Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(193,1300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1300, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1300.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.bs (of order \(12\), degree \(4\), 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: | \(10.3805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + \cdots + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 357.4 | ||
Root | \(-1.70974i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.357 |
Dual form | 1300.2.bs.d.193.4 |
$q$-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 \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(651\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{5}{12}\right)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.563138 | + | 2.10166i | 0.325128 | + | 1.21339i | 0.914183 | + | 0.405301i | \(0.132833\pi\) |
−0.589055 | + | 0.808093i | \(0.700500\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.25530 | + | 0.724750i | −0.474460 | + | 0.273930i | −0.718105 | − | 0.695935i | \(-0.754990\pi\) |
0.243645 | + | 0.969865i | \(0.421657\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.50178 | + | 0.867051i | −0.500592 | + | 0.289017i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.39230 | − | 1.17691i | 1.32433 | − | 0.354852i | 0.473730 | − | 0.880670i | \(-0.342907\pi\) |
0.850597 | + | 0.525818i | \(0.176241\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.25262 | + | 1.55579i | 0.902114 | + | 0.431498i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.20404 | + | 1.39442i | 1.26217 | + | 0.338196i | 0.827024 | − | 0.562166i | \(-0.190032\pi\) |
0.435141 | + | 0.900362i | \(0.356698\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.379384 | − | 1.41588i | 0.0870366 | − | 0.324825i | −0.908655 | − | 0.417547i | \(-0.862890\pi\) |
0.995692 | + | 0.0927216i | \(0.0295567\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.23009 | − | 2.23009i | −0.486645 | − | 0.486645i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.61547 | + | 0.968762i | −0.753877 | + | 0.202001i | −0.615237 | − | 0.788342i | \(-0.710940\pi\) |
−0.138640 | + | 0.990343i | \(0.544273\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.94761 | + | 1.94761i | 0.374818 | + | 0.374818i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.251591 | + | 0.145256i | 0.0467193 | + | 0.0269734i | 0.523178 | − | 0.852224i | \(-0.324746\pi\) |
−0.476458 | + | 0.879197i | \(0.658080\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.02636 | + | 1.02636i | −0.184340 | + | 0.184340i | −0.793244 | − | 0.608904i | \(-0.791609\pi\) |
0.608904 | + | 0.793244i | \(0.291609\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.94694 | + | 8.56835i | 0.861152 | + | 1.49156i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.21947 | − | 3.59081i | −1.02247 | − | 0.590326i | −0.107655 | − | 0.994188i | \(-0.534334\pi\) |
−0.914820 | + | 0.403862i | \(0.867667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.43806 | + | 7.71202i | −0.230274 | + | 1.23491i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.53542 | + | 9.46231i | 0.395966 | + | 1.47776i | 0.820129 | + | 0.572179i | \(0.193902\pi\) |
−0.424163 | + | 0.905586i | \(0.639432\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.36558 | − | 8.82848i | 0.360748 | − | 1.34633i | −0.512346 | − | 0.858779i | \(-0.671223\pi\) |
0.873094 | − | 0.487552i | \(-0.162110\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.46815i | 0.651747i | 0.945413 | + | 0.325874i | \(0.105658\pi\) | ||||
−0.945413 | + | 0.325874i | \(0.894342\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.44948 | + | 4.24262i | −0.349925 | + | 0.606088i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.7224i | 1.64146i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.60704 | + | 3.60704i | −0.495465 | + | 0.495465i | −0.910023 | − | 0.414558i | \(-0.863936\pi\) |
0.414558 | + | 0.910023i | \(0.363936\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.18934 | 0.422439 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.41208 | − | 1.45016i | −0.704593 | − | 0.188795i | −0.111306 | − | 0.993786i | \(-0.535503\pi\) |
−0.593287 | + | 0.804991i | \(0.702170\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00186 | + | 10.3955i | 0.768459 | + | 1.33101i | 0.938398 | + | 0.345556i | \(0.112310\pi\) |
−0.169939 | + | 0.985455i | \(0.554357\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.25679 | − | 2.17682i | 0.158341 | − | 0.274254i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.739961 | + | 1.28165i | −0.0904006 | + | 0.156578i | −0.907680 | − | 0.419664i | \(-0.862148\pi\) |
0.817279 | + | 0.576242i | \(0.195481\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.07202 | − | 7.05294i | −0.490213 | − | 0.849074i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.0787 | − | 2.96852i | −1.31480 | − | 0.352299i | −0.467771 | − | 0.883850i | \(-0.654943\pi\) |
−0.847026 | + | 0.531551i | \(0.821610\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.7133 | 1.37093 | 0.685466 | − | 0.728104i | \(-0.259598\pi\) | ||||
0.685466 | + | 0.728104i | \(0.259598\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.66070 | + | 4.66070i | −0.531136 | + | 0.531136i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 5.42877i | − | 0.610784i | −0.952227 | − | 0.305392i | \(-0.901212\pi\) | ||
0.952227 | − | 0.305392i | \(-0.0987876\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.59760 | + | 9.69532i | −0.621955 | + | 1.07726i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 12.0274i | − | 1.32018i | −0.751188 | − | 0.660088i | \(-0.770519\pi\) | ||
0.751188 | − | 0.660088i | \(-0.229481\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.163598 | + | 0.610558i | −0.0175396 | + | 0.0654587i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.62430 | − | 13.5261i | −0.384175 | − | 1.43376i | −0.839463 | − | 0.543416i | \(-0.817131\pi\) |
0.455288 | − | 0.890344i | \(-0.349536\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.21058 | + | 0.404351i | −0.546217 | + | 0.0423874i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.73505 | − | 1.57908i | −0.283611 | − | 0.163743i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.38955 | − | 9.33497i | −0.547226 | − | 0.947823i | −0.998463 | − | 0.0554189i | \(-0.982351\pi\) |
0.451237 | − | 0.892404i | \(-0.350983\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.57580 | + | 5.57580i | −0.560389 | + | 0.560389i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.04621 | + | 1.18138i | 0.203605 | + | 0.117552i | 0.598336 | − | 0.801245i | \(-0.295829\pi\) |
−0.394731 | + | 0.918797i | \(0.629162\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.28773 | − | 1.28773i | −0.126883 | − | 0.126883i | 0.640813 | − | 0.767697i | \(-0.278597\pi\) |
