0.233301i | \(-0.925047\pi\) |
0.284157 | − | 0.958778i | \(-0.408286\pi\) | |||||||
\(20\) | −4.00000 | −0.894427 | ||||||||
\(21\) | −6.00000 | + | 5.19615i | −1.30931 | + | 1.13389i | ||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 1.00000 | + | 1.73205i | 0.208514 | + | 0.361158i | 0.951247 | − | 0.308431i | \(-0.0998038\pi\) |
−0.742732 | + | 0.669588i | \(0.766471\pi\) | |||||||
\(24\) | −1.50000 | + | 2.59808i | −0.306186 | + | 0.530330i | ||||
\(25\) | −5.50000 | + | 9.52628i | −1.10000 | + | 1.90526i | ||||
\(26\) | −0.500000 | − | 0.866025i | −0.0980581 | − | 0.169842i | ||||
\(27\) | −9.00000 | −1.73205 | ||||||||
\(28\) | 2.00000 | − | 1.73205i | 0.377964 | − | 0.327327i | ||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | 6.00000 | + | 10.3923i | 1.09545 | + | 1.89737i | ||||
\(31\) | −2.00000 | + | 3.46410i | −0.359211 | + | 0.622171i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −1.50000 | − | 2.59808i | −0.261116 | − | 0.452267i | ||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | −2.00000 | − | 10.3923i | −0.338062 | − | 1.75662i | ||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | 1.00000 | + | 1.73205i | 0.164399 | + | 0.284747i | 0.936442 | − | 0.350823i | \(-0.114098\pi\) |
−0.772043 | + | 0.635571i | \(0.780765\pi\) | |||||||
\(38\) | 3.00000 | − | 5.19615i | 0.486664 | − | 0.842927i | ||||
\(39\) | −1.50000 | + | 2.59808i | −0.240192 | + | 0.416025i | ||||
\(40\) | −2.00000 | − | 3.46410i | −0.316228 | − | 0.547723i | ||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | −7.50000 | − | 2.59808i | −1.15728 | − | 0.400892i | ||||
\(43\) | 4.00000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | 0.500000 | + | 0.866025i | 0.0753778 | + | 0.130558i | ||||
\(45\) | 12.0000 | − | 20.7846i | 1.78885 | − | 3.09839i | ||||
\(46\) | −1.00000 | + | 1.73205i | −0.147442 | + | 0.255377i | ||||
\(47\) | −1.00000 | − | 1.73205i | −0.145865 | − | 0.252646i | 0.783830 | − | 0.620975i | \(-0.213263\pi\) |
−0.929695 | + | 0.368329i | \(0.879930\pi\) | |||||||
\(48\) | −3.00000 | −0.433013 | ||||||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | −11.0000 | −1.55563 | ||||||||
\(51\) | 3.00000 | + | 5.19615i | 0.420084 | + | 0.727607i | ||||
\(52\) | 0.500000 | − | 0.866025i | 0.0693375 | − | 0.120096i | ||||
\(53\) | 6.00000 | − | 10.3923i | 0.824163 | − | 1.42749i | −0.0783936 | − | 0.996922i | \(-0.524979\pi\) |
0.902557 | − | 0.430570i | \(-0.141688\pi\) | |||||||
\(54\) | −4.50000 | − | 7.79423i | −0.612372 | − | 1.06066i | ||||
\(55\) | 4.00000 | 0.539360 | ||||||||
\(56\) | 2.50000 | + | 0.866025i | 0.334077 | + | 0.115728i | ||||
\(57\) | −18.0000 | −2.38416 | ||||||||
\(58\) | 0.500000 | + | 0.866025i | 0.0656532 | + | 0.113715i | ||||
\(59\) | −4.50000 | + | 7.79423i | −0.585850 | + | 1.01472i | 0.408919 | + | 0.912571i | \(0.365906\pi\) |
−0.994769 | + | 0.102151i | \(0.967427\pi\) | |||||||
\(60\) | −6.00000 | + | 10.3923i | −0.774597 | + | 1.34164i | ||||
\(61\) | 2.50000 | + | 4.33013i | 0.320092 | + | 0.554416i | 0.980507 | − | 0.196485i | \(-0.0629528\pi\) |
−0.660415 | + | 0.750901i | \(0.729619\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | 3.00000 | + | 15.5885i | 0.377964 | + | 1.96396i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.00000 | − | 3.46410i | −0.248069 | − | 0.429669i | ||||
\(66\) | 1.50000 | − | 2.59808i | 0.184637 | − | 0.319801i | ||||
\(67\) | 4.50000 | − | 7.79423i | 0.549762 | − | 0.952217i | −0.448528 | − | 0.893769i | \(-0.648052\pi\) |
0.998290 | − | 0.0584478i | \(-0.0186151\pi\) | |||||||
\(68\) | −1.00000 | − | 1.73205i | −0.121268 | − | 0.210042i | ||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 8.00000 | − | 6.92820i | 0.956183 | − | 0.828079i | ||||
\(71\) | 4.00000 | 0.474713 | 0.237356 | − | 0.971423i | \(-0.423719\pi\) | ||||
0.237356 | + | 0.971423i | \(0.423719\pi\) | |||||||
\(72\) | 3.00000 | + | 5.19615i | 0.353553 | + | 0.612372i | ||||
\(73\) | 1.00000 | − | 1.73205i | 0.117041 | − | 0.202721i | −0.801553 | − | 0.597924i | \(-0.795992\pi\) |
0.918594 | + | 0.395203i | \(0.129326\pi\) | |||||||
\(74\) | −1.00000 | + | 1.73205i | −0.116248 | + | 0.201347i | ||||
\(75\) | 16.5000 | + | 28.5788i | 1.90526 | + | 3.30000i | ||||
\(76\) | 6.00000 | 0.688247 | ||||||||
\(77\) | −2.00000 | + | 1.73205i | −0.227921 | + | 0.197386i | ||||
\(78\) | −3.00000 | −0.339683 | ||||||||
\(79\) | 7.50000 | + | 12.9904i | 0.843816 | + | 1.46153i | 0.886646 | + | 0.462450i | \(0.153029\pi\) |
−0.0428296 | + | 0.999082i | \(0.513637\pi\) | |||||||
\(80\) | 2.00000 | − | 3.46410i | 0.223607 | − | 0.387298i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | −1.00000 | − | 1.73205i | −0.110432 | − | 0.191273i | ||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | −1.50000 | − | 7.79423i | −0.163663 | − | 0.850420i | ||||
\(85\) | −8.00000 | −0.867722 | ||||||||
\(86\) | 2.00000 | + | 3.46410i | 0.215666 | + | 0.373544i | ||||
\(87\) | 1.50000 | − | 2.59808i | 0.160817 | − | 0.278543i | ||||
\(88\) | −0.500000 | + | 0.866025i | −0.0533002 | + | 0.0923186i | ||||
\(89\) | −3.00000 | − | 5.19615i | −0.317999 | − | 0.550791i | 0.662071 | − | 0.749441i | \(-0.269678\pi\) |
−0.980071 | + | 0.198650i | \(0.936344\pi\) | |||||||
\(90\) | 24.0000 | 2.52982 | ||||||||
\(91\) | 2.50000 | + | 0.866025i | 0.262071 | + | 0.0907841i | ||||
\(92\) | −2.00000 | −0.208514 | ||||||||
\(93\) | 6.00000 | + | 10.3923i | 0.622171 | + | 1.07763i | ||||
\(94\) | 1.00000 | − | 1.73205i | 0.103142 | − | 0.178647i | ||||
\(95\) | 12.0000 | − | 20.7846i | 1.23117 | − | 2.13246i | ||||
\(96\) | −1.50000 | − | 2.59808i | −0.153093 | − | 0.265165i | ||||
\(97\) | −5.00000 | −0.507673 | −0.253837 | − | 0.967247i | \(-0.581693\pi\) | ||||
−0.253837 | + | 0.967247i | \(0.581693\pi\) | |||||||
\(98\) | −1.00000 | + | 6.92820i | −0.101015 | + | 0.699854i | ||||
\(99\) | −6.00000 | −0.603023 | ||||||||
\(100\) | −5.50000 | − | 9.52628i | −0.550000 | − | 0.952628i | ||||
\(101\) | 7.50000 | − | 12.9904i | 0.746278 | − | 1.29259i | −0.203317 | − | 0.979113i | \(-0.565172\pi\) |
0.949595 | − | 0.313478i | \(-0.101494\pi\) | |||||||
\(102\) | −3.00000 | + | 5.19615i | −0.297044 | + | 0.514496i | ||||
\(103\) | −6.00000 | − | 10.3923i | −0.591198 | − | 1.02398i | −0.994071 | − | 0.108729i | \(-0.965322\pi\) |
0.402874 | − | 0.915255i | \(-0.368011\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | −30.0000 | − | 10.3923i | −2.92770 | − | 1.01419i | ||||
\(106\) | 12.0000 | 1.16554 | ||||||||
\(107\) | −4.00000 | − | 6.92820i | −0.386695 | − | 0.669775i | 0.605308 | − | 0.795991i | \(-0.293050\pi\) |
−0.992003 | + | 0.126217i | \(0.959717\pi\) | |||||||
\(108\) | 4.50000 | − | 7.79423i | 0.433013 | − | 0.750000i | ||||
\(109\) | −5.00000 | + | 8.66025i | −0.478913 | + | 0.829502i | −0.999708 | − | 0.0241802i | \(-0.992302\pi\) |
0.520794 | + | 0.853682i | \(0.325636\pi\) | |||||||
\(110\) | 2.00000 | + | 3.46410i | 0.190693 | + | 0.330289i | ||||
\(111\) | 6.00000 | 0.569495 | ||||||||
\(112\) | 0.500000 | + | 2.59808i | 0.0472456 | + | 0.245495i | ||||
\(113\) | 17.0000 | 1.59923 | 0.799613 | − | 0.600516i | \(-0.205038\pi\) | ||||
0.799613 | + | 0.600516i | \(0.205038\pi\) | |||||||
\(114\) | −9.00000 | − | 15.5885i | −0.842927 | − | 1.45999i | ||||
\(115\) | −4.00000 | + | 6.92820i | −0.373002 | + | 0.646058i | ||||
\(116\) | −0.500000 | + | 0.866025i | −0.0464238 | + | 0.0804084i | ||||
\(117\) | 3.00000 | + | 5.19615i | 0.277350 | + | 0.480384i | ||||
\(118\) | −9.00000 | −0.828517 | ||||||||
\(119\) | 4.00000 | − | 3.46410i | 0.366679 | − | 0.317554i | ||||
\(120\) | −12.0000 | −1.09545 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | −2.50000 | + | 4.33013i | −0.226339 | + | 0.392031i | ||||
\(123\) | −3.00000 | + | 5.19615i | −0.270501 | + | 0.468521i | ||||
\(124\) | −2.00000 | − | 3.46410i | −0.179605 | − | 0.311086i | ||||
\(125\) | −24.0000 | −2.14663 | ||||||||
\(126\) | −12.0000 | + | 10.3923i | −1.06904 | + | 0.925820i | ||||
\(127\) | 5.00000 | 0.443678 | 0.221839 | − | 0.975083i | \(-0.428794\pi\) | ||||
0.221839 | + | 0.975083i | \(0.428794\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 6.00000 | − | 10.3923i | 0.528271 | − | 0.914991i | ||||
\(130\) | 2.00000 | − | 3.46410i | 0.175412 | − | 0.303822i | ||||
\(131\) | 9.00000 | + | 15.5885i | 0.786334 | + | 1.36197i | 0.928199 | + | 0.372084i | \(0.121357\pi\) |
−0.141865 | + | 0.989886i | \(0.545310\pi\) | |||||||
\(132\) | 3.00000 | 0.261116 | ||||||||
\(133\) | 3.00000 | + | 15.5885i | 0.260133 | + | 1.35169i | ||||
\(134\) | 9.00000 | 0.777482 | ||||||||
\(135\) | −18.0000 | − | 31.1769i | −1.54919 | − | 2.68328i | ||||
\(136\) | 1.00000 | − | 1.73205i | 0.0857493 | − | 0.148522i | ||||
\(137\) | 4.50000 | − | 7.79423i | 0.384461 | − | 0.665906i | −0.607233 | − | 0.794524i | \(-0.707721\pi\) |
0.991694 | + | 0.128618i | \(0.0410540\pi\) | |||||||
\(138\) | 3.00000 | + | 5.19615i | 0.255377 | + | 0.442326i | ||||
\(139\) | 8.00000 | 0.678551 | 0.339276 | − | 0.940687i | \(-0.389818\pi\) | ||||
0.339276 | + | 0.940687i | \(0.389818\pi\) | |||||||
\(140\) | 10.0000 | + | 3.46410i | 0.845154 | + | 0.292770i | ||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 2.00000 | + | 3.46410i | 0.167836 | + | 0.290701i | ||||
