Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(67,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(-0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.67 |
Dual form | 1078.2.e.s.177.1 |
$q$-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 \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||
\(3\) | −0.707107 | + | 1.22474i | −0.408248 | + | 0.707107i | −0.994694 | − | 0.102882i | \(-0.967194\pi\) |
0.586445 | + | 0.809989i | \(0.300527\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.707107 | + | 1.22474i | 0.316228 | + | 0.547723i | 0.979698 | − | 0.200480i | \(-0.0642503\pi\) |
−0.663470 | + | 0.748203i | \(0.730917\pi\) | |||||||
\(6\) | −1.41421 | −0.577350 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | −0.707107 | + | 1.22474i | −0.223607 | + | 0.387298i | ||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | −0.707107 | − | 1.22474i | −0.204124 | − | 0.353553i | ||||
\(13\) | −2.82843 | −0.784465 | −0.392232 | − | 0.919866i | \(-0.628297\pi\) | ||||
−0.392232 | + | 0.919866i | \(0.628297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.00000 | −0.516398 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.82843 | + | 4.89898i | −0.685994 | + | 1.18818i | 0.287129 | + | 0.957892i | \(0.407299\pi\) |
−0.973123 | + | 0.230285i | \(0.926034\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | 1.41421 | + | 2.44949i | 0.324443 | + | 0.561951i | 0.981399 | − | 0.191977i | \(-0.0614899\pi\) |
−0.656957 | + | 0.753928i | \(0.728157\pi\) | |||||||
\(20\) | −1.41421 | −0.316228 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 1.00000 | + | 1.73205i | 0.208514 | + | 0.361158i | 0.951247 | − | 0.308431i | \(-0.0998038\pi\) |
−0.742732 | + | 0.669588i | \(0.766471\pi\) | |||||||
\(24\) | 0.707107 | − | 1.22474i | 0.144338 | − | 0.250000i | ||||
\(25\) | 1.50000 | − | 2.59808i | 0.300000 | − | 0.519615i | ||||
\(26\) | −1.41421 | − | 2.44949i | −0.277350 | − | 0.480384i | ||||
\(27\) | −5.65685 | −1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | −1.00000 | − | 1.73205i | −0.182574 | − | 0.316228i | ||||
\(31\) | −0.707107 | + | 1.22474i | −0.127000 | + | 0.219971i | −0.922513 | − | 0.385966i | \(-0.873868\pi\) |
0.795513 | + | 0.605937i | \(0.207202\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0.707107 | + | 1.22474i | 0.123091 | + | 0.213201i | ||||
\(34\) | −5.65685 | −0.970143 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 1.00000 | + | 1.73205i | 0.164399 | + | 0.284747i | 0.936442 | − | 0.350823i | \(-0.114098\pi\) |
−0.772043 | + | 0.635571i | \(0.780765\pi\) | |||||||
\(38\) | −1.41421 | + | 2.44949i | −0.229416 | + | 0.397360i | ||||
\(39\) | 2.00000 | − | 3.46410i | 0.320256 | − | 0.554700i | ||||
\(40\) | −0.707107 | − | 1.22474i | −0.111803 | − | 0.193649i | ||||
\(41\) | −5.65685 | −0.883452 | −0.441726 | − | 0.897150i | \(-0.645634\pi\) | ||||
−0.441726 | + | 0.897150i | \(0.645634\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 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 | ||||
\(45\) | −0.707107 | + | 1.22474i | −0.105409 | + | 0.182574i | ||||
\(46\) | −1.00000 | + | 1.73205i | −0.147442 | + | 0.255377i | ||||
\(47\) | 2.12132 | + | 3.67423i | 0.309426 | + | 0.535942i | 0.978237 | − | 0.207491i | \(-0.0665296\pi\) |
−0.668811 | + | 0.743433i | \(0.733196\pi\) | |||||||
\(48\) | 1.41421 | 0.204124 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.00000 | 0.424264 | ||||||||
\(51\) | −4.00000 | − | 6.92820i | −0.560112 | − | 0.970143i | ||||
\(52\) | 1.41421 | − | 2.44949i | 0.196116 | − | 0.339683i | ||||
\(53\) | 6.00000 | − | 10.3923i | 0.824163 | − | 1.42749i | −0.0783936 | − | 0.996922i | \(-0.524979\pi\) |
0.902557 | − | 0.430570i | \(-0.141688\pi\) | |||||||
\(54\) | −2.82843 | − | 4.89898i | −0.384900 | − | 0.666667i | ||||
\(55\) | 1.41421 | 0.190693 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.00000 | −0.529813 | ||||||||
\(58\) | −3.00000 | − | 5.19615i | −0.393919 | − | 0.682288i | ||||
\(59\) | 2.12132 | − | 3.67423i | 0.276172 | − | 0.478345i | −0.694258 | − | 0.719726i | \(-0.744267\pi\) |
0.970430 | + | 0.241382i | \(0.0776006\pi\) | |||||||
\(60\) | 1.00000 | − | 1.73205i | 0.129099 | − | 0.223607i | ||||
\(61\) | −2.82843 | − | 4.89898i | −0.362143 | − | 0.627250i | 0.626170 | − | 0.779686i | \(-0.284621\pi\) |
−0.988313 | + | 0.152436i | \(0.951288\pi\) | |||||||
\(62\) | −1.41421 | −0.179605 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.00000 | − | 3.46410i | −0.248069 | − | 0.429669i | ||||
\(66\) | −0.707107 | + | 1.22474i | −0.0870388 | + | 0.150756i | ||||
\(67\) | 1.00000 | − | 1.73205i | 0.122169 | − | 0.211604i | −0.798454 | − | 0.602056i | \(-0.794348\pi\) |
0.920623 | + | 0.390453i | \(0.127682\pi\) | |||||||
\(68\) | −2.82843 | − | 4.89898i | −0.342997 | − | 0.594089i | ||||
\(69\) | −2.82843 | −0.340503 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.0000 | −1.18678 | −0.593391 | − | 0.804914i | \(-0.702211\pi\) | ||||
−0.593391 | + | 0.804914i | \(0.702211\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | −7.07107 | + | 12.2474i | −0.827606 | + | 1.43346i | 0.0723054 | + | 0.997383i | \(0.476964\pi\) |
−0.899911 | + | 0.436073i | \(0.856369\pi\) | |||||||
\(74\) | −1.00000 | + | 1.73205i | −0.116248 | + | 0.201347i | ||||
\(75\) | 2.12132 | + | 3.67423i | 0.244949 | + | 0.424264i | ||||
\(76\) | −2.82843 | −0.324443 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.00000 | 0.452911 | ||||||||
\(79\) | 4.00000 | + | 6.92820i | 0.450035 | + | 0.779484i | 0.998388 | − | 0.0567635i | \(-0.0180781\pi\) |
−0.548352 | + | 0.836247i | \(0.684745\pi\) | |||||||
\(80\) | 0.707107 | − | 1.22474i | 0.0790569 | − | 0.136931i | ||||
\(81\) | 2.50000 | − | 4.33013i | 0.277778 | − | 0.481125i | ||||
\(82\) | −2.82843 | − | 4.89898i | −0.312348 | − | 0.541002i | ||||
\(83\) | 2.82843 | 0.310460 | 0.155230 | − | 0.987878i | \(-0.450388\pi\) | ||||
0.155230 | + | 0.987878i | \(0.450388\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.00000 | −0.867722 | ||||||||
\(86\) | 2.00000 | + | 3.46410i | 0.215666 | + | 0.373544i | ||||
\(87\) | 4.24264 | − | 7.34847i | 0.454859 | − | 0.787839i | ||||
\(88\) | −0.500000 | + | 0.866025i | −0.0533002 | + | 0.0923186i | ||||
\(89\) | −3.53553 | − | 6.12372i | −0.374766 | − | 0.649113i | 0.615526 | − | 0.788116i | \(-0.288944\pi\) |
−0.990292 | + | 0.139003i | \(0.955610\pi\) | |||||||
\(90\) | −1.41421 | −0.149071 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.00000 | −0.208514 | ||||||||
\(93\) | −1.00000 | − | 1.73205i | −0.103695 | − | 0.179605i | ||||
\(94\) | −2.12132 | + | 3.67423i | −0.218797 | + | 0.378968i | ||||
\(95\) | −2.00000 | + | 3.46410i | −0.205196 | + | 0.355409i | ||||
\(96\) | 0.707107 | + | 1.22474i | 0.0721688 | + | 0.125000i | ||||
\(97\) | 15.5563 | 1.57951 | 0.789754 | − | 0.613424i | \(-0.210208\pi\) | ||||
0.789754 | + | 0.613424i | \(0.210208\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 1.50000 | + | 2.59808i | 0.150000 | + | 0.259808i | ||||
\(101\) | 1.41421 | − | 2.44949i | 0.140720 | − | 0.243733i | −0.787048 | − | 0.616891i | \(-0.788392\pi\) |
0.927768 | + | 0.373158i | \(0.121725\pi\) | |||||||
\(102\) | 4.00000 | − | 6.92820i | 0.396059 | − | 0.685994i | ||||
\(103\) | −2.12132 | − | 3.67423i | −0.209020 | − | 0.362033i | 0.742386 | − | 0.669972i | \(-0.233694\pi\) |
−0.951406 | + | 0.307939i | \(0.900361\pi\) | |||||||
\(104\) | 2.82843 | 0.277350 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.0000 | 1.16554 | ||||||||
\(107\) | 10.0000 | + | 17.3205i | 0.966736 | + | 1.67444i | 0.704875 | + | 0.709331i | \(0.251003\pi\) |
0.261861 | + | 0.965106i | \(0.415664\pi\) | |||||||
\(108\) | 2.82843 | − | 4.89898i | 0.272166 | − | 0.471405i | ||||
\(109\) | −5.00000 | + | 8.66025i | −0.478913 | + | 0.829502i | −0.999708 | − | 0.0241802i | \(-0.992302\pi\) |
0.520794 | + | 0.853682i | \(0.325636\pi\) | |||||||
\(110\) | 0.707107 | + | 1.22474i | 0.0674200 | + | 0.116775i | ||||
\(111\) | −2.82843 | −0.268462 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.0000 | −1.69330 | −0.846649 | − | 0.532152i | \(-0.821383\pi\) | ||||
−0.846649 | + | 0.532152i | \(0.821383\pi\) | |||||||
\(114\) | −2.00000 | − | 3.46410i | −0.187317 | − | 0.324443i | ||||
\(115\) | −1.41421 | + | 2.44949i | −0.131876 | + | 0.228416i | ||||
\(116\) | 3.00000 | − | 5.19615i | 0.278543 | − | 0.482451i | ||||
\(117\) | −1.41421 | − | 2.44949i | −0.130744 | − | 0.226455i | ||||
\(118\) | 4.24264 | 0.390567 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.00000 | 0.182574 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 2.82843 | − | 4.89898i | 0.256074 | − | 0.443533i | ||||
\(123\) | 4.00000 | − | 6.92820i | 0.360668 | − | 0.624695i | ||||