−0.767697 | + | 0.640813i | \(0.778597\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.2891 | + | 3.02490i | −1.09136 | + | 0.292428i | −0.759240 | − | 0.650811i | \(-0.774429\pi\) |
−0.332115 | + | 0.943239i | \(0.607762\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.52541 | + | 9.52541i | 0.912369 | + | 0.912369i | 0.996458 | − | 0.0840895i | \(-0.0267982\pi\) |
−0.0840895 | + | 0.996458i | \(0.526798\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.04425 | − | 15.0933i | 0.383863 | − | 1.43260i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.3917 | + | 3.58830i | 1.25979 | + | 0.337559i | 0.826109 | − | 0.563510i | \(-0.190549\pi\) |
0.433677 | + | 0.901069i | \(0.357216\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.23365 | + | 0.483743i | −0.576301 | + | 0.0447220i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.54326 | + | 2.02121i | −0.691489 | + | 0.185284i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.38086 | − | 4.83869i | 0.761897 | − | 0.439881i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −18.4588 | + | 10.6572i | −1.66437 | + | 0.960925i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.12904 | + | 4.21363i | 0.100186 | + | 0.373899i | 0.997755 | − | 0.0669757i | \(-0.0213350\pi\) |
−0.897569 | + | 0.440875i | \(0.854668\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 19.8866 | 1.75092 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.6339 | 1.27857 | 0.639286 | − | 0.768969i | \(-0.279230\pi\) | ||||
0.639286 | + | 0.768969i | \(0.279230\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.549917 | + | 2.05232i | 0.0476838 | + | 0.177958i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.671485 | + | 0.387682i | −0.0573689 | + | 0.0331219i | −0.528410 | − | 0.848989i | \(-0.677212\pi\) |
0.471041 | + | 0.882111i | \(0.343878\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.7398 | + | 11.3968i | −1.67431 | + | 0.966664i | −0.709132 | + | 0.705076i | \(0.750913\pi\) |
−0.965180 | + | 0.261588i | \(0.915754\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.39054 | + | 2.51619i | −0.790826 | + | 0.211901i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.1175 | + | 3.00543i | 1.34781 | + | 0.251327i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.2959 | − | 2.75879i | −0.849194 | − | 0.227541i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.79239 | − | 6.68928i | 0.146838 | − | 0.548007i | −0.852829 | − | 0.522191i | \(-0.825115\pi\) |
0.999667 | − | 0.0258163i | \(-0.00821850\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.60288 | − | 1.60288i | −0.130440 | − | 0.130440i | 0.638872 | − | 0.769313i | \(-0.279401\pi\) |
−0.769313 | + | 0.638872i | \(0.779401\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.02434 | + | 2.41806i | −0.729575 | + | 0.195489i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.08174 | + | 3.08174i | 0.245950 | + | 0.245950i | 0.819306 | − | 0.573356i | \(-0.194359\pi\) |
−0.573356 | + | 0.819306i | \(0.694359\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.61203 | − | 5.54951i | −0.762283 | − | 0.440104i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.83640 | − | 3.83640i | 0.302351 | − | 0.302351i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.985666 | − | 1.70722i | −0.0772033 | − | 0.133720i | 0.824839 | − | 0.565368i | \(-0.191266\pi\) |
−0.902042 | + | 0.431648i | \(0.857932\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.2648 | + | 7.65842i | 1.02646 | + | 0.592626i | 0.915968 | − | 0.401251i | \(-0.131425\pi\) |
0.110490 | + | 0.993877i | \(0.464758\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.15906 | + | 10.1208i | 0.627620 | + | 0.778520i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.657890 | + | 2.45528i | 0.0503101 | + | 0.187760i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.567617 | + | 2.11838i | −0.0431552 | + | 0.161057i | −0.984141 | − | 0.177389i | \(-0.943235\pi\) |
0.940986 | + | 0.338447i | \(0.109901\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 12.1910i | − | 0.916332i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.3526 | − | 21.3953i | 0.923275 | − | 1.59916i | 0.128963 | − | 0.991649i | \(-0.458835\pi\) |
0.794312 | − | 0.607510i | \(-0.207831\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 10.9512i | − | 0.813995i | −0.913429 | − | 0.406997i | \(-0.866576\pi\) | ||
0.913429 | − | 0.406997i | \(-0.133424\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.4680 | + | 18.4680i | −1.36519 | + | 1.36519i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.4988 | 1.79153 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.85638 | − | 1.03331i | −0.280510 | − | 0.0751625i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.3738 | − | 19.7000i | −0.822977 | − | 1.42544i | −0.903455 | − | 0.428682i | \(-0.858978\pi\) |
0.0804781 | − | 0.996756i | \(-0.474355\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.06182 | − | 8.76733i | 0.364358 | − | 0.631086i | −0.624315 | − | 0.781173i | \(-0.714622\pi\) |
0.988673 | + | 0.150086i | \(0.0479552\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.68286 | + | 4.64685i | −0.191146 | + | 0.331074i | −0.945630 | − | 0.325244i | \(-0.894554\pi\) |
0.754484 | + | 0.656318i | \(0.227887\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.93978 | + | 13.7521i | 0.562836 | + | 0.974861i | 0.997247 | + | 0.0741463i | \(0.0236232\pi\) |
−0.434411 | + | 0.900715i | \(0.643044\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.11029 | − | 0.833400i | −0.219383 | − | 0.0587835i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.421097 | −0.0295552 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.58966 | − | 4.58966i | 0.319003 | − | 0.319003i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 6.66546i | − | 0.461060i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.83794 | + | 17.0398i | −0.677272 | + | 1.17307i | 0.298528 | + | 0.954401i | \(0.403504\pi\) |
−0.975799 | + | 0.218668i | \(0.929829\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 24.9553i | − | 1.70991i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.544540 | − | 2.03225i | 0.0369658 | − | 0.137958i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.59618 | + | 24.6173i | 0.445729 | + | 1.66348i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.7573 | + | 12.6319i | 0.992687 | + | 0.849713i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.8536 | + | 10.8851i | 1.26253 | + | 0.728921i | 0.973563 | − | 0.228418i | \(-0.0733554\pi\) |
0.288965 | + | 0.957340i | \(0.406689\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.47032 | − | 4.27872i | −0.163961 | − | 0.283989i | 0.772325 | − | 0.635228i | \(-0.219094\pi\) |
−0.936286 | + | 0.351239i | \(0.885760\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.3403 | − | 12.3403i | 0.815468 | − | 0.815468i | −0.169980 | − | 0.985448i | \(-0.554370\pi\) |
