Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,2,Mod(47,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.y (of order \(12\), degree \(4\), 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: | \(4.59938315643\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 335.19 | ||
Character | \(\chi\) | \(=\) | 576.335 |
Dual form | 576.2.y.a.239.19 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | 1.58764 | + | 0.692394i | 0.916622 | + | 0.399754i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.83365 | − | 0.759273i | −1.26725 | − | 0.339557i | −0.438270 | − | 0.898843i | \(-0.644409\pi\) |
−0.828975 | + | 0.559286i | \(0.811075\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.41719 | + | 2.45465i | −0.535648 | + | 0.927769i | 0.463484 | + | 0.886105i | \(0.346599\pi\) |
−0.999132 | + | 0.0416640i | \(0.986734\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.04118 | + | 2.19854i | 0.680394 | + | 0.732847i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.794578 | + | 0.212907i | −0.239574 | + | 0.0641937i | −0.376608 | − | 0.926373i | \(-0.622910\pi\) |
0.137034 | + | 0.990566i | \(0.456243\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.22468 | + | 0.864050i | 0.894365 | + | 0.239644i | 0.676595 | − | 0.736356i | \(-0.263455\pi\) |
0.217770 | + | 0.976000i | \(0.430122\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.97308 | − | 3.16745i | −1.02585 | − | 0.817832i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.28589i | 1.76709i | 0.468348 | + | 0.883544i | \(0.344849\pi\) | ||||
−0.468348 | + | 0.883544i | \(0.655151\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.951758 | + | 0.951758i | 0.218348 | + | 0.218348i | 0.807802 | − | 0.589454i | \(-0.200657\pi\) |
−0.589454 | + | 0.807802i | \(0.700657\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.94957 | + | 2.91583i | −0.861866 | + | 0.636287i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.13217 | + | 2.96306i | −1.07013 | + | 0.617841i | −0.928218 | − | 0.372038i | \(-0.878659\pi\) |
−0.141915 | + | 0.989879i | \(0.545326\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.12293 | + | 1.80302i | 0.624585 | + | 0.360605i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.71840 | + | 4.90379i | 0.330706 | + | 0.943734i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.76813 | + | 0.473770i | −0.328334 | + | 0.0879768i | −0.419221 | − | 0.907884i | \(-0.637697\pi\) |
0.0908866 | + | 0.995861i | \(0.471030\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.05610 | + | 1.18709i | −0.369286 | + | 0.213207i | −0.673147 | − | 0.739509i | \(-0.735058\pi\) |
0.303860 | + | 0.952717i | \(0.401724\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.40892 | − | 0.212143i | −0.245261 | − | 0.0369293i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.87957 | − | 5.87957i | 0.993828 | − | 0.993828i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.03704 | + | 6.03704i | 0.992483 | + | 0.992483i | 0.999972 | − | 0.00748933i | \(-0.00238395\pi\) |
−0.00748933 | + | 0.999972i | \(0.502384\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.52135 | + | 3.60455i | 0.723996 | + | 0.577189i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.60866 | − | 7.98243i | −0.719751 | − | 1.24665i | −0.961098 | − | 0.276207i | \(-0.910923\pi\) |
0.241347 | − | 0.970439i | \(-0.422411\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.402483 | − | 1.50209i | −0.0613780 | − | 0.229066i | 0.928423 | − | 0.371526i | \(-0.121165\pi\) |
−0.989801 | + | 0.142460i | \(0.954499\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.11469 | − | 7.77970i | −0.613382 | − | 1.15973i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.85832 | − | 4.95075i | 0.416928 | − | 0.722141i | −0.578701 | − | 0.815540i | \(-0.696440\pi\) |
0.995629 | + | 0.0933994i | \(0.0297733\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.516861 | − | 0.895230i | −0.0738373 | − | 0.127890i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.04471 | + | 11.5674i | −0.706401 | + | 1.61975i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.50856 | − | 4.50856i | 0.619298 | − | 0.619298i | −0.326053 | − | 0.945351i | \(-0.605719\pi\) |
0.945351 | + | 0.326053i | \(0.105719\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.41321 | 0.325397 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.852054 | + | 2.17004i | 0.112857 | + | 0.287429i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.85508 | − | 10.6553i | 0.371700 | − | 1.38720i | −0.486407 | − | 0.873732i | \(-0.661693\pi\) |
0.858107 | − | 0.513471i | \(-0.171640\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.16531 | − | 8.08106i | −0.277240 | − | 1.03467i | −0.954325 | − | 0.298769i | \(-0.903424\pi\) |
0.677086 | − | 0.735904i | \(-0.263243\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.28938 | + | 1.89463i | −1.04436 | + | 0.238700i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.48155 | − | 4.89682i | −1.05201 | − | 0.607376i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.99423 | − | 11.1746i | 0.365804 | − | 1.36520i | −0.500524 | − | 0.865723i | \(-0.666859\pi\) |
0.866328 | − | 0.499476i | \(-0.166474\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.1996 | + | 1.15078i | −1.22789 | + | 0.138538i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.98978i | 0.354821i | 0.984137 | + | 0.177411i | \(0.0567721\pi\) | ||||
−0.984137 | + | 0.177411i | \(0.943228\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.7280i | 1.48970i | 0.667229 | + | 0.744852i | \(0.267480\pi\) | ||||
−0.667229 | + | 0.744852i | \(0.732520\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.70967 | + | 5.02484i | 0.428356 | + | 0.580219i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.603459 | − | 2.25214i | 0.0687705 | − | 0.256655i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.94529 | + | 5.16457i | 1.00642 | + | 0.581059i | 0.910143 | − | 0.414295i | \(-0.135972\pi\) |
0.0962815 | + | 0.995354i | \(0.469305\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.667162 | + | 8.97524i | −0.0741291 | + | 0.997249i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.00404 | + | 3.74713i | 0.110208 | + | 0.411301i | 0.998884 | − | 0.0472343i | \(-0.0150407\pi\) |
−0.888676 | + | 0.458536i | \(0.848374\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.53198 | − | 20.6456i | 0.600028 | − | 2.23933i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.13519 | − | 0.472070i | −0.336127 | − | 0.0506113i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.25017 | 0.980516 | 0.490258 | − | 0.871577i | \(-0.336903\pi\) | ||||
0.490258 | + | 0.871577i | \(0.336903\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.69092 | + | 6.69092i | −0.701399 | + | 0.701399i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.08627 | + | 0.461036i | −0.423727 | + | 0.0478072i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.97430 | − | 3.41959i | −0.202559 | − | 0.350843i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.148868 | − | 0.257847i | 0.0151153 | − | 0.0261804i | −0.858369 | − | 0.513033i | \(-0.828522\pi\) |
0.873484 | + | 0.486853i | \(0.161855\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.08996 | − | 1.31233i | −0.210049 | − | 0.131894i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.11843 | + | 7.90610i | 0.210792 | + | 0.786687i | 0.987606 | + | 0.156956i | \(0.0501681\pi\) |
−0.776814 | + | 0.629731i | \(0.783165\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.72414 | + | 9.91450i | 0.564016 | + | 0.976905i | 0.997140 | + | 0.0755707i | \(0.0240779\pi\) |
−0.433124 | + | 0.901334i | \(0.642589\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.4056 | − | 5.26364i | 1.30825 | − | 0.513678i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.174948 | + | 0.174948i | 0.0169128 | + | 0.0169128i | 0.715513 | − | 0.698600i | \(-0.246193\pi\) |
−0.698600 | + | 0.715513i | \(0.746193\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.50900 | − | 1.50900i | 0.144536 | − | 0.144536i | −0.631136 | − | 0.775672i | \(-0.717411\pi\) |
0.775672 | + | 0.631136i | \(0.217411\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.40461 | + | 13.7646i | 0.512983 | + | 1.30648i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.513633 | + | 0.296546i | −0.0483185 | + | 0.0278967i | −0.523965 | − | 0.851740i | \(-0.675548\pi\) |
