Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(289,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.j (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.447703281.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.4 | ||
Root | \(-1.38232 - 0.298668i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.289 |
Dual form | 546.2.j.c.529.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.75410 | − | 3.03819i | 0.784457 | − | 1.35872i | −0.144866 | − | 0.989451i | \(-0.546275\pi\) |
0.929323 | − | 0.369268i | \(-0.120391\pi\) | |||||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | −2.63641 | + | 0.222079i | −0.996471 | + | 0.0839380i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 1.75410 | − | 3.03819i | 0.554695 | − | 0.960759i | ||||
\(11\) | 3.20391 | − | 5.54934i | 0.966015 | − | 1.67319i | 0.259154 | − | 0.965836i | \(-0.416556\pi\) |
0.706862 | − | 0.707352i | \(-0.250110\pi\) | |||||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | −0.213022 | + | 3.59925i | −0.0590817 | + | 0.998253i | ||||
\(14\) | −2.63641 | + | 0.222079i | −0.704611 | + | 0.0593532i | ||||
\(15\) | 1.75410 | + | 3.03819i | 0.452906 | + | 0.784457i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.67781 | 1.13453 | 0.567267 | − | 0.823534i | \(-0.308001\pi\) | ||||
0.567267 | + | 0.823534i | \(0.308001\pi\) | |||||||
\(18\) | −0.500000 | − | 0.866025i | −0.117851 | − | 0.204124i | ||||
\(19\) | −2.61911 | − | 4.53642i | −0.600864 | − | 1.04073i | −0.992690 | − | 0.120688i | \(-0.961490\pi\) |
0.391826 | − | 0.920039i | \(-0.371843\pi\) | |||||||
\(20\) | 1.75410 | − | 3.03819i | 0.392228 | − | 0.679359i | ||||
\(21\) | 1.12588 | − | 2.39424i | 0.245687 | − | 0.522466i | ||||
\(22\) | 3.20391 | − | 5.54934i | 0.683076 | − | 1.18312i | ||||
\(23\) | −2.16961 | −0.452395 | −0.226197 | − | 0.974081i | \(-0.572629\pi\) | ||||
−0.226197 | + | 0.974081i | \(0.572629\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | −3.65372 | − | 6.32843i | −0.730745 | − | 1.26569i | ||||
\(26\) | −0.213022 | + | 3.59925i | −0.0417771 | + | 0.705872i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.63641 | + | 0.222079i | −0.498235 | + | 0.0419690i | ||||
\(29\) | −1.23033 | − | 2.13099i | −0.228467 | − | 0.395716i | 0.728887 | − | 0.684634i | \(-0.240038\pi\) |
−0.957354 | + | 0.288918i | \(0.906705\pi\) | |||||||
\(30\) | 1.75410 | + | 3.03819i | 0.320253 | + | 0.554695i | ||||
\(31\) | 4.46035 | + | 7.72555i | 0.801102 | + | 1.38755i | 0.918892 | + | 0.394510i | \(0.129086\pi\) |
−0.117790 | + | 0.993039i | \(0.537581\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.20391 | + | 5.54934i | 0.557729 | + | 0.966015i | ||||
\(34\) | 4.67781 | 0.802237 | ||||||||
\(35\) | −3.94981 | + | 8.39947i | −0.667640 | + | 1.41977i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 3.89962 | 0.641094 | 0.320547 | − | 0.947233i | \(-0.396133\pi\) | ||||
0.320547 | + | 0.947233i | \(0.396133\pi\) | |||||||
\(38\) | −2.61911 | − | 4.53642i | −0.424875 | − | 0.735905i | ||||
