Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(401,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.l (of order \(4\), 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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | 16.0.534694406811304329216.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 401.7 | ||
Root | \(-1.40501 + 0.161069i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.401 |
Dual form | 1600.2.l.h.1201.7 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 1.86033 | + | 1.86033i | 1.07406 | + | 1.07406i | 0.997029 | + | 0.0770310i | \(0.0245441\pi\) |
0.0770310 | + | 0.997029i | \(0.475456\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.61392i | 1.36593i | 0.730450 | + | 0.682966i | \(0.239310\pi\) | ||||
−0.730450 | + | 0.682966i | \(0.760690\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.92163i | 1.30721i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.0947876 | − | 0.0947876i | 0.0285795 | − | 0.0285795i | −0.692673 | − | 0.721252i | \(-0.743567\pi\) |
0.721252 | + | 0.692673i | \(0.243567\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.59462 | + | 2.59462i | 0.719618 | + | 0.719618i | 0.968527 | − | 0.248909i | \(-0.0800720\pi\) |
−0.248909 | + | 0.968527i | \(0.580072\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.89939 | −0.460671 | −0.230335 | − | 0.973111i | \(-0.573982\pi\) | ||||
−0.230335 | + | 0.973111i | \(0.573982\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.16418 | − | 2.16418i | −0.496496 | − | 0.496496i | 0.413849 | − | 0.910345i | \(-0.364184\pi\) |
−0.910345 | + | 0.413849i | \(0.864184\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.72307 | + | 6.72307i | −1.46709 | + | 1.46709i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.08251i | 1.05978i | 0.848068 | + | 0.529888i | \(0.177766\pi\) | ||||
−0.848068 | + | 0.529888i | \(0.822234\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.71452 | + | 1.71452i | −0.329960 | + | 0.329960i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.25896 | − | 1.25896i | −0.233784 | − | 0.233784i | 0.580486 | − | 0.814270i | \(-0.302863\pi\) |
−0.814270 | + | 0.580486i | \(0.802863\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.27453 | 0.228912 | 0.114456 | − | 0.993428i | \(-0.463488\pi\) | ||||
0.114456 | + | 0.993428i | \(0.463488\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.352672 | 0.0613923 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.25207 | − | 2.25207i | 0.370237 | − | 0.370237i | −0.497326 | − | 0.867564i | \(-0.665685\pi\) |
0.867564 | + | 0.497326i | \(0.165685\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.65368i | 1.54583i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 8.52451i | − | 1.33130i | −0.746262 | − | 0.665652i | \(-0.768153\pi\) | ||
0.746262 | − | 0.665652i | \(-0.231847\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.61439 | − | 1.61439i | 0.246192 | − | 0.246192i | −0.573214 | − | 0.819406i | \(-0.694304\pi\) |
0.819406 | + | 0.573214i | \(0.194304\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.53884 | −0.370328 | −0.185164 | − | 0.982708i | \(-0.559282\pi\) | ||||
−0.185164 | + | 0.982708i | \(0.559282\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.06040 | −0.865772 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.53349 | − | 3.53349i | −0.494788 | − | 0.494788i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.67100 | + | 5.67100i | −0.778971 | + | 0.778971i | −0.979656 | − | 0.200684i | \(-0.935683\pi\) |
0.200684 | + | 0.979656i | \(0.435683\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 8.05215i | − | 1.06653i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.81785 | + | 7.81785i | −1.01780 | + | 1.01780i | −0.0179591 | + | 0.999839i | \(0.505717\pi\) |
−0.999839 | + | 0.0179591i | \(0.994283\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.46410 | + | 3.46410i | 0.443533 | + | 0.443533i | 0.893197 | − | 0.449665i | \(-0.148457\pi\) |
−0.449665 | + | 0.893197i | \(0.648457\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −14.1724 | −1.78556 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.29856 | + | 6.29856i | 0.769491 | + | 0.769491i | 0.978017 | − | 0.208526i | \(-0.0668665\pi\) |
−0.208526 | + | 0.978017i | \(0.566866\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.45512 | + | 9.45512i | −1.13826 | + | 1.13826i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.3074i | 1.34194i | 0.741486 | + | 0.670968i | \(0.234121\pi\) | ||||
−0.741486 | + | 0.670968i | \(0.765879\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 16.1786i | − | 1.89356i | −0.321885 | − | 0.946779i | \(-0.604316\pi\) | ||
0.321885 | − | 0.946779i | \(-0.395684\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.342555 | + | 0.342555i | 0.0390377 | + | 0.0390377i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.13575 | 0.127782 | 0.0638908 | − | 0.997957i | \(-0.479649\pi\) | ||||
0.0638908 | + | 0.997957i | \(0.479649\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.38573 | 0.598414 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.75489 | + | 3.75489i | 0.412153 | + | 0.412153i | 0.882488 | − | 0.470335i | \(-0.155867\pi\) |
−0.470335 | + | 0.882488i | \(0.655867\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 4.68417i | − | 0.502196i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 3.98203i | − | 0.422094i | −0.977476 | − | 0.211047i | \(-0.932313\pi\) | ||
0.977476 | − | 0.211047i | \(-0.0676874\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.37674 | + | 9.37674i | −0.982950 | + | 0.982950i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.37103 | + | 2.37103i | 0.245865 | + | 0.245865i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.3042 | 1.04623 | 0.523117 | − | 0.852261i | \(-0.324769\pi\) | ||||
0.523117 | + | 0.852261i | \(0.324769\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.371721 | + | 0.371721i | 0.0373594 | + | 0.0373594i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.25896 | − | 1.25896i | 0.125272 | − | 0.125272i | −0.641691 | − | 0.766963i | \(-0.721767\pi\) |
0.766963 | + | 0.641691i | \(0.221767\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 10.8655i | − | 1.07061i | −0.844658 | − | 0.535306i | \(-0.820196\pi\) | ||
0.844658 | − | 0.535306i | \(-0.179804\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.48167 | − | 9.48167i | 0.916628 | − | 0.916628i | −0.0801549 | − | 0.996782i | \(-0.525541\pi\) |
0.996782 | + | 0.0801549i | \(0.0255415\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.57530 | + | 8.57530i | 0.821365 | + | 0.821365i | 0.986304 | − | 0.164939i | \(-0.0527427\pi\) |