0.985448 | + | 0.169980i | \(0.0543702\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.4198 | − | 7.17059i | −0.817164 | − | 0.471790i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.98171 | − | 7.98171i | −0.522899 | − | 0.522899i | 0.395547 | − | 0.918446i | \(-0.370555\pi\) |
−0.918446 | + | 0.395547i | \(0.870555\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.4094 | − | 3.05715i | 0.741122 | − | 0.198583i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.23426 | − | 4.23426i | −0.273891 | − | 0.273891i | 0.556773 | − | 0.830665i | \(-0.312039\pi\) |
−0.830665 | + | 0.556773i | \(0.812039\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.61985 | − | 20.9736i | 0.362006 | − | 1.35103i | −0.509428 | − | 0.860513i | \(-0.670143\pi\) |
0.871434 | − | 0.490512i | \(-0.163190\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5470 | − | 4.16582i | −0.997343 | − | 0.267237i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.43680 | − | 4.01508i | 0.218678 | − | 0.255473i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 25.2775 | − | 6.77308i | 1.60189 | − | 0.429226i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.8296 | − | 12.6033i | 1.37787 | − | 0.795514i | 0.385967 | − | 0.922513i | \(-0.373868\pi\) |
0.991903 | + | 0.126999i | \(0.0405345\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.7401 | + | 8.51018i | −0.926700 | + | 0.535030i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.26976 | − | 12.2029i | −0.203962 | − | 0.761197i | −0.989763 | − | 0.142718i | \(-0.954416\pi\) |
0.785801 | − | 0.618479i | \(-0.212251\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.4098 | 0.646831 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.503778 | −0.0311831 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.49468 | − | 13.0423i | −0.215491 | − | 0.804223i | −0.985993 | − | 0.166786i | \(-0.946661\pi\) |
0.770502 | − | 0.637437i | \(-0.220006\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 26.3862 | − | 15.2341i | 1.61481 | − | 0.932311i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.0205 | + | 8.09471i | −0.854842 | + | 0.493543i | −0.862282 | − | 0.506429i | \(-0.830965\pi\) |
0.00743940 | + | 0.999972i | \(0.497632\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.1884 | + | 2.99792i | −0.679647 | + | 0.182111i | −0.582096 | − | 0.813120i | \(-0.697767\pi\) |
−0.0975504 | + | 0.995231i | \(0.531101\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.78408 | − | 10.7232i | −0.229023 | − | 0.648995i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.9803 | + | 6.69346i | 1.50092 | + | 0.402171i | 0.913409 | − | 0.407043i | \(-0.133440\pi\) |
0.587514 | + | 0.809214i | \(0.300107\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.651458 | − | 2.43127i | 0.0390018 | − | 0.145557i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.6609 | − | 14.6609i | −0.874597 | − | 0.874597i | 0.118372 | − | 0.992969i | \(-0.462232\pi\) |
−0.992969 | + | 0.118372i | \(0.962232\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.27181 | − | 0.876680i | 0.194489 | − | 0.0521132i | −0.160259 | − | 0.987075i | \(-0.551233\pi\) |
0.354749 | + | 0.934962i | \(0.384566\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.0405 | − | 10.0405i | −0.592674 | − | 0.592674i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.4152 | + | 6.01323i | 0.612660 | + | 0.353719i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.5839 | − | 16.5839i | 0.972164 | − | 0.972164i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.6537 | − | 21.9169i | −0.739240 | − | 1.28040i | −0.952838 | − | 0.303479i | \(-0.901852\pi\) |
0.213599 | − | 0.976922i | \(-0.431482\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.8467 | + | 6.26232i | 0.629387 | + | 0.363377i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.2669 | − | 2.47388i | −0.767246 | − | 0.143068i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.42891 | + | 12.7969i | 0.197639 | + | 0.737600i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.33056 | + | 4.96571i | −0.0764386 | + | 0.285273i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.8252i | 0.731974i | 0.930620 | + | 0.365987i | \(0.119269\pi\) | ||||
−0.930620 | + | 0.365987i | \(0.880731\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.98119 | − | 3.43153i | 0.112706 | − | 0.195213i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.59622i | 0.0905134i | 0.998975 | + | 0.0452567i | \(0.0144106\pi\) | ||||
−0.998975 | + | 0.0452567i | \(0.985589\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.0754 | + | 19.0754i | −1.07821 | + | 1.07821i | −0.0815374 | + | 0.996670i | \(0.525983\pi\) |
−0.996670 | + | 0.0815374i | \(0.974017\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.6088 | −0.876680 | −0.438340 | − | 0.898809i | \(-0.644433\pi\) | ||||
−0.438340 | + | 0.898809i | \(0.644433\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.27602 | + | 0.341907i | 0.0714431 | + | 0.0191431i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.7146 | − | 22.0224i | −0.709660 | − | 1.22917i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.94866 | − | 6.83928i | 0.219709 | − | 0.380548i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.6551 | + | 25.3833i | −0.810426 | + | 1.40370i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.23829 | − | 5.60889i | −0.178533 | − | 0.309228i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.7600 | − | 6.90237i | −1.41590 | − | 0.379388i | −0.531870 | − | 0.846826i | \(-0.678511\pi\) |
−0.884026 | + | 0.467438i | \(0.845177\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.4537 | 0.682457 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.54193 | − | 1.54193i | 0.0839941 | − | 0.0839941i | −0.663861 | − | 0.747856i | \(-0.731084\pi\) |
0.747856 | + | 0.663861i | \(0.231084\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 30.1655i | 1.63837i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.30015 | + | 5.71602i | −0.178713 | + | 0.309540i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.2475i | − | 0.931279i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.59818 | − | 9.69655i | 0.139478 | − | 0.520538i | −0.860461 | − | 0.509516i | \(-0.829825\pi\) |
0.999939 | − | 0.0110226i | \(-0.00350868\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.70030 | − | 21.2738i | −0.305130 | − | 1.13876i | −0.932833 | − | 0.360308i | \(-0.882671\pi\) |
0.627703 | − | 0.778453i | \(-0.283995\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.30477 | + | 9.36491i | 0.176396 | + | 0.499862i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.9958 | + | 9.23518i | 0.851371 | + | 0.491539i | 0.861113 | − | 0.508414i | \(-0.169768\pi\) |
−0.00974252 | + | 0.999953i | \(0.503101\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.49579 | − | 14.7151i | −0.449645 | − | 0.778808i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.6227 | − | 15.6227i | 0.824534 | − | 0.824534i | −0.162220 | − | 0.986755i | \(-0.551865\pi\) |