\(39\) | −3.01053 | − | 1.98411i | −0.482071 | − | 0.317712i | ||||
\(40\) | 1.75410 | − | 3.03819i | 0.277347 | − | 0.480380i | ||||
\(41\) | 5.09300 | + | 8.82134i | 0.795393 | + | 1.37766i | 0.922589 | + | 0.385784i | \(0.126069\pi\) |
−0.127196 | + | 0.991878i | \(0.540598\pi\) | |||||||
\(42\) | 1.12588 | − | 2.39424i | 0.173727 | − | 0.369439i | ||||
\(43\) | −1.19338 | + | 2.06699i | −0.181988 | + | 0.315213i | −0.942558 | − | 0.334044i | \(-0.891587\pi\) |
0.760569 | + | 0.649257i | \(0.224920\pi\) | |||||||
\(44\) | 3.20391 | − | 5.54934i | 0.483008 | − | 0.836594i | ||||
\(45\) | −3.50820 | −0.522971 | ||||||||
\(46\) | −2.16961 | −0.319891 | ||||||||
\(47\) | −2.44070 | + | 4.22742i | −0.356013 | + | 0.616632i | −0.987291 | − | 0.158924i | \(-0.949197\pi\) |
0.631278 | + | 0.775557i | \(0.282531\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | 6.90136 | − | 1.17099i | 0.985909 | − | 0.167284i | ||||
\(50\) | −3.65372 | − | 6.32843i | −0.516714 | − | 0.894976i | ||||
\(51\) | −2.33890 | + | 4.05110i | −0.327512 | + | 0.567267i | ||||
\(52\) | −0.213022 | + | 3.59925i | −0.0295409 | + | 0.499127i | ||||
\(53\) | −1.05395 | − | 1.82549i | −0.144771 | − | 0.250750i | 0.784517 | − | 0.620108i | \(-0.212911\pi\) |
−0.929287 | + | 0.369358i | \(0.879578\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −11.2399 | − | 19.4682i | −1.51559 | − | 2.62509i | ||||
\(56\) | −2.63641 | + | 0.222079i | −0.352306 | + | 0.0296766i | ||||
\(57\) | 5.23821 | 0.693818 | ||||||||
\(58\) | −1.23033 | − | 2.13099i | −0.161550 | − | 0.279813i | ||||
\(59\) | −11.7946 | −1.53552 | −0.767761 | − | 0.640736i | \(-0.778629\pi\) | ||||
−0.767761 | + | 0.640736i | \(0.778629\pi\) | |||||||
\(60\) | 1.75410 | + | 3.03819i | 0.226453 | + | 0.392228i | ||||
\(61\) | −4.67781 | − | 8.10220i | −0.598932 | − | 1.03738i | −0.992979 | − | 0.118290i | \(-0.962259\pi\) |
0.394047 | − | 0.919090i | \(-0.371075\pi\) | |||||||
\(62\) | 4.46035 | + | 7.72555i | 0.566464 | + | 0.981145i | ||||
\(63\) | 1.51053 | + | 2.17216i | 0.190309 | + | 0.273667i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 10.5615 | + | 6.96065i | 1.31000 | + | 0.863362i | ||||
\(66\) | 3.20391 | + | 5.54934i | 0.394374 | + | 0.683076i | ||||
\(67\) | −3.64461 | + | 6.31265i | −0.445260 | + | 0.771213i | −0.998070 | − | 0.0620940i | \(-0.980222\pi\) |
0.552810 | + | 0.833307i | \(0.313555\pi\) | |||||||
\(68\) | 4.67781 | 0.567267 | ||||||||
\(69\) | 1.08480 | − | 1.87894i | 0.130595 | − | 0.226197i | ||||
\(70\) | −3.94981 | + | 8.39947i | −0.472093 | + | 1.00393i | ||||
\(71\) | 2.79339 | − | 4.83829i | 0.331514 | − | 0.574199i | −0.651295 | − | 0.758825i | \(-0.725774\pi\) |
0.982809 | + | 0.184625i | \(0.0591072\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 4.23175 | + | 7.32961i | 0.495289 | + | 0.857866i | 0.999985 | − | 0.00543110i | \(-0.00172878\pi\) |
−0.504696 | + | 0.863297i | \(0.668395\pi\) | |||||||
\(74\) | 3.89962 | 0.453322 | ||||||||