\(124\) | −0.707107 | − | 1.22474i | −0.0635001 | − | 0.109985i | ||||
\(125\) | 11.3137 | 1.01193 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.0000 | 1.06483 | 0.532414 | − | 0.846484i | \(-0.321285\pi\) | ||||
0.532414 | + | 0.846484i | \(0.321285\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −2.82843 | + | 4.89898i | −0.249029 | + | 0.431331i | ||||
\(130\) | 2.00000 | − | 3.46410i | 0.175412 | − | 0.303822i | ||||
\(131\) | 5.65685 | + | 9.79796i | 0.494242 | + | 0.856052i | 0.999978 | − | 0.00663646i | \(-0.00211246\pi\) |
−0.505736 | + | 0.862688i | \(0.668779\pi\) | |||||||
\(132\) | −1.41421 | −0.123091 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.00000 | 0.172774 | ||||||||
\(135\) | −4.00000 | − | 6.92820i | −0.344265 | − | 0.596285i | ||||
\(136\) | 2.82843 | − | 4.89898i | 0.242536 | − | 0.420084i | ||||
\(137\) | 1.00000 | − | 1.73205i | 0.0854358 | − | 0.147979i | −0.820141 | − | 0.572161i | \(-0.806105\pi\) |
0.905577 | + | 0.424182i | \(0.139438\pi\) | |||||||
\(138\) | −1.41421 | − | 2.44949i | −0.120386 | − | 0.208514i | ||||
\(139\) | 2.82843 | 0.239904 | 0.119952 | − | 0.992780i | \(-0.461726\pi\) | ||||
0.119952 | + | 0.992780i | \(0.461726\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | −5.00000 | − | 8.66025i | −0.419591 | − | 0.726752i | ||||
\(143\) | −1.41421 | + | 2.44949i | −0.118262 | + | 0.204837i | ||||
\(144\) | 0.500000 | − | 0.866025i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | −4.24264 | − | 7.34847i | −0.352332 | − | 0.610257i | ||||
\(146\) | −14.1421 | −1.17041 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | 5.00000 | + | 8.66025i | 0.409616 | + | 0.709476i | 0.994847 | − | 0.101391i | \(-0.0323294\pi\) |
−0.585231 | + | 0.810867i | \(0.698996\pi\) | |||||||
\(150\) | −2.12132 | + | 3.67423i | −0.173205 | + | 0.300000i | ||||
\(151\) | −8.00000 | + | 13.8564i | −0.651031 | + | 1.12762i | 0.331842 | + | 0.943335i | \(0.392330\pi\) |
−0.982873 | + | 0.184284i | \(0.941004\pi\) | |||||||
\(152\) | −1.41421 | − | 2.44949i | −0.114708 | − | 0.198680i | ||||
\(153\) | −5.65685 | −0.457330 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.00000 | −0.160644 | ||||||||
\(156\) | 2.00000 | + | 3.46410i | 0.160128 | + | 0.277350i | ||||
\(157\) | 9.19239 | − | 15.9217i | 0.733632 | − | 1.27069i | −0.221688 | − | 0.975118i | \(-0.571157\pi\) |
0.955321 | − | 0.295571i | \(-0.0955099\pi\) | |||||||
\(158\) | −4.00000 | + | 6.92820i | −0.318223 | + | 0.551178i | ||||
\(159\) | 8.48528 | + | 14.6969i | 0.672927 | + | 1.16554i | ||||
\(160\) | 1.41421 | 0.111803 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 5.00000 | 0.392837 | ||||||||
\(163\) | 11.0000 | + | 19.0526i | 0.861586 | + | 1.49231i | 0.870397 | + | 0.492350i | \(0.163862\pi\) |
−0.00881059 | + | 0.999961i | \(0.502805\pi\) | |||||||
\(164\) | 2.82843 | − | 4.89898i | 0.220863 | − | 0.382546i | ||||
\(165\) | −1.00000 | + | 1.73205i | −0.0778499 | + | 0.134840i | ||||
\(166\) | 1.41421 | + | 2.44949i | 0.109764 | + | 0.190117i | ||||
\(167\) | 11.3137 | 0.875481 | 0.437741 | − | 0.899101i | \(-0.355779\pi\) | ||||
0.437741 | + | 0.899101i | \(0.355779\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | −4.00000 | − | 6.92820i | −0.306786 | − | 0.531369i | ||||
\(171\) | −1.41421 | + | 2.44949i | −0.108148 | + | 0.187317i | ||||
\(172\) | −2.00000 | + | 3.46410i | −0.152499 | + | 0.264135i | ||||
\(173\) | 7.07107 | + | 12.2474i | 0.537603 | + | 0.931156i | 0.999032 | + | 0.0439792i | \(0.0140035\pi\) |
−0.461429 | + | 0.887177i | \(0.652663\pi\) | |||||||
\(174\) | 8.48528 | 0.643268 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 3.00000 | + | 5.19615i | 0.225494 | + | 0.390567i | ||||
\(178\) | 3.53553 | − | 6.12372i | 0.264999 | − | 0.458993i | ||||
\(179\) | −10.0000 | + | 17.3205i | −0.747435 | + | 1.29460i | 0.201613 | + | 0.979465i | \(0.435382\pi\) |
−0.949048 | + | 0.315130i | \(0.897952\pi\) | |||||||
\(180\) | −0.707107 | − | 1.22474i | −0.0527046 | − | 0.0912871i | ||||
\(181\) | −12.7279 | −0.946059 | −0.473029 | − | 0.881047i | \(-0.656840\pi\) | ||||
−0.473029 | + | 0.881047i | \(0.656840\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.00000 | 0.591377 | ||||||||
\(184\) | −1.00000 | − | 1.73205i | −0.0737210 | − | 0.127688i | ||||
\(185\) | −1.41421 | + | 2.44949i | −0.103975 | + | 0.180090i | ||||
\(186\) | 1.00000 | − | 1.73205i | 0.0733236 | − | 0.127000i | ||||
\(187\) | 2.82843 | + | 4.89898i | 0.206835 | + | 0.358249i | ||||
\(188\) | −4.24264 | −0.309426 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.00000 | −0.290191 | ||||||||
\(191\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(192\) | −0.707107 | + | 1.22474i | −0.0510310 | + | 0.0883883i | ||||
\(193\) | −3.00000 | + | 5.19615i | −0.215945 | + | 0.374027i | −0.953564 | − | 0.301189i | \(-0.902616\pi\) |
0.737620 | + | 0.675216i | \(0.235950\pi\) | |||||||
\(194\) | 7.77817 | + | 13.4722i | 0.558440 | + | 0.967247i | ||||
\(195\) | 5.65685 | 0.405096 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0.500000 | + | 0.866025i | 0.0355335 | + | 0.0615457i | ||||
\(199\) | 10.6066 | − | 18.3712i | 0.751882 | − | 1.30230i | −0.195027 | − | 0.980798i | \(-0.562480\pi\) |
0.946910 | − | 0.321500i | \(-0.104187\pi\) | |||||||
\(200\) | −1.50000 | + | 2.59808i | −0.106066 | + | 0.183712i | ||||
\(201\) | 1.41421 | + | 2.44949i | 0.0997509 | + | 0.172774i | ||||
\(202\) | 2.82843 | 0.199007 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 8.00000 | 0.560112 | ||||||||
\(205\) | −4.00000 | − | 6.92820i | −0.279372 | − | 0.483887i | ||||
\(206\) | 2.12132 | − | 3.67423i | 0.147799 | − | 0.255996i | ||||
\(207\) | −1.00000 | + | 1.73205i | −0.0695048 | + | 0.120386i | ||||
\(208\) | 1.41421 | + | 2.44949i | 0.0980581 | + | 0.169842i | ||||
\(209\) | 2.82843 | 0.195646 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28.0000 | 1.92760 | 0.963800 | − | 0.266627i | \(-0.0859092\pi\) | ||||
0.963800 | + | 0.266627i | \(0.0859092\pi\) | |||||||
\(212\) | 6.00000 | + | 10.3923i | 0.412082 | + | 0.713746i | ||||
\(213\) | 7.07107 | − | 12.2474i | 0.484502 | − | 0.839181i | ||||
\(214\) | −10.0000 | + | 17.3205i | −0.683586 | + | 1.18401i | ||||
\(215\) | 2.82843 | + | 4.89898i | 0.192897 | + | 0.334108i | ||||
\(216\) | 5.65685 | 0.384900 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.0000 | −0.677285 | ||||||||
\(219\) | −10.0000 | − | 17.3205i | −0.675737 | − | 1.17041i | ||||
\(220\) | −0.707107 | + | 1.22474i | −0.0476731 | + | 0.0825723i | ||||
\(221\) | 8.00000 | − | 13.8564i | 0.538138 | − | 0.932083i | ||||
\(222\) | −1.41421 | − | 2.44949i | −0.0949158 | − | 0.164399i | ||||
\(223\) | 15.5563 | 1.04173 | 0.520865 | − | 0.853639i | \(-0.325609\pi\) | ||||
0.520865 | + | 0.853639i | \(0.325609\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | 0.200000 | ||||||||
\(226\) | −9.00000 | − | 15.5885i | −0.598671 | − | 1.03693i | ||||
\(227\) | −14.1421 | + | 24.4949i | −0.938647 | + | 1.62578i | −0.170648 | + | 0.985332i | \(0.554586\pi\) |
−0.767999 | + | 0.640451i | \(0.778747\pi\) | |||||||
\(228\) | 2.00000 | − | 3.46410i | 0.132453 | − | 0.229416i | ||||
\(229\) | −2.12132 | − | 3.67423i | −0.140181 | − | 0.242800i | 0.787384 | − | 0.616463i | \(-0.211435\pi\) |
−0.927565 | + | 0.373663i | \(0.878102\pi\) | |||||||
\(230\) | −2.82843 | −0.186501 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.00000 | 0.393919 | ||||||||
\(233\) | −3.00000 | − | 5.19615i | −0.196537 | − | 0.340411i | 0.750867 | − | 0.660454i | \(-0.229636\pi\) |
−0.947403 | + | 0.320043i | \(0.896303\pi\) | |||||||
\(234\) | 1.41421 | − | 2.44949i | 0.0924500 | − | 0.160128i | ||||
\(235\) | −3.00000 | + | 5.19615i | −0.195698 | + | 0.338960i | ||||
\(236\) | 2.12132 | + | 3.67423i | 0.138086 | + | 0.239172i | ||||
\(237\) | −11.3137 | −0.734904 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.0000 | −1.03495 | −0.517477 | − | 0.855697i | \(-0.673129\pi\) | ||||
−0.517477 | + | 0.855697i | \(0.673129\pi\) | |||||||
\(240\) | 1.00000 | + | 1.73205i | 0.0645497 | + | 0.111803i | ||||
\(241\) | −2.82843 | + | 4.89898i | −0.182195 | + | 0.315571i | −0.942628 | − | 0.333846i | \(-0.891654\pi\) |
0.760433 | + | 0.649417i | \(0.224987\pi\) | |||||||
\(242\) | 0.500000 | − | 0.866025i | 0.0321412 | − | 0.0556702i | ||||
\(243\) | −4.94975 | − | 8.57321i | −0.317526 | − | 0.549972i | ||||
\(244\) | 5.65685 | 0.362143 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8.00000 | 0.510061 | ||||||||
\(247\) | −4.00000 | − | 6.92820i | −0.254514 | − | 0.440831i | ||||
\(248\) | 0.707107 | − | 1.22474i | 0.0449013 | − | 0.0777714i | ||||
\(249\) | −2.00000 | + | 3.46410i | −0.126745 | + | 0.219529i | ||||