0.475646 | + | 0.879637i | \(0.342214\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.7925 | − | 4.49955i | 1.56591 | − | 0.419585i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.68250 | + | 8.85327i | 0.432898 | + | 0.818485i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17.8843 | − | 10.3255i | −1.63945 | − | 0.946537i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.94025 | + | 5.16166i | −0.812750 | + | 0.469242i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.78989 | − | 15.8642i | −0.161389 | − | 1.43043i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.89158 | + | 2.89158i | 0.258631 | + | 0.258631i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.1816i | − | 1.25841i | −0.777240 | − | 0.629205i | \(-0.783381\pi\) | ||
0.777240 | − | 0.629205i | \(-0.216619\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.401039 | − | 2.66344i | 0.0353095 | − | 0.234503i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.86197 | − | 1.03481i | −0.337422 | − | 0.0904119i | 0.0861298 | − | 0.996284i | \(-0.472550\pi\) |
−0.423551 | + | 0.905872i | \(0.639217\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.68505 | + | 0.987407i | −0.319535 | + | 0.0856190i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.14602 | − | 15.2003i | −0.0986333 | − | 1.30824i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.98207 | − | 6.89714i | 0.340211 | − | 0.589262i | −0.644261 | − | 0.764806i | \(-0.722835\pi\) |
0.984472 | + | 0.175543i | \(0.0561682\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.3155 | − | 2.76404i | −0.874952 | − | 0.234443i | −0.206724 | − | 0.978399i | \(-0.566280\pi\) |
−0.668228 | + | 0.743957i | \(0.732947\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.96583 | − | 5.88091i | 0.670844 | − | 0.495262i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.74622 | −0.229651 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.36998 | 0.445953 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.200736 | − | 1.77917i | −0.0165564 | − | 0.146744i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.24117 | + | 1.13642i | 0.347450 | + | 0.0930990i | 0.428324 | − | 0.903625i | \(-0.359104\pi\) |
−0.0808734 | + | 0.996724i | \(0.525771\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.93783 | − | 12.0167i | 0.564592 | − | 0.977903i | −0.432495 | − | 0.901636i | \(-0.642367\pi\) |
0.997087 | − | 0.0762664i | \(-0.0242999\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −16.0183 | + | 14.8718i | −1.29501 | + | 1.20232i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.72758 | − | 1.80265i | 0.540372 | − | 0.144792i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.01560 | + | 1.61187i | 0.480097 | + | 0.128642i | 0.490748 | − | 0.871302i | \(-0.336724\pi\) |
−0.0106509 | + | 0.999943i | \(0.503390\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.2797 | − | 4.03625i | 0.815229 | − | 0.320096i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 16.7969i | − | 1.32378i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.39010 | − | 3.39010i | −0.265533 | − | 0.265533i | 0.561764 | − | 0.827297i | \(-0.310123\pi\) |
−0.827297 | + | 0.561764i | \(0.810123\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.83130 | + | 1.67089i | 0.298266 | + | 0.130079i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.58610 | + | 4.95718i | −0.664412 | + | 0.383598i | −0.793956 | − | 0.607975i | \(-0.791982\pi\) |
0.129544 | + | 0.991574i | \(0.458649\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.60636 | − | 0.927433i | −0.123566 | − | 0.0713410i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.149769 | + | 4.03519i | −0.0114531 | + | 0.308579i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.25249 | + | 1.94330i | −0.551396 | + | 0.147746i | −0.523751 | − | 0.851872i | \(-0.675468\pi\) |
−0.0276457 | + | 0.999618i | \(0.508801\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.85157 | + | 5.11046i | −0.669116 | + | 0.386314i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.9105 | − | 14.9399i | 0.895248 | − | 1.12295i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.604756 | − | 0.604756i | 0.0452016 | − | 0.0452016i | −0.684145 | − | 0.729346i | \(-0.739824\pi\) |
0.729346 | + | 0.684145i | \(0.239824\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.1716 | − | 10.1716i | −0.756048 | − | 0.756048i | 0.219553 | − | 0.975601i | \(-0.429540\pi\) |
−0.975601 | + | 0.219553i | \(0.929540\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.15755 | − | 14.3290i | 0.159490 | − | 1.05923i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.5231 | − | 21.6906i | −0.920714 | − | 1.59472i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.55121 | − | 5.78921i | −0.113436 | − | 0.423349i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −14.4724 | − | 2.73154i | −1.05271 | − | 0.198691i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.80282 | + | 10.0508i | −0.419877 | + | 0.727249i | −0.995927 | − | 0.0901660i | \(-0.971260\pi\) |
0.576049 | + | 0.817415i | \(0.304594\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.09572 | + | 8.82605i | 0.366798 | + | 0.635313i | 0.989063 | − | 0.147494i | \(-0.0471206\pi\) |
−0.622265 | + | 0.782807i | \(0.713787\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.0751 | − | 13.6470i | −0.721492 | − | 0.977278i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.32430 | − | 4.32430i | 0.308094 | − | 0.308094i | −0.536076 | − | 0.844170i | \(-0.680094\pi\) |
0.844170 | + | 0.536076i | \(0.180094\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 27.7260 | 1.96544 | 0.982720 | − | 0.185097i | \(-0.0592599\pi\) | ||||
0.982720 | + | 0.185097i | \(0.0592599\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.4910 | − | 15.6681i | 0.881047 | − | 1.10514i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.34284 | − | 5.01156i | 0.0942492 | − | 0.351743i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.99846 | + | 26.1186i | 0.488793 | + | 1.82420i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −16.9901 | − | 5.23515i | −1.18089 | − | 0.363868i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.958882 | − | 0.553611i | −0.0663272 | − | 0.0382940i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.10152 | + | 19.0391i | −0.351203 | + | 1.31071i | 0.533993 | + | 0.845489i | \(0.320691\pi\) |
−0.885196 | + | 0.465219i | \(0.845976\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.07010 | + | 4.74668i | −0.141841 | + | 0.325237i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.56197i | 0.311124i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 6.72933i | − | 0.456817i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.81282 | + | 20.2075i | −0.595515 | + | 1.36550i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.29538 | + | 23.4947i | −0.423473 | + | 1.58042i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.9074 | + | 6.29741i | 0.730416 | + | 0.421706i | 0.818574 | − | 0.574401i | \(-0.194765\pi\) |
−0.0881582 | + | 0.996106i | \(0.528098\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.41044 | + | 10.5462i | 0.160696 | + | 0.703079i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.12014 | + | 11.6445i | 0.207091 | + | 0.772874i | 0.988802 | + | 0.149233i | \(0.0476805\pi\) |
−0.781711 | + | 0.623641i | \(0.785653\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.46608 | − | 5.47149i | 0.0968814 | − | 0.361566i | −0.900417 | − | 0.435029i | \(-0.856738\pi\) |
0.997298 | + | 0.0734624i | \(0.0234049\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.51744 | − | 3.15775i | 0.165635 | − | 0.207764i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.1291 | −0.663580 | −0.331790 | − | 0.943353i | \(-0.607653\pi\) | ||||
−0.331790 | + | 0.943353i | \(0.607653\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.8584 | + | 11.8584i | −0.773558 | + | 0.773558i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.6260 | + | 14.3931i | 0.690230 | + | 0.934934i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.263562 | + | 0.456503i | 0.0170484 | + | 0.0295287i | 0.874424 | − | 0.485163i | \(-0.161240\pi\) |