\(75\) | 7.30745 | 0.843791 | ||||||||
\(76\) | −2.61911 | − | 4.53642i | −0.300432 | − | 0.520364i | ||||
\(77\) | −7.21444 | + | 15.3419i | −0.822162 | + | 1.74837i | ||||
\(78\) | −3.01053 | − | 1.98411i | −0.340876 | − | 0.224656i | ||||
\(79\) | 0.893764 | − | 1.54804i | 0.100556 | − | 0.174169i | −0.811358 | − | 0.584550i | \(-0.801271\pi\) |
0.911914 | + | 0.410381i | \(0.134604\pi\) | |||||||
\(80\) | 1.75410 | − | 3.03819i | 0.196114 | − | 0.339680i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 5.09300 | + | 8.82134i | 0.562428 | + | 0.974154i | ||||
\(83\) | −2.59218 | −0.284529 | −0.142264 | − | 0.989829i | \(-0.545438\pi\) | ||||
−0.142264 | + | 0.989829i | \(0.545438\pi\) | |||||||
\(84\) | 1.12588 | − | 2.39424i | 0.122844 | − | 0.261233i | ||||
\(85\) | 8.20533 | − | 14.2121i | 0.889993 | − | 1.54151i | ||||
\(86\) | −1.19338 | + | 2.06699i | −0.128685 | + | 0.222889i | ||||
\(87\) | 2.46066 | 0.263811 | ||||||||
\(88\) | 3.20391 | − | 5.54934i | 0.341538 | − | 0.591561i | ||||
\(89\) | 7.00752 | 0.742795 | 0.371398 | − | 0.928474i | \(-0.378879\pi\) | ||||
0.371398 | + | 0.928474i | \(0.378879\pi\) | |||||||
\(90\) | −3.50820 | −0.369796 | ||||||||
\(91\) | −0.237705 | − | 9.53643i | −0.0249182 | − | 0.999689i | ||||
\(92\) | −2.16961 | −0.226197 | ||||||||
\(93\) | −8.92069 | −0.925033 | ||||||||
\(94\) | −2.44070 | + | 4.22742i | −0.251739 | + | 0.436025i | ||||
\(95\) | −18.3767 | −1.88541 | ||||||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | −4.92513 | + | 8.53057i | −0.500071 | + | 0.866149i | 0.499929 | + | 0.866066i | \(0.333359\pi\) |
−1.00000 | 8.21569e-5i | \(0.999974\pi\) | ||||||||
\(98\) | 6.90136 | − | 1.17099i | 0.697143 | − | 0.118287i | ||||
\(99\) | −6.40782 | −0.644010 | ||||||||
\(100\) | −3.65372 | − | 6.32843i | −0.365372 | − | 0.632843i | ||||
\(101\) | −6.91016 | + | 11.9687i | −0.687586 | + | 1.19093i | 0.285030 | + | 0.958519i | \(0.407996\pi\) |
−0.972616 | + | 0.232416i | \(0.925337\pi\) | |||||||
\(102\) | −2.33890 | + | 4.05110i | −0.231586 | + | 0.401119i | ||||
\(103\) | −6.56658 | + | 11.3737i | −0.647025 | + | 1.12068i | 0.336805 | + | 0.941574i | \(0.390654\pi\) |
−0.983830 | + | 0.179105i | \(0.942680\pi\) | |||||||
\(104\) | −0.213022 | + | 3.59925i | −0.0208885 | + | 0.352936i | ||||
\(105\) | −5.29925 | − | 7.62037i | −0.517154 | − | 0.743672i | ||||
\(106\) | −1.05395 | − | 1.82549i | −0.102368 | − | 0.177307i | ||||
\(107\) | −9.76463 | −0.943983 | −0.471991 | − | 0.881603i | \(-0.656465\pi\) | ||||
−0.471991 | + | 0.881603i | \(0.656465\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 1.14786 | + | 1.98816i | 0.109945 | + | 0.190431i | 0.915748 | − | 0.401753i | \(-0.131599\pi\) |
−0.805803 | + | 0.592184i | \(0.798266\pi\) | |||||||
\(110\) | −11.2399 | − | 19.4682i | −1.07169 | − | 1.85622i | ||||
\(111\) | −1.94981 | + | 3.37717i | −0.185068 | + | 0.320547i | ||||
\(112\) | −2.63641 | + | 0.222079i | −0.249118 | + | 0.0209845i | ||||