\(250\) | 5.65685 | + | 9.79796i | 0.357771 | + | 0.619677i | ||||
\(251\) | 24.0416 | 1.51749 | 0.758747 | − | 0.651385i | \(-0.225812\pi\) | ||||
0.758747 | + | 0.651385i | \(0.225812\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.00000 | 0.125739 | ||||||||
\(254\) | 6.00000 | + | 10.3923i | 0.376473 | + | 0.652071i | ||||
\(255\) | 5.65685 | − | 9.79796i | 0.354246 | − | 0.613572i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −4.94975 | − | 8.57321i | −0.308757 | − | 0.534782i | 0.669334 | − | 0.742962i | \(-0.266580\pi\) |
−0.978091 | + | 0.208179i | \(0.933246\pi\) | |||||||
\(258\) | −5.65685 | −0.352180 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.00000 | 0.248069 | ||||||||
\(261\) | −3.00000 | − | 5.19615i | −0.185695 | − | 0.321634i | ||||
\(262\) | −5.65685 | + | 9.79796i | −0.349482 | + | 0.605320i | ||||
\(263\) | −12.0000 | + | 20.7846i | −0.739952 | + | 1.28163i | 0.212565 | + | 0.977147i | \(0.431818\pi\) |
−0.952517 | + | 0.304487i | \(0.901515\pi\) | |||||||
\(264\) | −0.707107 | − | 1.22474i | −0.0435194 | − | 0.0753778i | ||||
\(265\) | 16.9706 | 1.04249 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.0000 | 0.611990 | ||||||||
\(268\) | 1.00000 | + | 1.73205i | 0.0610847 | + | 0.105802i | ||||
\(269\) | −12.0208 | + | 20.8207i | −0.732922 | + | 1.26946i | 0.222707 | + | 0.974885i | \(0.428511\pi\) |
−0.955629 | + | 0.294573i | \(0.904823\pi\) | |||||||
\(270\) | 4.00000 | − | 6.92820i | 0.243432 | − | 0.421637i | ||||
\(271\) | 4.24264 | + | 7.34847i | 0.257722 | + | 0.446388i | 0.965631 | − | 0.259916i | \(-0.0836948\pi\) |
−0.707909 | + | 0.706303i | \(0.750361\pi\) | |||||||
\(272\) | 5.65685 | 0.342997 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.00000 | 0.120824 | ||||||||
\(275\) | −1.50000 | − | 2.59808i | −0.0904534 | − | 0.156670i | ||||
\(276\) | 1.41421 | − | 2.44949i | 0.0851257 | − | 0.147442i | ||||
\(277\) | 5.00000 | − | 8.66025i | 0.300421 | − | 0.520344i | −0.675810 | − | 0.737075i | \(-0.736206\pi\) |
0.976231 | + | 0.216731i | \(0.0695395\pi\) | |||||||
\(278\) | 1.41421 | + | 2.44949i | 0.0848189 | + | 0.146911i | ||||
\(279\) | −1.41421 | −0.0846668 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0000 | 1.07379 | 0.536895 | − | 0.843649i | \(-0.319597\pi\) | ||||
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(282\) | −3.00000 | − | 5.19615i | −0.178647 | − | 0.309426i | ||||
\(283\) | 8.48528 | − | 14.6969i | 0.504398 | − | 0.873642i | −0.495589 | − | 0.868557i | \(-0.665048\pi\) |
0.999987 | − | 0.00508540i | \(-0.00161874\pi\) | |||||||
\(284\) | 5.00000 | − | 8.66025i | 0.296695 | − | 0.513892i | ||||
\(285\) | −2.82843 | − | 4.89898i | −0.167542 | − | 0.290191i | ||||
\(286\) | −2.82843 | −0.167248 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −7.50000 | − | 12.9904i | −0.441176 | − | 0.764140i | ||||
\(290\) | 4.24264 | − | 7.34847i | 0.249136 | − | 0.431517i | ||||
\(291\) | −11.0000 | + | 19.0526i | −0.644831 | + | 1.11688i | ||||
\(292\) | −7.07107 | − | 12.2474i | −0.413803 | − | 0.716728i | ||||
\(293\) | −16.9706 | −0.991431 | −0.495715 | − | 0.868485i | \(-0.665094\pi\) | ||||
−0.495715 | + | 0.868485i | \(0.665094\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.00000 | 0.349334 | ||||||||
\(296\) | −1.00000 | − | 1.73205i | −0.0581238 | − | 0.100673i | ||||
\(297\) | −2.82843 | + | 4.89898i | −0.164122 | + | 0.284268i | ||||
\(298\) | −5.00000 | + | 8.66025i | −0.289642 | + | 0.501675i | ||||
\(299\) | −2.82843 | − | 4.89898i | −0.163572 | − | 0.283315i | ||||
\(300\) | −4.24264 | −0.244949 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −16.0000 | −0.920697 | ||||||||
\(303\) | 2.00000 | + | 3.46410i | 0.114897 | + | 0.199007i | ||||
\(304\) | 1.41421 | − | 2.44949i | 0.0811107 | − | 0.140488i | ||||
\(305\) | 4.00000 | − | 6.92820i | 0.229039 | − | 0.396708i | ||||
\(306\) | −2.82843 | − | 4.89898i | −0.161690 | − | 0.280056i | ||||
\(307\) | 11.3137 | 0.645707 | 0.322854 | − | 0.946449i | \(-0.395358\pi\) | ||||
0.322854 | + | 0.946449i | \(0.395358\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.00000 | 0.341328 | ||||||||
\(310\) | −1.00000 | − | 1.73205i | −0.0567962 | − | 0.0983739i | ||||
\(311\) | −4.94975 | + | 8.57321i | −0.280674 | + | 0.486142i | −0.971551 | − | 0.236830i | \(-0.923891\pi\) |
0.690877 | + | 0.722973i | \(0.257225\pi\) | |||||||
\(312\) | −2.00000 | + | 3.46410i | −0.113228 | + | 0.196116i | ||||
\(313\) | 13.4350 | + | 23.2702i | 0.759393 | + | 1.31531i | 0.943161 | + | 0.332337i | \(0.107837\pi\) |
−0.183768 | + | 0.982970i | \(0.558829\pi\) | |||||||
\(314\) | 18.3848 | 1.03751 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | 13.0000 | + | 22.5167i | 0.730153 | + | 1.26466i | 0.956818 | + | 0.290689i | \(0.0938844\pi\) |
−0.226665 | + | 0.973973i | \(0.572782\pi\) | |||||||
\(318\) | −8.48528 | + | 14.6969i | −0.475831 | + | 0.824163i | ||||
\(319\) | −3.00000 | + | 5.19615i | −0.167968 | + | 0.290929i | ||||
\(320\) | 0.707107 | + | 1.22474i | 0.0395285 | + | 0.0684653i | ||||
\(321\) | −28.2843 | −1.57867 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.0000 | −0.890264 | ||||||||
\(324\) | 2.50000 | + | 4.33013i | 0.138889 | + | 0.240563i | ||||
\(325\) | −4.24264 | + | 7.34847i | −0.235339 | + | 0.407620i | ||||
\(326\) | −11.0000 | + | 19.0526i | −0.609234 | + | 1.05522i | ||||
\(327\) | −7.07107 | − | 12.2474i | −0.391031 | − | 0.677285i | ||||
\(328\) | 5.65685 | 0.312348 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.00000 | −0.110096 | ||||||||
\(331\) | −14.0000 | − | 24.2487i | −0.769510 | − | 1.33283i | −0.937829 | − | 0.347097i | \(-0.887167\pi\) |
0.168320 | − | 0.985732i | \(-0.446166\pi\) | |||||||
\(332\) | −1.41421 | + | 2.44949i | −0.0776151 | + | 0.134433i | ||||
\(333\) | −1.00000 | + | 1.73205i | −0.0547997 | + | 0.0949158i | ||||
\(334\) | 5.65685 | + | 9.79796i | 0.309529 | + | 0.536120i | ||||
\(335\) | 2.82843 | 0.154533 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.00000 | −0.108947 | −0.0544735 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544735 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(338\) | −2.50000 | − | 4.33013i | −0.135982 | − | 0.235528i | ||||
\(339\) | 12.7279 | − | 22.0454i | 0.691286 | − | 1.19734i | ||||
\(340\) | 4.00000 | − | 6.92820i | 0.216930 | − | 0.375735i | ||||
\(341\) | 0.707107 | + | 1.22474i | 0.0382920 | + | 0.0663237i | ||||
\(342\) | −2.82843 | −0.152944 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.00000 | −0.215666 | ||||||||
\(345\) | −2.00000 | − | 3.46410i | −0.107676 | − | 0.186501i | ||||
\(346\) | −7.07107 | + | 12.2474i | −0.380143 | + | 0.658427i | ||||
\(347\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(348\) | 4.24264 | + | 7.34847i | 0.227429 | + | 0.393919i | ||||
\(349\) | 5.65685 | 0.302804 | 0.151402 | − | 0.988472i | \(-0.451621\pi\) | ||||
0.151402 | + | 0.988472i | \(0.451621\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.0000 | 0.854017 | ||||||||
\(352\) | −0.500000 | − | 0.866025i | −0.0266501 | − | 0.0461593i | ||||
\(353\) | 0.707107 | − | 1.22474i | 0.0376355 | − | 0.0651866i | −0.846594 | − | 0.532239i | \(-0.821351\pi\) |
0.884230 | + | 0.467052i | \(0.154684\pi\) | |||||||
\(354\) | −3.00000 | + | 5.19615i | −0.159448 | + | 0.276172i | ||||
\(355\) | −7.07107 | − | 12.2474i | −0.375293 | − | 0.650027i | ||||
\(356\) | 7.07107 | 0.374766 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.0000 | −1.05703 | ||||||||
\(359\) | −16.0000 | − | 27.7128i | −0.844448 | − | 1.46263i | −0.886100 | − | 0.463494i | \(-0.846596\pi\) |
0.0416523 | − | 0.999132i | \(-0.486738\pi\) | |||||||
\(360\) | 0.707107 | − | 1.22474i | 0.0372678 | − | 0.0645497i | ||||
\(361\) | 5.50000 | − | 9.52628i | 0.289474 | − | 0.501383i | ||||
\(362\) | −6.36396 | − | 11.0227i | −0.334482 | − | 0.579340i | ||||
\(363\) | 1.41421 | 0.0742270 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.0000 | −1.04685 | ||||||||
\(366\) | 4.00000 | + | 6.92820i | 0.209083 | + | 0.362143i | ||||
\(367\) | 14.8492 | − | 25.7196i | 0.775124 | − | 1.34255i | −0.159601 | − | 0.987182i | \(-0.551021\pi\) |
0.934725 | − | 0.355373i | \(-0.115646\pi\) | |||||||
\(368\) | 1.00000 | − | 1.73205i | 0.0521286 | − | 0.0902894i | ||||
\(369\) | −2.82843 | − | 4.89898i | −0.147242 | − | 0.255031i | ||||
\(370\) | −2.82843 | −0.147043 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.00000 | 0.103695 | ||||||||
\(373\) | 7.00000 | + | 12.1244i | 0.362446 | + | 0.627775i | 0.988363 | − | 0.152115i | \(-0.0486083\pi\) |
−0.625917 | + | 0.779890i | \(0.715275\pi\) | |||||||
\(374\) | −2.82843 | + | 4.89898i | −0.146254 | + | 0.253320i | ||||
\(375\) | −8.00000 | + | 13.8564i | −0.413118 | + | 0.715542i | ||||