−0.857375 | + | 0.514692i | \(0.827906\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.74338 | − | 16.8760i | 0.627626 | − | 1.08708i | −0.360400 | − | 0.932798i | \(-0.617360\pi\) |
0.988027 | − | 0.154283i | \(-0.0493068\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.27361 | + | 13.7875i | −0.466603 | + | 0.884467i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.784878 | + | 2.92920i | 0.0501440 | + | 0.187140i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.24675 | + | 3.89148i | 0.142957 | + | 0.247609i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.00044 | + | 6.64428i | −0.0634003 | + | 0.421064i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.9199 | + | 17.9199i | 1.13110 | + | 1.13110i | 0.989995 | + | 0.141101i | \(0.0450643\pi\) |
0.141101 | + | 0.989995i | \(0.454936\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.44706 | − | 3.44706i | 0.216715 | − | 0.216715i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 23.0777 | − | 28.9475i | 1.44518 | − | 1.81276i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.6152 | − | 8.43809i | 0.911671 | − | 0.526353i | 0.0307025 | − | 0.999529i | \(-0.490226\pi\) |
0.880968 | + | 0.473175i | \(0.156892\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −23.3744 | + | 6.26316i | −1.45242 | + | 0.389174i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.65068 | − | 2.92026i | −0.287870 | − | 0.180760i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.8065 | + | 10.8579i | 1.15966 | + | 0.669528i | 0.951222 | − | 0.308508i | \(-0.0998297\pi\) |
0.208435 | + | 0.978036i | \(0.433163\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.1989 | + | 9.35243i | −0.995090 | + | 0.574515i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.6859 | + | 6.40476i | 0.898763 | + | 0.391965i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.50729 | + | 3.50729i | 0.213843 | + | 0.213843i | 0.805898 | − | 0.592055i | \(-0.201683\pi\) |
−0.592055 | + | 0.805898i | \(0.701683\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.25749i | 0.137133i | 0.997647 | + | 0.0685665i | \(0.0218425\pi\) | ||||
−0.997647 | + | 0.0685665i | \(0.978157\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −15.2555 | + | 5.99000i | −0.923306 | + | 0.362531i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.86529 | − | 0.767751i | −0.172783 | − | 0.0462971i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.7581 | + | 4.75826i | −1.06698 | + | 0.285896i | −0.749251 | − | 0.662286i | \(-0.769586\pi\) |
−0.317727 | + | 0.948182i | \(0.602920\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.80673 | − | 2.09735i | −0.407508 | − | 0.125565i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.38270 | + | 7.59106i | −0.261450 | + | 0.452845i | −0.966627 | − | 0.256186i | \(-0.917534\pi\) |
0.705177 | + | 0.709031i | \(0.250867\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.6177 | + | 4.18474i | 0.928375 | + | 0.248757i | 0.691161 | − | 0.722700i | \(-0.257099\pi\) |
0.237213 | + | 0.971458i | \(0.423766\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.766769 | − | 6.79606i | −0.0454195 | − | 0.402564i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 26.1254 | 1.54213 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −36.0842 | −2.12260 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.414880 | − | 0.306292i | 0.0243207 | − | 0.0179552i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.1120 | + | 3.24540i | 0.707589 | + | 0.189598i | 0.594628 | − | 0.804001i | \(-0.297300\pi\) |
0.112962 | + | 0.993599i | \(0.463966\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.1806 | + | 28.0256i | −0.942070 | + | 1.63171i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.40945 | − | 3.53058i | −0.139810 | − | 0.204865i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −19.1098 | + | 5.12047i | −1.10515 | + | 0.296124i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.25749 | + | 1.14079i | 0.245397 | + | 0.0657540i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.11084 | + | 14.0188i | −0.121264 | + | 0.805360i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 24.5429i | 1.40532i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.9168 | − | 18.9168i | −1.07964 | − | 1.07964i | −0.996542 | − | 0.0830950i | \(-0.973519\pi\) |
−0.0830950 | − | 0.996542i | \(-0.526481\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.22311 | + | 19.7040i | 0.126468 | + | 1.12092i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.08666 | − | 2.93678i | 0.288438 | − | 0.166530i | −0.348799 | − | 0.937197i | \(-0.613411\pi\) |
0.637237 | + | 0.770668i | \(0.280077\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.3490 | − | 8.28438i | −0.811051 | − | 0.468261i | 0.0362694 | − | 0.999342i | \(-0.488453\pi\) |
−0.847321 | + | 0.531081i | \(0.821786\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 24.9277 | + | 0.925208i | 1.40452 | + | 0.0521296i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.73750 | + | 1.80531i | −0.378416 | + | 0.101396i | −0.443013 | − | 0.896515i | \(-0.646090\pi\) |
0.0645973 | + | 0.997911i | \(0.479424\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.30405 | − | 0.752894i | 0.0730128 | − | 0.0421540i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.156621 | + | 0.398886i | 0.00874171 | + | 0.0222636i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.93441 | + | 6.93441i | −0.385841 | + | 0.385841i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.51253 | + | 8.51253i | 0.472190 | + | 0.472190i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.44058 | − | 1.35092i | 0.190264 | − | 0.0747063i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.10156 | + | 14.0323i | 0.446653 | + | 0.773626i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.83736 | − | 21.7853i | −0.320850 | − | 1.19743i | −0.918418 | − | 0.395612i | \(-0.870533\pi\) |
0.597567 | − | 0.801819i | \(-0.296134\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.949988 | + | 25.5954i | −0.0520590 | + | 1.40262i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.9692 | + | 29.3915i | −0.927126 | + | 1.60583i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.04210 | + | 8.73317i | 0.274661 | + | 0.475726i | 0.970049 | − | 0.242908i | \(-0.0781012\pi\) |
−0.695389 | + | 0.718634i | \(0.744768\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.02079 | + | 0.115171i | −0.0554416 | + | 0.00625523i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.38099 | − | 1.38099i | 0.0747849 | − | 0.0747849i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9107 | −0.913093 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 29.7759 | + | 4.48341i | 1.60308 | + | 0.241379i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.70540 | − | 28.7569i | 0.413647 | − | 1.54375i | −0.373882 | − | 0.927476i | \(-0.621974\pi\) |
0.787530 | − | 0.616277i | \(-0.211360\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.31845 | − | 8.65259i | −0.124104 | − | 0.463163i | 0.875702 | − | 0.482852i | \(-0.160399\pi\) |
−0.999806 | + | 0.0196892i | \(0.993732\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.30416 | + | 17.2979i | 0.0696110 | + | 0.923294i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.1794 | + | 16.2694i | 1.49984 | + | 0.865933i | 1.00000 | 0.000184008i | \(-5.85715e-5\pi\) | |
0.499841 | + | 0.866117i | \(0.333392\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.27006 | − | 8.47197i | 0.120482 | − | 0.449645i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −21.2444 | − | 28.7761i | −1.12438 | − | 1.52299i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.581843i | 0.0307085i | 0.999882 | + | 0.0153542i | \(0.00488760\pi\) | ||||
−0.999882 | + | 0.0153542i | \(0.995112\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 17.1883i | − | 0.904648i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −17.7678 | + | 2.00466i | −0.932566 | + | 0.105217i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.66406 | − | 36.0668i | 0.505840 | − | 1.88782i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.68240 | − | 2.12603i | −0.192220 | − | 0.110978i | 0.400802 | − | 0.916165i | \(-0.368732\pi\) |