−0.164939 | + | 0.986304i | \(0.552743\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.37915 | 0.795314 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.5286 | −1.17860 | −0.589298 | − | 0.807916i | \(-0.700595\pi\) | ||||
−0.589298 | + | 0.807916i | \(0.700595\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.1751 | + | 10.1751i | −0.940691 | + | 0.940691i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 6.86425i | − | 0.629245i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9820i | 0.998366i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.8584 | − | 15.8584i | 1.42990 | − | 1.42990i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.94200 | −0.261061 | −0.130530 | − | 0.991444i | \(-0.541668\pi\) | ||||
−0.130530 | + | 0.991444i | \(0.541668\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.00658 | 0.528850 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.54333 | − | 6.54333i | −0.571693 | − | 0.571693i | 0.360908 | − | 0.932601i | \(-0.382467\pi\) |
−0.932601 | + | 0.360908i | \(0.882467\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.82116 | − | 7.82116i | 0.678180 | − | 0.678180i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.82513i | 0.155931i | 0.996956 | + | 0.0779657i | \(0.0248425\pi\) | ||||
−0.996956 | + | 0.0779657i | \(0.975158\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.36931 | + | 5.36931i | −0.455419 | + | 0.455419i | −0.897148 | − | 0.441729i | \(-0.854365\pi\) |
0.441729 | + | 0.897148i | \(0.354365\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.72307 | − | 4.72307i | −0.397754 | − | 0.397754i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.491875 | 0.0411327 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.2743 | − | 11.2743i | −0.929891 | − | 0.929891i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.37915 | + | 4.37915i | −0.358754 | + | 0.358754i | −0.863354 | − | 0.504600i | \(-0.831640\pi\) |
0.504600 | + | 0.863354i | \(0.331640\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 12.9610i | − | 1.05475i | −0.849631 | − | 0.527377i | \(-0.823176\pi\) | ||
0.849631 | − | 0.527377i | \(-0.176824\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 7.44871i | − | 0.602193i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.12723 | + | 9.12723i | 0.728432 | + | 0.728432i | 0.970307 | − | 0.241875i | \(-0.0777624\pi\) |
−0.241875 | + | 0.970307i | \(0.577762\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −21.0998 | −1.67332 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −18.3678 | −1.44758 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.15099 | − | 6.15099i | −0.481783 | − | 0.481783i | 0.423918 | − | 0.905701i | \(-0.360654\pi\) |
−0.905701 | + | 0.423918i | \(0.860654\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 0.710173i | − | 0.0549548i | −0.999622 | − | 0.0274774i | \(-0.991253\pi\) | ||
0.999622 | − | 0.0274774i | \(-0.00874743\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.464102i | 0.0357001i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.48709 | − | 8.48709i | 0.649024 | − | 0.649024i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.1773 | + | 14.1773i | 1.07788 | + | 1.07788i | 0.996700 | + | 0.0811779i | \(0.0258682\pi\) |
0.0811779 | + | 0.996700i | \(0.474132\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −29.0875 | −2.18635 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.00502 | + | 9.00502i | 0.673067 | + | 0.673067i | 0.958422 | − | 0.285355i | \(-0.0921115\pi\) |
−0.285355 | + | 0.958422i | \(0.592111\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.1872 | − | 14.1872i | 1.05452 | − | 1.05452i | 0.0560986 | − | 0.998425i | \(-0.482134\pi\) |
0.998425 | − | 0.0560986i | \(-0.0178661\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.8887i | 0.952761i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.180039 | + | 0.180039i | −0.0131657 | + | 0.0131657i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.19615 | − | 6.19615i | −0.450704 | − | 0.450704i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.9282 | −1.36960 | −0.684798 | − | 0.728733i | \(-0.740110\pi\) | ||||
−0.684798 | + | 0.728733i | \(0.740110\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.3880 | 1.53954 | 0.769772 | − | 0.638319i | \(-0.220370\pi\) | ||||
0.769772 | + | 0.638319i | \(0.220370\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.39341 | − | 6.39341i | 0.455511 | − | 0.455511i | −0.441667 | − | 0.897179i | \(-0.645613\pi\) |
0.897179 | + | 0.441667i | \(0.145613\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 5.85641i | − | 0.415150i | −0.978219 | − | 0.207575i | \(-0.933443\pi\) | ||
0.978219 | − | 0.207575i | \(-0.0665570\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.4347i | 1.65296i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.54979 | − | 4.54979i | 0.319333 | − | 0.319333i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −19.9317 | −1.38535 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.410274 | −0.0283793 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.2640 | + | 19.2640i | 1.32619 | + | 1.32619i | 0.908668 | + | 0.417520i | \(0.137100\pi\) |
0.417520 | + | 0.908668i | \(0.362900\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −21.0354 | + | 21.0354i | −1.44132 | + | 1.44132i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.60603i | 0.312678i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 30.0974 | − | 30.0974i | 2.03379 | − | 2.03379i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.92820 | − | 4.92820i | −0.331507 | − | 0.331507i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.1117 | −1.34678 | −0.673390 | − | 0.739287i | \(-0.735163\pi\) | ||||
−0.673390 | + | 0.739287i | \(0.735163\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.21430 | + | 4.21430i | 0.279713 | + | 0.279713i | 0.832994 | − | 0.553282i | \(-0.186625\pi\) |
−0.553282 | + | 0.832994i | \(0.686625\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.0304 | − | 18.0304i | 1.19148 | − | 1.19148i | 0.214833 | − | 0.976651i | \(-0.431079\pi\) |
0.976651 | − | 0.214833i | \(-0.0689207\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.27453i | 0.0838577i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 4.57839i | − | 0.299941i | −0.988691 | − | 0.149970i | \(-0.952082\pi\) | ||
0.988691 | − | 0.149970i | \(-0.0479178\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.11286 | + | 2.11286i | 0.137245 | + | 0.137245i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.3104 | 1.18440 | 0.592200 | − | 0.805791i | \(-0.298259\pi\) | ||||