\(376\) | −2.12132 | − | 3.67423i | −0.109399 | − | 0.189484i | ||||
\(377\) | 16.9706 | 0.874028 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.00000 | 0.308199 | 0.154100 | − | 0.988055i | \(-0.450752\pi\) | ||||
0.154100 | + | 0.988055i | \(0.450752\pi\) | |||||||
\(380\) | −2.00000 | − | 3.46410i | −0.102598 | − | 0.177705i | ||||
\(381\) | −8.48528 | + | 14.6969i | −0.434714 | + | 0.752947i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.4350 | + | 23.2702i | 0.686498 | + | 1.18905i | 0.972964 | + | 0.230959i | \(0.0741862\pi\) |
−0.286466 | + | 0.958091i | \(0.592480\pi\) | |||||||
\(384\) | −1.41421 | −0.0721688 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.00000 | −0.305392 | ||||||||
\(387\) | 2.00000 | + | 3.46410i | 0.101666 | + | 0.176090i | ||||
\(388\) | −7.77817 | + | 13.4722i | −0.394877 | + | 0.683947i | ||||
\(389\) | 14.0000 | − | 24.2487i | 0.709828 | − | 1.22946i | −0.255092 | − | 0.966917i | \(-0.582106\pi\) |
0.964921 | − | 0.262542i | \(-0.0845608\pi\) | |||||||
\(390\) | 2.82843 | + | 4.89898i | 0.143223 | + | 0.248069i | ||||
\(391\) | −11.3137 | −0.572159 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.0000 | −0.807093 | ||||||||
\(394\) | 9.00000 | + | 15.5885i | 0.453413 | + | 0.785335i | ||||
\(395\) | −5.65685 | + | 9.79796i | −0.284627 | + | 0.492989i | ||||
\(396\) | −0.500000 | + | 0.866025i | −0.0251259 | + | 0.0435194i | ||||
\(397\) | −12.0208 | − | 20.8207i | −0.603307 | − | 1.04496i | −0.992317 | − | 0.123725i | \(-0.960516\pi\) |
0.389009 | − | 0.921234i | \(-0.372817\pi\) | |||||||
\(398\) | 21.2132 | 1.06332 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | −0.150000 | ||||||||
\(401\) | −18.0000 | − | 31.1769i | −0.898877 | − | 1.55690i | −0.828932 | − | 0.559350i | \(-0.811051\pi\) |
−0.0699455 | − | 0.997551i | \(-0.522283\pi\) | |||||||
\(402\) | −1.41421 | + | 2.44949i | −0.0705346 | + | 0.122169i | ||||
\(403\) | 2.00000 | − | 3.46410i | 0.0996271 | − | 0.172559i | ||||
\(404\) | 1.41421 | + | 2.44949i | 0.0703598 | + | 0.121867i | ||||
\(405\) | 7.07107 | 0.351364 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.00000 | 0.0991363 | ||||||||
\(408\) | 4.00000 | + | 6.92820i | 0.198030 | + | 0.342997i | ||||
\(409\) | 15.5563 | − | 26.9444i | 0.769212 | − | 1.33231i | −0.168779 | − | 0.985654i | \(-0.553982\pi\) |
0.937991 | − | 0.346660i | \(-0.112684\pi\) | |||||||
\(410\) | 4.00000 | − | 6.92820i | 0.197546 | − | 0.342160i | ||||
\(411\) | 1.41421 | + | 2.44949i | 0.0697580 | + | 0.120824i | ||||
\(412\) | 4.24264 | 0.209020 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.00000 | −0.0982946 | ||||||||
\(415\) | 2.00000 | + | 3.46410i | 0.0981761 | + | 0.170046i | ||||
\(416\) | −1.41421 | + | 2.44949i | −0.0693375 | + | 0.120096i | ||||
\(417\) | −2.00000 | + | 3.46410i | −0.0979404 | + | 0.169638i | ||||
\(418\) | 1.41421 | + | 2.44949i | 0.0691714 | + | 0.119808i | ||||
\(419\) | 12.7279 | 0.621800 | 0.310900 | − | 0.950443i | \(-0.399370\pi\) | ||||
0.310900 | + | 0.950443i | \(0.399370\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.00000 | 0.389896 | 0.194948 | − | 0.980814i | \(-0.437546\pi\) | ||||
0.194948 | + | 0.980814i | \(0.437546\pi\) | |||||||
\(422\) | 14.0000 | + | 24.2487i | 0.681509 | + | 1.18041i | ||||
\(423\) | −2.12132 | + | 3.67423i | −0.103142 | + | 0.178647i | ||||
\(424\) | −6.00000 | + | 10.3923i | −0.291386 | + | 0.504695i | ||||
\(425\) | 8.48528 | + | 14.6969i | 0.411597 | + | 0.712906i | ||||
\(426\) | 14.1421 | 0.685189 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −20.0000 | −0.966736 | ||||||||
\(429\) | −2.00000 | − | 3.46410i | −0.0965609 | − | 0.167248i | ||||
\(430\) | −2.82843 | + | 4.89898i | −0.136399 | + | 0.236250i | ||||
\(431\) | 10.0000 | − | 17.3205i | 0.481683 | − | 0.834300i | −0.518096 | − | 0.855323i | \(-0.673359\pi\) |
0.999779 | + | 0.0210230i | \(0.00669232\pi\) | |||||||
\(432\) | 2.82843 | + | 4.89898i | 0.136083 | + | 0.235702i | ||||
\(433\) | −38.1838 | −1.83499 | −0.917497 | − | 0.397742i | \(-0.869794\pi\) | ||||
−0.917497 | + | 0.397742i | \(0.869794\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.0000 | 0.575356 | ||||||||
\(436\) | −5.00000 | − | 8.66025i | −0.239457 | − | 0.414751i | ||||
\(437\) | −2.82843 | + | 4.89898i | −0.135302 | + | 0.234350i | ||||
\(438\) | 10.0000 | − | 17.3205i | 0.477818 | − | 0.827606i | ||||
\(439\) | −12.7279 | − | 22.0454i | −0.607471 | − | 1.05217i | −0.991656 | − | 0.128914i | \(-0.958851\pi\) |
0.384185 | − | 0.923256i | \(-0.374482\pi\) | |||||||
\(440\) | −1.41421 | −0.0674200 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16.0000 | 0.761042 | ||||||||
\(443\) | 6.00000 | + | 10.3923i | 0.285069 | + | 0.493753i | 0.972626 | − | 0.232377i | \(-0.0746503\pi\) |
−0.687557 | + | 0.726130i | \(0.741317\pi\) | |||||||
\(444\) | 1.41421 | − | 2.44949i | 0.0671156 | − | 0.116248i | ||||
\(445\) | 5.00000 | − | 8.66025i | 0.237023 | − | 0.410535i | ||||
\(446\) | 7.77817 | + | 13.4722i | 0.368307 | + | 0.637927i | ||||
\(447\) | −14.1421 | −0.668900 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.0000 | −0.566315 | −0.283158 | − | 0.959073i | \(-0.591382\pi\) | ||||
−0.283158 | + | 0.959073i | \(0.591382\pi\) | |||||||
\(450\) | 1.50000 | + | 2.59808i | 0.0707107 | + | 0.122474i | ||||
\(451\) | −2.82843 | + | 4.89898i | −0.133185 | + | 0.230684i | ||||
\(452\) | 9.00000 | − | 15.5885i | 0.423324 | − | 0.733219i | ||||
\(453\) | −11.3137 | − | 19.5959i | −0.531564 | − | 0.920697i | ||||
\(454\) | −28.2843 | −1.32745 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.00000 | 0.187317 | ||||||||
\(457\) | −1.00000 | − | 1.73205i | −0.0467780 | − | 0.0810219i | 0.841688 | − | 0.539964i | \(-0.181562\pi\) |
−0.888466 | + | 0.458942i | \(0.848229\pi\) | |||||||
\(458\) | 2.12132 | − | 3.67423i | 0.0991228 | − | 0.171686i | ||||
\(459\) | 16.0000 | − | 27.7128i | 0.746816 | − | 1.29352i | ||||
\(460\) | −1.41421 | − | 2.44949i | −0.0659380 | − | 0.114208i | ||||
\(461\) | −28.2843 | −1.31733 | −0.658665 | − | 0.752436i | \(-0.728879\pi\) | ||||
−0.658665 | + | 0.752436i | \(0.728879\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.0000 | −0.650635 | −0.325318 | − | 0.945605i | \(-0.605471\pi\) | ||||
−0.325318 | + | 0.945605i | \(0.605471\pi\) | |||||||
\(464\) | 3.00000 | + | 5.19615i | 0.139272 | + | 0.241225i | ||||
\(465\) | 1.41421 | − | 2.44949i | 0.0655826 | − | 0.113592i | ||||
\(466\) | 3.00000 | − | 5.19615i | 0.138972 | − | 0.240707i | ||||
\(467\) | 2.12132 | + | 3.67423i | 0.0981630 | + | 0.170023i | 0.910924 | − | 0.412574i | \(-0.135370\pi\) |
−0.812761 | + | 0.582597i | \(0.802037\pi\) | |||||||
\(468\) | 2.82843 | 0.130744 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6.00000 | −0.276759 | ||||||||
\(471\) | 13.0000 | + | 22.5167i | 0.599008 | + | 1.03751i | ||||
\(472\) | −2.12132 | + | 3.67423i | −0.0976417 | + | 0.169120i | ||||
\(473\) | 2.00000 | − | 3.46410i | 0.0919601 | − | 0.159280i | ||||
\(474\) | −5.65685 | − | 9.79796i | −0.259828 | − | 0.450035i | ||||
\(475\) | 8.48528 | 0.389331 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.0000 | 0.549442 | ||||||||
\(478\) | −8.00000 | − | 13.8564i | −0.365911 | − | 0.633777i | ||||
\(479\) | 12.7279 | − | 22.0454i | 0.581554 | − | 1.00728i | −0.413742 | − | 0.910394i | \(-0.635778\pi\) |
0.995295 | − | 0.0968862i | \(-0.0308883\pi\) | |||||||
\(480\) | −1.00000 | + | 1.73205i | −0.0456435 | + | 0.0790569i | ||||
\(481\) | −2.82843 | − | 4.89898i | −0.128965 | − | 0.223374i | ||||
\(482\) | −5.65685 | −0.257663 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 11.0000 | + | 19.0526i | 0.499484 | + | 0.865132i | ||||
\(486\) | 4.94975 | − | 8.57321i | 0.224525 | − | 0.388889i | ||||
\(487\) | −5.00000 | + | 8.66025i | −0.226572 | + | 0.392434i | −0.956790 | − | 0.290780i | \(-0.906085\pi\) |
0.730218 | + | 0.683214i | \(0.239418\pi\) | |||||||
\(488\) | 2.82843 | + | 4.89898i | 0.128037 | + | 0.221766i | ||||
\(489\) | −31.1127 | −1.40696 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.00000 | 0.180517 | 0.0902587 | − | 0.995918i | \(-0.471231\pi\) | ||||
0.0902587 | + | 0.995918i | \(0.471231\pi\) | |||||||
\(492\) | 4.00000 | + | 6.92820i | 0.180334 | + | 0.312348i | ||||
\(493\) | 16.9706 | − | 29.3939i | 0.764316 | − | 1.32383i | ||||
\(494\) | 4.00000 | − | 6.92820i | 0.179969 | − | 0.311715i | ||||
\(495\) | 0.707107 | + | 1.22474i | 0.0317821 | + | 0.0550482i | ||||
\(496\) | 1.41421 | 0.0635001 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.00000 | −0.179244 | ||||||||
\(499\) | 15.0000 | + | 25.9808i | 0.671492 | + | 1.16306i | 0.977481 | + | 0.211024i | \(0.0676797\pi\) |
−0.305989 | + | 0.952035i | \(0.598987\pi\) | |||||||