\(143\) | −0.500000 | + | 0.866025i | −0.0418121 | + | 0.0724207i | ||||
\(144\) | −3.00000 | + | 5.19615i | −0.250000 | + | 0.433013i | ||||
\(145\) | 2.00000 | + | 3.46410i | 0.166091 | + | 0.287678i | ||||
\(146\) | 2.00000 | 0.165521 | ||||||||
\(147\) | 19.5000 | − | 7.79423i | 1.60833 | − | 0.642857i | ||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | 5.00000 | + | 8.66025i | 0.409616 | + | 0.709476i | 0.994847 | − | 0.101391i | \(-0.0323294\pi\) |
−0.585231 | + | 0.810867i | \(0.698996\pi\) | |||||||
\(150\) | −16.5000 | + | 28.5788i | −1.34722 | + | 2.33345i | ||||
\(151\) | −4.50000 | + | 7.79423i | −0.366205 | + | 0.634285i | −0.988969 | − | 0.148124i | \(-0.952676\pi\) |
0.622764 | + | 0.782410i | \(0.286010\pi\) | |||||||
\(152\) | 3.00000 | + | 5.19615i | 0.243332 | + | 0.421464i | ||||
\(153\) | 12.0000 | 0.970143 | ||||||||
\(154\) | −2.50000 | − | 0.866025i | −0.201456 | − | 0.0697863i | ||||
\(155\) | −16.0000 | −1.28515 | ||||||||
\(156\) | −1.50000 | − | 2.59808i | −0.120096 | − | 0.208013i | ||||
\(157\) | −2.00000 | + | 3.46410i | −0.159617 | + | 0.276465i | −0.934731 | − | 0.355357i | \(-0.884359\pi\) |
0.775113 | + | 0.631822i | \(0.217693\pi\) | |||||||
\(158\) | −7.50000 | + | 12.9904i | −0.596668 | + | 1.03346i | ||||
\(159\) | −18.0000 | − | 31.1769i | −1.42749 | − | 2.47249i | ||||
\(160\) | 4.00000 | 0.316228 | ||||||||
\(161\) | −1.00000 | − | 5.19615i | −0.0788110 | − | 0.409514i | ||||
\(162\) | −9.00000 | −0.707107 | ||||||||
\(163\) | −6.50000 | − | 11.2583i | −0.509119 | − | 0.881820i | −0.999944 | − | 0.0105623i | \(-0.996638\pi\) |
0.490825 | − | 0.871258i | \(-0.336695\pi\) | |||||||
\(164\) | 1.00000 | − | 1.73205i | 0.0780869 | − | 0.135250i | ||||
\(165\) | 6.00000 | − | 10.3923i | 0.467099 | − | 0.809040i | ||||
\(166\) | −3.00000 | − | 5.19615i | −0.232845 | − | 0.403300i | ||||
\(167\) | −17.0000 | −1.31550 | −0.657750 | − | 0.753237i | \(-0.728492\pi\) | ||||
−0.657750 | + | 0.753237i | \(0.728492\pi\) | |||||||
\(168\) | 6.00000 | − | 5.19615i | 0.462910 | − | 0.400892i | ||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | −4.00000 | − | 6.92820i | −0.306786 | − | 0.531369i | ||||
\(171\) | −18.0000 | + | 31.1769i | −1.37649 | + | 2.38416i | ||||
\(172\) | −2.00000 | + | 3.46410i | −0.152499 | + | 0.264135i | ||||
\(173\) | 2.50000 | + | 4.33013i | 0.190071 | + | 0.329213i | 0.945274 | − | 0.326278i | \(-0.105795\pi\) |
−0.755202 | + | 0.655492i | \(0.772461\pi\) | |||||||
\(174\) | 3.00000 | 0.227429 | ||||||||
\(175\) | 22.0000 | − | 19.0526i | 1.66304 | − | 1.44024i | ||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 13.5000 | + | 23.3827i | 1.01472 | + | 1.75755i | ||||
\(178\) | 3.00000 | − | 5.19615i | 0.224860 | − | 0.389468i | ||||
\(179\) | −6.50000 | + | 11.2583i | −0.485833 | + | 0.841487i | −0.999867 | − | 0.0162823i | \(-0.994817\pi\) |
0.514035 | + | 0.857769i | \(0.328150\pi\) | |||||||
\(180\) | 12.0000 | + | 20.7846i | 0.894427 | + | 1.54919i | ||||
\(181\) | −22.0000 | −1.63525 | −0.817624 | − | 0.575753i | \(-0.804709\pi\) | ||||
−0.817624 | + | 0.575753i | \(0.804709\pi\) | |||||||
\(182\) | 0.500000 | + | 2.59808i | 0.0370625 | + | 0.192582i | ||||
\(183\) | 15.0000 | 1.10883 | ||||||||
\(184\) | −1.00000 | − | 1.73205i | −0.0737210 | − | 0.127688i | ||||
\(185\) | −4.00000 | + | 6.92820i | −0.294086 | + | 0.509372i | ||||
\(186\) | −6.00000 | + | 10.3923i | −0.439941 | + | 0.762001i | ||||
\(187\) | 1.00000 | + | 1.73205i | 0.0731272 | + | 0.126660i | ||||
\(188\) | 2.00000 | 0.145865 | ||||||||
\(189\) | 22.5000 | + | 7.79423i | 1.63663 | + | 0.566947i | ||||
\(190\) | 24.0000 | 1.74114 | ||||||||
\(191\) | −7.00000 | − | 12.1244i | −0.506502 | − | 0.877288i | −0.999972 | − | 0.00752447i | \(-0.997605\pi\) |
0.493469 | − | 0.869763i | \(-0.335728\pi\) | |||||||
\(192\) | 1.50000 | − | 2.59808i | 0.108253 | − | 0.187500i | ||||
\(193\) | 11.0000 | − | 19.0526i | 0.791797 | − | 1.37143i | −0.133056 | − | 0.991109i | \(-0.542479\pi\) |
0.924853 | − | 0.380325i | \(-0.124188\pi\) | |||||||
\(194\) | −2.50000 | − | 4.33013i | −0.179490 | − | 0.310885i | ||||
\(195\) | −12.0000 | −0.859338 | ||||||||
\(196\) | −6.50000 | + | 2.59808i | −0.464286 | + | 0.185577i | ||||
\(197\) | −3.00000 | −0.213741 | −0.106871 | − | 0.994273i | \(-0.534083\pi\) | ||||
−0.106871 | + | 0.994273i | \(0.534083\pi\) | |||||||
\(198\) | −3.00000 | − | 5.19615i | −0.213201 | − | 0.369274i | ||||
\(199\) | −5.00000 | + | 8.66025i | −0.354441 | + | 0.613909i | −0.987022 | − | 0.160585i | \(-0.948662\pi\) |
0.632581 | + | 0.774494i | \(0.281995\pi\) | |||||||
\(200\) | 5.50000 | − | 9.52628i | 0.388909 | − | 0.673610i | ||||
\(201\) | −13.5000 | − | 23.3827i | −0.952217 | − | 1.64929i | ||||
\(202\) | 15.0000 | 1.05540 | ||||||||
\(203\) | −2.50000 | − | 0.866025i | −0.175466 | − | 0.0607831i | ||||
\(204\) | −6.00000 | −0.420084 | ||||||||
\(205\) | −4.00000 | − | 6.92820i | −0.279372 | − | 0.483887i | ||||
\(206\) | 6.00000 | − | 10.3923i | 0.418040 | − | 0.724066i | ||||
\(207\) | 6.00000 | − | 10.3923i | 0.417029 | − | 0.722315i | ||||
\(208\) | 0.500000 | + | 0.866025i | 0.0346688 | + | 0.0600481i | ||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | −6.00000 | − | 31.1769i | −0.414039 | − | 2.15141i | ||||
\(211\) | −14.0000 | −0.963800 | −0.481900 | − | 0.876226i | \(-0.660053\pi\) | ||||
−0.481900 | + | 0.876226i | \(0.660053\pi\) | |||||||
\(212\) | 6.00000 | + | 10.3923i | 0.412082 | + | 0.713746i | ||||
\(213\) | 6.00000 | − | 10.3923i | 0.411113 | − | 0.712069i | ||||
\(214\) | 4.00000 | − | 6.92820i | 0.273434 | − | 0.473602i | ||||
\(215\) | 8.00000 | + | 13.8564i | 0.545595 | + | 0.944999i | ||||
\(216\) | 9.00000 | 0.612372 | ||||||||
\(217\) | 8.00000 | − | 6.92820i | 0.543075 | − | 0.470317i | ||||
\(218\) | −10.0000 | −0.677285 | ||||||||
\(219\) | −3.00000 | − | 5.19615i | −0.202721 | − | 0.351123i | ||||
\(220\) | −2.00000 | + | 3.46410i | −0.134840 | + | 0.233550i | ||||
\(221\) | 1.00000 | − | 1.73205i | 0.0672673 | − | 0.116510i | ||||
\(222\) | 3.00000 | + | 5.19615i | 0.201347 | + | 0.348743i | ||||
\(223\) | −26.0000 | −1.74109 | −0.870544 | − | 0.492090i | \(-0.836233\pi\) | ||||
−0.870544 | + | 0.492090i | \(0.836233\pi\) | |||||||
\(224\) | −2.00000 | + | 1.73205i | −0.133631 | + | 0.115728i | ||||
\(225\) | 66.0000 | 4.40000 | ||||||||
\(226\) | 8.50000 | + | 14.7224i | 0.565412 | + | 0.979322i | ||||
\(227\) | −5.00000 | + | 8.66025i | −0.331862 | + | 0.574801i | −0.982877 | − | 0.184263i | \(-0.941010\pi\) |
0.651015 | + | 0.759065i | \(0.274343\pi\) | |||||||
\(228\) | 9.00000 | − | 15.5885i | 0.596040 | − | 1.03237i | ||||
\(229\) | 8.00000 | + | 13.8564i | 0.528655 | + | 0.915657i | 0.999442 | + | 0.0334101i | \(0.0106368\pi\) |
−0.470787 | + | 0.882247i | \(0.656030\pi\) | |||||||
\(230\) | −8.00000 | −0.527504 | ||||||||
\(231\) | 1.50000 | + | 7.79423i | 0.0986928 | + | 0.512823i | ||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | −3.00000 | − | 5.19615i | −0.196537 | − | 0.340411i | 0.750867 | − | 0.660454i | \(-0.229636\pi\) |
−0.947403 | + | 0.320043i | \(0.896303\pi\) | |||||||
\(234\) | −3.00000 | + | 5.19615i | −0.196116 | + | 0.339683i | ||||
\(235\) | 4.00000 | − | 6.92820i | 0.260931 | − | 0.451946i | ||||
\(236\) | −4.50000 | − | 7.79423i | −0.292925 | − | 0.507361i | ||||
\(237\) | 45.0000 | 2.92306 | ||||||||
\(238\) | 5.00000 | + | 1.73205i | 0.324102 | + | 0.112272i | ||||
\(239\) | 19.0000 | 1.22901 | 0.614504 | − | 0.788914i | \(-0.289356\pi\) | ||||
0.614504 | + | 0.788914i | \(0.289356\pi\) | |||||||
\(240\) | −6.00000 | − | 10.3923i | −0.387298 | − | 0.670820i | ||||
\(241\) | −15.0000 | + | 25.9808i | −0.966235 | + | 1.67357i | −0.259975 | + | 0.965615i | \(0.583714\pi\) |
−0.706260 | + | 0.707953i | \(0.749619\pi\) | |||||||
\(242\) | 0.500000 | − | 0.866025i | 0.0321412 | − | 0.0556702i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.00000 | −0.320092 | ||||||||
\(245\) | −4.00000 | + | 27.7128i | −0.255551 | + | 1.77051i | ||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | 3.00000 | + | 5.19615i | 0.190885 | + | 0.330623i | ||||
\(248\) | 2.00000 | − | 3.46410i | 0.127000 | − | 0.219971i | ||||
\(249\) | −9.00000 | + | 15.5885i | −0.570352 | + | 0.987878i | ||||
\(250\) | −12.0000 | − | 20.7846i | −0.758947 | − | 1.31453i | ||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | −15.0000 | − | 5.19615i | −0.944911 | − | 0.327327i | ||||
\(253\) | 2.00000 | 0.125739 | ||||||||
\(254\) | 2.50000 | + | 4.33013i | 0.156864 | + | 0.271696i | ||||
\(255\) | −12.0000 | + | 20.7846i | −0.751469 | + | 1.30158i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 10.5000 | + | 18.1865i | 0.654972 | + | 1.13444i | 0.981901 | + | 0.189396i | \(0.0606529\pi\) |
−0.326929 | + | 0.945049i | \(0.606014\pi\) | |||||||
\(258\) | 12.0000 | 0.747087 | ||||||||
\(259\) | −1.00000 | − | 5.19615i | −0.0621370 | − | 0.322873i | ||||
\(260\) | 4.00000 | 0.248069 | ||||||||
\(261\) | −3.00000 | − | 5.19615i | −0.185695 | − | 0.321634i | ||||
\(262\) | −9.00000 | + | 15.5885i | −0.556022 | + | 0.963058i | ||||
\(263\) | −1.50000 | + | 2.59808i | −0.0924940 | + | 0.160204i | −0.908560 | − | 0.417755i | \(-0.862817\pi\) |
0.816066 | + | 0.577959i | \(0.196151\pi\) | |||||||
\(264\) | 1.50000 | + | 2.59808i | 0.0923186 | + | 0.159901i | ||||