0.592200 | + | 0.805791i | \(0.298259\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.31393 | −0.599963 | −0.299982 | − | 0.953945i | \(-0.596981\pi\) | ||||
−0.299982 | + | 0.953945i | \(0.596981\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.1628 | + | 15.1628i | 0.972693 | + | 0.972693i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 11.2304i | − | 0.714575i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.9706i | 0.885353i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.2156 | − | 14.2156i | 0.897281 | − | 0.897281i | −0.0979143 | − | 0.995195i | \(-0.531217\pi\) |
0.995195 | + | 0.0979143i | \(0.0312171\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.481758 | + | 0.481758i | 0.0302879 | + | 0.0302879i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.1347 | 1.06883 | 0.534416 | − | 0.845222i | \(-0.320532\pi\) | ||||
0.534416 | + | 0.845222i | \(0.320532\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.13878 | + | 8.13878i | 0.505719 | + | 0.505719i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.93719 | − | 4.93719i | 0.305604 | − | 0.305604i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.11593i | 0.315462i | 0.987482 | + | 0.157731i | \(0.0504179\pi\) | ||||
−0.987482 | + | 0.157731i | \(0.949582\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.40788 | − | 7.40788i | 0.453355 | − | 0.453355i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.1506 | − | 19.1506i | −1.16763 | − | 1.16763i | −0.982763 | − | 0.184870i | \(-0.940814\pi\) |
−0.184870 | − | 0.982763i | \(-0.559186\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.72066 | −0.286760 | −0.143380 | − | 0.989668i | \(-0.545797\pi\) | ||||
−0.143380 | + | 0.989668i | \(0.545797\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −34.8876 | −2.11149 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.8887 | + | 12.8887i | −0.774408 | + | 0.774408i | −0.978874 | − | 0.204466i | \(-0.934454\pi\) |
0.204466 | + | 0.978874i | \(0.434454\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.99822i | 0.299235i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 16.4934i | − | 0.983913i | −0.870620 | − | 0.491956i | \(-0.836282\pi\) | ||
0.870620 | − | 0.491956i | \(-0.163718\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.69771 | + | 7.69771i | −0.457581 | + | 0.457581i | −0.897861 | − | 0.440279i | \(-0.854879\pi\) |
0.440279 | + | 0.897861i | \(0.354879\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 30.8069 | 1.81847 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.3923 | −0.787783 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19.1692 | + | 19.1692i | 1.12372 | + | 1.12372i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.75538 | − | 5.75538i | 0.336233 | − | 0.336233i | −0.518715 | − | 0.854947i | \(-0.673589\pi\) |
0.854947 | + | 0.518715i | \(0.173589\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.325031i | 0.0188602i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.1872 | + | 13.1872i | −0.762634 | + | 0.762634i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.83427 | + | 5.83427i | 0.336282 | + | 0.336282i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.68417 | 0.269098 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.60547 | + | 9.60547i | 0.548213 | + | 0.548213i | 0.925924 | − | 0.377711i | \(-0.123289\pi\) |
−0.377711 | + | 0.925924i | \(0.623289\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.2134 | − | 20.2134i | 1.14990 | − | 1.14990i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 20.3415i | − | 1.15346i | −0.816934 | − | 0.576731i | \(-0.804328\pi\) | ||
0.816934 | − | 0.576731i | \(-0.195672\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.6414i | 1.44934i | 0.689097 | + | 0.724669i | \(0.258007\pi\) | ||||
−0.689097 | + | 0.724669i | \(0.741993\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.945994 | − | 0.945994i | −0.0531323 | − | 0.0531323i | 0.680041 | − | 0.733174i | \(-0.261962\pi\) |
−0.733174 | + | 0.680041i | \(0.761962\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.238668 | −0.0133629 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 35.2780 | 1.96903 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.11062 | + | 4.11062i | 0.228721 | + | 0.228721i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 31.9057i | 1.76439i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 9.17515i | − | 0.505843i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.16418 | + | 6.16418i | −0.338814 | + | 0.338814i | −0.855921 | − | 0.517107i | \(-0.827009\pi\) |
0.517107 | + | 0.855921i | \(0.327009\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.83176 | + | 8.83176i | 0.483977 | + | 0.483977i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.2333 | 1.53797 | 0.768983 | − | 0.639269i | \(-0.220763\pi\) | ||||
0.768983 | + | 0.639269i | \(0.220763\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −23.3074 | − | 23.3074i | −1.26588 | − | 1.26588i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.120809 | − | 0.120809i | 0.00654219 | − | 0.00654219i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.39562i | 0.183346i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.0548 | + | 13.0548i | −0.700816 | + | 0.700816i | −0.964586 | − | 0.263770i | \(-0.915034\pi\) |
0.263770 | + | 0.964586i | \(0.415034\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.3080 | + | 20.3080i | 1.08706 | + | 1.08706i | 0.995830 | + | 0.0912314i | \(0.0290803\pi\) |
0.0912314 | + | 0.995830i | \(0.470920\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.89708 | −0.474891 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.6814 | 0.994310 | 0.497155 | − | 0.867662i | \(-0.334378\pi\) | ||||
0.497155 | + | 0.867662i | \(0.334378\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.7697 | − | 12.7697i | 0.675847 | − | 0.675847i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 16.4072i | − | 0.865937i | −0.901409 | − | 0.432968i | \(-0.857466\pi\) | ||
0.901409 | − | 0.432968i | \(-0.142534\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 9.63268i | − | 0.506983i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −20.4302 | + | 20.4302i | −1.07231 | + | 1.07231i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.58049 | −0.186900 | −0.0934500 | − | 0.995624i | \(-0.529790\pi\) | ||||
−0.0934500 | + | 0.995624i | \(0.529790\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 33.4299 | 1.74029 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.4945 | − | 20.4945i | −1.06402 | − | 1.06402i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.72985 | + | 8.72985i | −0.452015 | + | 0.452015i | −0.896023 | − | 0.444008i | \(-0.853556\pi\) |