\(113\) | 1.96268 | − | 3.39947i | 0.184634 | − | 0.319795i | −0.758819 | − | 0.651301i | \(-0.774223\pi\) |
0.943453 | + | 0.331506i | \(0.107557\pi\) | |||||||
\(114\) | 5.23821 | 0.490604 | ||||||||
\(115\) | −3.80571 | + | 6.59168i | −0.354884 | + | 0.614677i | ||||
\(116\) | −1.23033 | − | 2.13099i | −0.114233 | − | 0.197858i | ||||
\(117\) | 3.22356 | − | 1.61514i | 0.298018 | − | 0.149320i | ||||
\(118\) | −11.7946 | −1.08578 | ||||||||
\(119\) | −12.3326 | + | 1.03884i | −1.13053 | + | 0.0952306i | ||||
\(120\) | 1.75410 | + | 3.03819i | 0.160127 | + | 0.277347i | ||||
\(121\) | −15.0301 | − | 26.0329i | −1.36637 | − | 2.36662i | ||||
\(122\) | −4.67781 | − | 8.10220i | −0.423509 | − | 0.733539i | ||||
\(123\) | −10.1860 | −0.918441 | ||||||||
\(124\) | 4.46035 | + | 7.72555i | 0.400551 | + | 0.693774i | ||||
\(125\) | −8.09497 | −0.724036 | ||||||||
\(126\) | 1.51053 | + | 2.17216i | 0.134569 | + | 0.193512i | ||||
\(127\) | 3.51196 | + | 6.08289i | 0.311636 | + | 0.539769i | 0.978717 | − | 0.205216i | \(-0.0657898\pi\) |
−0.667081 | + | 0.744985i | \(0.732457\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −1.19338 | − | 2.06699i | −0.105071 | − | 0.181988i | ||||
\(130\) | 10.5615 | + | 6.96065i | 0.926309 | + | 0.610489i | ||||
\(131\) | −4.56251 | + | 7.90250i | −0.398628 | + | 0.690444i | −0.993557 | − | 0.113334i | \(-0.963847\pi\) |
0.594929 | + | 0.803778i | \(0.297180\pi\) | |||||||
\(132\) | 3.20391 | + | 5.54934i | 0.278865 | + | 0.483008i | ||||
\(133\) | 7.91249 | + | 11.3782i | 0.686100 | + | 0.986619i | ||||
\(134\) | −3.64461 | + | 6.31265i | −0.314846 | + | 0.545330i | ||||
\(135\) | 1.75410 | − | 3.03819i | 0.150969 | − | 0.261486i | ||||
\(136\) | 4.67781 | 0.401119 | ||||||||
\(137\) | 15.0674 | 1.28730 | 0.643648 | − | 0.765322i | \(-0.277420\pi\) | ||||
0.643648 | + | 0.765322i | \(0.277420\pi\) | |||||||
\(138\) | 1.08480 | − | 1.87894i | 0.0923447 | − | 0.159946i | ||||
\(139\) | 7.02519 | − | 12.1680i | 0.595869 | − | 1.03208i | −0.397555 | − | 0.917578i | \(-0.630141\pi\) |
0.993424 | − | 0.114497i | \(-0.0365255\pi\) | |||||||
\(140\) | −3.94981 | + | 8.39947i | −0.333820 | + | 0.709885i | ||||
\(141\) | −2.44070 | − | 4.22742i | −0.205544 | − | 0.356013i | ||||
\(142\) | 2.79339 | − | 4.83829i | 0.234416 | − | 0.406020i | ||||
\(143\) | 19.2910 | + | 12.7138i | 1.61319 | + | 1.06318i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | −8.63248 | −0.716889 | ||||||||
\(146\) | 4.23175 | + | 7.32961i | 0.350222 | + | 0.606603i | ||||
\(147\) | −2.43658 | + | 6.56225i | −0.200966 | + | 0.541245i | ||||
\(148\) | 3.89962 | 0.320547 | ||||||||
\(149\) | −0.614668 | − | 1.06464i | −0.0503555 | − | 0.0872183i | 0.839749 | − | 0.542975i | \(-0.182702\pi\) |
−0.890104 | + | 0.455757i | \(0.849369\pi\) | |||||||
\(150\) | 7.30745 | 0.596650 | ||||||||
\(151\) | 8.17245 | + | 14.1551i | 0.665065 | + | 1.15193i | 0.979268 | + | 0.202570i | \(0.0649294\pi\) |
−0.314203 | + | 0.949356i | \(0.601737\pi\) | |||||||
\(152\) | −2.61911 | − | 4.53642i | −0.212438 | − | 0.367953i | ||||