\(265\) | 48.0000 | 2.94862 | ||||||||
\(266\) | −12.0000 | + | 10.3923i | −0.735767 | + | 0.637193i | ||||
\(267\) | −18.0000 | −1.10158 | ||||||||
\(268\) | 4.50000 | + | 7.79423i | 0.274881 | + | 0.476108i | ||||
\(269\) | −6.00000 | + | 10.3923i | −0.365826 | + | 0.633630i | −0.988908 | − | 0.148527i | \(-0.952547\pi\) |
0.623082 | + | 0.782157i | \(0.285880\pi\) | |||||||
\(270\) | 18.0000 | − | 31.1769i | 1.09545 | − | 1.89737i | ||||
\(271\) | −12.5000 | − | 21.6506i | −0.759321 | − | 1.31518i | −0.943197 | − | 0.332233i | \(-0.892198\pi\) |
0.183876 | − | 0.982949i | \(-0.441135\pi\) | |||||||
\(272\) | 2.00000 | 0.121268 | ||||||||
\(273\) | 6.00000 | − | 5.19615i | 0.363137 | − | 0.314485i | ||||
\(274\) | 9.00000 | 0.543710 | ||||||||
\(275\) | 5.50000 | + | 9.52628i | 0.331662 | + | 0.574456i | ||||
\(276\) | −3.00000 | + | 5.19615i | −0.180579 | + | 0.312772i | ||||
\(277\) | 1.50000 | − | 2.59808i | 0.0901263 | − | 0.156103i | −0.817438 | − | 0.576017i | \(-0.804606\pi\) |
0.907564 | + | 0.419914i | \(0.137940\pi\) | |||||||
\(278\) | 4.00000 | + | 6.92820i | 0.239904 | + | 0.415526i | ||||
\(279\) | 24.0000 | 1.43684 | ||||||||
\(280\) | 2.00000 | + | 10.3923i | 0.119523 | + | 0.621059i | ||||
\(281\) | −10.0000 | −0.596550 | −0.298275 | − | 0.954480i | \(-0.596411\pi\) | ||||
−0.298275 | + | 0.954480i | \(0.596411\pi\) | |||||||
\(282\) | −3.00000 | − | 5.19615i | −0.178647 | − | 0.309426i | ||||
\(283\) | 3.00000 | − | 5.19615i | 0.178331 | − | 0.308879i | −0.762978 | − | 0.646425i | \(-0.776263\pi\) |
0.941309 | + | 0.337546i | \(0.109597\pi\) | |||||||
\(284\) | −2.00000 | + | 3.46410i | −0.118678 | + | 0.205557i | ||||
\(285\) | −36.0000 | − | 62.3538i | −2.13246 | − | 3.69352i | ||||
\(286\) | −1.00000 | −0.0591312 | ||||||||
\(287\) | 5.00000 | + | 1.73205i | 0.295141 | + | 0.102240i | ||||
\(288\) | −6.00000 | −0.353553 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | −2.00000 | + | 3.46410i | −0.117444 | + | 0.203419i | ||||
\(291\) | −7.50000 | + | 12.9904i | −0.439658 | + | 0.761510i | ||||
\(292\) | 1.00000 | + | 1.73205i | 0.0585206 | + | 0.101361i | ||||
\(293\) | −6.00000 | −0.350524 | −0.175262 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175262 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(294\) | 16.5000 | + | 12.9904i | 0.962300 | + | 0.757614i | ||||
\(295\) | −36.0000 | −2.09600 | ||||||||
\(296\) | −1.00000 | − | 1.73205i | −0.0581238 | − | 0.100673i | ||||
\(297\) | −4.50000 | + | 7.79423i | −0.261116 | + | 0.452267i | ||||
\(298\) | −5.00000 | + | 8.66025i | −0.289642 | + | 0.501675i | ||||
\(299\) | −1.00000 | − | 1.73205i | −0.0578315 | − | 0.100167i | ||||
\(300\) | −33.0000 | −1.90526 | ||||||||
\(301\) | −10.0000 | − | 3.46410i | −0.576390 | − | 0.199667i | ||||
\(302\) | −9.00000 | −0.517892 | ||||||||
\(303\) | −22.5000 | − | 38.9711i | −1.29259 | − | 2.23883i | ||||
\(304\) | −3.00000 | + | 5.19615i | −0.172062 | + | 0.298020i | ||||
\(305\) | −10.0000 | + | 17.3205i | −0.572598 | + | 0.991769i | ||||
\(306\) | 6.00000 | + | 10.3923i | 0.342997 | + | 0.594089i | ||||
\(307\) | 32.0000 | 1.82634 | 0.913168 | − | 0.407583i | \(-0.133628\pi\) | ||||
0.913168 | + | 0.407583i | \(0.133628\pi\) | |||||||
\(308\) | −0.500000 | − | 2.59808i | −0.0284901 | − | 0.148039i | ||||
\(309\) | −36.0000 | −2.04797 | ||||||||
\(310\) | −8.00000 | − | 13.8564i | −0.454369 | − | 0.786991i | ||||
\(311\) | 14.0000 | − | 24.2487i | 0.793867 | − | 1.37502i | −0.129689 | − | 0.991555i | \(-0.541398\pi\) |
0.923556 | − | 0.383464i | \(-0.125269\pi\) | |||||||
\(312\) | 1.50000 | − | 2.59808i | 0.0849208 | − | 0.147087i | ||||
\(313\) | −0.500000 | − | 0.866025i | −0.0282617 | − | 0.0489506i | 0.851549 | − | 0.524276i | \(-0.175664\pi\) |
−0.879810 | + | 0.475325i | \(0.842331\pi\) | |||||||
\(314\) | −4.00000 | −0.225733 | ||||||||
\(315\) | −48.0000 | + | 41.5692i | −2.70449 | + | 2.34216i | ||||
\(316\) | −15.0000 | −0.843816 | ||||||||
\(317\) | 6.00000 | + | 10.3923i | 0.336994 | + | 0.583690i | 0.983866 | − | 0.178908i | \(-0.0572566\pi\) |
−0.646872 | + | 0.762598i | \(0.723923\pi\) | |||||||
\(318\) | 18.0000 | − | 31.1769i | 1.00939 | − | 1.74831i | ||||
\(319\) | 0.500000 | − | 0.866025i | 0.0279946 | − | 0.0484881i | ||||
\(320\) | 2.00000 | + | 3.46410i | 0.111803 | + | 0.193649i | ||||
\(321\) | −24.0000 | −1.33955 | ||||||||
\(322\) | 4.00000 | − | 3.46410i | 0.222911 | − | 0.193047i | ||||
\(323\) | 12.0000 | 0.667698 | ||||||||
\(324\) | −4.50000 | − | 7.79423i | −0.250000 | − | 0.433013i | ||||
\(325\) | 5.50000 | − | 9.52628i | 0.305085 | − | 0.528423i | ||||
\(326\) | 6.50000 | − | 11.2583i | 0.360002 | − | 0.623541i | ||||
\(327\) | 15.0000 | + | 25.9808i | 0.829502 | + | 1.43674i | ||||
\(328\) | 2.00000 | 0.110432 | ||||||||
\(329\) | 1.00000 | + | 5.19615i | 0.0551318 | + | 0.286473i | ||||
\(330\) | 12.0000 | 0.660578 | ||||||||
\(331\) | −3.50000 | − | 6.06218i | −0.192377 | − | 0.333207i | 0.753660 | − | 0.657264i | \(-0.228286\pi\) |
−0.946038 | + | 0.324057i | \(0.894953\pi\) | |||||||
\(332\) | 3.00000 | − | 5.19615i | 0.164646 | − | 0.285176i | ||||
\(333\) | 6.00000 | − | 10.3923i | 0.328798 | − | 0.569495i | ||||
\(334\) | −8.50000 | − | 14.7224i | −0.465099 | − | 0.805576i | ||||
\(335\) | 36.0000 | 1.96689 | ||||||||
\(336\) | 7.50000 | + | 2.59808i | 0.409159 | + | 0.141737i | ||||
\(337\) | −30.0000 | −1.63420 | −0.817102 | − | 0.576493i | \(-0.804421\pi\) | ||||
−0.817102 | + | 0.576493i | \(0.804421\pi\) | |||||||
\(338\) | −6.00000 | − | 10.3923i | −0.326357 | − | 0.565267i | ||||
\(339\) | 25.5000 | − | 44.1673i | 1.38497 | − | 2.39884i | ||||
\(340\) | 4.00000 | − | 6.92820i | 0.216930 | − | 0.375735i | ||||
\(341\) | 2.00000 | + | 3.46410i | 0.108306 | + | 0.187592i | ||||
\(342\) | −36.0000 | −1.94666 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | −4.00000 | −0.215666 | ||||||||
\(345\) | 12.0000 | + | 20.7846i | 0.646058 | + | 1.11901i | ||||
\(346\) | −2.50000 | + | 4.33013i | −0.134401 | + | 0.232789i | ||||
\(347\) | 14.0000 | − | 24.2487i | 0.751559 | − | 1.30174i | −0.195507 | − | 0.980702i | \(-0.562635\pi\) |
0.947067 | − | 0.321037i | \(-0.104031\pi\) | |||||||
\(348\) | 1.50000 | + | 2.59808i | 0.0804084 | + | 0.139272i | ||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | 27.5000 | + | 9.52628i | 1.46994 | + | 0.509201i | ||||
\(351\) | 9.00000 | 0.480384 | ||||||||
\(352\) | −0.500000 | − | 0.866025i | −0.0266501 | − | 0.0461593i | ||||
\(353\) | 9.00000 | − | 15.5885i | 0.479022 | − | 0.829690i | −0.520689 | − | 0.853746i | \(-0.674325\pi\) |
0.999711 | + | 0.0240566i | \(0.00765819\pi\) | |||||||
\(354\) | −13.5000 | + | 23.3827i | −0.717517 | + | 1.24278i | ||||
\(355\) | 8.00000 | + | 13.8564i | 0.424596 | + | 0.735422i | ||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | −3.00000 | − | 15.5885i | −0.158777 | − | 0.825029i | ||||
\(358\) | −13.0000 | −0.687071 | ||||||||
\(359\) | 15.5000 | + | 26.8468i | 0.818059 | + | 1.41692i | 0.907111 | + | 0.420892i | \(0.138283\pi\) |
−0.0890519 | + | 0.996027i | \(0.528384\pi\) | |||||||
\(360\) | −12.0000 | + | 20.7846i | −0.632456 | + | 1.09545i | ||||
\(361\) | −8.50000 | + | 14.7224i | −0.447368 | + | 0.774865i | ||||
\(362\) | −11.0000 | − | 19.0526i | −0.578147 | − | 1.00138i | ||||
\(363\) | −3.00000 | −0.157459 | ||||||||
\(364\) | −2.00000 | + | 1.73205i | −0.104828 | + | 0.0907841i | ||||
\(365\) | 8.00000 | 0.418739 | ||||||||
\(366\) | 7.50000 | + | 12.9904i | 0.392031 | + | 0.679018i | ||||
\(367\) | 7.00000 | − | 12.1244i | 0.365397 | − | 0.632886i | −0.623443 | − | 0.781869i | \(-0.714267\pi\) |
0.988840 | + | 0.148983i | \(0.0475999\pi\) | |||||||
\(368\) | 1.00000 | − | 1.73205i | 0.0521286 | − | 0.0902894i | ||||
\(369\) | 6.00000 | + | 10.3923i | 0.312348 | + | 0.541002i | ||||
\(370\) | −8.00000 | −0.415900 | ||||||||
\(371\) | −24.0000 | + | 20.7846i | −1.24602 | + | 1.07908i | ||||
\(372\) | −12.0000 | −0.622171 | ||||||||
\(373\) | 3.50000 | + | 6.06218i | 0.181223 | + | 0.313888i | 0.942297 | − | 0.334777i | \(-0.108661\pi\) |
−0.761074 | + | 0.648665i | \(0.775328\pi\) | |||||||
\(374\) | −1.00000 | + | 1.73205i | −0.0517088 | + | 0.0895622i | ||||
\(375\) | −36.0000 | + | 62.3538i | −1.85903 | + | 3.21994i | ||||
\(376\) | 1.00000 | + | 1.73205i | 0.0515711 | + | 0.0893237i | ||||
\(377\) | −1.00000 | −0.0515026 | ||||||||
\(378\) | 4.50000 | + | 23.3827i | 0.231455 | + | 1.20268i | ||||
\(379\) | −29.0000 | −1.48963 | −0.744815 | − | 0.667271i | \(-0.767462\pi\) | ||||
−0.744815 | + | 0.667271i | \(0.767462\pi\) | |||||||
\(380\) | 12.0000 | + | 20.7846i | 0.615587 | + | 1.06623i | ||||
\(381\) | 7.50000 | − | 12.9904i | 0.384237 | − | 0.665517i | ||||
\(382\) | 7.00000 | − | 12.1244i | 0.358151 | − | 0.620336i | ||||
\(383\) | −4.00000 | − | 6.92820i | −0.204390 | − | 0.354015i | 0.745548 | − | 0.666452i | \(-0.232188\pi\) |
−0.949938 | + | 0.312437i | \(0.898855\pi\) | |||||||
\(384\) | 3.00000 | 0.153093 | ||||||||
\(385\) | −10.0000 | − | 3.46410i | −0.509647 | − | 0.176547i | ||||
\(386\) | 22.0000 | 1.11977 | ||||||||
\(387\) | −12.0000 | − | 20.7846i | −0.609994 | − | 1.05654i | ||||
\(388\) | 2.50000 | − | 4.33013i | 0.126918 | − | 0.219829i | ||||