0.986755 | + | 0.162220i | \(0.0518655\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.5937 | + | 8.42568i | 0.768089 | + | 0.443457i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.8889 | + | 14.8889i | 0.781463 | + | 0.781463i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −36.1290 | + | 9.68075i | −1.88592 | + | 0.505331i | −0.886858 | + | 0.462041i | \(0.847117\pi\) |
−0.999063 | + | 0.0432899i | \(0.986216\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.0119 | − | 12.0119i | −0.625316 | − | 0.625316i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.91373 | − | 7.14212i | 0.0993557 | − | 0.370801i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.1071 | − | 4.04794i | −0.782218 | − | 0.209595i | −0.154455 | − | 0.988000i | \(-0.549362\pi\) |
−0.627762 | + | 0.778405i | \(0.716029\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.592342 | + | 0.863884i | 0.0305072 | + | 0.0444923i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.09134 | − | 1.09627i | 0.210158 | − | 0.0563117i | −0.152204 | − | 0.988349i | \(-0.548637\pi\) |
0.362362 | + | 0.932037i | \(0.381970\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.21981 | + | 4.74571i | −0.421114 | + | 0.243130i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.5287 | + | 7.23343i | −0.640185 | + | 0.369611i | −0.784686 | − | 0.619894i | \(-0.787176\pi\) |
0.144501 | + | 0.989505i | \(0.453842\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.10216 | + | 15.3095i | 0.208525 | + | 0.778225i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.89275 | −0.197370 | −0.0986852 | − | 0.995119i | \(-0.531464\pi\) | ||||
−0.0986852 | + | 0.995119i | \(0.531464\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.1659 | −1.01983 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.24093 | + | 30.7556i | 0.415700 | + | 1.55141i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.921577 | − | 0.532073i | 0.0462526 | − | 0.0267040i | −0.476695 | − | 0.879069i | \(-0.658166\pi\) |
0.522948 | + | 0.852365i | \(0.324832\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.00359 | + | 2.31148i | −0.200430 | + | 0.115719i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.6698 | − | 5.27051i | 0.982263 | − | 0.263197i | 0.268266 | − | 0.963345i | \(-0.413549\pi\) |
0.713997 | + | 0.700148i | \(0.246883\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.93516 | + | 1.74156i | −0.245838 | + | 0.0867535i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −31.5438 | − | 8.45214i | −1.56357 | − | 0.418957i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.49767 | − | 20.5176i | 0.271842 | − | 1.01453i | −0.686085 | − | 0.727521i | \(-0.740672\pi\) |
0.957928 | − | 0.287009i | \(-0.0926610\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.19292 | − | 1.19292i | −0.0588422 | − | 0.0588422i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.84481 | − | 2.10201i | 0.386018 | − | 0.103433i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −35.0685 | − | 35.0685i | −1.71731 | − | 1.71731i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.58399 | − | 2.06922i | −0.175089 | − | 0.101088i | 0.409894 | − | 0.912133i | \(-0.365566\pi\) |
−0.584983 | + | 0.811045i | \(0.698899\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.3449 | − | 14.3449i | 0.699129 | − | 0.699129i | −0.265094 | − | 0.964223i | \(-0.585403\pi\) |
0.964223 | + | 0.265094i | \(0.0854029\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.87412 | − | 6.71017i | −0.188366 | − | 0.326260i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.0683 | − | 8.69969i | −0.729207 | − | 0.421008i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.75998 | + | 35.5660i | 0.133253 | + | 1.71714i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.87880 | − | 25.6720i | −0.331340 | − | 1.23658i | −0.907783 | − | 0.419440i | \(-0.862226\pi\) |
0.576443 | − | 0.817137i | \(-0.304440\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.86366 | − | 14.4194i | 0.185676 | − | 0.692951i | −0.808809 | − | 0.588071i | \(-0.799888\pi\) |
0.994485 | − | 0.104880i | \(-0.0334458\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.48660i | 0.262460i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.947472 | + | 1.64107i | −0.0452204 | + | 0.0783240i | −0.887750 | − | 0.460327i | \(-0.847732\pi\) |
0.842529 | + | 0.538651i | \(0.181066\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 8.49528i | − | 0.404537i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.19043 | − | 9.19043i | 0.436651 | − | 0.436651i | −0.454232 | − | 0.890883i | \(-0.650086\pi\) |
0.890883 | + | 0.454232i | \(0.150086\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.0680 | 0.712690 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.59242 | + | 1.23053i | 0.216730 | + | 0.0580725i | 0.365550 | − | 0.930792i | \(-0.380881\pi\) |
−0.148820 | + | 0.988864i | \(0.547548\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.2726 | + | 38.5773i | 1.04878 | + | 1.81653i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.46606 | − | 4.27135i | 0.115866 | − | 0.200686i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.5494 | − | 21.7363i | 0.587038 | − | 1.01678i | −0.407580 | − | 0.913169i | \(-0.633627\pi\) |
0.994618 | − | 0.103610i | \(-0.0330393\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.41967 | + | 12.8512i | 0.346321 | + | 0.599845i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.24463 | + | 0.333498i | 0.0579683 | + | 0.0155326i | 0.287687 | − | 0.957725i | \(-0.407114\pi\) |
−0.229718 | + | 0.973257i | \(0.573780\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.0066 | −0.976260 | −0.488130 | − | 0.872771i | \(-0.662321\pi\) | ||||
−0.488130 | + | 0.872771i | \(0.662321\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.95409 | + | 7.95409i | −0.368071 | + | 0.368071i | −0.866773 | − | 0.498702i | \(-0.833810\pi\) |
0.498702 | + | 0.866773i | \(0.333810\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 2.14514i | − | 0.0990536i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.74133 | + | 8.21222i | −0.218469 | + | 0.378399i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 41.5614i | − | 1.91099i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.28948 | − | 8.54445i | 0.104828 | − | 0.391223i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.51597 | − | 20.5859i | −0.252031 | − | 0.940592i | −0.969718 | − | 0.244227i | \(-0.921466\pi\) |
0.717687 | − | 0.696366i | \(-0.245201\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.6430 | − | 21.3557i | −0.667664 | − | 0.973736i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.2232 | + | 5.90239i | 0.465173 | + | 0.268568i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.1379 | + | 26.2196i | 0.685963 | + | 1.18812i | 0.973133 | + | 0.230243i | \(0.0739520\pi\) |