0.444008 | + | 0.896023i | \(0.353556\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 6.53307i | − | 0.336470i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.11276 | − | 6.11276i | 0.313991 | − | 0.313991i | −0.532462 | − | 0.846454i | \(-0.678733\pi\) |
0.846454 | + | 0.532462i | \(0.178733\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.47309 | − | 5.47309i | −0.280395 | − | 0.280395i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.31434 | 0.373745 | 0.186873 | − | 0.982384i | \(-0.440165\pi\) | ||||
0.186873 | + | 0.982384i | \(0.440165\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.33103 | + | 6.33103i | 0.321824 | + | 0.321824i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.74166 | − | 9.74166i | 0.493922 | − | 0.493922i | −0.415618 | − | 0.909539i | \(-0.636435\pi\) |
0.909539 | + | 0.415618i | \(0.136435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 9.65368i | − | 0.488207i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 24.3454i | − | 1.22807i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.04203 | − | 8.04203i | −0.403618 | − | 0.403618i | 0.475888 | − | 0.879506i | \(-0.342127\pi\) |
−0.879506 | + | 0.475888i | \(0.842127\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 29.0998 | 1.45681 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.77627 | −0.338391 | −0.169195 | − | 0.985583i | \(-0.554117\pi\) | ||||
−0.169195 | + | 0.985583i | \(0.554117\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.30691 | + | 3.30691i | 0.164729 | + | 0.164729i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 0.426936i | − | 0.0211624i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 16.2601i | − | 0.804010i | −0.915637 | − | 0.402005i | \(-0.868313\pi\) | ||
0.915637 | − | 0.402005i | \(-0.131687\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.39534 | + | 3.39534i | −0.167480 | + | 0.167480i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −28.2531 | − | 28.2531i | −1.39024 | − | 1.39024i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.9773 | −0.978295 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.1408 | − | 10.1408i | −0.495409 | − | 0.495409i | 0.414596 | − | 0.910005i | \(-0.363923\pi\) |
−0.910005 | + | 0.414596i | \(0.863923\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.5849 | + | 13.5849i | −0.662088 | + | 0.662088i | −0.955872 | − | 0.293784i | \(-0.905085\pi\) |
0.293784 | + | 0.955872i | \(0.405085\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 9.95637i | − | 0.484095i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.5190 | + | 12.5190i | −0.605836 | + | 0.605836i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.915049 | + | 0.915049i | 0.0441790 | + | 0.0441790i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.37612 | −0.0662853 | −0.0331427 | − | 0.999451i | \(-0.510552\pi\) | ||||
−0.0331427 | + | 0.999451i | \(0.510552\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.9307 | 0.957810 | 0.478905 | − | 0.877867i | \(-0.341034\pi\) | ||||
0.478905 | + | 0.877867i | \(0.341034\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.9994 | − | 10.9994i | 0.526175 | − | 0.526175i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 25.4133i | − | 1.21291i | −0.795117 | − | 0.606455i | \(-0.792591\pi\) | ||
0.795117 | − | 0.606455i | \(-0.207409\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 23.7666i | − | 1.13174i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.7208 | − | 24.7208i | 1.17452 | − | 1.17452i | 0.193402 | − | 0.981120i | \(-0.438048\pi\) |
0.981120 | − | 0.193402i | \(-0.0619522\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.2933 | −0.770646 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.62743 | −0.265575 | −0.132787 | − | 0.991145i | \(-0.542393\pi\) | ||||
−0.132787 | + | 0.991145i | \(0.542393\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.808017 | − | 0.808017i | −0.0380481 | − | 0.0380481i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 24.1117 | − | 24.1117i | 1.13287 | − | 1.13287i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 26.6040i | − | 1.24448i | −0.782825 | − | 0.622241i | \(-0.786222\pi\) | ||
0.782825 | − | 0.622241i | \(-0.213778\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.25656 | − | 3.25656i | 0.152003 | − | 0.152003i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.9468 | + | 11.9468i | 0.556418 | + | 0.556418i | 0.928286 | − | 0.371868i | \(-0.121283\pi\) |
−0.371868 | + | 0.928286i | \(0.621283\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.530134 | −0.0246374 | −0.0123187 | − | 0.999924i | \(-0.503921\pi\) | ||||
−0.0123187 | + | 0.999924i | \(0.503921\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.4219 | − | 11.4219i | −0.528542 | − | 0.528542i | 0.391595 | − | 0.920138i | \(-0.371923\pi\) |
−0.920138 | + | 0.391595i | \(0.871923\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.7625 | + | 22.7625i | −1.05107 | + | 1.05107i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 33.9592i | 1.56476i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 0.306048i | − | 0.0140721i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −22.2395 | − | 22.2395i | −1.01828 | − | 1.01828i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.37434 | 0.291251 | 0.145625 | − | 0.989340i | \(-0.453481\pi\) | ||||
0.145625 | + | 0.989340i | \(0.453481\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.6865 | 0.532859 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −34.1700 | − | 34.1700i | −1.55479 | − | 1.55479i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 31.3203i | − | 1.41926i | −0.704575 | − | 0.709629i | \(-0.748862\pi\) | ||
0.704575 | − | 0.709629i | \(-0.251138\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 22.8857i | − | 1.03493i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.0893 | + | 14.0893i | −0.635843 | + | 0.635843i | −0.949527 | − | 0.313684i | \(-0.898437\pi\) |
0.313684 | + | 0.949527i | \(0.398437\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.39127 | + | 2.39127i | 0.107697 | + | 0.107697i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −40.8639 | −1.83299 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.30233 | − | 2.30233i | −0.103067 | − | 0.103067i | 0.653693 | − | 0.756760i | \(-0.273219\pi\) |
−0.756760 | + | 0.653693i | \(0.773219\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.32115 | − | 1.32115i | 0.0590248 | − | 0.0590248i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 14.7556i | − | 0.657921i | −0.944344 | − | 0.328961i | \(-0.893302\pi\) | ||