−0.593021 | + | 0.805187i | \(0.702065\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.14259 | − | 26.4259i | 0.423886 | − | 1.37568i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.67743 | + | 17.4564i | 0.242840 | + | 0.906291i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.61385 | + | 6.02298i | −0.0835621 | + | 0.311858i | −0.995038 | − | 0.0994955i | \(-0.968277\pi\) |
0.911476 | + | 0.411353i | \(0.134944\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.58867 | + | 6.59289i | 0.133678 | + | 0.340456i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.11102 | −0.314733 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.99791 | − | 8.99791i | 0.462192 | − | 0.462192i | −0.437182 | − | 0.899373i | \(-0.644023\pi\) |
0.899373 | + | 0.437182i | \(0.144023\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.81923 | − | 22.5152i | 0.503054 | − | 1.15349i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.35960 | − | 7.55105i | −0.222765 | − | 0.385840i | 0.732882 | − | 0.680356i | \(-0.238175\pi\) |
−0.955647 | + | 0.294516i | \(0.904842\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.41998 | + | 5.92357i | −0.174298 | + | 0.301893i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.48086 | − | 3.95090i | 0.126109 | − | 0.200836i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.20893 | + | 26.9041i | 0.365507 | + | 1.36409i | 0.866732 | + | 0.498774i | \(0.166216\pi\) |
−0.501225 | + | 0.865317i | \(0.667117\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.5886 | − | 37.3925i | −1.09178 | − | 1.89102i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.41490 | − | 4.31691i | −0.273146 | − | 0.217759i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21.4265 | − | 21.4265i | −1.07808 | − | 1.07808i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.82319 | − | 3.82319i | 0.191880 | − | 0.191880i | −0.604628 | − | 0.796508i | \(-0.706678\pi\) |
0.796508 | + | 0.604628i | \(0.206678\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.53420 | − | 0.983866i | −0.327119 | − | 0.0492549i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.9442 | + | 14.4015i | −1.24565 | + | 0.719178i | −0.970239 | − | 0.242148i | \(-0.922148\pi\) |
−0.275414 | + | 0.961326i | \(0.588815\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.65596 | + | 2.05141i | −0.381371 | + | 0.102188i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.70516 | − | 24.9261i | 0.432563 | − | 1.23859i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.08222 | − | 3.51157i | −0.301485 | − | 0.174062i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.11179 | − | 5.26069i | 0.450549 | − | 0.260125i | −0.257513 | − | 0.966275i | \(-0.582903\pi\) |
0.708062 | + | 0.706150i | \(0.249570\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.0976 | − | 8.19299i | 0.547405 | − | 0.404131i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 22.1088 | + | 22.1088i | 1.08790 | + | 1.08790i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 11.3804i | − | 0.558642i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.4635 | − | 11.5307i | −0.708281 | − | 0.564661i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.4024 | + | 3.32320i | 0.605895 | + | 0.162349i | 0.548708 | − | 0.836014i | \(-0.315120\pi\) |
0.0571875 | + | 0.998363i | \(0.481787\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.21476 | + | 2.46909i | −0.449100 | + | 0.120336i | −0.476278 | − | 0.879295i | \(-0.658015\pi\) |
0.0271782 | + | 0.999631i | \(0.491348\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 16.7188 | − | 3.82125i | 0.812894 | − | 0.185795i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.1366 | + | 22.7533i | −0.637220 | + | 1.10370i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.9048 | + | 6.13732i | 1.10844 | + | 0.297006i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.36000 | − | 1.90147i | −0.210503 | − | 0.0918037i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.4451 | 0.792131 | 0.396065 | − | 0.918222i | \(-0.370375\pi\) | ||||
0.396065 | + | 0.918222i | \(0.370375\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.51715 | −0.169023 | −0.0845116 | − | 0.996422i | \(-0.526933\pi\) | ||||
−0.0845116 | + | 0.996422i | \(0.526933\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.52558 | + | 3.71814i | 0.408770 | + | 0.178271i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.70471 | − | 2.06447i | −0.368566 | − | 0.0987570i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.4483 | + | 18.0969i | −0.498668 | + | 0.863719i | −0.999999 | − | 0.00153725i | \(-0.999511\pi\) |
0.501331 | + | 0.865256i | \(0.332844\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.913192 | − | 2.96367i | 0.0434854 | − | 0.141127i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.6793 | + | 2.86151i | −0.507389 | + | 0.135954i | −0.503427 | − | 0.864038i | \(-0.667928\pi\) |
−0.00396162 | + | 0.999992i | \(0.501261\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −26.2117 | − | 7.02341i | −1.24255 | − | 0.332941i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.94659 | + | 4.74078i | 0.281264 | + | 0.224231i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 17.5860i | − | 0.829933i | −0.909837 | − | 0.414966i | \(-0.863793\pi\) | ||
0.909837 | − | 0.414966i | \(-0.136207\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.36145 | + | 5.36145i | 0.252461 | + | 0.252461i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.3350 | − | 14.2744i | 0.908439 | − | 0.670670i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 24.0399 | − | 13.8795i | 1.12701 | − | 0.650680i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.6606 | + | 10.7737i | 0.872905 | + | 0.503972i | 0.868313 | − | 0.496017i | \(-0.165205\pi\) |
0.00459262 | + | 0.999989i | \(0.498538\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −35.7285 | + | 12.5201i | −1.66766 | + | 0.584386i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.9925 | + | 4.55312i | −0.791419 | + | 0.212060i | −0.631813 | − | 0.775121i | \(-0.717689\pi\) |
−0.159606 | + | 0.987181i | \(0.551022\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.4389 | + | 10.6457i | −0.856930 | + | 0.494749i | −0.862983 | − | 0.505233i | \(-0.831407\pi\) |
0.00605328 | + | 0.999982i | \(0.498073\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.9291 | + | 1.79618i | 0.553199 | + | 0.0832960i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.62864 | − | 2.62864i | 0.121639 | − | 0.121639i | −0.643667 | − | 0.765306i | \(-0.722588\pi\) |
0.765306 | + | 0.643667i | \(0.222588\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.1864 | + | 23.1864i | 1.07065 | + | 1.07065i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.43453 | + | 6.72423i | 0.388643 | + | 0.309836i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.639608 | + | 1.10783i | 0.0294092 | + | 0.0509382i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.25623 | + | 4.68831i | 0.0576398 | + | 0.215115i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 19.1150 | + | 0.709466i | 0.875217 | + | 0.0324842i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.7530 | − | 18.6247i | 0.491317 | − | 0.850986i | −0.508633 | − | 0.860983i | \(-0.669849\pi\) |
0.999950 | + | 0.00999740i | \(0.00318233\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.2512 | + | 24.6838i | 0.649799 | + | 1.12548i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.6301 | − | 26.6674i | 0.529187 | − | 1.21341i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.617616 | + | 0.617616i | −0.0280445 | + | 0.0280445i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.6445 | 0.663607 | 0.331804 | − | 0.943348i | \(-0.392343\pi\) | ||||
0.331804 | + | 0.943348i | \(0.392343\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.03496 | − | 7.72953i | −0.137246 | − | 0.349541i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.3160 | + | 42.2317i | −0.510682 | + | 1.90589i | −0.0975209 | + | 0.995233i | \(0.531091\pi\) |
−0.413161 | + | 0.910658i | \(0.635575\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.45183 | − | 12.8824i | −0.155463 | − | 0.580195i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.92579 | + | 5.30553i | 0.221398 | + | 0.238466i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.33885 | − | 4.23708i | −0.329192 | − | 0.190059i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.12060 | − | 7.91419i | 0.0949311 | − | 0.354288i | −0.902078 | − | 0.431573i | \(-0.857959\pi\) |