−0.287171 | + | 0.957879i | \(0.592715\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.03294 | − | 3.03294i | 0.137154 | − | 0.137154i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.93926 | + | 4.58373i | 0.358294 | + | 0.206861i | 0.668332 | − | 0.743863i | \(-0.267009\pi\) |
−0.310038 | + | 0.950724i | \(0.600342\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.10674 | + | 1.10674i | 0.0498451 | + | 0.0498451i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.0585 | − | 4.30287i | 0.720324 | − | 0.193010i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.0223 | − | 15.0223i | −0.672489 | − | 0.672489i | 0.285800 | − | 0.958289i | \(-0.407741\pi\) |
−0.958289 | + | 0.285800i | \(0.907741\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.62550 | + | 32.1908i | −0.385359 | + | 1.43818i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.2502 | − | 7.30167i | −1.21503 | − | 0.325565i | −0.406294 | − | 0.913742i | \(-0.633179\pi\) |
−0.808732 | + | 0.588177i | \(0.799846\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.6757 | + | 22.8470i | −0.740595 | + | 1.01467i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.9997 | + | 2.94735i | −0.487552 | + | 0.130639i | −0.494217 | − | 0.869339i | \(-0.664545\pi\) |
0.00666482 | + | 0.999978i | \(0.497879\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.7037 | + | 8.48918i | −0.650453 | + | 0.375539i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.49648 | − | 2.01869i | 0.154373 | − | 0.0891275i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.25863 | + | 19.6255i | 0.231274 | + | 0.863127i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.77176 | −0.209457 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.2904 | −1.15180 | −0.575902 | − | 0.817519i | \(-0.695349\pi\) | ||||
−0.575902 | + | 0.817519i | \(0.695349\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.15518 | + | 22.9715i | 0.269147 | + | 1.00447i | 0.959663 | + | 0.281154i | \(0.0907172\pi\) |
−0.690515 | + | 0.723318i | \(0.742616\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.77241 | + | 3.91005i | −0.295011 | + | 0.170324i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.78547 | + | 4.49495i | −0.338499 | + | 0.195432i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.38511 | − | 2.51473i | 0.407279 | − | 0.109130i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.47459 | + | 34.7219i | −0.280445 | + | 1.50397i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 51.9218 | + | 13.9124i | 2.24059 | + | 0.600365i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.76564 | + | 21.5176i | −0.248343 | + | 0.926831i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.1348 | + | 13.1348i | 0.564708 | + | 0.564708i | 0.930641 | − | 0.365933i | \(-0.119250\pi\) |
−0.365933 | + | 0.930641i | \(0.619250\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.0157 | − | 6.16703i | 0.987697 | − | 0.264653i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.2880 | + | 19.2880i | 0.824696 | + | 0.824696i | 0.986777 | − | 0.162081i | \(-0.0518207\pi\) |
−0.162081 | + | 0.986777i | \(0.551821\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.0269 | − | 10.4078i | −0.769369 | − | 0.444196i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.301115 | − | 0.301115i | 0.0128279 | − | 0.0128279i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.93450 | + | 6.81475i | 0.167312 | + | 0.289793i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.72959 | − | 0.998577i | −0.0732849 | − | 0.0423111i | 0.462910 | − | 0.886405i | \(-0.346805\pi\) |
−0.536195 | + | 0.844094i | \(0.680139\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.4296 | − | 25.0353i | 0.906375 | − | 1.05888i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.7962 | + | 51.4882i | 0.582477 | + | 2.17383i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.28516 | − | 8.52834i | 0.0963081 | − | 0.359427i | −0.900906 | − | 0.434013i | \(-0.857097\pi\) |
0.997215 | + | 0.0745867i | \(0.0237637\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 16.2274i | − | 0.681488i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.7930 | + | 22.1581i | −0.536309 | + | 0.928914i | 0.462790 | + | 0.886468i | \(0.346848\pi\) |
−0.999099 | + | 0.0424461i | \(0.986485\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.2404i | 0.721487i | 0.932665 | + | 0.360744i | \(0.117477\pi\) | ||||
−0.932665 | + | 0.360744i | \(0.882523\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 34.9976 | − | 34.9976i | 1.46205 | − | 1.46205i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.8547 | 1.49265 | 0.746325 | − | 0.665581i | \(-0.231816\pi\) | ||||
0.746325 | + | 0.665581i | \(0.231816\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.2765 | + | 5.70101i | 0.884219 | + | 0.236926i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.71684 | + | 15.0980i | 0.361636 | + | 0.626371i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.5980 | + | 20.0883i | −0.480340 | + | 0.831974i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.6192 | + | 20.1251i | −0.479577 | + | 0.830652i | −0.999726 | − | 0.0234240i | \(-0.992543\pi\) |
0.520149 | + | 0.854076i | \(0.325877\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.06382 | + | 1.84259i | 0.0438339 | + | 0.0759226i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.2769 | − | 3.02164i | −0.463871 | − | 0.124294i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.9013 | 0.776182 | 0.388091 | − | 0.921621i | \(-0.373135\pi\) | ||||
0.388091 | + | 0.921621i | \(0.373135\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.4311 | + | 24.4311i | −0.999897 | + | 0.999897i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.9904i | 1.47053i | 0.677781 | + | 0.735264i | \(0.262942\pi\) | ||||
−0.677781 | + | 0.735264i | \(0.737058\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.79547 | + | 8.30599i | −0.195611 | + | 0.338808i | −0.947101 | − | 0.320937i | \(-0.896002\pi\) |
0.751490 | + | 0.659745i | \(0.229336\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 2.56633i | − | 0.104509i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.4598 | − | 46.5006i | 0.505728 | − | 1.88740i | 0.0468517 | − | 0.998902i | \(-0.485081\pi\) |
0.458876 | − | 0.888500i | \(-0.348252\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.237136 | − | 0.885003i | −0.00960923 | − | 0.0358621i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.95149 | + | 14.5332i | −0.281227 | + | 0.587950i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.4121 | + | 12.3623i | 0.864825 | + | 0.499307i | 0.865625 | − | 0.500693i | \(-0.166921\pi\) |
−0.000800300 | 1.00000i | \(0.500255\pi\) | ||||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.9719 | − | 34.5924i | −0.804040 | − | 1.39264i | −0.916937 | − | 0.399031i | \(-0.869346\pi\) |