0.944344 | − | 0.328961i | \(-0.106698\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.863380 | + | 0.863380i | −0.0383441 | + | 0.0383441i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.03042 | + | 8.03042i | 0.355942 | + | 0.355942i | 0.862315 | − | 0.506373i | \(-0.169014\pi\) |
−0.506373 | + | 0.862315i | \(0.669014\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 58.4680 | 2.58647 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.42107 | 0.327648 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.240650 | + | 0.240650i | −0.0105838 | + | 0.0105838i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 52.7487i | 2.31541i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 13.7417i | − | 0.602033i | −0.953619 | − | 0.301017i | \(-0.902674\pi\) | ||
0.953619 | − | 0.301017i | \(-0.0973259\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.77116 | + | 6.77116i | −0.296082 | + | 0.296082i | −0.839477 | − | 0.543395i | \(-0.817139\pi\) |
0.543395 | + | 0.839477i | \(0.317139\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.42083 | −0.105453 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.83186 | −0.123124 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −30.6587 | − | 30.6587i | −1.33047 | − | 1.33047i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.1179 | − | 22.1179i | 0.958030 | − | 0.958030i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 33.5046i | 1.44583i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.574451 | + | 0.574451i | −0.0247434 | + | 0.0247434i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.82599 | + | 7.82599i | 0.336465 | + | 0.336465i | 0.855035 | − | 0.518570i | \(-0.173535\pi\) |
−0.518570 | + | 0.855035i | \(0.673535\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 52.7855 | 2.26524 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.1263 | − | 16.1263i | −0.689511 | − | 0.689511i | 0.272613 | − | 0.962124i | \(-0.412112\pi\) |
−0.962124 | + | 0.272613i | \(0.912112\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.5849 | + | 13.5849i | −0.579790 | + | 0.579790i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.44924i | 0.232146i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.10450i | 0.174541i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.7333 | + | 13.7333i | 0.581897 | + | 0.581897i | 0.935424 | − | 0.353527i | \(-0.115018\pi\) |
−0.353527 | + | 0.935424i | \(0.615018\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.37745 | 0.354328 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.669862 | −0.0282816 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.2023 | − | 13.2023i | −0.556412 | − | 0.556412i | 0.371872 | − | 0.928284i | \(-0.378716\pi\) |
−0.928284 | + | 0.371872i | \(0.878716\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.4636i | 0.817393i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 7.32481i | − | 0.307072i | −0.988143 | − | 0.153536i | \(-0.950934\pi\) | ||
0.988143 | − | 0.153536i | \(-0.0490661\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.1916 | − | 22.1916i | 0.928688 | − | 0.928688i | −0.0689332 | − | 0.997621i | \(-0.521960\pi\) |
0.997621 | + | 0.0689332i | \(0.0219595\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −35.2126 | − | 35.2126i | −1.47103 | − | 1.47103i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.39473 | 0.391108 | 0.195554 | − | 0.980693i | \(-0.437350\pi\) | ||||
0.195554 | + | 0.980693i | \(0.437350\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 39.7887 | + | 39.7887i | 1.65356 | + | 1.65356i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.5699 | + | 13.5699i | −0.562973 | + | 0.562973i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.07508i | 0.0445253i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.7246 | − | 10.7246i | 0.442650 | − | 0.442650i | −0.450252 | − | 0.892902i | \(-0.648666\pi\) |
0.892902 | + | 0.450252i | \(0.148666\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.75830 | − | 2.75830i | −0.113654 | − | 0.113654i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.7876 | 0.978493 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −38.2253 | −1.56973 | −0.784863 | − | 0.619670i | \(-0.787267\pi\) | ||||
−0.784863 | + | 0.619670i | \(0.787267\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.8948 | − | 10.8948i | 0.445896 | − | 0.445896i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 41.5801i | − | 1.69892i | −0.527656 | − | 0.849458i | \(-0.676929\pi\) | ||
0.527656 | − | 0.849458i | \(-0.323071\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.1081i | 0.942599i | 0.881973 | + | 0.471299i | \(0.156215\pi\) | ||||
−0.881973 | + | 0.471299i | \(0.843785\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −24.7006 | + | 24.7006i | −1.00589 | + | 1.00589i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.1150 | 0.613500 | 0.306750 | − | 0.951790i | \(-0.400759\pi\) | ||||
0.306750 | + | 0.951790i | \(0.400759\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16.9282 | 0.685965 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.58732 | − | 6.58732i | −0.266494 | − | 0.266494i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.18710 | − | 1.18710i | 0.0479466 | − | 0.0479466i | −0.682727 | − | 0.730674i | \(-0.739206\pi\) |
0.730674 | + | 0.682727i | \(0.239206\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 5.23711i | − | 0.210838i | −0.994428 | − | 0.105419i | \(-0.966382\pi\) | ||
0.994428 | − | 0.105419i | \(-0.0336184\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.52847 | + | 6.52847i | −0.262401 | + | 0.262401i | −0.826029 | − | 0.563628i | \(-0.809405\pi\) |
0.563628 | + | 0.826029i | \(0.309405\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.71408 | − | 8.71408i | −0.349684 | − | 0.349684i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.3907 | 0.576553 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.763244 | − | 0.763244i | −0.0304810 | − | 0.0304810i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.27756 | + | 4.27756i | −0.170557 | + | 0.170557i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.7193i | 0.864633i | 0.901722 | + | 0.432316i | \(0.142304\pi\) | ||||
−0.901722 | + | 0.432316i | \(0.857696\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 71.6746i | 2.84881i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.7244 | − | 15.7244i | −0.623025 | − | 0.623025i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −44.3432 | −1.75419 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −45.3927 | −1.79291 | −0.896453 | − | 0.443139i | \(-0.853865\pi\) | ||||