0.997009 | + | 0.0772856i | \(0.0246253\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.0639 | + | 1.92525i | −0.762360 | + | 0.0860137i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.90408i | − | 0.0848988i | −0.999099 | − | 0.0424494i | \(-0.986484\pi\) | ||
0.999099 | − | 0.0424494i | \(-0.0135161\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 24.0116i | − | 1.06850i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.90817 | − | 2.58466i | −0.0847447 | − | 0.114789i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.95009 | + | 7.27785i | −0.0864364 | + | 0.322585i | −0.995582 | − | 0.0938926i | \(-0.970069\pi\) |
0.909146 | + | 0.416478i | \(0.136736\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −31.2428 | − | 18.0381i | −1.38210 | − | 0.797957i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.03172 | + | 6.30272i | −0.133854 | + | 0.278272i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.69237 | − | 32.4404i | −0.383032 | − | 1.42949i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.21711 | + | 4.54231i | −0.0535284 | + | 0.199771i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.8598 | − | 1.93633i | −0.564484 | − | 0.0849954i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.5974 | 1.29669 | 0.648343 | − | 0.761349i | \(-0.275462\pi\) | ||||
0.648343 | + | 0.761349i | \(0.275462\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.1710 | + | 29.1710i | −1.27556 | + | 1.27556i | −0.332431 | + | 0.943128i | \(0.607869\pi\) |
−0.943128 | + | 0.332431i | \(0.892131\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −17.5915 | + | 1.98477i | −0.767757 | + | 0.0866226i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.64900 | − | 14.9805i | −0.376756 | − | 0.652561i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.05948 | − | 10.4953i | 0.263456 | − | 0.456318i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 29.2539 | − | 15.4724i | 1.26951 | − | 0.671445i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.96422 | − | 29.7229i | −0.344969 | − | 1.28744i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.362907 | − | 0.628573i | −0.0156898 | − | 0.0271756i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.37886 | − | 0.541403i | 0.0595023 | − | 0.0233633i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.601287 | + | 0.601287i | 0.0258993 | + | 0.0258993i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.87135 | − | 7.87135i | 0.338416 | − | 0.338416i | −0.517355 | − | 0.855771i | \(-0.673083\pi\) |
0.855771 | + | 0.517355i | \(0.173083\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.10603 | − | 23.1915i | −0.390777 | − | 0.995243i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.42173 | + | 3.13024i | −0.232241 | + | 0.134085i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.05052 | + | 0.817385i | −0.130431 | + | 0.0349488i | −0.323444 | − | 0.946247i | \(-0.604841\pi\) |
0.193013 | + | 0.981196i | \(0.438174\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.3467 | − | 21.2554i | 0.569625 | − | 0.907159i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.13375 | − | 1.23192i | −0.0909007 | − | 0.0524816i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −25.3544 | + | 14.6384i | −1.07818 | + | 0.622486i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.86364 | − | 43.1077i | −0.206450 | − | 1.82982i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.4110 | − | 22.4110i | −0.949583 | − | 0.949583i | 0.0492055 | − | 0.998789i | \(-0.484331\pi\) |
−0.998789 | + | 0.0492055i | \(0.984331\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5.19151i | − | 0.219577i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.54565 | − | 10.2652i | 0.0652574 | − | 0.433398i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 30.2910 | + | 8.11646i | 1.27661 | + | 0.342068i | 0.832561 | − | 0.553933i | \(-0.186873\pi\) |
0.444053 | + | 0.896000i | \(0.353540\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.68061 | − | 0.450319i | 0.0707039 | − | 0.0189450i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −21.0855 | − | 14.3573i | −0.885510 | − | 0.602949i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.78787 | + | 4.82873i | −0.116874 | + | 0.202431i | −0.918527 | − | 0.395358i | \(-0.870621\pi\) |
0.801654 | + | 0.597789i | \(0.203954\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.1186 | + | 5.39076i | 0.841937 | + | 0.225596i | 0.653915 | − | 0.756568i | \(-0.273126\pi\) |
0.188023 | + | 0.982165i | \(0.439792\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.1719 | + | 11.9391i | −0.675590 | + | 0.498765i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.3699 | −0.891185 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.3551 | 0.847394 | 0.423697 | − | 0.905804i | \(-0.360732\pi\) | ||||
0.423697 | + | 0.905804i | \(0.360732\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.97905 | + | 17.5408i | 0.0822465 | + | 0.728971i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.6208 | − | 2.84584i | −0.440626 | − | 0.118065i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.62250 | + | 4.54230i | −0.108613 | + | 0.188123i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.54651 | − | 28.6423i | −0.270665 | − | 1.18421i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.5741 | − | 8.19230i | 1.26193 | − | 0.338132i | 0.434994 | − | 0.900433i | \(-0.356750\pi\) |
0.826933 | + | 0.562301i | \(0.190084\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.08673 | − | 0.827087i | −0.127186 | − | 0.0340795i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.85953 | − | 3.87130i | 0.405567 | − | 0.159244i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 18.8148i | − | 0.772633i | −0.922366 | − | 0.386317i | \(-0.873747\pi\) | ||
0.922366 | − | 0.386317i | \(-0.126253\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 42.8379 | + | 42.8379i | 1.75618 | + | 1.75618i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 44.0187 | + | 19.1973i | 1.80157 | + | 0.785693i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.618276 | + | 0.356962i | −0.0252621 | + | 0.0145851i | −0.512578 | − | 0.858641i | \(-0.671309\pi\) |
0.487316 | + | 0.873226i | \(0.337976\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.9427 | + | 23.0610i | 1.62930 | + | 0.940676i | 0.984302 | + | 0.176490i | \(0.0564742\pi\) |
0.644996 | + | 0.764186i | \(0.276859\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 30.6796 | − | 16.2265i | 1.24937 | − | 0.660794i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 29.2526 | − | 7.83822i | 1.18929 | − | 0.318669i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.9512 | − | 14.9830i | 1.05333 | − | 0.608139i | 0.129749 | − | 0.991547i | \(-0.458583\pi\) |
0.923579 | + | 0.383408i | \(0.125250\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.60193 | − | 7.02676i | 0.227001 | − | 0.284739i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.4948 | − | 13.4948i | 0.545943 | − | 0.545943i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.31839 | − | 4.31839i | −0.174418 | − | 0.174418i | 0.614499 | − | 0.788917i | \(-0.289358\pi\) |
−0.788917 | + | 0.614499i | \(0.789358\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.97336 | + | 46.3125i | −0.281193 | + | 1.86750i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.3245 | + | 24.8108i | 0.576683 | + | 0.998844i | 0.995857 | + | 0.0909377i | \(0.0289864\pi\) |
−0.419174 | + | 0.907906i | \(0.637680\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.44181 | − | 31.5053i | −0.339305 | − | 1.26630i | −0.899126 | − | 0.437690i | \(-0.855797\pi\) |
0.559821 | − | 0.828614i | \(-0.310870\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −23.3493 | − | 20.0754i | −0.936977 | − | 0.805597i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.1093 | + | 22.7059i | −0.525211 | + | 0.909693i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.0133 | − | 26.0039i | −0.600533 | − | 1.04015i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.13904 | − | 1.54286i | −0.0454888 | − | 0.0616158i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −43.9852 | + | 43.9852i | −1.75380 | + | 1.75380i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.5062 | −0.776529 | −0.388265 | − | 0.921548i | \(-0.626925\pi\) | ||||