0.112897 | − | 0.993607i | \(-0.463987\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.50369 | + | 3.50369i | −0.140825 | + | 0.140825i | −0.774005 | − | 0.633180i | \(-0.781749\pi\) |
0.633180 | + | 0.774005i | \(0.281749\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.92830 | − | 5.15476i | −0.358280 | − | 0.206853i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.3526 | + | 14.3526i | 0.575025 | + | 0.575025i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14.0085 | − | 3.75358i | 0.559447 | − | 0.149903i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −27.3593 | − | 27.3593i | −1.09089 | − | 1.09089i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.78921 | − | 17.8736i | 0.190656 | − | 0.711536i | −0.802693 | − | 0.596392i | \(-0.796600\pi\) |
0.993349 | − | 0.115144i | \(-0.0367330\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −41.3520 | − | 11.0802i | −1.64360 | − | 0.440400i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.5678 | + | 9.98875i | −0.577198 | + | 0.395769i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19.2116 | − | 5.14772i | 0.759998 | − | 0.203641i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.75083 | + | 3.89760i | −0.266642 | + | 0.153946i | −0.627361 | − | 0.778729i | \(-0.715865\pi\) |
0.360719 | + | 0.932675i | \(0.382531\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.4142 | − | 13.5182i | 0.923367 | − | 0.533106i | 0.0386590 | − | 0.999252i | \(-0.487691\pi\) |
0.884708 | + | 0.466147i | \(0.154358\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.97989 | − | 37.2455i | −0.392350 | − | 1.46427i | −0.826247 | − | 0.563308i | \(-0.809529\pi\) |
0.433897 | − | 0.900962i | \(-0.357138\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.4782 | −1.00011 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.57775 | 0.179416 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.90149 | + | 22.0247i | 0.230943 | + | 0.861891i | 0.979936 | + | 0.199313i | \(0.0638711\pi\) |
−0.748993 | + | 0.662578i | \(0.769462\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −17.5907 | + | 10.1560i | −0.686278 | + | 0.396223i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.33308 | + | 5.38846i | −0.363565 | + | 0.209905i | −0.670644 | − | 0.741780i | \(-0.733982\pi\) |
0.307078 | + | 0.951684i | \(0.400649\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.0956 | − | 11.0115i | 1.59843 | − | 0.428299i | 0.653865 | − | 0.756611i | \(-0.273146\pi\) |
0.944569 | + | 0.328312i | \(0.106480\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −18.2375 | + | 38.1284i | −0.708287 | + | 1.48079i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.05034 | − | 0.281437i | −0.0406692 | − | 0.0108973i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.2596 | + | 45.7536i | −0.473985 | + | 1.76894i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38.5966 | + | 38.5966i | 1.49000 | + | 1.49000i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.4138 | + | 4.66602i | −0.671254 | + | 0.179862i | −0.578320 | − | 0.815810i | \(-0.696291\pi\) |
−0.0929342 | + | 0.995672i | \(0.529625\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.4931 | + | 17.4931i | 0.672315 | + | 0.672315i | 0.958249 | − | 0.285934i | \(-0.0923038\pi\) |
−0.285934 | + | 0.958249i | \(0.592304\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.5310 | + | 7.81215i | 0.519274 | + | 0.299803i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.60129 | − | 7.60129i | 0.291282 | − | 0.291282i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.02842 | − | 1.78127i | −0.0393514 | − | 0.0681586i | 0.845679 | − | 0.533692i | \(-0.179196\pi\) |
−0.885030 | + | 0.465533i | \(0.845862\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 32.8843 | + | 18.9858i | 1.25462 | + | 0.724353i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17.3441 | + | 6.12054i | −0.660757 | + | 0.233174i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.568099 | − | 2.12017i | −0.0216115 | − | 0.0806552i | 0.954278 | − | 0.298921i | \(-0.0966267\pi\) |
−0.975889 | + | 0.218266i | \(0.929960\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.95826 | − | 11.0404i | 0.112375 | − | 0.419390i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 52.7777i | 1.99910i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.2800 | − | 21.2696i | 0.464474 | − | 0.804492i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 25.9991i | − | 0.981972i | −0.871168 | − | 0.490986i | \(-0.836637\pi\) | ||
0.871168 | − | 0.490986i | \(-0.163363\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.44372 | + | 7.44372i | −0.280745 | + | 0.280745i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.42482 | −0.128803 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.7979 | + | 10.3959i | 1.45709 | + | 0.390425i | 0.898482 | − | 0.439010i | \(-0.144671\pi\) |
0.558603 | + | 0.829435i | \(0.311337\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.70702 | + | 8.15280i | 0.176527 | + | 0.305754i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.71648 | − | 4.70508i | 0.101733 | − | 0.176207i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.51450 | − | 11.2834i | 0.243288 | − | 0.421388i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.6884 | − | 20.2450i | −0.435905 | − | 0.755010i | 0.561464 | − | 0.827501i | \(-0.310238\pi\) |
−0.997369 | + | 0.0724910i | \(0.976905\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.54976 | + | 0.683207i | 0.0949582 | + | 0.0254440i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 47.2440 | 1.75702 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.9556 | − | 18.9556i | 0.703024 | − | 0.703024i | −0.262034 | − | 0.965059i | \(-0.584393\pi\) |
0.965059 | + | 0.262034i | \(0.0843934\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.43494i | − | 0.0531459i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.6212 | − | 42.6452i | 0.910648 | − | 1.57729i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 48.4953i | 1.79122i | 0.444845 | + | 0.895608i | \(0.353259\pi\) | ||||
−0.444845 | + | 0.895608i | \(0.646741\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.74174 | + | 6.50025i | −0.0641577 | + | 0.239440i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.74097 | + | 6.49738i | 0.0640425 | + | 0.239010i | 0.990526 | − | 0.137326i | \(-0.0438507\pi\) |
−0.926483 | + | 0.376335i | \(0.877184\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.3737 | + | 4.96194i | 0.381088 | + | 0.182281i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.9313 | − | 11.5074i | −0.731209 | − | 0.422164i | 0.0876550 | − | 0.996151i | \(-0.472063\pi\) |
−0.818864 | + | 0.573987i | \(0.805396\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.4284 | + | 18.0624i | 0.381553 | + | 0.660870i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.9789 | − | 11.9789i | 0.437700 | − | 0.437700i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.0748 | − | 8.12611i | −0.513598 | − | 0.296526i | 0.220713 | − | 0.975339i | \(-0.429161\pi\) |