−0.896453 | + | 0.443139i | \(0.853865\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.5408 | + | 20.5408i | 0.810049 | + | 0.810049i | 0.984641 | − | 0.174592i | \(-0.0558607\pi\) |
−0.174592 | + | 0.984641i | \(0.555861\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.7472i | 1.24811i | 0.781379 | + | 0.624056i | \(0.214516\pi\) | ||||
−0.781379 | + | 0.624056i | \(0.785484\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.48207i | 0.0581764i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.56873 | + | 8.56873i | −0.335835 | + | 0.335835i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.30078 | + | 4.30078i | 0.168302 | + | 0.168302i | 0.786233 | − | 0.617930i | \(-0.212029\pi\) |
−0.617930 | + | 0.786233i | \(0.712029\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 63.4463 | 2.47527 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.2156 | − | 18.2156i | −0.709579 | − | 0.709579i | 0.256868 | − | 0.966447i | \(-0.417310\pi\) |
−0.966447 | + | 0.256868i | \(0.917310\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.7679 | + | 19.7679i | −0.768883 | + | 0.768883i | −0.977910 | − | 0.209027i | \(-0.932970\pi\) |
0.209027 | + | 0.977910i | \(0.432970\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 18.3361i | − | 0.712116i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.39869 | − | 6.39869i | 0.247758 | − | 0.247758i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −37.4144 | − | 37.4144i | −1.44652 | − | 1.44652i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.656708 | 0.0253519 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.43246 | −0.325047 | −0.162524 | − | 0.986705i | \(-0.551963\pi\) | ||||
−0.162524 | + | 0.986705i | \(0.551963\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.8693 | + | 20.8693i | −0.802073 | + | 0.802073i | −0.983419 | − | 0.181346i | \(-0.941954\pi\) |
0.181346 | + | 0.983419i | \(0.441954\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 37.2386i | 1.42909i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.6799i | 0.600856i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.4398 | + | 16.4398i | −0.629051 | + | 0.629051i | −0.947829 | − | 0.318778i | \(-0.896728\pi\) |
0.318778 | + | 0.947829i | \(0.396728\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 67.0849 | 2.55945 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −29.4282 | −1.12112 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.4076 | − | 17.4076i | −0.662216 | − | 0.662216i | 0.293686 | − | 0.955902i | \(-0.405118\pi\) |
−0.955902 | + | 0.293686i | \(0.905118\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.34337 | + | 1.34337i | −0.0510304 | + | 0.0510304i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.1914i | 0.613293i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.51731 | − | 8.51731i | 0.322154 | − | 0.322154i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.3888 | − | 25.3888i | −0.958920 | − | 0.958920i | 0.0402687 | − | 0.999189i | \(-0.487179\pi\) |
−0.999189 | + | 0.0402687i | \(0.987179\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.74773 | −0.367643 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.54979 | + | 4.54979i | 0.171113 | + | 0.171113i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.6201 | + | 17.6201i | −0.661738 | + | 0.661738i | −0.955790 | − | 0.294051i | \(-0.904996\pi\) |
0.294051 | + | 0.955790i | \(0.404996\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.45398i | 0.167037i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.47779i | 0.242595i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 34.0633 | + | 34.0633i | 1.27212 | + | 1.27212i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −42.6068 | −1.58896 | −0.794482 | − | 0.607287i | \(-0.792258\pi\) | ||||
−0.794482 | + | 0.607287i | \(0.792258\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 39.2671 | 1.46238 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.3269 | − | 17.3269i | −0.644396 | − | 0.644396i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 50.5830i | − | 1.87602i | −0.346609 | − | 0.938010i | \(-0.612667\pi\) | ||
0.346609 | − | 0.938010i | \(-0.387333\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 40.2583i | 1.49105i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.06636 | + | 3.06636i | −0.113413 | + | 0.113413i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.17299 | + | 6.17299i | 0.228005 | + | 0.228005i | 0.811859 | − | 0.583854i | \(-0.198456\pi\) |
−0.583854 | + | 0.811859i | \(0.698456\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.19405 | 0.0439834 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.8974 | + | 22.8974i | 0.842293 | + | 0.842293i | 0.989157 | − | 0.146864i | \(-0.0469178\pi\) |
−0.146864 | + | 0.989157i | \(0.546918\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.8923 | − | 20.8923i | 0.767497 | − | 0.767497i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.8975i | 0.436478i | 0.975895 | + | 0.218239i | \(0.0700312\pi\) | ||||
−0.975895 | + | 0.218239i | \(0.929969\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.7253 | + | 14.7253i | −0.538770 | + | 0.538770i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 34.2660 | + | 34.2660i | 1.25205 | + | 1.25205i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.4102 | −0.854250 | −0.427125 | − | 0.904193i | \(-0.640474\pi\) | ||||
−0.427125 | + | 0.904193i | \(0.640474\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 52.8913 | 1.92747 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.3218 | + | 11.3218i | −0.411496 | + | 0.411496i | −0.882260 | − | 0.470763i | \(-0.843979\pi\) |
0.470763 | + | 0.882260i | \(0.343979\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.79246i | 0.0650620i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.53590i | 0.309426i | 0.987959 | + | 0.154713i | \(0.0494453\pi\) | ||||
−0.987959 | + | 0.154713i | \(0.950555\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30.9904 | + | 30.9904i | −1.12193 | + | 1.12193i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −40.5687 | −1.46485 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.8384 | 0.643270 | 0.321635 | − | 0.946864i | \(-0.395768\pi\) | ||||
0.321635 | + | 0.946864i | \(0.395768\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31.8761 | + | 31.8761i | 1.14799 | + | 1.14799i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.9457 | + | 23.9457i | −0.861267 | + | 0.861267i | −0.991485 | − | 0.130219i | \(-0.958432\pi\) |