\(389\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(390\) | −6.00000 | − | 10.3923i | −0.303822 | − | 0.526235i | ||||
\(391\) | −4.00000 | −0.202289 | ||||||||
\(392\) | −5.50000 | − | 4.33013i | −0.277792 | − | 0.218704i | ||||
\(393\) | 54.0000 | 2.72394 | ||||||||
\(394\) | −1.50000 | − | 2.59808i | −0.0755689 | − | 0.130889i | ||||
\(395\) | −30.0000 | + | 51.9615i | −1.50946 | + | 2.61447i | ||||
\(396\) | 3.00000 | − | 5.19615i | 0.150756 | − | 0.261116i | ||||
\(397\) | 15.0000 | + | 25.9808i | 0.752828 | + | 1.30394i | 0.946447 | + | 0.322860i | \(0.104644\pi\) |
−0.193618 | + | 0.981077i | \(0.562022\pi\) | |||||||
\(398\) | −10.0000 | −0.501255 | ||||||||
\(399\) | 45.0000 | + | 15.5885i | 2.25282 | + | 0.780399i | ||||
\(400\) | 11.0000 | 0.550000 | ||||||||
\(401\) | −7.50000 | − | 12.9904i | −0.374532 | − | 0.648709i | 0.615725 | − | 0.787961i | \(-0.288863\pi\) |
−0.990257 | + | 0.139253i | \(0.955530\pi\) | |||||||
\(402\) | 13.5000 | − | 23.3827i | 0.673319 | − | 1.16622i | ||||
\(403\) | 2.00000 | − | 3.46410i | 0.0996271 | − | 0.172559i | ||||
\(404\) | 7.50000 | + | 12.9904i | 0.373139 | + | 0.646296i | ||||
\(405\) | −36.0000 | −1.78885 | ||||||||
\(406\) | −0.500000 | − | 2.59808i | −0.0248146 | − | 0.128940i | ||||
\(407\) | 2.00000 | 0.0991363 | ||||||||
\(408\) | −3.00000 | − | 5.19615i | −0.148522 | − | 0.257248i | ||||
\(409\) | 16.0000 | − | 27.7128i | 0.791149 | − | 1.37031i | −0.134107 | − | 0.990967i | \(-0.542817\pi\) |
0.925256 | − | 0.379344i | \(-0.123850\pi\) | |||||||
\(410\) | 4.00000 | − | 6.92820i | 0.197546 | − | 0.342160i | ||||
\(411\) | −13.5000 | − | 23.3827i | −0.665906 | − | 1.15338i | ||||
\(412\) | 12.0000 | 0.591198 | ||||||||
\(413\) | 18.0000 | − | 15.5885i | 0.885722 | − | 0.767058i | ||||
\(414\) | 12.0000 | 0.589768 | ||||||||
\(415\) | −12.0000 | − | 20.7846i | −0.589057 | − | 1.02028i | ||||
\(416\) | −0.500000 | + | 0.866025i | −0.0245145 | + | 0.0424604i | ||||
\(417\) | 12.0000 | − | 20.7846i | 0.587643 | − | 1.01783i | ||||
\(418\) | −3.00000 | − | 5.19615i | −0.146735 | − | 0.254152i | ||||
\(419\) | −20.0000 | −0.977064 | −0.488532 | − | 0.872546i | \(-0.662467\pi\) | ||||
−0.488532 | + | 0.872546i | \(0.662467\pi\) | |||||||
\(420\) | 24.0000 | − | 20.7846i | 1.17108 | − | 1.01419i | ||||
\(421\) | −20.0000 | −0.974740 | −0.487370 | − | 0.873195i | \(-0.662044\pi\) | ||||
−0.487370 | + | 0.873195i | \(0.662044\pi\) | |||||||
\(422\) | −7.00000 | − | 12.1244i | −0.340755 | − | 0.590204i | ||||
\(423\) | −6.00000 | + | 10.3923i | −0.291730 | + | 0.505291i | ||||
\(424\) | −6.00000 | + | 10.3923i | −0.291386 | + | 0.504695i | ||||
\(425\) | −11.0000 | − | 19.0526i | −0.533578 | − | 0.924185i | ||||
\(426\) | 12.0000 | 0.581402 | ||||||||
\(427\) | −2.50000 | − | 12.9904i | −0.120983 | − | 0.628649i | ||||
\(428\) | 8.00000 | 0.386695 | ||||||||
\(429\) | 1.50000 | + | 2.59808i | 0.0724207 | + | 0.125436i | ||||
\(430\) | −8.00000 | + | 13.8564i | −0.385794 | + | 0.668215i | ||||
\(431\) | −0.500000 | + | 0.866025i | −0.0240842 | + | 0.0417150i | −0.877816 | − | 0.478997i | \(-0.841000\pi\) |
0.853732 | + | 0.520712i | \(0.174334\pi\) | |||||||
\(432\) | 4.50000 | + | 7.79423i | 0.216506 | + | 0.375000i | ||||
\(433\) | −10.0000 | −0.480569 | −0.240285 | − | 0.970702i | \(-0.577241\pi\) | ||||
−0.240285 | + | 0.970702i | \(0.577241\pi\) | |||||||
\(434\) | 10.0000 | + | 3.46410i | 0.480015 | + | 0.166282i | ||||
\(435\) | 12.0000 | 0.575356 | ||||||||
\(436\) | −5.00000 | − | 8.66025i | −0.239457 | − | 0.414751i | ||||
\(437\) | 6.00000 | − | 10.3923i | 0.287019 | − | 0.497131i | ||||
\(438\) | 3.00000 | − | 5.19615i | 0.143346 | − | 0.248282i | ||||
\(439\) | 2.50000 | + | 4.33013i | 0.119318 | + | 0.206666i | 0.919498 | − | 0.393095i | \(-0.128596\pi\) |
−0.800179 | + | 0.599761i | \(0.795262\pi\) | |||||||
\(440\) | −4.00000 | −0.190693 | ||||||||
\(441\) | 6.00000 | − | 41.5692i | 0.285714 | − | 1.97949i | ||||
\(442\) | 2.00000 | 0.0951303 | ||||||||
\(443\) | 6.00000 | + | 10.3923i | 0.285069 | + | 0.493753i | 0.972626 | − | 0.232377i | \(-0.0746503\pi\) |
−0.687557 | + | 0.726130i | \(0.741317\pi\) | |||||||
\(444\) | −3.00000 | + | 5.19615i | −0.142374 | + | 0.246598i | ||||
\(445\) | 12.0000 | − | 20.7846i | 0.568855 | − | 0.985285i | ||||
\(446\) | −13.0000 | − | 22.5167i | −0.615568 | − | 1.06619i | ||||
\(447\) | 30.0000 | 1.41895 | ||||||||
\(448\) | −2.50000 | − | 0.866025i | −0.118114 | − | 0.0409159i | ||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | 33.0000 | + | 57.1577i | 1.55563 | + | 2.69444i | ||||
\(451\) | −1.00000 | + | 1.73205i | −0.0470882 | + | 0.0815591i | ||||
\(452\) | −8.50000 | + | 14.7224i | −0.399806 | + | 0.692485i | ||||
\(453\) | 13.5000 | + | 23.3827i | 0.634285 | + | 1.09861i | ||||
\(454\) | −10.0000 | −0.469323 | ||||||||
\(455\) | 2.00000 | + | 10.3923i | 0.0937614 | + | 0.487199i | ||||
\(456\) | 18.0000 | 0.842927 | ||||||||
\(457\) | −1.00000 | − | 1.73205i | −0.0467780 | − | 0.0810219i | 0.841688 | − | 0.539964i | \(-0.181562\pi\) |
−0.888466 | + | 0.458942i | \(0.848229\pi\) | |||||||
\(458\) | −8.00000 | + | 13.8564i | −0.373815 | + | 0.647467i | ||||
\(459\) | 9.00000 | − | 15.5885i | 0.420084 | − | 0.727607i | ||||
\(460\) | −4.00000 | − | 6.92820i | −0.186501 | − | 0.323029i | ||||
\(461\) | −3.00000 | −0.139724 | −0.0698620 | − | 0.997557i | \(-0.522256\pi\) | ||||
−0.0698620 | + | 0.997557i | \(0.522256\pi\) | |||||||
\(462\) | −6.00000 | + | 5.19615i | −0.279145 | + | 0.241747i | ||||
\(463\) | −14.0000 | −0.650635 | −0.325318 | − | 0.945605i | \(-0.605471\pi\) | ||||
−0.325318 | + | 0.945605i | \(0.605471\pi\) | |||||||
\(464\) | −0.500000 | − | 0.866025i | −0.0232119 | − | 0.0402042i | ||||
\(465\) | −24.0000 | + | 41.5692i | −1.11297 | + | 1.92773i | ||||
\(466\) | 3.00000 | − | 5.19615i | 0.138972 | − | 0.240707i | ||||
\(467\) | 6.00000 | + | 10.3923i | 0.277647 | + | 0.480899i | 0.970799 | − | 0.239892i | \(-0.0771121\pi\) |
−0.693153 | + | 0.720791i | \(0.743779\pi\) | |||||||
\(468\) | −6.00000 | −0.277350 | ||||||||
\(469\) | −18.0000 | + | 15.5885i | −0.831163 | + | 0.719808i | ||||
\(470\) | 8.00000 | 0.369012 | ||||||||
\(471\) | 6.00000 | + | 10.3923i | 0.276465 | + | 0.478852i | ||||
\(472\) | 4.50000 | − | 7.79423i | 0.207129 | − | 0.358758i | ||||
\(473\) | 2.00000 | − | 3.46410i | 0.0919601 | − | 0.159280i | ||||
\(474\) | 22.5000 | + | 38.9711i | 1.03346 | + | 1.79000i | ||||
\(475\) | 66.0000 | 3.02829 | ||||||||
\(476\) | 1.00000 | + | 5.19615i | 0.0458349 | + | 0.238165i | ||||
\(477\) | −72.0000 | −3.29665 | ||||||||
\(478\) | 9.50000 | + | 16.4545i | 0.434520 | + | 0.752611i | ||||
\(479\) | 18.5000 | − | 32.0429i | 0.845287 | − | 1.46408i | −0.0400855 | − | 0.999196i | \(-0.512763\pi\) |
0.885372 | − | 0.464883i | \(-0.153904\pi\) | |||||||
\(480\) | 6.00000 | − | 10.3923i | 0.273861 | − | 0.474342i | ||||
\(481\) | −1.00000 | − | 1.73205i | −0.0455961 | − | 0.0789747i | ||||
\(482\) | −30.0000 | −1.36646 | ||||||||
\(483\) | −15.0000 | − | 5.19615i | −0.682524 | − | 0.236433i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −10.0000 | − | 17.3205i | −0.454077 | − | 0.786484i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.00000 | − | 3.46410i | 0.0906287 | − | 0.156973i | −0.817147 | − | 0.576429i | \(-0.804446\pi\) |
0.907776 | + | 0.419456i | \(0.137779\pi\) | |||||||
\(488\) | −2.50000 | − | 4.33013i | −0.113170 | − | 0.196016i | ||||
\(489\) | −39.0000 | −1.76364 | ||||||||
\(490\) | −26.0000 | + | 10.3923i | −1.17456 | + | 0.469476i | ||||
\(491\) | 18.0000 | 0.812329 | 0.406164 | − | 0.913800i | \(-0.366866\pi\) | ||||
0.406164 | + | 0.913800i | \(0.366866\pi\) | |||||||
\(492\) | −3.00000 | − | 5.19615i | −0.135250 | − | 0.234261i | ||||
\(493\) | −1.00000 | + | 1.73205i | −0.0450377 | + | 0.0780076i | ||||
\(494\) | −3.00000 | + | 5.19615i | −0.134976 | + | 0.233786i | ||||
\(495\) | −12.0000 | − | 20.7846i | −0.539360 | − | 0.934199i | ||||
\(496\) | 4.00000 | 0.179605 | ||||||||
\(497\) | −10.0000 | − | 3.46410i | −0.448561 | − | 0.155386i | ||||
\(498\) | −18.0000 | −0.806599 | ||||||||
\(499\) | 8.00000 | + | 13.8564i | 0.358129 | + | 0.620298i | 0.987648 | − | 0.156687i | \(-0.0500814\pi\) |
−0.629519 | + | 0.776985i | \(0.716748\pi\) | |||||||
\(500\) | 12.0000 | − | 20.7846i | 0.536656 | − | 0.929516i | ||||
\(501\) | −25.5000 | + | 44.1673i | −1.13926 | + | 1.97325i | ||||
\(502\) | 6.00000 | + | 10.3923i | 0.267793 | + | 0.463831i | ||||
\(503\) | −21.0000 | −0.936344 | −0.468172 | − | 0.883637i | \(-0.655087\pi\) | ||||
−0.468172 | + | 0.883637i | \(0.655087\pi\) | |||||||
\(504\) | −3.00000 | − | 15.5885i | −0.133631 | − | 0.694365i | ||||
\(505\) | 60.0000 | 2.66996 | ||||||||
\(506\) | 1.00000 | + | 1.73205i | 0.0444554 | + | 0.0769991i | ||||
\(507\) | −18.0000 | + | 31.1769i | −0.799408 | + | 1.38462i | ||||
\(508\) | −2.50000 | + | 4.33013i | −0.110920 | + | 0.192118i | ||||
\(509\) | −1.00000 | − | 1.73205i | −0.0443242 | − | 0.0767718i | 0.843012 | − | 0.537895i | \(-0.180780\pi\) |
−0.887336 | + | 0.461123i | \(0.847447\pi\) | |||||||
\(510\) | −24.0000 | −1.06274 | ||||||||
\(511\) | −4.00000 | + | 3.46410i | −0.176950 | + | 0.153243i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 27.0000 | + | 46.7654i | 1.19208 | + | 2.06474i | ||||