−0.734311 | + | 0.678813i | \(0.762495\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 38.7809 | + | 38.7809i | 1.41326 | + | 1.41326i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.9153 | + | 6.40809i | −0.869218 | + | 0.232906i | −0.665749 | − | 0.746175i | \(-0.731888\pi\) |
−0.203468 | + | 0.979082i | \(0.565221\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −26.1862 | − | 26.1862i | −0.950499 | − | 0.950499i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.77474 | + | 17.8196i | −0.173084 | + | 0.645960i | 0.823786 | + | 0.566901i | \(0.191858\pi\) |
−0.996870 | + | 0.0790582i | \(0.974809\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.8608 | − | 5.05374i | −0.682807 | − | 0.182958i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.3473 | − | 13.1369i | −0.554159 | − | 0.474345i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.7050 | + | 10.3710i | −1.39574 | + | 0.373987i | −0.876812 | − | 0.480833i | \(-0.840335\pi\) |
−0.518926 | + | 0.854819i | \(0.673668\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.8050 | − | 13.7439i | 0.857318 | − | 0.494973i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.6228 | + | 11.9066i | −0.741750 | + | 0.428250i | −0.822705 | − | 0.568468i | \(-0.807536\pi\) |
0.0809550 | + | 0.996718i | \(0.474203\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.86213 | + | 21.8778i | 0.210303 | + | 0.784861i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.3594 | 0.514479 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −52.1545 | −1.86624 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.207099 | + | 0.772904i | 0.00740112 | + | 0.0276213i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.78665 | + | 3.34092i | −0.206272 | + | 0.119091i | −0.599577 | − | 0.800317i | \(-0.704665\pi\) |
0.393306 | + | 0.919408i | \(0.371331\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 25.4425 | − | 14.6892i | 0.905778 | − | 0.522951i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.4113 | + | 5.20123i | −0.690185 | + | 0.184935i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.34854 | + | 43.1503i | 0.118910 | + | 1.53231i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −25.8557 | − | 6.92801i | −0.915856 | − | 0.245403i | −0.230043 | − | 0.973181i | \(-0.573887\pi\) |
−0.685813 | + | 0.727778i | \(0.740553\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.23048 | + | 23.2525i | −0.220418 | + | 0.822613i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.1707 | + | 17.1707i | 0.606696 | + | 0.606696i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 51.4481 | − | 13.7855i | 1.81556 | − | 0.486479i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24.9078 | − | 24.9078i | −0.876796 | − | 0.876796i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.00929 | + | 5.20152i | 0.316750 | + | 0.182876i | 0.649943 | − | 0.759983i | \(-0.274793\pi\) |
−0.333193 | + | 0.942859i | \(0.608126\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.88418 | + | 2.88418i | −0.101277 | + | 0.101277i | −0.755930 | − | 0.654653i | \(-0.772815\pi\) |
0.654653 | + | 0.755930i | \(0.272815\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.6012 | − | 21.8260i | −0.441944 | − | 0.765470i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.6026 | − | 6.69877i | −0.405924 | − | 0.234360i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.47453 | − | 5.12508i | 0.261181 | − | 0.179085i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.80641 | − | 14.2057i | −0.132845 | − | 0.495783i | 0.867153 | − | 0.498042i | \(-0.165948\pi\) |
−0.999997 | + | 0.00225931i | \(0.999281\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.90567 | − | 25.7723i | 0.240717 | − | 0.898366i | −0.734772 | − | 0.678315i | \(-0.762711\pi\) |
0.975488 | − | 0.220052i | \(-0.0706227\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.9935i | 0.556148i | 0.960560 | + | 0.278074i | \(0.0896961\pi\) | ||||
−0.960560 | + | 0.278074i | \(0.910304\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.7937 | + | 18.6953i | −0.374882 | + | 0.649314i | −0.990309 | − | 0.138879i | \(-0.955650\pi\) |
0.615428 | + | 0.788193i | \(0.288983\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 56.2695i | 1.95197i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.6632 | + | 18.6632i | −0.646640 | + | 0.646640i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.99791 | −0.138188 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −52.3906 | − | 14.0380i | −1.80872 | − | 0.484646i | −0.813439 | − | 0.581650i | \(-0.802407\pi\) |
−0.995284 | + | 0.0970040i | \(0.969074\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.4578 | − | 25.0416i | −0.498545 | − | 0.863505i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.5562 | − | 39.0684i | 0.776875 | − | 1.34559i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.01368 | + | 12.1481i | −0.240993 | + | 0.417412i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.68497 | + | 6.38255i | 0.126468 | + | 0.219049i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.9649 | + | 6.95728i | 0.890066 | + | 0.238493i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.9281 | −0.613848 | −0.306924 | − | 0.951734i | \(-0.599300\pi\) | ||||
−0.306924 | + | 0.951734i | \(0.599300\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.9470 | + | 35.9470i | −1.22793 | + | 1.22793i | −0.263179 | + | 0.964747i | \(0.584771\pi\) |
−0.964747 | + | 0.263179i | \(0.915229\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.8361i | 1.39331i | 0.717406 | + | 0.696655i | \(0.245329\pi\) | ||||
−0.717406 | + | 0.696655i | \(0.754671\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.4476 | − | 26.7560i | 0.526452 | − | 0.911841i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1.61377i | − | 0.0549334i | −0.999623 | − | 0.0274667i | \(-0.991256\pi\) | ||
0.999623 | − | 0.0274667i | \(-0.00874403\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.77256 | + | 25.2755i | −0.230008 | + | 0.858402i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.38919 | − | 23.8448i | −0.216738 | − | 0.808878i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.40078 | + | 3.01750i | −0.149115 | + | 0.102244i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.1878 | + | 9.34603i | 0.547874 | + | 0.316315i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.7214 | − | 30.6943i | −0.598409 | − | 1.03647i | −0.993056 | − | 0.117642i | \(-0.962467\pi\) |
0.394647 | − | 0.918833i | \(-0.370867\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 38.9361 | − | 38.9361i | 1.31328 | − | 1.31328i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.1387 | + | 7.00829i | 0.408964 | + | 0.236115i | 0.690344 | − | 0.723481i | \(-0.257459\pi\) |