0.130219 | + | 0.991485i | \(0.458432\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 30.2816i | 1.08635i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.4485 | + | 18.4485i | −0.660988 | + | 0.660988i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.07180 | + | 1.07180i | 0.0383519 | + | 0.0383519i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.31705 | 0.154279 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.3914 | + | 32.3914i | 1.15463 | + | 1.15463i | 0.985614 | + | 0.169014i | \(0.0540582\pi\) |
0.169014 | + | 0.985614i | \(0.445942\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.51731 | + | 9.51731i | −0.338825 | + | 0.338825i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 45.2775i | − | 1.60988i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.9761i | 0.638348i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.92658 | − | 1.92658i | −0.0682428 | − | 0.0682428i | 0.672162 | − | 0.740404i | \(-0.265366\pi\) |
−0.740404 | + | 0.672162i | \(0.765366\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.82225 | 0.170599 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.6160 | 0.551765 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.53353 | − | 1.53353i | −0.0541170 | − | 0.0541170i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 71.2527i | − | 2.50822i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 49.8993i | 1.75437i | 0.480157 | + | 0.877183i | \(0.340580\pi\) | ||||
−0.480157 | + | 0.877183i | \(0.659420\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.9363 | + | 22.9363i | −0.805401 | + | 0.805401i | −0.983934 | − | 0.178533i | \(-0.942865\pi\) |
0.178533 | + | 0.983934i | \(0.442865\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.78196 | − | 8.78196i | −0.307997 | − | 0.307997i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.98764 | −0.244467 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −36.7721 | − | 36.7721i | −1.28492 | − | 1.28492i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.7321 | − | 10.7321i | 0.374551 | − | 0.374551i | −0.494581 | − | 0.869132i | \(-0.664678\pi\) |
0.869132 | + | 0.494581i | \(0.164678\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.56875i | 0.298688i | 0.988785 | + | 0.149344i | \(0.0477162\pi\) | ||||
−0.988785 | + | 0.149344i | \(0.952284\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.0841 | − | 10.0841i | 0.350660 | − | 0.350660i | −0.509695 | − | 0.860355i | \(-0.670242\pi\) |
0.860355 | + | 0.509695i | \(0.170242\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.656708 | − | 0.656708i | −0.0228084 | − | 0.0228084i | 0.695611 | − | 0.718419i | \(-0.255134\pi\) |
−0.718419 | + | 0.695611i | \(0.755134\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −47.9544 | −1.66352 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.5111 | 0.398836 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.18521 | + | 2.18521i | −0.0755318 | + | 0.0755318i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.41206i | 0.186845i | 0.995627 | + | 0.0934225i | \(0.0297807\pi\) | ||||
−0.995627 | + | 0.0934225i | \(0.970219\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 25.8300i | − | 0.890690i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 30.6831 | − | 30.6831i | 1.05678 | − | 1.05678i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −39.6882 | −1.36370 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.6405 | −0.982939 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.4461 | + | 11.4461i | 0.392368 | + | 0.392368i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.0301 | + | 17.0301i | −0.583098 | + | 0.583098i | −0.935753 | − | 0.352655i | \(-0.885279\pi\) |
0.352655 | + | 0.935753i | \(0.385279\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 53.1079i | 1.81413i | 0.420988 | + | 0.907066i | \(0.361683\pi\) | ||||
−0.420988 | + | 0.907066i | \(0.638317\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.7609 | + | 10.7609i | −0.367158 | + | 0.367158i | −0.866440 | − | 0.499282i | \(-0.833597\pi\) |
0.499282 | + | 0.866440i | \(0.333597\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 57.3108 | + | 57.3108i | 1.95315 | + | 1.95315i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.2106 | 0.722016 | 0.361008 | − | 0.932563i | \(-0.382433\pi\) | ||||
0.361008 | + | 0.932563i | \(0.382433\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −24.9141 | − | 24.9141i | −0.846126 | − | 0.846126i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.107655 | − | 0.107655i | 0.00365194 | − | 0.00365194i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.6847i | 1.10748i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 40.4093i | 1.36765i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.6041 | − | 25.6041i | −0.864589 | − | 0.864589i | 0.127278 | − | 0.991867i | \(-0.459376\pi\) |
−0.991867 | + | 0.127278i | \(0.959376\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21.4138 | 0.722268 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.0675 | −0.440255 | −0.220128 | − | 0.975471i | \(-0.570647\pi\) | ||||
−0.220128 | + | 0.975471i | \(0.570647\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.1957 | − | 12.1957i | −0.410419 | − | 0.410419i | 0.471466 | − | 0.881884i | \(-0.343725\pi\) |
−0.881884 | + | 0.471466i | \(0.843725\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.3716i | 1.22124i | 0.791924 | + | 0.610619i | \(0.209079\pi\) | ||||
−0.791924 | + | 0.610619i | \(0.790921\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 10.6322i | − | 0.356591i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.510500 | − | 0.510500i | 0.0171024 | − | 0.0171024i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.49449 | + | 5.49449i | 0.183866 | + | 0.183866i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −49.0649 | −1.63823 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.60458 | − | 1.60458i | −0.0535159 | − | 0.0535159i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.7715 | − | 10.7715i | 0.358849 | − | 0.358849i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 21.7073i | 0.722373i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.4831 | + | 35.4831i | −1.17820 | + | 1.17820i | −0.197996 | + | 0.980203i | \(0.563443\pi\) |
−0.980203 | + | 0.197996i | \(0.936557\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.93719 | + | 4.93719i | 0.163756 | + | 0.163756i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.6536 | −0.750547 | −0.375274 | − | 0.926914i | \(-0.622451\pi\) | ||||
−0.375274 | + | 0.926914i | \(0.622451\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.711834 | 0.0235583 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23.6470 | − | 23.6470i | 0.780894 | − | 0.780894i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.9532i | 0.658195i | 0.944296 | + | 0.329097i | \(0.106744\pi\) | ||||