\(514\) | −10.5000 | + | 18.1865i | −0.463135 | + | 0.802174i | ||||
\(515\) | 24.0000 | − | 41.5692i | 1.05757 | − | 1.83176i | ||||
\(516\) | 6.00000 | + | 10.3923i | 0.264135 | + | 0.457496i | ||||
\(517\) | −2.00000 | −0.0879599 | ||||||||
\(518\) | 4.00000 | − | 3.46410i | 0.175750 | − | 0.152204i | ||||
\(519\) | 15.0000 | 0.658427 | ||||||||
\(520\) | 2.00000 | + | 3.46410i | 0.0877058 | + | 0.151911i | ||||
\(521\) | 13.0000 | − | 22.5167i | 0.569540 | − | 0.986473i | −0.427071 | − | 0.904218i | \(-0.640455\pi\) |
0.996611 | − | 0.0822547i | \(-0.0262121\pi\) | |||||||
\(522\) | 3.00000 | − | 5.19615i | 0.131306 | − | 0.227429i | ||||
\(523\) | −10.0000 | − | 17.3205i | −0.437269 | − | 0.757373i | 0.560208 | − | 0.828352i | \(-0.310721\pi\) |
−0.997478 | + | 0.0709788i | \(0.977388\pi\) | |||||||
\(524\) | −18.0000 | −0.786334 | ||||||||
\(525\) | −16.5000 | − | 85.7365i | −0.720119 | − | 3.74185i | ||||
\(526\) | −3.00000 | −0.130806 | ||||||||
\(527\) | −4.00000 | − | 6.92820i | −0.174243 | − | 0.301797i | ||||
\(528\) | −1.50000 | + | 2.59808i | −0.0652791 | + | 0.113067i | ||||
\(529\) | 9.50000 | − | 16.4545i | 0.413043 | − | 0.715412i | ||||
\(530\) | 24.0000 | + | 41.5692i | 1.04249 | + | 1.80565i | ||||
\(531\) | 54.0000 | 2.34340 | ||||||||
\(532\) | −15.0000 | − | 5.19615i | −0.650332 | − | 0.225282i | ||||
\(533\) | 2.00000 | 0.0866296 | ||||||||
\(534\) | −9.00000 | − | 15.5885i | −0.389468 | − | 0.674579i | ||||
\(535\) | 16.0000 | − | 27.7128i | 0.691740 | − | 1.19813i | ||||
\(536\) | −4.50000 | + | 7.79423i | −0.194370 | + | 0.336659i | ||||
\(537\) | 19.5000 | + | 33.7750i | 0.841487 | + | 1.45750i | ||||
\(538\) | −12.0000 | −0.517357 | ||||||||
\(539\) | 6.50000 | − | 2.59808i | 0.279975 | − | 0.111907i | ||||
\(540\) | 36.0000 | 1.54919 | ||||||||
\(541\) | 12.5000 | + | 21.6506i | 0.537417 | + | 0.930834i | 0.999042 | + | 0.0437584i | \(0.0139332\pi\) |
−0.461625 | + | 0.887075i | \(0.652733\pi\) | |||||||
\(542\) | 12.5000 | − | 21.6506i | 0.536921 | − | 0.929974i | ||||
\(543\) | −33.0000 | + | 57.1577i | −1.41617 | + | 2.45287i | ||||
\(544\) | 1.00000 | + | 1.73205i | 0.0428746 | + | 0.0742611i | ||||
\(545\) | −40.0000 | −1.71341 | ||||||||
\(546\) | 7.50000 | + | 2.59808i | 0.320970 | + | 0.111187i | ||||
\(547\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(548\) | 4.50000 | + | 7.79423i | 0.192230 | + | 0.332953i | ||||
\(549\) | 15.0000 | − | 25.9808i | 0.640184 | − | 1.10883i | ||||
\(550\) | −5.50000 | + | 9.52628i | −0.234521 | + | 0.406202i | ||||
\(551\) | −3.00000 | − | 5.19615i | −0.127804 | − | 0.221364i | ||||
\(552\) | −6.00000 | −0.255377 | ||||||||
\(553\) | −7.50000 | − | 38.9711i | −0.318932 | − | 1.65722i | ||||
\(554\) | 3.00000 | 0.127458 | ||||||||
\(555\) | 12.0000 | + | 20.7846i | 0.509372 | + | 0.882258i | ||||
\(556\) | −4.00000 | + | 6.92820i | −0.169638 | + | 0.293821i | ||||
\(557\) | −19.0000 | + | 32.9090i | −0.805056 | + | 1.39440i | 0.111198 | + | 0.993798i | \(0.464531\pi\) |
−0.916253 | + | 0.400599i | \(0.868802\pi\) | |||||||
\(558\) | 12.0000 | + | 20.7846i | 0.508001 | + | 0.879883i | ||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | −8.00000 | + | 6.92820i | −0.338062 | + | 0.292770i | ||||
\(561\) | 6.00000 | 0.253320 | ||||||||
\(562\) | −5.00000 | − | 8.66025i | −0.210912 | − | 0.365311i | ||||
\(563\) | −13.0000 | + | 22.5167i | −0.547885 | + | 0.948964i | 0.450535 | + | 0.892759i | \(0.351233\pi\) |
−0.998419 | + | 0.0562051i | \(0.982100\pi\) | |||||||
\(564\) | 3.00000 | − | 5.19615i | 0.126323 | − | 0.218797i | ||||
\(565\) | 34.0000 | + | 58.8897i | 1.43039 | + | 2.47751i | ||||
\(566\) | 6.00000 | 0.252199 | ||||||||
\(567\) | 18.0000 | − | 15.5885i | 0.755929 | − | 0.654654i | ||||
\(568\) | −4.00000 | −0.167836 | ||||||||
\(569\) | −18.0000 | − | 31.1769i | −0.754599 | − | 1.30700i | −0.945573 | − | 0.325409i | \(-0.894498\pi\) |
0.190974 | − | 0.981595i | \(-0.438835\pi\) | |||||||
\(570\) | 36.0000 | − | 62.3538i | 1.50787 | − | 2.61171i | ||||
\(571\) | 10.0000 | − | 17.3205i | 0.418487 | − | 0.724841i | −0.577301 | − | 0.816532i | \(-0.695894\pi\) |
0.995788 | + | 0.0916910i | \(0.0292272\pi\) | |||||||
\(572\) | −0.500000 | − | 0.866025i | −0.0209061 | − | 0.0362103i | ||||
\(573\) | −42.0000 | −1.75458 | ||||||||
\(574\) | 1.00000 | + | 5.19615i | 0.0417392 | + | 0.216883i | ||||
\(575\) | −22.0000 | −0.917463 | ||||||||
\(576\) | −3.00000 | − | 5.19615i | −0.125000 | − | 0.216506i | ||||
\(577\) | 3.50000 | − | 6.06218i | 0.145707 | − | 0.252372i | −0.783930 | − | 0.620850i | \(-0.786788\pi\) |
0.929636 | + | 0.368478i | \(0.120121\pi\) | |||||||
\(578\) | −6.50000 | + | 11.2583i | −0.270364 | + | 0.468285i | ||||
\(579\) | −33.0000 | − | 57.1577i | −1.37143 | − | 2.37539i | ||||
\(580\) | −4.00000 | −0.166091 | ||||||||
\(581\) | 15.0000 | + | 5.19615i | 0.622305 | + | 0.215573i | ||||
\(582\) | −15.0000 | −0.621770 | ||||||||
\(583\) | −6.00000 | − | 10.3923i | −0.248495 | − | 0.430405i | ||||
\(584\) | −1.00000 | + | 1.73205i | −0.0413803 | + | 0.0716728i | ||||
\(585\) | −12.0000 | + | 20.7846i | −0.496139 | + | 0.859338i | ||||
\(586\) | −3.00000 | − | 5.19615i | −0.123929 | − | 0.214651i | ||||
\(587\) | −3.00000 | −0.123823 | −0.0619116 | − | 0.998082i | \(-0.519720\pi\) | ||||
−0.0619116 | + | 0.998082i | \(0.519720\pi\) | |||||||
\(588\) | −3.00000 | + | 20.7846i | −0.123718 | + | 0.857143i | ||||
\(589\) | 24.0000 | 0.988903 | ||||||||
\(590\) | −18.0000 | − | 31.1769i | −0.741048 | − | 1.28353i | ||||
\(591\) | −4.50000 | + | 7.79423i | −0.185105 | + | 0.320612i | ||||
\(592\) | 1.00000 | − | 1.73205i | 0.0410997 | − | 0.0711868i | ||||
\(593\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(594\) | −9.00000 | −0.369274 | ||||||||
\(595\) | 20.0000 | + | 6.92820i | 0.819920 | + | 0.284029i | ||||
\(596\) | −10.0000 | −0.409616 | ||||||||
\(597\) | 15.0000 | + | 25.9808i | 0.613909 | + | 1.06332i | ||||
\(598\) | 1.00000 | − | 1.73205i | 0.0408930 | − | 0.0708288i | ||||
\(599\) | 12.0000 | − | 20.7846i | 0.490307 | − | 0.849236i | −0.509631 | − | 0.860393i | \(-0.670218\pi\) |
0.999938 | + | 0.0111569i | \(0.00355143\pi\) | |||||||
\(600\) | −16.5000 | − | 28.5788i | −0.673610 | − | 1.16673i | ||||
\(601\) | 26.0000 | 1.06056 | 0.530281 | − | 0.847822i | \(-0.322086\pi\) | ||||
0.530281 | + | 0.847822i | \(0.322086\pi\) | |||||||
\(602\) | −2.00000 | − | 10.3923i | −0.0815139 | − | 0.423559i | ||||
\(603\) | −54.0000 | −2.19905 | ||||||||
\(604\) | −4.50000 | − | 7.79423i | −0.183102 | − | 0.317143i | ||||
\(605\) | 2.00000 | − | 3.46410i | 0.0813116 | − | 0.140836i | ||||
\(606\) | 22.5000 | − | 38.9711i | 0.914000 | − | 1.58309i | ||||
\(607\) | 8.00000 | + | 13.8564i | 0.324710 | + | 0.562414i | 0.981454 | − | 0.191700i | \(-0.0614000\pi\) |
−0.656744 | + | 0.754114i | \(0.728067\pi\) | |||||||
\(608\) | −6.00000 | −0.243332 | ||||||||
\(609\) | −6.00000 | + | 5.19615i | −0.243132 | + | 0.210559i | ||||
\(610\) | −20.0000 | −0.809776 | ||||||||
\(611\) | 1.00000 | + | 1.73205i | 0.0404557 | + | 0.0700713i | ||||
\(612\) | −6.00000 | + | 10.3923i | −0.242536 | + | 0.420084i | ||||
\(613\) | −11.0000 | + | 19.0526i | −0.444286 | + | 0.769526i | −0.998002 | − | 0.0631797i | \(-0.979876\pi\) |
0.553716 | + | 0.832705i | \(0.313209\pi\) | |||||||
\(614\) | 16.0000 | + | 27.7128i | 0.645707 | + | 1.11840i | ||||
\(615\) | −24.0000 | −0.967773 | ||||||||
\(616\) | 2.00000 | − | 1.73205i | 0.0805823 | − | 0.0697863i | ||||
\(617\) | −27.0000 | −1.08698 | −0.543490 | − | 0.839416i | \(-0.682897\pi\) | ||||
−0.543490 | + | 0.839416i | \(0.682897\pi\) | |||||||
\(618\) | −18.0000 | − | 31.1769i | −0.724066 | − | 1.25412i | ||||
\(619\) | −10.0000 | + | 17.3205i | −0.401934 | + | 0.696170i | −0.993959 | − | 0.109749i | \(-0.964995\pi\) |
0.592025 | + | 0.805919i | \(0.298329\pi\) | |||||||
\(620\) | 8.00000 | − | 13.8564i | 0.321288 | − | 0.556487i | ||||
\(621\) | −9.00000 | − | 15.5885i | −0.361158 | − | 0.625543i | ||||
\(622\) | 28.0000 | 1.12270 | ||||||||
\(623\) | 3.00000 | + | 15.5885i | 0.120192 | + | 0.624538i | ||||
\(624\) | 3.00000 | 0.120096 | ||||||||
\(625\) | −20.5000 | − | 35.5070i | −0.820000 | − | 1.42028i | ||||
\(626\) | 0.500000 | − | 0.866025i | 0.0199840 | − | 0.0346133i | ||||
\(627\) | −9.00000 | + | 15.5885i | −0.359425 | + | 0.622543i | ||||
\(628\) | −2.00000 | − | 3.46410i | −0.0798087 | − | 0.138233i | ||||
\(629\) | −4.00000 | −0.159490 | ||||||||
\(630\) | −60.0000 | − | 20.7846i | −2.39046 | − | 0.828079i | ||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | −7.50000 | − | 12.9904i | −0.298334 | − | 0.516730i | ||||
\(633\) | −21.0000 | + | 36.3731i | −0.834675 | + | 1.44570i | ||||
\(634\) | −6.00000 | + | 10.3923i | −0.238290 | + | 0.412731i | ||||
\(635\) | 10.0000 | + | 17.3205i | 0.396838 | + | 0.687343i | ||||
\(636\) | 36.0000 | 1.42749 | ||||||||
\(637\) | −5.50000 | − | 4.33013i | −0.217918 | − | 0.171566i | ||||
\(638\) | 1.00000 | 0.0395904 | ||||||||
\(639\) | −12.0000 | − | 20.7846i | −0.474713 | − | 0.822226i | ||||
\(640\) | −2.00000 | + | 3.46410i | −0.0790569 | + | 0.136931i | ||||
\(641\) | −4.50000 | + | 7.79423i | −0.177739 | + | 0.307854i | −0.941106 | − | 0.338112i | \(-0.890212\pi\) |
0.763367 | + | 0.645966i | \(0.223545\pi\) | |||||||