−0.281381 | + | 0.959596i | \(0.590792\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.3985 | + | 34.3985i | 1.15760 | + | 1.15760i | 0.984990 | + | 0.172612i | \(0.0552206\pi\) |
0.172612 | + | 0.984990i | \(0.444779\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.1266 | − | 11.8237i | 1.48163 | − | 0.397000i | 0.574725 | − | 0.818346i | \(-0.305109\pi\) |
0.906900 | + | 0.421346i | \(0.138442\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.47111 | − | 4.47111i | −0.149956 | − | 0.149956i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.1758 | + | 49.1726i | −0.441405 | + | 1.64734i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.32637 | + | 1.69515i | 0.211704 | + | 0.0567259i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.27185 | − | 29.2757i | −0.0758548 | − | 0.977488i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.407308 | + | 0.109138i | −0.0135845 | + | 0.00363996i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.8009 | + | 13.7415i | −0.792923 | + | 0.457794i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −24.9637 | + | 14.4128i | −0.830741 | + | 0.479629i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.5412 | − | 50.5364i | −0.449628 | − | 1.67804i | −0.703419 | − | 0.710776i | \(-0.748344\pi\) |
0.253790 | − | 0.967259i | \(-0.418323\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.09726 | −0.135898 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.3525 | 0.608044 | 0.304022 | − | 0.952665i | \(-0.401670\pi\) | ||||
0.304022 | + | 0.952665i | \(0.401670\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.1552 | − | 52.8278i | −0.468468 | − | 1.74835i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.3700 | + | 10.6059i | −0.606632 | + | 0.350239i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.0739 | + | 21.9820i | −1.25594 | + | 0.725118i | −0.972283 | − | 0.233807i | \(-0.924882\pi\) |
−0.283659 | + | 0.958925i | \(0.591548\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.9543 | + | 7.22238i | −0.888174 | + | 0.237985i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −31.4163 | − | 26.8915i | −1.03408 | − | 0.885146i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.05040 | + | 0.817352i | 0.100188 | + | 0.0268454i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.147215 | + | 0.549414i | −0.00482997 | + | 0.0180257i | −0.968299 | − | 0.249795i | \(-0.919637\pi\) |
0.963469 | + | 0.267821i | \(0.0863035\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.07774 | + | 5.07774i | 0.166416 | + | 0.166416i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.35471 | + | 0.898893i | −0.109828 | + | 0.0294284i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.91585 | + | 6.91585i | 0.225931 | + | 0.225931i | 0.810990 | − | 0.585059i | \(-0.198929\pi\) |
−0.585059 | + | 0.810990i | \(0.698929\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −50.8322 | − | 29.3480i | −1.65885 | − | 0.957736i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.12906 | + | 4.12906i | −0.134604 | + | 0.134604i | −0.771198 | − | 0.636595i | \(-0.780342\pi\) |
0.636595 | + | 0.771198i | \(0.280342\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.3334 | − | 31.7545i | −0.597019 | − | 1.03407i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.3027 | + | 7.68029i | 0.432278 | + | 0.249576i | 0.700317 | − | 0.713832i | \(-0.253042\pi\) |
−0.268039 | + | 0.963408i | \(0.586375\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 38.0987 | + | 18.2233i | 1.23674 | + | 0.591554i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.78994 | − | 32.8045i | −0.285033 | − | 1.06376i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.70449 | − | 6.36124i | 0.0552138 | − | 0.206061i | −0.932808 | − | 0.360373i | \(-0.882649\pi\) |
0.988022 | + | 0.154312i | \(0.0493161\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.87429i | 0.0929127i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.561945 | − | 0.973318i | 0.0181462 | − | 0.0314301i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.8932i | 0.932038i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.3309 | − | 14.3309i | 0.461807 | − | 0.461807i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.220203 | 0.00708125 | 0.00354063 | − | 0.999994i | \(-0.498873\pi\) | ||||
0.00354063 | + | 0.999994i | \(0.498873\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.5975 | + | 4.44728i | 0.533188 | + | 0.142867i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.8799 | − | 41.3611i | −0.766341 | − | 1.32734i | −0.939534 | − | 0.342454i | \(-0.888742\pi\) |
0.173193 | − | 0.984888i | \(-0.444592\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.5197 | − | 28.6129i | 0.529596 | − | 0.917287i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.69292 | + | 8.12838i | −0.150140 | + | 0.260050i | −0.931279 | − | 0.364307i | \(-0.881306\pi\) |
0.781139 | + | 0.624357i | \(0.214639\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −31.8380 | − | 55.1450i | −1.01755 | − | 1.76244i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −22.5640 | − | 6.04602i | −0.720415 | − | 0.193035i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.2960 | −0.583553 | −0.291776 | − | 0.956487i | \(-0.594246\pi\) | ||||
−0.291776 | + | 0.956487i | \(0.594246\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.96437 | − | 9.96437i | 0.317170 | − | 0.317170i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34.2108i | 1.08784i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.30731 | − | 5.72843i | 0.105060 | − | 0.181970i | −0.808703 | − | 0.588218i | \(-0.799830\pi\) |
0.913763 | + | 0.406248i | \(0.133163\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 58.0257i | − | 1.84139i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.50791 | − | 20.5558i | 0.174437 | − | 0.651009i | −0.822209 | − | 0.569185i | \(-0.807259\pi\) |
0.996647 | − | 0.0818241i | \(-0.0260746\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.11960 | − | 19.1066i | −0.161977 | − | 0.604507i |
(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 | 1300.2.bs.d.357.4 | 20 | ||
5.2 | odd | 4 | 260.2.bf.c.253.4 | yes | 20 | ||
5.3 | odd | 4 | 1300.2.bn.d.1293.2 | 20 | |||
5.4 | even | 2 | 260.2.bk.c.97.2 | yes | 20 | ||
13.11 | odd | 12 | 1300.2.bn.d.557.2 | 20 | |||
65.24 | odd | 12 | 260.2.bf.c.37.4 | ✓ | 20 | ||
65.37 | even | 12 | 260.2.bk.c.193.2 | yes | 20 | ||
65.63 | even | 12 | inner | 1300.2.bs.d.193.4 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.bf.c.37.4 | ✓ | 20 | 65.24 | odd | 12 | ||
260.2.bf.c.253.4 | yes | 20 | 5.2 | odd | 4 | ||
260.2.bk.c.97.2 | yes | 20 | 5.4 | even | 2 | ||
260.2.bk.c.193.2 | yes | 20 | 65.37 | even | 12 | ||
1300.2.bn.d.557.2 | 20 | 13.11 | odd | 12 | |||
1300.2.bn.d.1293.2 | 20 | 5.3 | odd | 4 | |||
1300.2.bs.d.193.4 | 20 | 65.63 | even | 12 | inner | ||
1300.2.bs.d.357.4 | 20 | 1.1 | even | 1 | trivial |