\(500\) | −5.65685 | + | 9.79796i | −0.252982 | + | 0.438178i | ||||
\(501\) | −8.00000 | + | 13.8564i | −0.357414 | + | 0.619059i | ||||
\(502\) | 12.0208 | + | 20.8207i | 0.536515 | + | 0.929272i | ||||
\(503\) | −19.7990 | −0.882793 | −0.441397 | − | 0.897312i | \(-0.645517\pi\) | ||||
−0.441397 | + | 0.897312i | \(0.645517\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.00000 | 0.177998 | ||||||||
\(506\) | 1.00000 | + | 1.73205i | 0.0444554 | + | 0.0769991i | ||||
\(507\) | 3.53553 | − | 6.12372i | 0.157019 | − | 0.271964i | ||||
\(508\) | −6.00000 | + | 10.3923i | −0.266207 | + | 0.461084i | ||||
\(509\) | 2.12132 | + | 3.67423i | 0.0940259 | + | 0.162858i | 0.909202 | − | 0.416356i | \(-0.136693\pi\) |
−0.815176 | + | 0.579214i | \(0.803360\pi\) | |||||||
\(510\) | 11.3137 | 0.500979 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −8.00000 | − | 13.8564i | −0.353209 | − | 0.611775i | ||||
\(514\) | 4.94975 | − | 8.57321i | 0.218324 | − | 0.378148i | ||||
\(515\) | 3.00000 | − | 5.19615i | 0.132196 | − | 0.228970i | ||||
\(516\) | −2.82843 | − | 4.89898i | −0.124515 | − | 0.215666i | ||||
\(517\) | 4.24264 | 0.186591 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.0000 | −0.877903 | ||||||||
\(520\) | 2.00000 | + | 3.46410i | 0.0877058 | + | 0.151911i | ||||
\(521\) | −7.77817 | + | 13.4722i | −0.340768 | + | 0.590228i | −0.984576 | − | 0.174960i | \(-0.944020\pi\) |
0.643808 | + | 0.765187i | \(0.277354\pi\) | |||||||
\(522\) | 3.00000 | − | 5.19615i | 0.131306 | − | 0.227429i | ||||
\(523\) | −8.48528 | − | 14.6969i | −0.371035 | − | 0.642652i | 0.618690 | − | 0.785635i | \(-0.287664\pi\) |
−0.989725 | + | 0.142983i | \(0.954331\pi\) | |||||||
\(524\) | −11.3137 | −0.494242 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | −4.00000 | − | 6.92820i | −0.174243 | − | 0.301797i | ||||
\(528\) | 0.707107 | − | 1.22474i | 0.0307729 | − | 0.0533002i | ||||
\(529\) | 9.50000 | − | 16.4545i | 0.413043 | − | 0.715412i | ||||
\(530\) | 8.48528 | + | 14.6969i | 0.368577 | + | 0.638394i | ||||
\(531\) | 4.24264 | 0.184115 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.0000 | 0.693037 | ||||||||
\(534\) | 5.00000 | + | 8.66025i | 0.216371 | + | 0.374766i | ||||
\(535\) | −14.1421 | + | 24.4949i | −0.611418 | + | 1.05901i | ||||
\(536\) | −1.00000 | + | 1.73205i | −0.0431934 | + | 0.0748132i | ||||
\(537\) | −14.1421 | − | 24.4949i | −0.610278 | − | 1.05703i | ||||
\(538\) | −24.0416 | −1.03651 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 8.00000 | 0.344265 | ||||||||
\(541\) | 9.00000 | + | 15.5885i | 0.386940 | + | 0.670200i | 0.992036 | − | 0.125952i | \(-0.0401986\pi\) |
−0.605096 | + | 0.796152i | \(0.706865\pi\) | |||||||
\(542\) | −4.24264 | + | 7.34847i | −0.182237 | + | 0.315644i | ||||
\(543\) | 9.00000 | − | 15.5885i | 0.386227 | − | 0.668965i | ||||
\(544\) | 2.82843 | + | 4.89898i | 0.121268 | + | 0.210042i | ||||
\(545\) | −14.1421 | −0.605783 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.0000 | 1.19719 | 0.598597 | − | 0.801050i | \(-0.295725\pi\) | ||||
0.598597 | + | 0.801050i | \(0.295725\pi\) | |||||||
\(548\) | 1.00000 | + | 1.73205i | 0.0427179 | + | 0.0739895i | ||||
\(549\) | 2.82843 | − | 4.89898i | 0.120714 | − | 0.209083i | ||||
\(550\) | 1.50000 | − | 2.59808i | 0.0639602 | − | 0.110782i | ||||
\(551\) | −8.48528 | − | 14.6969i | −0.361485 | − | 0.626111i | ||||
\(552\) | 2.82843 | 0.120386 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 10.0000 | 0.424859 | ||||||||
\(555\) | −2.00000 | − | 3.46410i | −0.0848953 | − | 0.147043i | ||||
\(556\) | −1.41421 | + | 2.44949i | −0.0599760 | + | 0.103882i | ||||
\(557\) | 9.00000 | − | 15.5885i | 0.381342 | − | 0.660504i | −0.609912 | − | 0.792469i | \(-0.708795\pi\) |
0.991254 | + | 0.131965i | \(0.0421286\pi\) | |||||||
\(558\) | −0.707107 | − | 1.22474i | −0.0299342 | − | 0.0518476i | ||||
\(559\) | −11.3137 | −0.478519 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.00000 | −0.337760 | ||||||||
\(562\) | 9.00000 | + | 15.5885i | 0.379642 | + | 0.657559i | ||||
\(563\) | −7.07107 | + | 12.2474i | −0.298010 | + | 0.516168i | −0.975681 | − | 0.219197i | \(-0.929656\pi\) |
0.677671 | + | 0.735366i | \(0.262990\pi\) | |||||||
\(564\) | 3.00000 | − | 5.19615i | 0.126323 | − | 0.218797i | ||||
\(565\) | −12.7279 | − | 22.0454i | −0.535468 | − | 0.927457i | ||||
\(566\) | 16.9706 | 0.713326 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.0000 | 0.419591 | ||||||||
\(569\) | 3.00000 | + | 5.19615i | 0.125767 | + | 0.217834i | 0.922032 | − | 0.387113i | \(-0.126528\pi\) |
−0.796266 | + | 0.604947i | \(0.793194\pi\) | |||||||
\(570\) | 2.82843 | − | 4.89898i | 0.118470 | − | 0.205196i | ||||
\(571\) | −4.00000 | + | 6.92820i | −0.167395 | + | 0.289936i | −0.937503 | − | 0.347977i | \(-0.886869\pi\) |
0.770108 | + | 0.637913i | \(0.220202\pi\) | |||||||
\(572\) | −1.41421 | − | 2.44949i | −0.0591312 | − | 0.102418i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.00000 | 0.250217 | ||||||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | −14.8492 | + | 25.7196i | −0.618182 | + | 1.07072i | 0.371635 | + | 0.928379i | \(0.378797\pi\) |
−0.989817 | + | 0.142344i | \(0.954536\pi\) | |||||||
\(578\) | 7.50000 | − | 12.9904i | 0.311959 | − | 0.540329i | ||||
\(579\) | −4.24264 | − | 7.34847i | −0.176318 | − | 0.305392i | ||||
\(580\) | 8.48528 | 0.352332 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −22.0000 | −0.911929 | ||||||||
\(583\) | −6.00000 | − | 10.3923i | −0.248495 | − | 0.430405i | ||||
\(584\) | 7.07107 | − | 12.2474i | 0.292603 | − | 0.506803i | ||||
\(585\) | 2.00000 | − | 3.46410i | 0.0826898 | − | 0.143223i | ||||
\(586\) | −8.48528 | − | 14.6969i | −0.350524 | − | 0.607125i | ||||
\(587\) | 1.41421 | 0.0583708 | 0.0291854 | − | 0.999574i | \(-0.490709\pi\) | ||||
0.0291854 | + | 0.999574i | \(0.490709\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.00000 | −0.164817 | ||||||||
\(590\) | 3.00000 | + | 5.19615i | 0.123508 | + | 0.213922i | ||||
\(591\) | −12.7279 | + | 22.0454i | −0.523557 | + | 0.906827i | ||||
\(592\) | 1.00000 | − | 1.73205i | 0.0410997 | − | 0.0711868i | ||||
\(593\) | 9.89949 | + | 17.1464i | 0.406524 | + | 0.704119i | 0.994497 | − | 0.104760i | \(-0.0334076\pi\) |
−0.587974 | + | 0.808880i | \(0.700074\pi\) | |||||||
\(594\) | −5.65685 | −0.232104 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.0000 | −0.409616 | ||||||||
\(597\) | 15.0000 | + | 25.9808i | 0.613909 | + | 1.06332i | ||||
\(598\) | 2.82843 | − | 4.89898i | 0.115663 | − | 0.200334i | ||||
\(599\) | −9.00000 | + | 15.5885i | −0.367730 | + | 0.636927i | −0.989210 | − | 0.146503i | \(-0.953198\pi\) |
0.621480 | + | 0.783430i | \(0.286532\pi\) | |||||||
\(600\) | −2.12132 | − | 3.67423i | −0.0866025 | − | 0.150000i | ||||
\(601\) | −45.2548 | −1.84598 | −0.922992 | − | 0.384820i | \(-0.874263\pi\) | ||||
−0.922992 | + | 0.384820i | \(0.874263\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.00000 | 0.0814463 | ||||||||
\(604\) | −8.00000 | − | 13.8564i | −0.325515 | − | 0.563809i | ||||
\(605\) | 0.707107 | − | 1.22474i | 0.0287480 | − | 0.0497930i | ||||
\(606\) | −2.00000 | + | 3.46410i | −0.0812444 | + | 0.140720i | ||||
\(607\) | −16.9706 | − | 29.3939i | −0.688814 | − | 1.19306i | −0.972222 | − | 0.234061i | \(-0.924798\pi\) |
0.283408 | − | 0.958999i | \(-0.408535\pi\) | |||||||
\(608\) | 2.82843 | 0.114708 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.00000 | 0.323911 | ||||||||
\(611\) | −6.00000 | − | 10.3923i | −0.242734 | − | 0.420428i | ||||
\(612\) | 2.82843 | − | 4.89898i | 0.114332 | − | 0.198030i | ||||
\(613\) | 17.0000 | − | 29.4449i | 0.686624 | − | 1.18927i | −0.286300 | − | 0.958140i | \(-0.592425\pi\) |
0.972924 | − | 0.231127i | \(-0.0742412\pi\) | |||||||
\(614\) | 5.65685 | + | 9.79796i | 0.228292 | + | 0.395413i | ||||
\(615\) | 11.3137 | 0.456213 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.00000 | −0.241551 | −0.120775 | − | 0.992680i | \(-0.538538\pi\) | ||||
−0.120775 | + | 0.992680i | \(0.538538\pi\) | |||||||
\(618\) | 3.00000 | + | 5.19615i | 0.120678 | + | 0.209020i | ||||
\(619\) | 6.36396 | − | 11.0227i | 0.255789 | − | 0.443040i | −0.709320 | − | 0.704886i | \(-0.750998\pi\) |
0.965110 | + | 0.261846i | \(0.0843314\pi\) | |||||||
\(620\) | 1.00000 | − | 1.73205i | 0.0401610 | − | 0.0695608i | ||||
\(621\) | −5.65685 | − | 9.79796i | −0.227002 | − | 0.393179i | ||||
\(622\) | −9.89949 | −0.396934 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.00000 | −0.160128 | ||||||||
\(625\) | 0.500000 | + | 0.866025i | 0.0200000 | + | 0.0346410i | ||||
\(626\) | −13.4350 | + | 23.2702i | −0.536972 | + | 0.930062i | ||||
\(627\) | −2.00000 | + | 3.46410i | −0.0798723 | + | 0.138343i | ||||