−0.388265 | + | 0.921548i | \(0.626925\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −21.2819 | + | 26.6950i | −0.845881 | + | 1.06103i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.7677 | + | 40.1855i | −0.427302 | + | 1.59471i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.893188 | − | 3.33342i | −0.0353894 | − | 0.132075i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.57315 | + | 6.10267i | −0.260030 | + | 0.241418i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.569361 | + | 0.328721i | 0.0224884 | + | 0.0129837i | 0.511202 | − | 0.859461i | \(-0.329200\pi\) |
−0.488714 | + | 0.872444i | \(0.662534\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.29265 | − | 23.4845i | 0.248158 | − | 0.926138i | −0.723612 | − | 0.690207i | \(-0.757519\pi\) |
0.971770 | − | 0.235931i | \(-0.0758138\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.15868 | + | 7.24276i | −0.124373 | + | 0.285183i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 21.5984i | − | 0.849122i | −0.905399 | − | 0.424561i | \(-0.860428\pi\) | ||
0.905399 | − | 0.424561i | \(-0.139572\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.07434i | 0.356199i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.65935 | − | 10.6837i | 0.182614 | − | 0.418728i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.2092 | − | 38.1014i | 0.399519 | − | 1.49102i | −0.414427 | − | 0.910082i | \(-0.636018\pi\) |
0.813946 | − | 0.580941i | \(-0.197315\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.1577 | + | 5.86458i | 0.396896 | + | 0.229148i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −27.9831 | + | 25.9802i | −1.09173 | + | 1.01359i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.62321 | − | 13.5220i | −0.141140 | − | 0.526742i | −0.999897 | − | 0.0143586i | \(-0.995429\pi\) |
0.858757 | − | 0.512383i | \(-0.171237\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.7578 | − | 40.1488i | 0.418432 | − | 1.56161i | −0.359430 | − | 0.933172i | \(-0.617029\pi\) |
0.777861 | − | 0.628436i | \(-0.216305\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −26.2623 | + | 32.9421i | −1.01994 | + | 1.27937i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.1918 | 0.434001 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.67055 | − | 7.67055i | 0.297005 | − | 0.297005i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.9568 | + | 17.5503i | 0.500937 | + | 0.678532i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.44102 | + | 5.96002i | 0.132839 | + | 0.230084i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.88063 | − | 4.98940i | 0.111040 | − | 0.192327i | −0.805150 | − | 0.593072i | \(-0.797915\pi\) |
0.916190 | + | 0.400744i | \(0.131248\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.47521 | + | 18.4125i | −0.133761 | + | 0.708696i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.27316 | − | 27.1438i | −0.279530 | − | 1.04322i | −0.952744 | − | 0.303773i | \(-0.901754\pi\) |
0.673214 | − | 0.739447i | \(-0.264913\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.421949 | + | 0.730837i | 0.0161929 | + | 0.0280469i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.10895 | + | 20.6476i | −0.119135 | + | 0.791219i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.50875 | + | 4.50875i | 0.172522 | + | 0.172522i | 0.788087 | − | 0.615564i | \(-0.211072\pi\) |
−0.615564 | + | 0.788087i | \(0.711072\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.5206 | + | 16.5206i | −0.631219 | + | 0.631219i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.11603 | − | 7.67163i | 0.233341 | − | 0.292691i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.4343 | − | 10.6430i | 0.702290 | − | 0.405467i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.90941 | + | 2.65522i | −0.376972 | + | 0.101009i | −0.442329 | − | 0.896853i | \(-0.645848\pi\) |
0.0653578 | + | 0.997862i | \(0.479181\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.18319 | − | 3.27029i | 0.234880 | − | 0.124228i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 27.1319 | + | 15.6646i | 1.02917 | + | 0.594193i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 58.1591 | − | 33.5782i | 2.20293 | − | 1.27186i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16.0813 | − | 7.01333i | −0.608252 | − | 0.265269i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.5518 | − | 16.5518i | −0.625154 | − | 0.625154i | 0.321691 | − | 0.946845i | \(-0.395749\pi\) |
−0.946845 | + | 0.321691i | \(0.895749\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.4916i | 0.433414i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −27.0376 | + | 10.6162i | −1.01829 | + | 0.399828i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −22.4089 | − | 6.00445i | −0.842774 | − | 0.225821i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −40.2743 | + | 10.7915i | −1.51253 | + | 0.405282i | −0.917276 | − | 0.398253i | \(-0.869617\pi\) |
−0.595257 | + | 0.803535i | \(0.702950\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.90445 | + | 30.2084i | 0.258937 | + | 1.13290i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.03484 | − | 12.1847i | 0.263457 | − | 0.456320i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.78182 | + | 2.08513i | 0.291023 | + | 0.0779795i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.102361 | + | 0.907249i | 0.00382274 | + | 0.0338818i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.8494 | −1.00131 | −0.500656 | − | 0.865646i | \(-0.666908\pi\) | ||||
−0.500656 | + | 0.865646i | \(0.666908\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.4488 | −1.20846 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 27.1538 | − | 20.0467i | 1.00986 | − | 0.745547i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.37597 | − | 1.70843i | −0.236797 | − | 0.0634497i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.1681 | − | 21.0758i | 0.451290 | − | 0.781657i | −0.547176 | − | 0.837017i | \(-0.684297\pi\) |
0.998466 | + | 0.0553600i | \(0.0176306\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.0942 | + | 16.8533i | −0.781268 | + | 0.624196i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.9440 | − | 2.93245i | 0.404780 | − | 0.108460i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.8512 | − | 5.85501i | −0.807093 | − | 0.216260i | −0.168397 | − | 0.985719i | \(-0.553859\pi\) |
−0.638696 | + | 0.769459i | \(0.720526\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.782063 | + | 5.19396i | −0.0288468 | + | 0.191582i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.51661i | 0.350549i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.6742 | + | 12.6742i | 0.466230 | + | 0.466230i | 0.900691 | − | 0.434461i | \(-0.143061\pi\) |
−0.434461 | + | 0.900691i | \(0.643061\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.872580 | + | 7.73389i | 0.0320550 | + | 0.284112i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.2864 | + | 14.5991i | −0.927667 | + | 0.535589i | −0.886073 | − | 0.463546i | \(-0.846577\pi\) |
−0.0415943 | + | 0.999135i | \(0.513244\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.1551 | − | 6.44042i | −0.408692 | − | 0.235959i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.18880 | + | 9.85601i | −0.226436 | + | 0.360612i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.677369 | + | 0.181500i | −0.0247505 | + | 0.00663188i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.9864 | + | 13.8486i | −0.875277 | + | 0.505341i | −0.869098 | − | 0.494639i | \(-0.835300\pi\) |
−0.00617885 | + | 0.999981i | \(0.501967\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.0427 | + | 40.8580i | 0.584628 | + | 1.48895i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28.7833 | + | 28.7833i | −1.04753 | + | 1.04753i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.84906 | − | 6.84906i | −0.248933 | − | 0.248933i | 0.571599 | − | 0.820533i | \(-0.306323\pi\) |