\(642\) | −12.0000 | − | 20.7846i | −0.473602 | − | 0.820303i | ||||
\(643\) | 1.00000 | 0.0394362 | 0.0197181 | − | 0.999806i | \(-0.493723\pi\) | ||||
0.0197181 | + | 0.999806i | \(0.493723\pi\) | |||||||
\(644\) | 5.00000 | + | 1.73205i | 0.197028 | + | 0.0682524i | ||||
\(645\) | 48.0000 | 1.89000 | ||||||||
\(646\) | 6.00000 | + | 10.3923i | 0.236067 | + | 0.408880i | ||||
\(647\) | −12.0000 | + | 20.7846i | −0.471769 | + | 0.817127i | −0.999478 | − | 0.0322975i | \(-0.989718\pi\) |
0.527710 | + | 0.849425i | \(0.323051\pi\) | |||||||
\(648\) | 4.50000 | − | 7.79423i | 0.176777 | − | 0.306186i | ||||
\(649\) | 4.50000 | + | 7.79423i | 0.176640 | + | 0.305950i | ||||
\(650\) | 11.0000 | 0.431455 | ||||||||
\(651\) | −6.00000 | − | 31.1769i | −0.235159 | − | 1.22192i | ||||
\(652\) | 13.0000 | 0.509119 | ||||||||
\(653\) | −11.0000 | − | 19.0526i | −0.430463 | − | 0.745584i | 0.566450 | − | 0.824096i | \(-0.308316\pi\) |
−0.996913 | + | 0.0785119i | \(0.974983\pi\) | |||||||
\(654\) | −15.0000 | + | 25.9808i | −0.586546 | + | 1.01593i | ||||
\(655\) | −36.0000 | + | 62.3538i | −1.40664 | + | 2.43637i | ||||
\(656\) | 1.00000 | + | 1.73205i | 0.0390434 | + | 0.0676252i | ||||
\(657\) | −12.0000 | −0.468165 | ||||||||
\(658\) | −4.00000 | + | 3.46410i | −0.155936 | + | 0.135045i | ||||
\(659\) | −32.0000 | −1.24654 | −0.623272 | − | 0.782006i | \(-0.714197\pi\) | ||||
−0.623272 | + | 0.782006i | \(0.714197\pi\) | |||||||
\(660\) | 6.00000 | + | 10.3923i | 0.233550 | + | 0.404520i | ||||
\(661\) | 5.00000 | − | 8.66025i | 0.194477 | − | 0.336845i | −0.752252 | − | 0.658876i | \(-0.771032\pi\) |
0.946729 | + | 0.322031i | \(0.104366\pi\) | |||||||
\(662\) | 3.50000 | − | 6.06218i | 0.136031 | − | 0.235613i | ||||
\(663\) | −3.00000 | − | 5.19615i | −0.116510 | − | 0.201802i | ||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | −48.0000 | + | 41.5692i | −1.86136 | + | 1.61199i | ||||
\(666\) | 12.0000 | 0.464991 | ||||||||
\(667\) | 1.00000 | + | 1.73205i | 0.0387202 | + | 0.0670653i | ||||
\(668\) | 8.50000 | − | 14.7224i | 0.328875 | − | 0.569628i | ||||
\(669\) | −39.0000 | + | 67.5500i | −1.50783 | + | 2.61163i | ||||
\(670\) | 18.0000 | + | 31.1769i | 0.695401 | + | 1.20447i | ||||
\(671\) | 5.00000 | 0.193023 | ||||||||
\(672\) | 1.50000 | + | 7.79423i | 0.0578638 | + | 0.300669i | ||||
\(673\) | 16.0000 | 0.616755 | 0.308377 | − | 0.951264i | \(-0.400214\pi\) | ||||
0.308377 | + | 0.951264i | \(0.400214\pi\) | |||||||
\(674\) | −15.0000 | − | 25.9808i | −0.577778 | − | 1.00074i | ||||
\(675\) | 49.5000 | − | 85.7365i | 1.90526 | − | 3.30000i | ||||
\(676\) | 6.00000 | − | 10.3923i | 0.230769 | − | 0.399704i | ||||
\(677\) | −19.0000 | − | 32.9090i | −0.730229 | − | 1.26479i | −0.956785 | − | 0.290796i | \(-0.906080\pi\) |
0.226556 | − | 0.973998i | \(-0.427253\pi\) | |||||||
\(678\) | 51.0000 | 1.95864 | ||||||||
\(679\) | 12.5000 | + | 4.33013i | 0.479706 | + | 0.166175i | ||||
\(680\) | 8.00000 | 0.306786 | ||||||||
\(681\) | 15.0000 | + | 25.9808i | 0.574801 | + | 0.995585i | ||||
\(682\) | −2.00000 | + | 3.46410i | −0.0765840 | + | 0.132647i | ||||
\(683\) | 16.5000 | − | 28.5788i | 0.631355 | − | 1.09354i | −0.355920 | − | 0.934516i | \(-0.615832\pi\) |
0.987275 | − | 0.159022i | \(-0.0508342\pi\) | |||||||
\(684\) | −18.0000 | − | 31.1769i | −0.688247 | − | 1.19208i | ||||
\(685\) | 36.0000 | 1.37549 | ||||||||
\(686\) | 8.50000 | − | 16.4545i | 0.324532 | − | 0.628235i | ||||
\(687\) | 48.0000 | 1.83131 | ||||||||
\(688\) | −2.00000 | − | 3.46410i | −0.0762493 | − | 0.132068i | ||||
\(689\) | −6.00000 | + | 10.3923i | −0.228582 | + | 0.395915i | ||||
\(690\) | −12.0000 | + | 20.7846i | −0.456832 | + | 0.791257i | ||||
\(691\) | −7.50000 | − | 12.9904i | −0.285313 | − | 0.494177i | 0.687372 | − | 0.726306i | \(-0.258764\pi\) |
−0.972685 | + | 0.232128i | \(0.925431\pi\) | |||||||
\(692\) | −5.00000 | −0.190071 | ||||||||
\(693\) | 15.0000 | + | 5.19615i | 0.569803 | + | 0.197386i | ||||
\(694\) | 28.0000 | 1.06287 | ||||||||
\(695\) | 16.0000 | + | 27.7128i | 0.606915 | + | 1.05121i | ||||
\(696\) | −1.50000 | + | 2.59808i | −0.0568574 | + | 0.0984798i | ||||
\(697\) | 2.00000 | − | 3.46410i | 0.0757554 | − | 0.131212i | ||||
\(698\) | 1.00000 | + | 1.73205i | 0.0378506 | + | 0.0655591i | ||||
\(699\) | −18.0000 | −0.680823 | ||||||||
\(700\) | 5.50000 | + | 28.5788i | 0.207880 | + | 1.08018i | ||||
\(701\) | 39.0000 | 1.47301 | 0.736505 | − | 0.676432i | \(-0.236475\pi\) | ||||
0.736505 | + | 0.676432i | \(0.236475\pi\) | |||||||
\(702\) | 4.50000 | + | 7.79423i | 0.169842 | + | 0.294174i | ||||
\(703\) | 6.00000 | − | 10.3923i | 0.226294 | − | 0.391953i | ||||
\(704\) | 0.500000 | − | 0.866025i | 0.0188445 | − | 0.0326396i | ||||
\(705\) | −12.0000 | − | 20.7846i | −0.451946 | − | 0.782794i | ||||
\(706\) | 18.0000 | 0.677439 | ||||||||
\(707\) | −30.0000 | + | 25.9808i | −1.12827 | + | 0.977107i | ||||
\(708\) | −27.0000 | −1.01472 | ||||||||
\(709\) | −3.00000 | − | 5.19615i | −0.112667 | − | 0.195146i | 0.804178 | − | 0.594389i | \(-0.202606\pi\) |
−0.916845 | + | 0.399244i | \(0.869273\pi\) | |||||||
\(710\) | −8.00000 | + | 13.8564i | −0.300235 | + | 0.520022i | ||||
\(711\) | 45.0000 | − | 77.9423i | 1.68763 | − | 2.92306i | ||||
\(712\) | 3.00000 | + | 5.19615i | 0.112430 | + | 0.194734i | ||||
\(713\) | −8.00000 | −0.299602 | ||||||||
\(714\) | 12.0000 | − | 10.3923i | 0.449089 | − | 0.388922i | ||||
\(715\) | −4.00000 | −0.149592 | ||||||||
\(716\) | −6.50000 | − | 11.2583i | −0.242916 | − | 0.420744i | ||||
\(717\) | 28.5000 | − | 49.3634i | 1.06435 | − | 1.84351i | ||||
\(718\) | −15.5000 | + | 26.8468i | −0.578455 | + | 1.00191i | ||||
\(719\) | 13.0000 | + | 22.5167i | 0.484818 | + | 0.839730i | 0.999848 | − | 0.0174426i | \(-0.00555244\pi\) |
−0.515030 | + | 0.857172i | \(0.672219\pi\) | |||||||
\(720\) | −24.0000 | −0.894427 | ||||||||
\(721\) | 6.00000 | + | 31.1769i | 0.223452 | + | 1.16109i | ||||
\(722\) | −17.0000 | −0.632674 | ||||||||
\(723\) | 45.0000 | + | 77.9423i | 1.67357 | + | 2.89870i | ||||
\(724\) | 11.0000 | − | 19.0526i | 0.408812 | − | 0.708083i | ||||
\(725\) | −5.50000 | + | 9.52628i | −0.204265 | + | 0.353797i | ||||
\(726\) | −1.50000 | − | 2.59808i | −0.0556702 | − | 0.0964237i | ||||
\(727\) | −34.0000 | −1.26099 | −0.630495 | − | 0.776193i | \(-0.717148\pi\) | ||||
−0.630495 | + | 0.776193i | \(0.717148\pi\) | |||||||
\(728\) | −2.50000 | − | 0.866025i | −0.0926562 | − | 0.0320970i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 4.00000 | + | 6.92820i | 0.148047 | + | 0.256424i | ||||
\(731\) | −4.00000 | + | 6.92820i | −0.147945 | + | 0.256249i | ||||
\(732\) | −7.50000 | + | 12.9904i | −0.277208 | + | 0.480138i | ||||
\(733\) | 0.500000 | + | 0.866025i | 0.0184679 | + | 0.0319874i | 0.875112 | − | 0.483921i | \(-0.160788\pi\) |
−0.856644 | + | 0.515908i | \(0.827454\pi\) | |||||||
\(734\) | 14.0000 | 0.516749 | ||||||||
\(735\) | 66.0000 | + | 51.9615i | 2.43445 | + | 1.91663i | ||||
\(736\) | 2.00000 | 0.0737210 | ||||||||
\(737\) | −4.50000 | − | 7.79423i | −0.165760 | − | 0.287104i | ||||
\(738\) | −6.00000 | + | 10.3923i | −0.220863 | + | 0.382546i | ||||
\(739\) | −9.00000 | + | 15.5885i | −0.331070 | + | 0.573431i | −0.982722 | − | 0.185088i | \(-0.940743\pi\) |
0.651652 | + | 0.758518i | \(0.274076\pi\) | |||||||
\(740\) | −4.00000 | − | 6.92820i | −0.147043 | − | 0.254686i | ||||
\(741\) | 18.0000 | 0.661247 | ||||||||
\(742\) | −30.0000 | − | 10.3923i | −1.10133 | − | 0.381514i | ||||
\(743\) | 36.0000 | 1.32071 | 0.660356 | − | 0.750953i | \(-0.270405\pi\) | ||||
0.660356 | + | 0.750953i | \(0.270405\pi\) | |||||||
\(744\) | −6.00000 | − | 10.3923i | −0.219971 | − | 0.381000i | ||||
\(745\) | −20.0000 | + | 34.6410i | −0.732743 | + | 1.26915i | ||||
\(746\) | −3.50000 | + | 6.06218i | −0.128144 | + | 0.221952i | ||||
\(747\) | 18.0000 | + | 31.1769i | 0.658586 | + | 1.14070i | ||||
\(748\) | −2.00000 | −0.0731272 | ||||||||
\(749\) | 4.00000 | + | 20.7846i | 0.146157 | + | 0.759453i | ||||
\(750\) | −72.0000 | −2.62907 | ||||||||
\(751\) | 22.0000 | + | 38.1051i | 0.802791 | + | 1.39048i | 0.917772 | + | 0.397108i | \(0.129986\pi\) |
−0.114981 | + | 0.993368i | \(0.536681\pi\) | |||||||
\(752\) | −1.00000 | + | 1.73205i | −0.0364662 | + | 0.0631614i | ||||
\(753\) | 18.0000 | − | 31.1769i | 0.655956 | − | 1.13615i | ||||
\(754\) | −0.500000 | − | 0.866025i | −0.0182089 | − | 0.0315388i | ||||
\(755\) | −36.0000 | −1.31017 | ||||||||
\(756\) | −18.0000 | + | 15.5885i | −0.654654 | + | 0.566947i | ||||
\(757\) | 26.0000 | 0.944986 | 0.472493 | − | 0.881334i | \(-0.343354\pi\) | ||||
0.472493 | + | 0.881334i | \(0.343354\pi\) | |||||||
\(758\) | −14.5000 | − | 25.1147i | −0.526664 | − | 0.912208i | ||||
\(759\) | 3.00000 | − | 5.19615i | 0.108893 | − | 0.188608i | ||||
\(760\) | −12.0000 | + | 20.7846i | −0.435286 | + | 0.753937i | ||||
\(761\) | −27.0000 | − | 46.7654i | −0.978749 | − | 1.69524i | −0.666962 | − | 0.745091i | \(-0.732406\pi\) |
−0.311787 | − | 0.950152i | \(-0.600927\pi\) | |||||||
\(762\) | 15.0000 | 0.543393 | ||||||||
\(763\) | 20.0000 | − | 17.3205i | 0.724049 | − | 0.627044i | ||||
\(764\) | 14.0000 | 0.506502 | ||||||||
\(765\) | 24.0000 | + | 41.5692i | 0.867722 | + | 1.50294i | ||||