\(628\) | 9.19239 | + | 15.9217i | 0.366816 | + | 0.635344i | ||||
\(629\) | −11.3137 | −0.451107 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | −4.00000 | − | 6.92820i | −0.159111 | − | 0.275589i | ||||
\(633\) | −19.7990 | + | 34.2929i | −0.786939 | + | 1.36302i | ||||
\(634\) | −13.0000 | + | 22.5167i | −0.516296 | + | 0.894251i | ||||
\(635\) | 8.48528 | + | 14.6969i | 0.336728 | + | 0.583230i | ||||
\(636\) | −16.9706 | −0.672927 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.00000 | −0.237542 | ||||||||
\(639\) | −5.00000 | − | 8.66025i | −0.197797 | − | 0.342594i | ||||
\(640\) | −0.707107 | + | 1.22474i | −0.0279508 | + | 0.0484123i | ||||
\(641\) | −15.0000 | + | 25.9808i | −0.592464 | + | 1.02618i | 0.401435 | + | 0.915888i | \(0.368512\pi\) |
−0.993899 | + | 0.110291i | \(0.964822\pi\) | |||||||
\(642\) | −14.1421 | − | 24.4949i | −0.558146 | − | 0.966736i | ||||
\(643\) | 12.7279 | 0.501940 | 0.250970 | − | 0.967995i | \(-0.419250\pi\) | ||||
0.250970 | + | 0.967995i | \(0.419250\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.00000 | −0.315000 | ||||||||
\(646\) | −8.00000 | − | 13.8564i | −0.314756 | − | 0.545173i | ||||
\(647\) | 20.5061 | − | 35.5176i | 0.806178 | − | 1.39634i | −0.109315 | − | 0.994007i | \(-0.534866\pi\) |
0.915493 | − | 0.402334i | \(-0.131801\pi\) | |||||||
\(648\) | −2.50000 | + | 4.33013i | −0.0982093 | + | 0.170103i | ||||
\(649\) | −2.12132 | − | 3.67423i | −0.0832691 | − | 0.144226i | ||||
\(650\) | −8.48528 | −0.332820 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −22.0000 | −0.861586 | ||||||||
\(653\) | 24.0000 | + | 41.5692i | 0.939193 | + | 1.62673i | 0.766982 | + | 0.641669i | \(0.221758\pi\) |
0.172211 | + | 0.985060i | \(0.444909\pi\) | |||||||
\(654\) | 7.07107 | − | 12.2474i | 0.276501 | − | 0.478913i | ||||
\(655\) | −8.00000 | + | 13.8564i | −0.312586 | + | 0.541415i | ||||
\(656\) | 2.82843 | + | 4.89898i | 0.110432 | + | 0.191273i | ||||
\(657\) | −14.1421 | −0.551737 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.00000 | −0.155818 | −0.0779089 | − | 0.996960i | \(-0.524824\pi\) | ||||
−0.0779089 | + | 0.996960i | \(0.524824\pi\) | |||||||
\(660\) | −1.00000 | − | 1.73205i | −0.0389249 | − | 0.0674200i | ||||
\(661\) | 19.0919 | − | 33.0681i | 0.742588 | − | 1.28620i | −0.208725 | − | 0.977974i | \(-0.566931\pi\) |
0.951313 | − | 0.308226i | \(-0.0997353\pi\) | |||||||
\(662\) | 14.0000 | − | 24.2487i | 0.544125 | − | 0.942453i | ||||
\(663\) | 11.3137 | + | 19.5959i | 0.439388 | + | 0.761042i | ||||
\(664\) | −2.82843 | −0.109764 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.00000 | −0.0774984 | ||||||||
\(667\) | −6.00000 | − | 10.3923i | −0.232321 | − | 0.402392i | ||||
\(668\) | −5.65685 | + | 9.79796i | −0.218870 | + | 0.379094i | ||||
\(669\) | −11.0000 | + | 19.0526i | −0.425285 | + | 0.736614i | ||||
\(670\) | 1.41421 | + | 2.44949i | 0.0546358 | + | 0.0946320i | ||||
\(671\) | −5.65685 | −0.218380 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.00000 | 0.0770943 | 0.0385472 | − | 0.999257i | \(-0.487727\pi\) | ||||
0.0385472 | + | 0.999257i | \(0.487727\pi\) | |||||||
\(674\) | −1.00000 | − | 1.73205i | −0.0385186 | − | 0.0667161i | ||||
\(675\) | −8.48528 | + | 14.6969i | −0.326599 | + | 0.565685i | ||||
\(676\) | 2.50000 | − | 4.33013i | 0.0961538 | − | 0.166543i | ||||
\(677\) | 15.5563 | + | 26.9444i | 0.597879 | + | 1.03556i | 0.993134 | + | 0.116985i | \(0.0373230\pi\) |
−0.395255 | + | 0.918572i | \(0.629344\pi\) | |||||||
\(678\) | 25.4558 | 0.977626 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 8.00000 | 0.306786 | ||||||||
\(681\) | −20.0000 | − | 34.6410i | −0.766402 | − | 1.32745i | ||||
\(682\) | −0.707107 | + | 1.22474i | −0.0270765 | + | 0.0468979i | ||||
\(683\) | 6.00000 | − | 10.3923i | 0.229584 | − | 0.397650i | −0.728101 | − | 0.685470i | \(-0.759597\pi\) |
0.957685 | + | 0.287819i | \(0.0929302\pi\) | |||||||
\(684\) | −1.41421 | − | 2.44949i | −0.0540738 | − | 0.0936586i | ||||
\(685\) | 2.82843 | 0.108069 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.00000 | 0.228914 | ||||||||
\(688\) | −2.00000 | − | 3.46410i | −0.0762493 | − | 0.132068i | ||||
\(689\) | −16.9706 | + | 29.3939i | −0.646527 | + | 1.11982i | ||||
\(690\) | 2.00000 | − | 3.46410i | 0.0761387 | − | 0.131876i | ||||
\(691\) | −16.2635 | − | 28.1691i | −0.618691 | − | 1.07160i | −0.989725 | − | 0.142985i | \(-0.954330\pi\) |
0.371034 | − | 0.928619i | \(-0.379003\pi\) | |||||||
\(692\) | −14.1421 | −0.537603 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.00000 | + | 3.46410i | 0.0758643 | + | 0.131401i | ||||
\(696\) | −4.24264 | + | 7.34847i | −0.160817 | + | 0.278543i | ||||
\(697\) | 16.0000 | − | 27.7128i | 0.606043 | − | 1.04970i | ||||
\(698\) | 2.82843 | + | 4.89898i | 0.107058 | + | 0.185429i | ||||
\(699\) | 8.48528 | 0.320943 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.0000 | −0.377695 | −0.188847 | − | 0.982006i | \(-0.560475\pi\) | ||||
−0.188847 | + | 0.982006i | \(0.560475\pi\) | |||||||
\(702\) | 8.00000 | + | 13.8564i | 0.301941 | + | 0.522976i | ||||
\(703\) | −2.82843 | + | 4.89898i | −0.106676 | + | 0.184769i | ||||
\(704\) | 0.500000 | − | 0.866025i | 0.0188445 | − | 0.0326396i | ||||
\(705\) | −4.24264 | − | 7.34847i | −0.159787 | − | 0.276759i | ||||
\(706\) | 1.41421 | 0.0532246 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.00000 | −0.225494 | ||||||||
\(709\) | 4.00000 | + | 6.92820i | 0.150223 | + | 0.260194i | 0.931309 | − | 0.364229i | \(-0.118667\pi\) |
−0.781086 | + | 0.624423i | \(0.785334\pi\) | |||||||
\(710\) | 7.07107 | − | 12.2474i | 0.265372 | − | 0.459639i | ||||
\(711\) | −4.00000 | + | 6.92820i | −0.150012 | + | 0.259828i | ||||
\(712\) | 3.53553 | + | 6.12372i | 0.132500 | + | 0.229496i | ||||
\(713\) | −2.82843 | −0.105925 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.00000 | −0.149592 | ||||||||
\(716\) | −10.0000 | − | 17.3205i | −0.373718 | − | 0.647298i | ||||
\(717\) | 11.3137 | − | 19.5959i | 0.422518 | − | 0.731823i | ||||
\(718\) | 16.0000 | − | 27.7128i | 0.597115 | − | 1.03423i | ||||
\(719\) | −7.77817 | − | 13.4722i | −0.290077 | − | 0.502428i | 0.683751 | − | 0.729716i | \(-0.260348\pi\) |
−0.973828 | + | 0.227288i | \(0.927014\pi\) | |||||||
\(720\) | 1.41421 | 0.0527046 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 11.0000 | 0.409378 | ||||||||
\(723\) | −4.00000 | − | 6.92820i | −0.148762 | − | 0.257663i | ||||
\(724\) | 6.36396 | − | 11.0227i | 0.236515 | − | 0.409656i | ||||
\(725\) | −9.00000 | + | 15.5885i | −0.334252 | + | 0.578941i | ||||
\(726\) | 0.707107 | + | 1.22474i | 0.0262432 | + | 0.0454545i | ||||
\(727\) | 32.5269 | 1.20636 | 0.603178 | − | 0.797606i | \(-0.293901\pi\) | ||||
0.603178 | + | 0.797606i | \(0.293901\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | −10.0000 | − | 17.3205i | −0.370117 | − | 0.641061i | ||||
\(731\) | −11.3137 | + | 19.5959i | −0.418453 | + | 0.724781i | ||||
\(732\) | −4.00000 | + | 6.92820i | −0.147844 | + | 0.256074i | ||||
\(733\) | −8.48528 | − | 14.6969i | −0.313411 | − | 0.542844i | 0.665687 | − | 0.746231i | \(-0.268138\pi\) |
−0.979098 | + | 0.203387i | \(0.934805\pi\) | |||||||
\(734\) | 29.6985 | 1.09619 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.00000 | 0.0737210 | ||||||||
\(737\) | −1.00000 | − | 1.73205i | −0.0368355 | − | 0.0638009i | ||||
\(738\) | 2.82843 | − | 4.89898i | 0.104116 | − | 0.180334i | ||||
\(739\) | 12.0000 | − | 20.7846i | 0.441427 | − | 0.764574i | −0.556369 | − | 0.830936i | \(-0.687806\pi\) |
0.997796 | + | 0.0663614i | \(0.0211390\pi\) | |||||||
\(740\) | −1.41421 | − | 2.44949i | −0.0519875 | − | 0.0900450i | ||||
\(741\) | 11.3137 | 0.415619 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −48.0000 | −1.76095 | −0.880475 | − | 0.474093i | \(-0.842776\pi\) | ||||
−0.880475 | + | 0.474093i | \(0.842776\pi\) | |||||||
\(744\) | 1.00000 | + | 1.73205i | 0.0366618 | + | 0.0635001i | ||||
\(745\) | −7.07107 | + | 12.2474i | −0.259064 | + | 0.448712i | ||||
\(746\) | −7.00000 | + | 12.1244i | −0.256288 | + | 0.443904i | ||||
\(747\) | 1.41421 | + | 2.44949i | 0.0517434 | + | 0.0896221i | ||||
\(748\) | −5.65685 | −0.206835 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −16.0000 | −0.584237 | ||||||||
\(751\) | −13.0000 | − | 22.5167i | −0.474377 | − | 0.821645i | 0.525193 | − | 0.850983i | \(-0.323993\pi\) |
−0.999570 | + | 0.0293387i | \(0.990660\pi\) | |||||||
\(752\) | 2.12132 | − | 3.67423i | 0.0773566 | − | 0.133986i | ||||
\(753\) | −17.0000 | + | 29.4449i | −0.619514 | + | 1.07303i | ||||
\(754\) | 8.48528 | + | 14.6969i | 0.309016 | + | 0.535231i | ||||