−0.820533 | + | 0.571599i | \(0.806323\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.85940 | − | 3.08595i | 0.285278 | − | 0.112013i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.92685 | + | 11.9977i | 0.251098 | + | 0.434915i | 0.963828 | − | 0.266523i | \(-0.0858750\pi\) |
−0.712730 | + | 0.701438i | \(0.752542\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.56553 | + | 5.84262i | 0.0566758 | + | 0.211517i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 56.6821 | − | 29.9792i | 2.04934 | − | 1.08390i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.4134 | − | 31.8930i | 0.664871 | − | 1.15159i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.15368 | + | 8.92644i | 0.185846 | + | 0.321896i | 0.943861 | − | 0.330342i | \(-0.107164\pi\) |
−0.758015 | + | 0.652237i | \(0.773831\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.0461 | − | 3.27714i | 1.04607 | − | 0.118023i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.0684 | − | 29.0684i | 1.04552 | − | 1.04552i | 0.0466043 | − | 0.998913i | \(-0.485160\pi\) |
0.998913 | − | 0.0466043i | \(-0.0148400\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.56139 | −0.307534 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −41.4467 | − | 6.24069i | −1.48689 | − | 0.223884i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.21101 | − | 11.9837i | 0.115046 | − | 0.429359i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.636543 | − | 2.37561i | −0.0227773 | − | 0.0850060i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.36162 | − | 7.85642i | −0.191609 | − | 0.280765i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.8222 | − | 9.13496i | −0.564719 | − | 0.326041i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.63526 | + | 35.9593i | −0.343460 | + | 1.28181i | 0.550941 | + | 0.834544i | \(0.314269\pi\) |
−0.894401 | + | 0.447266i | \(0.852398\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.3399 | + | 30.2599i | 0.795321 | + | 1.07728i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.68105i | − | 0.0597712i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 27.9297i | − | 0.991814i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −32.1935 | + | 3.63225i | −1.14179 | + | 0.128823i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.51421 | − | 9.38318i | 0.0890580 | − | 0.332369i | −0.906994 | − | 0.421144i | \(-0.861629\pi\) |
0.996052 | + | 0.0887752i | \(0.0282953\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.0706 | + | 20.8254i | 1.27609 | + | 0.736749i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.8813 | + | 20.3369i | 0.667137 | + | 0.718568i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.70988 | − | 10.1134i | −0.0956297 | − | 0.356895i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.7534 | + | 47.5965i | −0.449500 | + | 1.67756i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.13987 | + | 7.99673i | 0.110529 | + | 0.281498i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.1867 | −0.463620 | −0.231810 | − | 0.972761i | \(-0.574465\pi\) | ||||
−0.231810 | + | 0.972761i | \(0.574465\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.0093 | − | 11.0093i | 0.386587 | − | 0.386587i | −0.486881 | − | 0.873468i | \(-0.661865\pi\) |
0.873468 | + | 0.486881i | \(0.161865\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.56307 | + | 3.58408i | −0.0548194 | + | 0.125699i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.03233 | + | 12.1804i | 0.246332 | + | 0.426659i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.04656 | − | 1.81269i | 0.0366144 | − | 0.0634179i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −28.3677 | − | 1.05288i | −0.991246 | − | 0.0367907i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.11987 | − | 4.17943i | −0.0390839 | − | 0.145863i | 0.943627 | − | 0.331012i | \(-0.107390\pi\) |
−0.982711 | + | 0.185149i | \(0.940723\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.8576 | − | 41.3225i | −0.831622 | − | 1.44041i | −0.896751 | − | 0.442535i | \(-0.854079\pi\) |
0.0651287 | − | 0.997877i | \(-0.479254\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.01745 | − | 3.20282i | −0.139870 | − | 0.111508i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.38625 | − | 1.38625i | −0.0482045 | − | 0.0482045i | 0.682594 | − | 0.730798i | \(-0.260852\pi\) |
−0.730798 | + | 0.682594i | \(0.760852\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.8345 | + | 21.8345i | −0.758345 | + | 0.758345i | −0.976021 | − | 0.217676i | \(-0.930152\pi\) |
0.217676 | + | 0.976021i | \(0.430152\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −31.4879 | − | 4.74119i | −1.09230 | − | 0.164470i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.52255 | − | 3.76580i | 0.225993 | − | 0.130477i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28.0938 | − | 7.52771i | 0.972227 | − | 0.260507i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.35442 | − | 8.04278i | −0.323336 | − | 0.277999i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.8914 | + | 16.1031i | 0.962916 | + | 0.555940i | 0.897069 | − | 0.441890i | \(-0.145692\pi\) |
0.0658470 | + | 0.997830i | \(0.479025\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.2129 | + | 12.8246i | −0.765962 | + | 0.442228i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.2141 | + | 9.01729i | −0.420678 | + | 0.310572i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.84768 | + | 3.84768i | 0.132364 | + | 0.132364i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 29.2602i | − | 1.00539i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21.8977 | + | 17.4574i | 0.751527 | + | 0.599138i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −48.8712 | − | 13.0950i | −1.67528 | − | 0.448891i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44.9166 | − | 12.0354i | 1.53791 | − | 0.412083i | 0.612323 | − | 0.790608i | \(-0.290235\pi\) |
0.925591 | + | 0.378525i | \(0.123569\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.48820 | − | 11.3206i | 0.119294 | − | 0.387156i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.0139 | − | 17.3446i | 0.342068 | − | 0.592480i | −0.642748 | − | 0.766077i | \(-0.722206\pi\) |
0.984817 | + | 0.173598i | \(0.0555392\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.6956 | − | 4.47358i | −0.569648 | − | 0.152637i | −0.0375129 | − | 0.999296i | \(-0.511944\pi\) |
−0.532135 | + | 0.846659i | \(0.678610\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 41.4776 | + | 18.0891i | 1.41355 | + | 0.616474i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.4242 | −0.831410 | −0.415705 | − | 0.909499i | \(-0.636465\pi\) | ||||
−0.415705 | + | 0.909499i | \(0.636465\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.0265 | 0.748923 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −57.2886 | − | 24.9845i | −1.94562 | − | 0.848518i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.20731 | − | 2.19914i | −0.278414 | − | 0.0746007i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.3109 | − | 33.4474i | 0.654324 | − | 1.13332i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.870754 | − | 0.199020i | 0.0294705 | − | 0.00673580i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.1957 | + | 2.99989i | −0.378485 | + | 0.101415i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.5743 | + | 9.26415i | 1.16749 | + | 0.312828i | 0.789954 | − | 0.613167i | \(-0.210105\pi\) |
0.377537 | + | 0.925995i | \(0.376771\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.9823 | + | 13.5388i | 0.572800 | + | 0.456651i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.8264i | 1.54393i | 0.635664 | + | 0.771966i | \(0.280726\pi\) | ||||
−0.635664 | + | 0.771966i | \(0.719274\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.22790 | − | 7.22790i | −0.243238 | − | 0.243238i | 0.574950 | − | 0.818188i | \(-0.305021\pi\) |
−0.818188 | + | 0.574950i | \(0.805021\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −45.0936 | + | 33.2911i | −1.51581 | + | 1.11907i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.9502 | − | 21.3332i | 1.24067 | − | 0.716300i | 0.271438 | − | 0.962456i | \(-0.412501\pi\) |