\(766\) | 4.00000 | − | 6.92820i | 0.144526 | − | 0.250326i | ||||
\(767\) | 4.50000 | − | 7.79423i | 0.162486 | − | 0.281433i | ||||
\(768\) | 1.50000 | + | 2.59808i | 0.0541266 | + | 0.0937500i | ||||
\(769\) | −38.0000 | −1.37032 | −0.685158 | − | 0.728395i | \(-0.740267\pi\) | ||||
−0.685158 | + | 0.728395i | \(0.740267\pi\) | |||||||
\(770\) | −2.00000 | − | 10.3923i | −0.0720750 | − | 0.374513i | ||||
\(771\) | 63.0000 | 2.26889 | ||||||||
\(772\) | 11.0000 | + | 19.0526i | 0.395899 | + | 0.685717i | ||||
\(773\) | 12.0000 | − | 20.7846i | 0.431610 | − | 0.747570i | −0.565402 | − | 0.824815i | \(-0.691279\pi\) |
0.997012 | + | 0.0772449i | \(0.0246123\pi\) | |||||||
\(774\) | 12.0000 | − | 20.7846i | 0.431331 | − | 0.747087i | ||||
\(775\) | −22.0000 | − | 38.1051i | −0.790263 | − | 1.36878i | ||||
\(776\) | 5.00000 | 0.179490 | ||||||||
\(777\) | −15.0000 | − | 5.19615i | −0.538122 | − | 0.186411i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.00000 | + | 10.3923i | 0.214972 | + | 0.372343i | ||||
\(780\) | 6.00000 | − | 10.3923i | 0.214834 | − | 0.372104i | ||||
\(781\) | 2.00000 | − | 3.46410i | 0.0715656 | − | 0.123955i | ||||
\(782\) | −2.00000 | − | 3.46410i | −0.0715199 | − | 0.123876i | ||||
\(783\) | −9.00000 | −0.321634 | ||||||||
\(784\) | 1.00000 | − | 6.92820i | 0.0357143 | − | 0.247436i | ||||
\(785\) | −16.0000 | −0.571064 | ||||||||
\(786\) | 27.0000 | + | 46.7654i | 0.963058 | + | 1.66807i | ||||
\(787\) | 11.0000 | − | 19.0526i | 0.392108 | − | 0.679150i | −0.600620 | − | 0.799535i | \(-0.705079\pi\) |
0.992727 | + | 0.120384i | \(0.0384127\pi\) | |||||||
\(788\) | 1.50000 | − | 2.59808i | 0.0534353 | − | 0.0925526i | ||||
\(789\) | 4.50000 | + | 7.79423i | 0.160204 | + | 0.277482i | ||||
\(790\) | −60.0000 | −2.13470 | ||||||||
\(791\) | −42.5000 | − | 14.7224i | −1.51113 | − | 0.523469i | ||||
\(792\) | 6.00000 | 0.213201 | ||||||||
\(793\) | −2.50000 | − | 4.33013i | −0.0887776 | − | 0.153767i | ||||
\(794\) | −15.0000 | + | 25.9808i | −0.532330 | + | 0.922023i | ||||
\(795\) | 72.0000 | − | 124.708i | 2.55358 | − | 4.42292i | ||||
\(796\) | −5.00000 | − | 8.66025i | −0.177220 | − | 0.306955i | ||||
\(797\) | 38.0000 | 1.34603 | 0.673015 | − | 0.739629i | \(-0.264999\pi\) | ||||
0.673015 | + | 0.739629i | \(0.264999\pi\) | |||||||
\(798\) | 9.00000 | + | 46.7654i | 0.318597 | + | 1.65548i | ||||
\(799\) | 4.00000 | 0.141510 | ||||||||
\(800\) | 5.50000 | + | 9.52628i | 0.194454 | + | 0.336805i | ||||
\(801\) | −18.0000 | + | 31.1769i | −0.635999 | + | 1.10158i | ||||
\(802\) | 7.50000 | − | 12.9904i | 0.264834 | − | 0.458706i | ||||
\(803\) | −1.00000 | − | 1.73205i | −0.0352892 | − | 0.0611227i | ||||
\(804\) | 27.0000 | 0.952217 | ||||||||
\(805\) | 16.0000 | − | 13.8564i | 0.563926 | − | 0.488374i | ||||
\(806\) | 4.00000 | 0.140894 | ||||||||
\(807\) | 18.0000 | + | 31.1769i | 0.633630 | + | 1.09748i | ||||
\(808\) | −7.50000 | + | 12.9904i | −0.263849 | + | 0.457000i | ||||
\(809\) | 24.0000 | − | 41.5692i | 0.843795 | − | 1.46150i | −0.0428684 | − | 0.999081i | \(-0.513650\pi\) |
0.886664 | − | 0.462415i | \(-0.153017\pi\) | |||||||
\(810\) | −18.0000 | − | 31.1769i | −0.632456 | − | 1.09545i | ||||
\(811\) | −28.0000 | −0.983213 | −0.491606 | − | 0.870817i | \(-0.663590\pi\) | ||||
−0.491606 | + | 0.870817i | \(0.663590\pi\) | |||||||
\(812\) | 2.00000 | − | 1.73205i | 0.0701862 | − | 0.0607831i | ||||
\(813\) | −75.0000 | −2.63036 | ||||||||
\(814\) | 1.00000 | + | 1.73205i | 0.0350500 | + | 0.0607083i | ||||
\(815\) | 26.0000 | − | 45.0333i | 0.910740 | − | 1.57745i | ||||
\(816\) | 3.00000 | − | 5.19615i | 0.105021 | − | 0.181902i | ||||
\(817\) | −12.0000 | − | 20.7846i | −0.419827 | − | 0.727161i | ||||
\(818\) | 32.0000 | 1.11885 | ||||||||
\(819\) | −3.00000 | − | 15.5885i | −0.104828 | − | 0.544705i | ||||
\(820\) | 8.00000 | 0.279372 | ||||||||
\(821\) | 7.50000 | + | 12.9904i | 0.261752 | + | 0.453367i | 0.966708 | − | 0.255884i | \(-0.0823665\pi\) |
−0.704956 | + | 0.709251i | \(0.749033\pi\) | |||||||
\(822\) | 13.5000 | − | 23.3827i | 0.470867 | − | 0.815565i | ||||
\(823\) | −19.0000 | + | 32.9090i | −0.662298 | + | 1.14713i | 0.317712 | + | 0.948187i | \(0.397086\pi\) |
−0.980010 | + | 0.198947i | \(0.936248\pi\) | |||||||
\(824\) | 6.00000 | + | 10.3923i | 0.209020 | + | 0.362033i | ||||
\(825\) | 33.0000 | 1.14891 | ||||||||
\(826\) | 22.5000 | + | 7.79423i | 0.782875 | + | 0.271196i | ||||
\(827\) | −22.0000 | −0.765015 | −0.382507 | − | 0.923952i | \(-0.624939\pi\) | ||||
−0.382507 | + | 0.923952i | \(0.624939\pi\) | |||||||
\(828\) | 6.00000 | + | 10.3923i | 0.208514 | + | 0.361158i | ||||
\(829\) | −8.00000 | + | 13.8564i | −0.277851 | + | 0.481253i | −0.970851 | − | 0.239686i | \(-0.922956\pi\) |
0.692999 | + | 0.720938i | \(0.256289\pi\) | |||||||
\(830\) | 12.0000 | − | 20.7846i | 0.416526 | − | 0.721444i | ||||
\(831\) | −4.50000 | − | 7.79423i | −0.156103 | − | 0.270379i | ||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | −13.0000 | + | 5.19615i | −0.450423 | + | 0.180036i | ||||
\(834\) | 24.0000 | 0.831052 | ||||||||
\(835\) | −34.0000 | − | 58.8897i | −1.17662 | − | 2.03796i | ||||
\(836\) | 3.00000 | − | 5.19615i | 0.103757 | − | 0.179713i | ||||
\(837\) | 18.0000 | − | 31.1769i | 0.622171 | − | 1.07763i | ||||
\(838\) | −10.0000 | − | 17.3205i | −0.345444 | − | 0.598327i | ||||
\(839\) | 54.0000 | 1.86429 | 0.932144 | − | 0.362089i | \(-0.117936\pi\) | ||||
0.932144 | + | 0.362089i | \(0.117936\pi\) | |||||||
\(840\) | 30.0000 | + | 10.3923i | 1.03510 | + | 0.358569i | ||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | −10.0000 | − | 17.3205i | −0.344623 | − | 0.596904i | ||||
\(843\) | −15.0000 | + | 25.9808i | −0.516627 | + | 0.894825i | ||||
\(844\) | 7.00000 | − | 12.1244i | 0.240950 | − | 0.417338i | ||||
\(845\) | −24.0000 | − | 41.5692i | −0.825625 | − | 1.43002i | ||||
\(846\) | −12.0000 | −0.412568 | ||||||||
\(847\) | 0.500000 | + | 2.59808i | 0.0171802 | + | 0.0892710i | ||||
\(848\) | −12.0000 | −0.412082 | ||||||||
\(849\) | −9.00000 | − | 15.5885i | −0.308879 | − | 0.534994i | ||||
\(850\) | 11.0000 | − | 19.0526i | 0.377297 | − | 0.653497i | ||||
\(851\) | −2.00000 | + | 3.46410i | −0.0685591 | + | 0.118748i | ||||
\(852\) | 6.00000 | + | 10.3923i | 0.205557 | + | 0.356034i | ||||
\(853\) | 50.0000 | 1.71197 | 0.855984 | − | 0.517003i | \(-0.172952\pi\) | ||||
0.855984 | + | 0.517003i | \(0.172952\pi\) | |||||||
\(854\) | 10.0000 | − | 8.66025i | 0.342193 | − | 0.296348i | ||||
\(855\) | −144.000 | −4.92470 | ||||||||
\(856\) | 4.00000 | + | 6.92820i | 0.136717 | + | 0.236801i | ||||
\(857\) | 2.00000 | − | 3.46410i | 0.0683187 | − | 0.118331i | −0.829843 | − | 0.557998i | \(-0.811570\pi\) |
0.898161 | + | 0.439666i | \(0.144903\pi\) | |||||||
\(858\) | −1.50000 | + | 2.59808i | −0.0512092 | + | 0.0886969i | ||||
\(859\) | 8.50000 | + | 14.7224i | 0.290016 | + | 0.502323i | 0.973813 | − | 0.227349i | \(-0.0730059\pi\) |
−0.683797 | + | 0.729672i | \(0.739673\pi\) | |||||||
\(860\) | −16.0000 | −0.545595 | ||||||||
\(861\) | 12.0000 | − | 10.3923i | 0.408959 | − | 0.354169i | ||||
\(862\) | −1.00000 | −0.0340601 | ||||||||
\(863\) | −5.00000 | − | 8.66025i | −0.170202 | − | 0.294798i | 0.768288 | − | 0.640104i | \(-0.221109\pi\) |
−0.938490 | + | 0.345305i | \(0.887775\pi\) | |||||||
\(864\) | −4.50000 | + | 7.79423i | −0.153093 | + | 0.265165i | ||||
\(865\) | −10.0000 | + | 17.3205i | −0.340010 | + | 0.588915i | ||||
\(866\) | −5.00000 | − | 8.66025i | −0.169907 | − | 0.294287i | ||||
\(867\) | 39.0000 | 1.32451 | ||||||||
\(868\) | 2.00000 | + | 10.3923i | 0.0678844 | + | 0.352738i | ||||
\(869\) | 15.0000 | 0.508840 | ||||||||
\(870\) | 6.00000 | + | 10.3923i | 0.203419 | + | 0.352332i | ||||
\(871\) | −4.50000 | + | 7.79423i | −0.152477 | + | 0.264097i | ||||
\(872\) | 5.00000 | − | 8.66025i | 0.169321 | − | 0.293273i | ||||
\(873\) | 15.0000 | + | 25.9808i | 0.507673 | + | 0.879316i | ||||
\(874\) | 12.0000 | 0.405906 | ||||||||
\(875\) | 60.0000 | + | 20.7846i | 2.02837 | + | 0.702648i | ||||
\(876\) | 6.00000 | 0.202721 | ||||||||
\(877\) | −12.5000 | − | 21.6506i | −0.422095 | − | 0.731090i | 0.574049 | − | 0.818821i | \(-0.305372\pi\) |
−0.996144 | + | 0.0877308i | \(0.972038\pi\) | |||||||
\(878\) | −2.50000 | + | 4.33013i | −0.0843709 | + | 0.146135i | ||||
\(879\) | −9.00000 | + | 15.5885i | −0.303562 | + | 0.525786i | ||||
\(880\) | −2.00000 | − | 3.46410i | −0.0674200 | − | 0.116775i | ||||
\(881\) | 9.00000 | 0.303218 | 0.151609 | − | 0.988441i | \(-0.451555\pi\) | ||||
0.151609 | + | 0.988441i | \(0.451555\pi\) | |||||||
\(882\) | 39.0000 | − | 15.5885i | 1.31320 | − | 0.524891i | ||||
\(883\) | 1.00000 | 0.0336527 | 0.0168263 | − | 0.999858i | \(-0.494644\pi\) | ||||
0.0168263 | + | 0.999858i | \(0.494644\pi\) | |||||||
\(884\) | 1.00000 | + | 1.73205i | 0.0336336 | + | 0.0582552i | ||||
\(885\) | −54.0000 | + | 93.5307i | −1.81519 | + | 3.14400i | ||||
\(886\) | −6.00000 | + | 10.3923i | −0.201574 | + | 0.349136i | ||||
\(887\) | 8.50000 | + | 14.7224i | 0.285402 | + | 0.494331i | 0.972707 | − | 0.232038i | \(-0.0745395\pi\) |
−0.687305 | + | 0.726369i | \(0.741206\pi\) | |||||||
\(888\) | −6.00000 | −0.201347 | ||||||||
\(889\) | −12.5000 | − | 4.33013i | −0.419237 | − | 0.145228i | ||||