\(755\) | −22.6274 | −0.823496 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −44.0000 | −1.59921 | −0.799604 | − | 0.600528i | \(-0.794957\pi\) | ||||
−0.799604 | + | 0.600528i | \(0.794957\pi\) | |||||||
\(758\) | 3.00000 | + | 5.19615i | 0.108965 | + | 0.188733i | ||||
\(759\) | −1.41421 | + | 2.44949i | −0.0513327 | + | 0.0889108i | ||||
\(760\) | 2.00000 | − | 3.46410i | 0.0725476 | − | 0.125656i | ||||
\(761\) | 12.7279 | + | 22.0454i | 0.461387 | + | 0.799145i | 0.999030 | − | 0.0440268i | \(-0.0140187\pi\) |
−0.537644 | + | 0.843172i | \(0.680685\pi\) | |||||||
\(762\) | −16.9706 | −0.614779 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.00000 | − | 6.92820i | −0.144620 | − | 0.250490i | ||||
\(766\) | −13.4350 | + | 23.2702i | −0.485427 | + | 0.840785i | ||||
\(767\) | −6.00000 | + | 10.3923i | −0.216647 | + | 0.375244i | ||||
\(768\) | −0.707107 | − | 1.22474i | −0.0255155 | − | 0.0441942i | ||||
\(769\) | −8.48528 | −0.305987 | −0.152994 | − | 0.988227i | \(-0.548891\pi\) | ||||
−0.152994 | + | 0.988227i | \(0.548891\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.0000 | 0.504198 | ||||||||
\(772\) | −3.00000 | − | 5.19615i | −0.107972 | − | 0.187014i | ||||
\(773\) | −0.707107 | + | 1.22474i | −0.0254329 | + | 0.0440510i | −0.878462 | − | 0.477813i | \(-0.841430\pi\) |
0.853029 | + | 0.521864i | \(0.174763\pi\) | |||||||
\(774\) | −2.00000 | + | 3.46410i | −0.0718885 | + | 0.124515i | ||||
\(775\) | 2.12132 | + | 3.67423i | 0.0762001 | + | 0.131982i | ||||
\(776\) | −15.5563 | −0.558440 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 28.0000 | 1.00385 | ||||||||
\(779\) | −8.00000 | − | 13.8564i | −0.286630 | − | 0.496457i | ||||
\(780\) | −2.82843 | + | 4.89898i | −0.101274 | + | 0.175412i | ||||
\(781\) | −5.00000 | + | 8.66025i | −0.178914 | + | 0.309888i | ||||
\(782\) | −5.65685 | − | 9.79796i | −0.202289 | − | 0.350374i | ||||
\(783\) | 33.9411 | 1.21296 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 26.0000 | 0.927980 | ||||||||
\(786\) | −8.00000 | − | 13.8564i | −0.285351 | − | 0.494242i | ||||
\(787\) | 21.2132 | − | 36.7423i | 0.756169 | − | 1.30972i | −0.188622 | − | 0.982050i | \(-0.560402\pi\) |
0.944791 | − | 0.327673i | \(-0.106265\pi\) | |||||||
\(788\) | −9.00000 | + | 15.5885i | −0.320612 | + | 0.555316i | ||||
\(789\) | −16.9706 | − | 29.3939i | −0.604168 | − | 1.04645i | ||||
\(790\) | −11.3137 | −0.402524 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | 8.00000 | + | 13.8564i | 0.284088 | + | 0.492055i | ||||
\(794\) | 12.0208 | − | 20.8207i | 0.426603 | − | 0.738898i | ||||
\(795\) | −12.0000 | + | 20.7846i | −0.425596 | + | 0.737154i | ||||
\(796\) | 10.6066 | + | 18.3712i | 0.375941 | + | 0.651149i | ||||
\(797\) | 18.3848 | 0.651222 | 0.325611 | − | 0.945504i | \(-0.394430\pi\) | ||||
0.325611 | + | 0.945504i | \(0.394430\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | −1.50000 | − | 2.59808i | −0.0530330 | − | 0.0918559i | ||||
\(801\) | 3.53553 | − | 6.12372i | 0.124922 | − | 0.216371i | ||||
\(802\) | 18.0000 | − | 31.1769i | 0.635602 | − | 1.10090i | ||||
\(803\) | 7.07107 | + | 12.2474i | 0.249533 | + | 0.432203i | ||||
\(804\) | −2.82843 | −0.0997509 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.00000 | 0.140894 | ||||||||
\(807\) | −17.0000 | − | 29.4449i | −0.598428 | − | 1.03651i | ||||
\(808\) | −1.41421 | + | 2.44949i | −0.0497519 | + | 0.0861727i | ||||
\(809\) | 3.00000 | − | 5.19615i | 0.105474 | − | 0.182687i | −0.808458 | − | 0.588555i | \(-0.799697\pi\) |
0.913932 | + | 0.405868i | \(0.133031\pi\) | |||||||
\(810\) | 3.53553 | + | 6.12372i | 0.124226 | + | 0.215166i | ||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.0000 | −0.420858 | ||||||||
\(814\) | 1.00000 | + | 1.73205i | 0.0350500 | + | 0.0607083i | ||||
\(815\) | −15.5563 | + | 26.9444i | −0.544915 | + | 0.943821i | ||||
\(816\) | −4.00000 | + | 6.92820i | −0.140028 | + | 0.242536i | ||||
\(817\) | 5.65685 | + | 9.79796i | 0.197908 | + | 0.342787i | ||||
\(818\) | 31.1127 | 1.08783 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.00000 | 0.279372 | ||||||||
\(821\) | −17.0000 | − | 29.4449i | −0.593304 | − | 1.02763i | −0.993784 | − | 0.111327i | \(-0.964490\pi\) |
0.400480 | − | 0.916306i | \(-0.368843\pi\) | |||||||
\(822\) | −1.41421 | + | 2.44949i | −0.0493264 | + | 0.0854358i | ||||
\(823\) | 16.0000 | − | 27.7128i | 0.557725 | − | 0.966008i | −0.439961 | − | 0.898017i | \(-0.645008\pi\) |
0.997686 | − | 0.0679910i | \(-0.0216589\pi\) | |||||||
\(824\) | 2.12132 | + | 3.67423i | 0.0738997 | + | 0.127998i | ||||
\(825\) | 4.24264 | 0.147710 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.00000 | −0.278187 | −0.139094 | − | 0.990279i | \(-0.544419\pi\) | ||||
−0.139094 | + | 0.990279i | \(0.544419\pi\) | |||||||
\(828\) | −1.00000 | − | 1.73205i | −0.0347524 | − | 0.0601929i | ||||
\(829\) | −17.6777 | + | 30.6186i | −0.613971 | + | 1.06343i | 0.376593 | + | 0.926379i | \(0.377095\pi\) |
−0.990564 | + | 0.137050i | \(0.956238\pi\) | |||||||
\(830\) | −2.00000 | + | 3.46410i | −0.0694210 | + | 0.120241i | ||||
\(831\) | 7.07107 | + | 12.2474i | 0.245293 | + | 0.424859i | ||||
\(832\) | −2.82843 | −0.0980581 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.00000 | −0.138509 | ||||||||
\(835\) | 8.00000 | + | 13.8564i | 0.276851 | + | 0.479521i | ||||
\(836\) | −1.41421 | + | 2.44949i | −0.0489116 | + | 0.0847174i | ||||
\(837\) | 4.00000 | − | 6.92820i | 0.138260 | − | 0.239474i | ||||
\(838\) | 6.36396 | + | 11.0227i | 0.219839 | + | 0.380773i | ||||
\(839\) | 43.8406 | 1.51355 | 0.756773 | − | 0.653678i | \(-0.226775\pi\) | ||||
0.756773 | + | 0.653678i | \(0.226775\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 4.00000 | + | 6.92820i | 0.137849 | + | 0.238762i | ||||
\(843\) | −12.7279 | + | 22.0454i | −0.438373 | + | 0.759284i | ||||
\(844\) | −14.0000 | + | 24.2487i | −0.481900 | + | 0.834675i | ||||
\(845\) | −3.53553 | − | 6.12372i | −0.121626 | − | 0.210663i | ||||
\(846\) | −4.24264 | −0.145865 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −12.0000 | −0.412082 | ||||||||
\(849\) | 12.0000 | + | 20.7846i | 0.411839 | + | 0.713326i | ||||
\(850\) | −8.48528 | + | 14.6969i | −0.291043 | + | 0.504101i | ||||
\(851\) | −2.00000 | + | 3.46410i | −0.0685591 | + | 0.118748i | ||||
\(852\) | 7.07107 | + | 12.2474i | 0.242251 | + | 0.419591i | ||||
\(853\) | 2.82843 | 0.0968435 | 0.0484218 | − | 0.998827i | \(-0.484581\pi\) | ||||
0.0484218 | + | 0.998827i | \(0.484581\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.00000 | −0.136797 | ||||||||
\(856\) | −10.0000 | − | 17.3205i | −0.341793 | − | 0.592003i | ||||
\(857\) | −4.24264 | + | 7.34847i | −0.144926 | + | 0.251019i | −0.929345 | − | 0.369212i | \(-0.879628\pi\) |
0.784419 | + | 0.620231i | \(0.212961\pi\) | |||||||
\(858\) | 2.00000 | − | 3.46410i | 0.0682789 | − | 0.118262i | ||||
\(859\) | 19.0919 | + | 33.0681i | 0.651407 | + | 1.12827i | 0.982782 | + | 0.184770i | \(0.0591541\pi\) |
−0.331375 | + | 0.943499i | \(0.607513\pi\) | |||||||
\(860\) | −5.65685 | −0.192897 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.0000 | 0.681203 | ||||||||
\(863\) | 16.0000 | + | 27.7128i | 0.544646 | + | 0.943355i | 0.998629 | + | 0.0523446i | \(0.0166694\pi\) |
−0.453983 | + | 0.891010i | \(0.649997\pi\) | |||||||
\(864\) | −2.82843 | + | 4.89898i | −0.0962250 | + | 0.166667i | ||||
\(865\) | −10.0000 | + | 17.3205i | −0.340010 | + | 0.588915i | ||||
\(866\) | −19.0919 | − | 33.0681i | −0.648769 | − | 1.12370i | ||||
\(867\) | 21.2132 | 0.720438 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.00000 | 0.271381 | ||||||||
\(870\) | 6.00000 | + | 10.3923i | 0.203419 | + | 0.352332i | ||||
\(871\) | −2.82843 | + | 4.89898i | −0.0958376 | + | 0.165996i | ||||
\(872\) | 5.00000 | − | 8.66025i | 0.169321 | − | 0.293273i | ||||
\(873\) | 7.77817 | + | 13.4722i | 0.263251 | + | 0.455965i | ||||
\(874\) | −5.65685 | −0.191346 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 20.0000 | 0.675737 | ||||||||
\(877\) | 5.00000 | + | 8.66025i | 0.168838 | + | 0.292436i | 0.938012 | − | 0.346604i | \(-0.112665\pi\) |
−0.769174 | + | 0.639040i | \(0.779332\pi\) | |||||||
\(878\) | 12.7279 | − | 22.0454i | 0.429547 | − | 0.743996i | ||||
\(879\) | 12.0000 | − | 20.7846i | 0.404750 | − | 0.701047i | ||||
\(880\) | −0.707107 | − | 1.22474i | −0.0238366 | − | 0.0412861i | ||||
\(881\) | −4.24264 | −0.142938 | −0.0714691 | − | 0.997443i | \(-0.522769\pi\) | ||||
−0.0714691 | + | 0.997443i | \(0.522769\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.0000 | 1.21150 | 0.605748 | − | 0.795656i | \(-0.292874\pi\) | ||||
0.605748 | + | 0.795656i | \(0.292874\pi\) | |||||||
\(884\) | 8.00000 | + | 13.8564i | 0.269069 | + | 0.466041i | ||||