0.969230 | + | 0.246156i | \(0.0791676\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 34.8107 | + | 20.0980i | 1.16751 | + | 0.674065i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.38077 | − | 7.27357i | −0.0462577 | − | 0.243674i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.43234 | − | 1.99149i | 0.248714 | − | 0.0666426i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.17284 | + | 1.25449i | −0.0726300 | + | 0.0419330i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −33.8849 | − | 5.10210i | −1.13138 | − | 0.170354i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.07305 | − | 3.07305i | 0.102492 | − | 0.102492i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.8489 | + | 32.8489i | 1.09435 | + | 1.09435i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.96946 | + | 4.75902i | 0.198651 | + | 0.158370i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.0997 | + | 36.5457i | 0.701376 | + | 1.21482i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.4458 | + | 38.9844i | 0.346848 | + | 1.29445i | 0.890438 | + | 0.455104i | \(0.150398\pi\) |
−0.543590 | + | 0.839351i | \(0.682935\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.0578 | + | 20.7953i | −0.433099 | + | 0.689735i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.6553 | − | 39.2402i | 0.750605 | − | 1.30009i | −0.196925 | − | 0.980419i | \(-0.563095\pi\) |
0.947530 | − | 0.319667i | \(-0.103571\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.59558 | − | 2.76362i | −0.0528060 | − | 0.0914626i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −16.9934 | + | 38.9652i | −0.561784 | + | 1.28815i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.01324 | − | 8.01324i | 0.264621 | − | 0.264621i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.91688 | 0.129206 | 0.0646030 | − | 0.997911i | \(-0.479422\pi\) | ||||
0.0646030 | + | 0.997911i | \(0.479422\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.9351 | − | 43.1308i | −0.558030 | − | 1.42121i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.58332 | + | 9.64107i | −0.0850309 | + | 0.317340i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.96831 | + | 29.7381i | 0.261996 | + | 0.977784i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.1134 | + | 32.8221i | −0.332169 | + | 1.07802i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.7214 | − | 7.92207i | −0.450185 | − | 0.259915i | 0.257723 | − | 0.966219i | \(-0.417028\pi\) |
−0.707908 | + | 0.706304i | \(0.750361\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.360116 | − | 1.34397i | 0.0118023 | − | 0.0440468i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.1092 | − | 1.14057i | 0.330960 | − | 0.0373407i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.5824i | 0.575005i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 38.0380i | − | 1.24265i | −0.783554 | − | 0.621324i | \(-0.786595\pi\) | ||
0.783554 | − | 0.621324i | \(-0.213405\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.0449 | − | 23.0877i | −0.556239 | − | 0.753439i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.2570 | + | 49.4756i | −0.432164 | + | 1.61286i | 0.315598 | + | 0.948893i | \(0.397795\pi\) |
−0.747762 | + | 0.663966i | \(0.768872\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 47.3048 | + | 27.3115i | 1.54046 | + | 0.889384i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 38.9356 | + | 18.7287i | 1.26657 | + | 0.609245i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.24080 | − | 15.8269i | −0.137808 | − | 0.514305i | −0.999971 | − | 0.00767376i | \(-0.997557\pi\) |
0.862163 | − | 0.506631i | \(-0.169109\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.9977 | + | 41.0438i | −0.356999 | + | 1.33234i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.9467 | − | 1.79883i | −0.387398 | − | 0.0583311i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.2107 | −0.622295 | −0.311147 | − | 0.950362i | \(-0.600713\pi\) | ||||
−0.311147 | + | 0.950362i | \(0.600713\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.0744 | − | 24.0744i | 0.779030 | − | 0.779030i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.59166 | − | 0.292405i | 0.0837764 | − | 0.00945211i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.2867 | + | 19.5491i | 0.364466 | + | 0.631274i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.6816 | + | 21.9652i | −0.409085 | + | 0.708556i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.0275297 | + | 0.741729i | −0.000887134 | + | 0.0239019i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.73809 | − | 28.8789i | −0.249098 | − | 0.929646i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.0779 | + | 29.5798i | 0.549188 | + | 0.951222i | 0.998330 | + | 0.0577615i | \(0.0183963\pi\) |
−0.449142 | + | 0.893460i | \(0.648270\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.8107 | + | 6.20798i | −0.507912 | + | 0.199429i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.2022 | + | 20.2022i | 0.648318 | + | 0.648318i | 0.952586 | − | 0.304268i | \(-0.0984119\pi\) |
−0.304268 | + | 0.952586i | \(0.598412\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.4038 | − | 21.4038i | 0.686175 | − | 0.686175i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.62078 | + | 19.4088i | 0.244060 | + | 0.621580i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.37615 | + | 4.25862i | −0.235984 | + | 0.136245i | −0.613329 | − | 0.789827i | \(-0.710170\pi\) |
0.377346 | + | 0.926072i | \(0.376837\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.34998 | + | 1.96942i | −0.234906 | + | 0.0629430i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.39776 | + | 0.237457i | 0.204265 | + | 0.00758141i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −47.6844 | − | 27.5306i | −1.52090 | − | 0.878090i | −0.999696 | − | 0.0246553i | \(-0.992151\pi\) |
−0.521200 | − | 0.853435i | \(-0.674515\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.5369 | + | 8.97021i | −0.495045 | + | 0.285815i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.14644 | + | 27.8877i | 0.100152 | + | 0.887675i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.51638 | + | 6.51638i | 0.207209 | + | 0.207209i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 61.9180i | 1.96689i | 0.181210 | + | 0.983444i | \(0.441999\pi\) | ||||
−0.181210 | + | 0.983444i | \(0.558001\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.81643 | − | 38.6290i | 0.184579 | − | 1.22585i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −78.5655 | − | 21.0516i | −2.49069 | − | 0.667380i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.3680 | − | 4.65375i | 0.550051 | − | 0.147386i | 0.0269194 | − | 0.999638i | \(-0.491430\pi\) |
0.523132 | + | 0.852252i | \(0.324764\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −19.2303 | + | 39.9784i | −0.608420 | + | 1.26486i |
(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 | 576.2.y.a.335.19 | 88 | ||
3.2 | odd | 2 | 1728.2.z.a.143.20 | 88 | |||
4.3 | odd | 2 | 144.2.u.a.11.18 | ✓ | 88 | ||
9.4 | even | 3 | 1728.2.z.a.719.20 | 88 | |||
9.5 | odd | 6 | inner | 576.2.y.a.527.15 | 88 | ||
12.11 | even | 2 | 432.2.v.a.251.5 | 88 | |||
16.3 | odd | 4 | inner | 576.2.y.a.47.15 | 88 | ||
16.13 | even | 4 | 144.2.u.a.83.11 | yes | 88 | ||
36.23 | even | 6 | 144.2.u.a.59.11 | yes | 88 | ||
36.31 | odd | 6 | 432.2.v.a.395.12 | 88 | |||
48.29 | odd | 4 | 432.2.v.a.35.12 | 88 | |||
48.35 | even | 4 | 1728.2.z.a.1007.20 | 88 | |||
144.13 | even | 12 | 432.2.v.a.179.5 | 88 | |||
144.67 | odd | 12 | 1728.2.z.a.1583.20 | 88 | |||
144.77 | odd | 12 | 144.2.u.a.131.18 | yes | 88 | ||
144.131 | even | 12 | inner | 576.2.y.a.239.19 | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.u.a.11.18 | ✓ | 88 | 4.3 | odd | 2 | ||
144.2.u.a.59.11 | yes | 88 | 36.23 | even | 6 | ||
144.2.u.a.83.11 | yes | 88 | 16.13 | even | 4 | ||
144.2.u.a.131.18 | yes | 88 | 144.77 | odd | 12 | ||
432.2.v.a.35.12 | 88 | 48.29 | odd | 4 | |||
432.2.v.a.179.5 | 88 | 144.13 | even | 12 | |||
432.2.v.a.251.5 | 88 | 12.11 | even | 2 | |||
432.2.v.a.395.12 | 88 | 36.31 | odd | 6 | |||
576.2.y.a.47.15 | 88 | 16.3 | odd | 4 | inner | ||
576.2.y.a.239.19 | 88 | 144.131 | even | 12 | inner | ||
576.2.y.a.335.19 | 88 | 1.1 | even | 1 | trivial | ||
576.2.y.a.527.15 | 88 | 9.5 | odd | 6 | inner | ||
1728.2.z.a.143.20 | 88 | 3.2 | odd | 2 | |||
1728.2.z.a.719.20 | 88 | 9.4 | even | 3 | |||
1728.2.z.a.1007.20 | 88 | 48.35 | even | 4 | |||
1728.2.z.a.1583.20 | 88 | 144.67 | odd | 12 |