\(890\) | 24.0000 | 0.804482 | ||||||||
\(891\) | 4.50000 | + | 7.79423i | 0.150756 | + | 0.261116i | ||||
\(892\) | 13.0000 | − | 22.5167i | 0.435272 | − | 0.753914i | ||||
\(893\) | −6.00000 | + | 10.3923i | −0.200782 | + | 0.347765i | ||||
\(894\) | 15.0000 | + | 25.9808i | 0.501675 | + | 0.868927i | ||||
\(895\) | −52.0000 | −1.73817 | ||||||||
\(896\) | −0.500000 | − | 2.59808i | −0.0167038 | − | 0.0867956i | ||||
\(897\) | −6.00000 | −0.200334 | ||||||||
\(898\) | 15.0000 | + | 25.9808i | 0.500556 | + | 0.866989i | ||||
\(899\) | −2.00000 | + | 3.46410i | −0.0667037 | + | 0.115534i | ||||
\(900\) | −33.0000 | + | 57.1577i | −1.10000 | + | 1.90526i | ||||
\(901\) | 12.0000 | + | 20.7846i | 0.399778 | + | 0.692436i | ||||
\(902\) | −2.00000 | −0.0665927 | ||||||||
\(903\) | −24.0000 | + | 20.7846i | −0.798670 | + | 0.691669i | ||||
\(904\) | −17.0000 | −0.565412 | ||||||||
\(905\) | −44.0000 | − | 76.2102i | −1.46261 | − | 2.53331i | ||||
\(906\) | −13.5000 | + | 23.3827i | −0.448507 | + | 0.776838i | ||||
\(907\) | −22.0000 | + | 38.1051i | −0.730498 | + | 1.26526i | 0.226173 | + | 0.974087i | \(0.427379\pi\) |
−0.956671 | + | 0.291172i | \(0.905955\pi\) | |||||||
\(908\) | −5.00000 | − | 8.66025i | −0.165931 | − | 0.287401i | ||||
\(909\) | −90.0000 | −2.98511 | ||||||||
\(910\) | −8.00000 | + | 6.92820i | −0.265197 | + | 0.229668i | ||||
\(911\) | −54.0000 | −1.78910 | −0.894550 | − | 0.446968i | \(-0.852504\pi\) | ||||
−0.894550 | + | 0.446968i | \(0.852504\pi\) | |||||||
\(912\) | 9.00000 | + | 15.5885i | 0.298020 | + | 0.516185i | ||||
\(913\) | −3.00000 | + | 5.19615i | −0.0992855 | + | 0.171968i | ||||
\(914\) | 1.00000 | − | 1.73205i | 0.0330771 | − | 0.0572911i | ||||
\(915\) | 30.0000 | + | 51.9615i | 0.991769 | + | 1.71780i | ||||
\(916\) | −16.0000 | −0.528655 | ||||||||
\(917\) | −9.00000 | − | 46.7654i | −0.297206 | − | 1.54433i | ||||
\(918\) | 18.0000 | 0.594089 | ||||||||
\(919\) | 12.0000 | + | 20.7846i | 0.395843 | + | 0.685621i | 0.993208 | − | 0.116348i | \(-0.0371189\pi\) |
−0.597365 | + | 0.801970i | \(0.703786\pi\) | |||||||
\(920\) | 4.00000 | − | 6.92820i | 0.131876 | − | 0.228416i | ||||
\(921\) | 48.0000 | − | 83.1384i | 1.58165 | − | 2.73950i | ||||
\(922\) | −1.50000 | − | 2.59808i | −0.0493999 | − | 0.0855631i | ||||
\(923\) | −4.00000 | −0.131662 | ||||||||
\(924\) | −7.50000 | − | 2.59808i | −0.246732 | − | 0.0854704i | ||||
\(925\) | −22.0000 | −0.723356 | ||||||||
\(926\) | −7.00000 | − | 12.1244i | −0.230034 | − | 0.398431i | ||||
\(927\) | −36.0000 | + | 62.3538i | −1.18240 | + | 2.04797i | ||||
\(928\) | 0.500000 | − | 0.866025i | 0.0164133 | − | 0.0284287i | ||||
\(929\) | 16.5000 | + | 28.5788i | 0.541347 | + | 0.937641i | 0.998827 | + | 0.0484211i | \(0.0154190\pi\) |
−0.457480 | + | 0.889220i | \(0.651248\pi\) | |||||||
\(930\) | −48.0000 | −1.57398 | ||||||||
\(931\) | 6.00000 | − | 41.5692i | 0.196642 | − | 1.36238i | ||||
\(932\) | 6.00000 | 0.196537 | ||||||||
\(933\) | −42.0000 | − | 72.7461i | −1.37502 | − | 2.38160i | ||||
\(934\) | −6.00000 | + | 10.3923i | −0.196326 | + | 0.340047i | ||||
\(935\) | −4.00000 | + | 6.92820i | −0.130814 | + | 0.226576i | ||||
\(936\) | −3.00000 | − | 5.19615i | −0.0980581 | − | 0.169842i | ||||
\(937\) | −12.0000 | −0.392023 | −0.196011 | − | 0.980602i | \(-0.562799\pi\) | ||||
−0.196011 | + | 0.980602i | \(0.562799\pi\) | |||||||
\(938\) | −22.5000 | − | 7.79423i | −0.734651 | − | 0.254491i | ||||
\(939\) | −3.00000 | −0.0979013 | ||||||||
\(940\) | 4.00000 | + | 6.92820i | 0.130466 | + | 0.225973i | ||||
\(941\) | −27.5000 | + | 47.6314i | −0.896474 | + | 1.55274i | −0.0645052 | + | 0.997917i | \(0.520547\pi\) |
−0.831969 | + | 0.554822i | \(0.812786\pi\) | |||||||
\(942\) | −6.00000 | + | 10.3923i | −0.195491 | + | 0.338600i | ||||
\(943\) | −2.00000 | − | 3.46410i | −0.0651290 | − | 0.112807i | ||||
\(944\) | 9.00000 | 0.292925 | ||||||||
\(945\) | 18.0000 | + | 93.5307i | 0.585540 | + | 3.04256i | ||||
\(946\) | 4.00000 | 0.130051 | ||||||||
\(947\) | 8.00000 | + | 13.8564i | 0.259965 | + | 0.450273i | 0.966232 | − | 0.257673i | \(-0.0829556\pi\) |
−0.706267 | + | 0.707945i | \(0.749622\pi\) | |||||||
\(948\) | −22.5000 | + | 38.9711i | −0.730766 | + | 1.26572i | ||||
\(949\) | −1.00000 | + | 1.73205i | −0.0324614 | + | 0.0562247i | ||||
\(950\) | 33.0000 | + | 57.1577i | 1.07066 | + | 1.85444i | ||||
\(951\) | 36.0000 | 1.16738 | ||||||||
\(952\) | −4.00000 | + | 3.46410i | −0.129641 | + | 0.112272i | ||||
\(953\) | 56.0000 | 1.81402 | 0.907009 | − | 0.421111i | \(-0.138360\pi\) | ||||
0.907009 | + | 0.421111i | \(0.138360\pi\) | |||||||
\(954\) | −36.0000 | − | 62.3538i | −1.16554 | − | 2.01878i | ||||
\(955\) | 28.0000 | − | 48.4974i | 0.906059 | − | 1.56934i | ||||
\(956\) | −9.50000 | + | 16.4545i | −0.307252 | + | 0.532176i | ||||
\(957\) | −1.50000 | − | 2.59808i | −0.0484881 | − | 0.0839839i | ||||
\(958\) | 37.0000 | 1.19542 | ||||||||
\(959\) | −18.0000 | + | 15.5885i | −0.581250 | + | 0.503378i | ||||
\(960\) | 12.0000 | 0.387298 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 1.00000 | − | 1.73205i | 0.0322413 | − | 0.0558436i | ||||
\(963\) | −24.0000 | + | 41.5692i | −0.773389 | + | 1.33955i | ||||
\(964\) | −15.0000 | − | 25.9808i | −0.483117 | − | 0.836784i | ||||
\(965\) | 88.0000 | 2.83282 | ||||||||
\(966\) | −3.00000 | − | 15.5885i | −0.0965234 | − | 0.501550i | ||||
\(967\) | 56.0000 | 1.80084 | 0.900419 | − | 0.435023i | \(-0.143260\pi\) | ||||
0.900419 | + | 0.435023i | \(0.143260\pi\) | |||||||
\(968\) | 0.500000 | + | 0.866025i | 0.0160706 | + | 0.0278351i | ||||
\(969\) | 18.0000 | − | 31.1769i | 0.578243 | − | 1.00155i | ||||
\(970\) | 10.0000 | − | 17.3205i | 0.321081 | − | 0.556128i | ||||
\(971\) | 6.50000 | + | 11.2583i | 0.208595 | + | 0.361297i | 0.951272 | − | 0.308353i | \(-0.0997776\pi\) |
−0.742677 | + | 0.669650i | \(0.766444\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.0000 | − | 6.92820i | −0.641171 | − | 0.222108i | ||||
\(974\) | 4.00000 | 0.128168 | ||||||||
\(975\) | −16.5000 | − | 28.5788i | −0.528423 | − | 0.915255i | ||||
\(976\) | 2.50000 | − | 4.33013i | 0.0800230 | − | 0.138604i | ||||
\(977\) | −7.00000 | + | 12.1244i | −0.223950 | + | 0.387893i | −0.956004 | − | 0.293354i | \(-0.905229\pi\) |
0.732054 | + | 0.681247i | \(0.238562\pi\) | |||||||
\(978\) | −19.5000 | − | 33.7750i | −0.623541 | − | 1.08001i | ||||
\(979\) | −6.00000 | −0.191761 | ||||||||
\(980\) | −22.0000 | − | 17.3205i | −0.702764 | − | 0.553283i | ||||
\(981\) | 60.0000 | 1.91565 | ||||||||
\(982\) | 9.00000 | + | 15.5885i | 0.287202 | + | 0.497448i | ||||
\(983\) | −9.00000 | + | 15.5885i | −0.287055 | + | 0.497195i | −0.973106 | − | 0.230360i | \(-0.926010\pi\) |
0.686050 | + | 0.727554i | \(0.259343\pi\) | |||||||
\(984\) | 3.00000 | − | 5.19615i | 0.0956365 | − | 0.165647i | ||||
\(985\) | −6.00000 | − | 10.3923i | −0.191176 | − | 0.331126i | ||||
\(986\) | −2.00000 | −0.0636930 | ||||||||
\(987\) | 15.0000 | + | 5.19615i | 0.477455 | + | 0.165395i | ||||
\(988\) | −6.00000 | −0.190885 | ||||||||
\(989\) | 4.00000 | + | 6.92820i | 0.127193 | + | 0.220304i | ||||
\(990\) | 12.0000 | − | 20.7846i | 0.381385 | − | 0.660578i | ||||
\(991\) | 10.0000 | − | 17.3205i | 0.317660 | − | 0.550204i | −0.662339 | − | 0.749204i | \(-0.730436\pi\) |
0.979999 | + | 0.199000i | \(0.0637695\pi\) | |||||||
\(992\) | 2.00000 | + | 3.46410i | 0.0635001 | + | 0.109985i | ||||
\(993\) | −21.0000 | −0.666415 | ||||||||
\(994\) | −2.00000 | − | 10.3923i | −0.0634361 | − | 0.329624i | ||||
\(995\) | −40.0000 | −1.26809 | ||||||||
\(996\) | −9.00000 | − | 15.5885i | −0.285176 | − | 0.493939i | ||||
\(997\) | 21.0000 | − | 36.3731i | 0.665077 | − | 1.15195i | −0.314188 | − | 0.949361i | \(-0.601732\pi\) |
0.979265 | − | 0.202586i | \(-0.0649345\pi\) | |||||||
\(998\) | −8.00000 | + | 13.8564i | −0.253236 | + | 0.438617i | ||||
\(999\) | −9.00000 | − | 15.5885i | −0.284747 | − | 0.493197i |
(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 | 154.2.e.d.67.1 | yes | 2 | |
3.2 | odd | 2 | 1386.2.k.a.991.1 | 2 | |||
4.3 | odd | 2 | 1232.2.q.a.529.1 | 2 | |||
7.2 | even | 3 | inner | 154.2.e.d.23.1 | ✓ | 2 | |
7.3 | odd | 6 | 1078.2.a.f.1.1 | 1 | |||
7.4 | even | 3 | 1078.2.a.a.1.1 | 1 | |||
7.5 | odd | 6 | 1078.2.e.g.177.1 | 2 | |||
7.6 | odd | 2 | 1078.2.e.g.67.1 | 2 | |||
21.2 | odd | 6 | 1386.2.k.a.793.1 | 2 | |||
21.11 | odd | 6 | 9702.2.a.cg.1.1 | 1 | |||
21.17 | even | 6 | 9702.2.a.bb.1.1 | 1 | |||
28.3 | even | 6 | 8624.2.a.d.1.1 | 1 | |||
28.11 | odd | 6 | 8624.2.a.bd.1.1 | 1 | |||
28.23 | odd | 6 | 1232.2.q.a.177.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.e.d.23.1 | ✓ | 2 | 7.2 | even | 3 | inner | |
154.2.e.d.67.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1078.2.a.a.1.1 | 1 | 7.4 | even | 3 | |||
1078.2.a.f.1.1 | 1 | 7.3 | odd | 6 | |||
1078.2.e.g.67.1 | 2 | 7.6 | odd | 2 | |||
1078.2.e.g.177.1 | 2 | 7.5 | odd | 6 | |||
1232.2.q.a.177.1 | 2 | 28.23 | odd | 6 | |||
1232.2.q.a.529.1 | 2 | 4.3 | odd | 2 | |||
1386.2.k.a.793.1 | 2 | 21.2 | odd | 6 | |||
1386.2.k.a.991.1 | 2 | 3.2 | odd | 2 | |||
8624.2.a.d.1.1 | 1 | 28.3 | even | 6 | |||
8624.2.a.bd.1.1 | 1 | 28.11 | odd | 6 | |||
9702.2.a.bb.1.1 | 1 | 21.17 | even | 6 | |||
9702.2.a.cg.1.1 | 1 | 21.11 | odd | 6 |