\(885\) | −4.24264 | + | 7.34847i | −0.142615 | + | 0.247016i | ||||
\(886\) | −6.00000 | + | 10.3923i | −0.201574 | + | 0.349136i | ||||
\(887\) | 24.0416 | + | 41.6413i | 0.807239 | + | 1.39818i | 0.914769 | + | 0.403977i | \(0.132372\pi\) |
−0.107530 | + | 0.994202i | \(0.534294\pi\) | |||||||
\(888\) | 2.82843 | 0.0949158 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 10.0000 | 0.335201 | ||||||||
\(891\) | −2.50000 | − | 4.33013i | −0.0837532 | − | 0.145065i | ||||
\(892\) | −7.77817 | + | 13.4722i | −0.260433 | + | 0.451082i | ||||
\(893\) | −6.00000 | + | 10.3923i | −0.200782 | + | 0.347765i | ||||
\(894\) | −7.07107 | − | 12.2474i | −0.236492 | − | 0.409616i | ||||
\(895\) | −28.2843 | −0.945439 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.00000 | 0.267112 | ||||||||
\(898\) | −6.00000 | − | 10.3923i | −0.200223 | − | 0.346796i | ||||
\(899\) | 4.24264 | − | 7.34847i | 0.141500 | − | 0.245085i | ||||
\(900\) | −1.50000 | + | 2.59808i | −0.0500000 | + | 0.0866025i | ||||
\(901\) | 33.9411 | + | 58.7878i | 1.13074 | + | 1.95850i | ||||
\(902\) | −5.65685 | −0.188353 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.0000 | 0.598671 | ||||||||
\(905\) | −9.00000 | − | 15.5885i | −0.299170 | − | 0.518178i | ||||
\(906\) | 11.3137 | − | 19.5959i | 0.375873 | − | 0.651031i | ||||
\(907\) | 13.0000 | − | 22.5167i | 0.431658 | − | 0.747653i | −0.565358 | − | 0.824845i | \(-0.691262\pi\) |
0.997016 | + | 0.0771920i | \(0.0245954\pi\) | |||||||
\(908\) | −14.1421 | − | 24.4949i | −0.469323 | − | 0.812892i | ||||
\(909\) | 2.82843 | 0.0938130 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.0000 | 0.993944 | 0.496972 | − | 0.867766i | \(-0.334445\pi\) | ||||
0.496972 | + | 0.867766i | \(0.334445\pi\) | |||||||
\(912\) | 2.00000 | + | 3.46410i | 0.0662266 | + | 0.114708i | ||||
\(913\) | 1.41421 | − | 2.44949i | 0.0468036 | − | 0.0810663i | ||||
\(914\) | 1.00000 | − | 1.73205i | 0.0330771 | − | 0.0572911i | ||||
\(915\) | 5.65685 | + | 9.79796i | 0.187010 | + | 0.323911i | ||||
\(916\) | 4.24264 | 0.140181 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 32.0000 | 1.05616 | ||||||||
\(919\) | −16.0000 | − | 27.7128i | −0.527791 | − | 0.914161i | −0.999475 | − | 0.0323936i | \(-0.989687\pi\) |
0.471684 | − | 0.881768i | \(-0.343646\pi\) | |||||||
\(920\) | 1.41421 | − | 2.44949i | 0.0466252 | − | 0.0807573i | ||||
\(921\) | −8.00000 | + | 13.8564i | −0.263609 | + | 0.456584i | ||||
\(922\) | −14.1421 | − | 24.4949i | −0.465746 | − | 0.806696i | ||||
\(923\) | 28.2843 | 0.930988 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | −7.00000 | − | 12.1244i | −0.230034 | − | 0.398431i | ||||
\(927\) | 2.12132 | − | 3.67423i | 0.0696733 | − | 0.120678i | ||||
\(928\) | −3.00000 | + | 5.19615i | −0.0984798 | + | 0.170572i | ||||
\(929\) | −7.77817 | − | 13.4722i | −0.255194 | − | 0.442008i | 0.709754 | − | 0.704449i | \(-0.248806\pi\) |
−0.964948 | + | 0.262441i | \(0.915473\pi\) | |||||||
\(930\) | 2.82843 | 0.0927478 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6.00000 | 0.196537 | ||||||||
\(933\) | −7.00000 | − | 12.1244i | −0.229170 | − | 0.396934i | ||||
\(934\) | −2.12132 | + | 3.67423i | −0.0694117 | + | 0.120225i | ||||
\(935\) | −4.00000 | + | 6.92820i | −0.130814 | + | 0.226576i | ||||
\(936\) | 1.41421 | + | 2.44949i | 0.0462250 | + | 0.0800641i | ||||
\(937\) | 25.4558 | 0.831606 | 0.415803 | − | 0.909455i | \(-0.363501\pi\) | ||||
0.415803 | + | 0.909455i | \(0.363501\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −38.0000 | −1.24008 | ||||||||
\(940\) | −3.00000 | − | 5.19615i | −0.0978492 | − | 0.169480i | ||||
\(941\) | 11.3137 | − | 19.5959i | 0.368816 | − | 0.638809i | −0.620564 | − | 0.784155i | \(-0.713096\pi\) |
0.989381 | + | 0.145347i | \(0.0464298\pi\) | |||||||
\(942\) | −13.0000 | + | 22.5167i | −0.423563 | + | 0.733632i | ||||
\(943\) | −5.65685 | − | 9.79796i | −0.184213 | − | 0.319065i | ||||
\(944\) | −4.24264 | −0.138086 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.00000 | 0.130051 | ||||||||
\(947\) | −6.00000 | − | 10.3923i | −0.194974 | − | 0.337705i | 0.751918 | − | 0.659256i | \(-0.229129\pi\) |
−0.946892 | + | 0.321552i | \(0.895796\pi\) | |||||||
\(948\) | 5.65685 | − | 9.79796i | 0.183726 | − | 0.318223i | ||||
\(949\) | 20.0000 | − | 34.6410i | 0.649227 | − | 1.12449i | ||||
\(950\) | 4.24264 | + | 7.34847i | 0.137649 | + | 0.238416i | ||||
\(951\) | −36.7696 | −1.19233 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42.0000 | −1.36051 | −0.680257 | − | 0.732974i | \(-0.738132\pi\) | ||||
−0.680257 | + | 0.732974i | \(0.738132\pi\) | |||||||
\(954\) | 6.00000 | + | 10.3923i | 0.194257 | + | 0.336463i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 8.00000 | − | 13.8564i | 0.258738 | − | 0.448148i | ||||
\(957\) | −4.24264 | − | 7.34847i | −0.137145 | − | 0.237542i | ||||
\(958\) | 25.4558 | 0.822441 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.00000 | −0.0645497 | ||||||||
\(961\) | 14.5000 | + | 25.1147i | 0.467742 | + | 0.810153i | ||||
\(962\) | 2.82843 | − | 4.89898i | 0.0911922 | − | 0.157949i | ||||
\(963\) | −10.0000 | + | 17.3205i | −0.322245 | + | 0.558146i | ||||
\(964\) | −2.82843 | − | 4.89898i | −0.0910975 | − | 0.157786i | ||||
\(965\) | −8.48528 | −0.273151 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.0000 | 0.900419 | 0.450210 | − | 0.892923i | \(-0.351349\pi\) | ||||
0.450210 | + | 0.892923i | \(0.351349\pi\) | |||||||
\(968\) | 0.500000 | + | 0.866025i | 0.0160706 | + | 0.0278351i | ||||
\(969\) | 11.3137 | − | 19.5959i | 0.363449 | − | 0.629512i | ||||
\(970\) | −11.0000 | + | 19.0526i | −0.353189 | + | 0.611741i | ||||
\(971\) | 13.4350 | + | 23.2702i | 0.431151 | + | 0.746775i | 0.996973 | − | 0.0777526i | \(-0.0247744\pi\) |
−0.565822 | + | 0.824527i | \(0.691441\pi\) | |||||||
\(972\) | 9.89949 | 0.317526 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −10.0000 | −0.320421 | ||||||||
\(975\) | −6.00000 | − | 10.3923i | −0.192154 | − | 0.332820i | ||||
\(976\) | −2.82843 | + | 4.89898i | −0.0905357 | + | 0.156813i | ||||
\(977\) | −14.0000 | + | 24.2487i | −0.447900 | + | 0.775785i | −0.998249 | − | 0.0591494i | \(-0.981161\pi\) |
0.550349 | + | 0.834934i | \(0.314494\pi\) | |||||||
\(978\) | −15.5563 | − | 26.9444i | −0.497437 | − | 0.861586i | ||||
\(979\) | −7.07107 | −0.225992 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.0000 | −0.319275 | ||||||||
\(982\) | 2.00000 | + | 3.46410i | 0.0638226 | + | 0.110544i | ||||
\(983\) | 28.9914 | − | 50.2145i | 0.924681 | − | 1.60160i | 0.132609 | − | 0.991168i | \(-0.457665\pi\) |
0.792073 | − | 0.610427i | \(-0.209002\pi\) | |||||||
\(984\) | −4.00000 | + | 6.92820i | −0.127515 | + | 0.220863i | ||||
\(985\) | 12.7279 | + | 22.0454i | 0.405545 | + | 0.702425i | ||||
\(986\) | 33.9411 | 1.08091 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.00000 | 0.254514 | ||||||||
\(989\) | 4.00000 | + | 6.92820i | 0.127193 | + | 0.220304i | ||||
\(990\) | −0.707107 | + | 1.22474i | −0.0224733 | + | 0.0389249i | ||||
\(991\) | −25.0000 | + | 43.3013i | −0.794151 | + | 1.37551i | 0.129226 | + | 0.991615i | \(0.458751\pi\) |
−0.923377 | + | 0.383895i | \(0.874582\pi\) | |||||||
\(992\) | 0.707107 | + | 1.22474i | 0.0224507 | + | 0.0388857i | ||||
\(993\) | 39.5980 | 1.25660 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30.0000 | 0.951064 | ||||||||
\(996\) | −2.00000 | − | 3.46410i | −0.0633724 | − | 0.109764i | ||||
\(997\) | 29.6985 | − | 51.4393i | 0.940560 | − | 1.62910i | 0.176155 | − | 0.984362i | \(-0.443634\pi\) |
0.764405 | − | 0.644736i | \(-0.223033\pi\) | |||||||
\(998\) | −15.0000 | + | 25.9808i | −0.474817 | + | 0.822407i | ||||
\(999\) | −5.65685 | − | 9.79796i | −0.178975 | − | 0.309994i |
(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 | 1078.2.e.s.67.1 | 4 | ||
7.2 | even | 3 | inner | 1078.2.e.s.177.1 | 4 | ||
7.3 | odd | 6 | 1078.2.a.q.1.1 | ✓ | 2 | ||
7.4 | even | 3 | 1078.2.a.q.1.2 | yes | 2 | ||
7.5 | odd | 6 | inner | 1078.2.e.s.177.2 | 4 | ||
7.6 | odd | 2 | inner | 1078.2.e.s.67.2 | 4 | ||
21.11 | odd | 6 | 9702.2.a.dq.1.2 | 2 | |||
21.17 | even | 6 | 9702.2.a.dq.1.1 | 2 | |||
28.3 | even | 6 | 8624.2.a.bw.1.2 | 2 | |||
28.11 | odd | 6 | 8624.2.a.bw.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1078.2.a.q.1.1 | ✓ | 2 | 7.3 | odd | 6 | ||
1078.2.a.q.1.2 | yes | 2 | 7.4 | even | 3 | ||
1078.2.e.s.67.1 | 4 | 1.1 | even | 1 | trivial | ||
1078.2.e.s.67.2 | 4 | 7.6 | odd | 2 | inner | ||
1078.2.e.s.177.1 | 4 | 7.2 | even | 3 | inner | ||
1078.2.e.s.177.2 | 4 | 7.5 | odd | 6 | inner | ||
8624.2.a.bw.1.1 | 2 | 28.11 | odd | 6 | |||
8624.2.a.bw.1.2 | 2 | 28.3 | even | 6 | |||
9702.2.a.dq.1.1 | 2 | 21.17 | even | 6 | |||
9702.2.a.dq.1.2 | 2 | 21.11 | odd | 6 |