−0.944296 | + | 0.329097i | \(0.893256\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 35.7386i | 1.17763i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29.3383 | + | 29.3383i | −0.965681 | + | 0.965681i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 42.6105 | 1.39951 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.0293 | −0.361859 | −0.180929 | − | 0.983496i | \(-0.557911\pi\) | ||||
−0.180929 | + | 0.983496i | \(0.557911\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.1158 | + | 13.1158i | 0.429853 | + | 0.429853i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 37.8418 | − | 37.8418i | 1.23889 | − | 1.23889i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 36.6851i | − | 1.19845i | −0.800581 | − | 0.599225i | \(-0.795476\pi\) | ||
0.800581 | − | 0.599225i | \(-0.204524\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −47.7014 | + | 47.7014i | −1.55668 | + | 1.55668i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.8618 | − | 26.8618i | −0.875671 | − | 0.875671i | 0.117412 | − | 0.993083i | \(-0.462540\pi\) |
−0.993083 | + | 0.117412i | \(0.962540\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 43.3258 | 1.41088 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42.0944 | − | 42.0944i | −1.36788 | − | 1.36788i | −0.863451 | − | 0.504433i | \(-0.831701\pi\) |
−0.504433 | − | 0.863451i | \(-0.668299\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 41.9772 | − | 41.9772i | 1.36264 | − | 1.36264i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 3.51971i | − | 0.114135i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.32619i | 0.172532i | 0.996272 | + | 0.0862661i | \(0.0274935\pi\) | ||||
−0.996272 | + | 0.0862661i | \(0.972506\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.444001 | − | 0.444001i | −0.0143525 | − | 0.0143525i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.59587 | −0.212992 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.3756 | −0.947599 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 37.1836 | + | 37.1836i | 1.19822 | + | 1.19822i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.9668i | 0.963667i | 0.876263 | + | 0.481833i | \(0.160029\pi\) | ||||
−0.876263 | + | 0.481833i | \(0.839971\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.2942i | 0.491320i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.750872 | + | 0.750872i | −0.0240966 | + | 0.0240966i | −0.719052 | − | 0.694956i | \(-0.755424\pi\) |
0.694956 | + | 0.719052i | \(0.255424\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.4043 | − | 19.4043i | −0.622072 | − | 0.622072i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.2513 | −0.839854 | −0.419927 | − | 0.907558i | \(-0.637944\pi\) | ||||
−0.419927 | + | 0.907558i | \(0.637944\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.377447 | − | 0.377447i | −0.0120633 | − | 0.0120633i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −33.6291 | + | 33.6291i | −1.07370 | + | 1.07370i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 13.0227i | − | 0.415360i | −0.978197 | − | 0.207680i | \(-0.933409\pi\) | ||
0.978197 | − | 0.207680i | \(-0.0665913\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 17.0688 | − | 17.0688i | 0.543305 | − | 0.543305i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.20514 | + | 8.20514i | 0.260908 | + | 0.260908i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.7487 | −1.42149 | −0.710744 | − | 0.703451i | \(-0.751642\pi\) | ||||
−0.710744 | + | 0.703451i | \(0.751642\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −22.9348 | −0.727813 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.2387 | + | 21.2387i | −0.672637 | + | 0.672637i | −0.958323 | − | 0.285686i | \(-0.907778\pi\) |
0.285686 | + | 0.958323i | \(0.407778\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.72244i | 0.244327i |
(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 | 1600.2.l.h.401.7 | 16 | ||
4.3 | odd | 2 | 400.2.l.i.301.6 | 16 | |||
5.2 | odd | 4 | 320.2.q.c.209.7 | 16 | |||
5.3 | odd | 4 | 320.2.q.c.209.2 | 16 | |||
5.4 | even | 2 | inner | 1600.2.l.h.401.2 | 16 | ||
16.5 | even | 4 | inner | 1600.2.l.h.1201.7 | 16 | ||
16.11 | odd | 4 | 400.2.l.i.101.6 | 16 | |||
20.3 | even | 4 | 80.2.q.c.29.2 | ✓ | 16 | ||
20.7 | even | 4 | 80.2.q.c.29.7 | yes | 16 | ||
20.19 | odd | 2 | 400.2.l.i.301.3 | 16 | |||
40.3 | even | 4 | 640.2.q.e.289.2 | 16 | |||
40.13 | odd | 4 | 640.2.q.f.289.7 | 16 | |||
40.27 | even | 4 | 640.2.q.e.289.7 | 16 | |||
40.37 | odd | 4 | 640.2.q.f.289.2 | 16 | |||
60.23 | odd | 4 | 720.2.bm.f.109.7 | 16 | |||
60.47 | odd | 4 | 720.2.bm.f.109.2 | 16 | |||
80.3 | even | 4 | 640.2.q.e.609.7 | 16 | |||
80.13 | odd | 4 | 640.2.q.f.609.2 | 16 | |||
80.27 | even | 4 | 80.2.q.c.69.2 | yes | 16 | ||
80.37 | odd | 4 | 320.2.q.c.49.2 | 16 | |||
80.43 | even | 4 | 80.2.q.c.69.7 | yes | 16 | ||
80.53 | odd | 4 | 320.2.q.c.49.7 | 16 | |||
80.59 | odd | 4 | 400.2.l.i.101.3 | 16 | |||
80.67 | even | 4 | 640.2.q.e.609.2 | 16 | |||
80.69 | even | 4 | inner | 1600.2.l.h.1201.2 | 16 | ||
80.77 | odd | 4 | 640.2.q.f.609.7 | 16 | |||
240.107 | odd | 4 | 720.2.bm.f.469.7 | 16 | |||
240.203 | odd | 4 | 720.2.bm.f.469.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.q.c.29.2 | ✓ | 16 | 20.3 | even | 4 | ||
80.2.q.c.29.7 | yes | 16 | 20.7 | even | 4 | ||
80.2.q.c.69.2 | yes | 16 | 80.27 | even | 4 | ||
80.2.q.c.69.7 | yes | 16 | 80.43 | even | 4 | ||
320.2.q.c.49.2 | 16 | 80.37 | odd | 4 | |||
320.2.q.c.49.7 | 16 | 80.53 | odd | 4 | |||
320.2.q.c.209.2 | 16 | 5.3 | odd | 4 | |||
320.2.q.c.209.7 | 16 | 5.2 | odd | 4 | |||
400.2.l.i.101.3 | 16 | 80.59 | odd | 4 | |||
400.2.l.i.101.6 | 16 | 16.11 | odd | 4 | |||
400.2.l.i.301.3 | 16 | 20.19 | odd | 2 | |||
400.2.l.i.301.6 | 16 | 4.3 | odd | 2 | |||
640.2.q.e.289.2 | 16 | 40.3 | even | 4 | |||
640.2.q.e.289.7 | 16 | 40.27 | even | 4 | |||
640.2.q.e.609.2 | 16 | 80.67 | even | 4 | |||
640.2.q.e.609.7 | 16 | 80.3 | even | 4 | |||
640.2.q.f.289.2 | 16 | 40.37 | odd | 4 | |||
640.2.q.f.289.7 | 16 | 40.13 | odd | 4 | |||
640.2.q.f.609.2 | 16 | 80.13 | odd | 4 | |||
640.2.q.f.609.7 | 16 | 80.77 | odd | 4 | |||
720.2.bm.f.109.2 | 16 | 60.47 | odd | 4 | |||
720.2.bm.f.109.7 | 16 | 60.23 | odd | 4 | |||
720.2.bm.f.469.2 | 16 | 240.203 | odd | 4 | |||
720.2.bm.f.469.7 | 16 | 240.107 | odd | 4 | |||
1600.2.l.h.401.2 | 16 | 5.4 | even | 2 | inner | ||
1600.2.l.h.401.7 | 16 | 1.1 | even | 1 | trivial | ||
1600.2.l.h.1201.2 | 16 | 80.69 | even | 4 | inner | ||
1600.2.l.h.1201.7 | 16 | 16.5 | even | 4 | inner |