\(153\) | −2.33890 | − | 4.05110i | −0.189089 | − | 0.327512i | ||||
\(154\) | −7.21444 | + | 15.3419i | −0.581356 | + | 1.23628i | ||||
\(155\) | 31.2955 | 2.51372 | ||||||||
\(156\) | −3.01053 | − | 1.98411i | −0.241036 | − | 0.158856i | ||||
\(157\) | −7.98494 | − | 13.8303i | −0.637267 | − | 1.10378i | −0.986030 | − | 0.166568i | \(-0.946731\pi\) |
0.348763 | − | 0.937211i | \(-0.386602\pi\) | |||||||
\(158\) | 0.893764 | − | 1.54804i | 0.0711040 | − | 0.123156i | ||||
\(159\) | 2.10789 | 0.167167 | ||||||||
\(160\) | 1.75410 | − | 3.03819i | 0.138674 | − | 0.240190i | ||||
\(161\) | 5.71999 | − | 0.481825i | 0.450798 | − | 0.0379731i | ||||
\(162\) | −0.500000 | + | 0.866025i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | −3.89316 | − | 6.74316i | −0.304936 | − | 0.528165i | 0.672311 | − | 0.740269i | \(-0.265302\pi\) |
−0.977247 | + | 0.212104i | \(0.931968\pi\) | |||||||
\(164\) | 5.09300 | + | 8.82134i | 0.397697 | + | 0.688831i | ||||
\(165\) | 22.4799 | 1.75006 | ||||||||
\(166\) | −2.59218 | −0.201192 | ||||||||
\(167\) | 3.32333 | + | 5.75618i | 0.257167 | + | 0.445427i | 0.965482 | − | 0.260470i | \(-0.0838776\pi\) |
−0.708315 | + | 0.705897i | \(0.750544\pi\) | |||||||
\(168\) | 1.12588 | − | 2.39424i | 0.0868636 | − | 0.184720i | ||||
\(169\) | −12.9092 | − | 1.53344i | −0.993019 | − | 0.117957i | ||||
\(170\) | 8.20533 | − | 14.2121i | 0.629320 | − | 1.09001i | ||||
\(171\) | −2.61911 | + | 4.53642i | −0.200288 | + | 0.346909i | ||||
\(172\) | −1.19338 | + | 2.06699i | −0.0909942 | + | 0.157607i | ||||
\(173\) | 7.30337 | + | 12.6498i | 0.555265 | + | 0.961747i | 0.997883 | + | 0.0650369i | \(0.0207165\pi\) |
−0.442618 | + | 0.896710i | \(0.645950\pi\) | |||||||
\(174\) | 2.46066 | 0.186542 | ||||||||
\(175\) | 11.0381 | + | 15.8730i | 0.834405 | + | 1.19988i | ||||
\(176\) | 3.20391 | − | 5.54934i | 0.241504 | − | 0.418297i | ||||
\(177\) | 5.89729 | − | 10.2144i | 0.443267 | − | 0.767761i | ||||
\(178\) | 7.00752 | 0.525236 | ||||||||
\(179\) | 7.06425 | − | 12.2356i | 0.528006 | − | 0.914534i | −0.471460 | − | 0.881887i | \(-0.656273\pi\) |
0.999467 | − | 0.0326468i | \(-0.0103937\pi\) | |||||||
\(180\) | −3.50820 | −0.261486 | ||||||||
\(181\) | −13.6453 | −1.01425 | −0.507124 | − | 0.861873i | \(-0.669291\pi\) | ||||
−0.507124 | + | 0.861873i | \(0.669291\pi\) | |||||||
\(182\) | −0.237705 | − | 9.53643i | −0.0176198 | − | 0.706887i | ||||
\(183\) | 9.35561 | 0.691587 | ||||||||
\(184\) | −2.16961 | −0.159946 | ||||||||
\(185\) | 6.84033 | − | 11.8478i | 0.502911 | − | 0.871067i | ||||
\(186\) | −8.92069 | −0.654097 | ||||||||
\(187\) | 14.9873 | − | 25.9587i | 1.09598 | − | 1.89829i | ||||
\(188\) | −2.44070 | + | 4.22742i | −0.178006 | + | 0.308316i | ||||
\(189\) | −2.63641 | + | 0.222079i | −0.191771 | + | 0.0161539i | ||||
\(190\) | −18.3767 | −1.33318 | ||||||||
\(191\) | 1.21572 | + | 2.10569i | 0.0879666 | + | 0.152363i | 0.906652 | − | 0.421880i | \(-0.138630\pi\) |
−0.818685 | + | 0.574243i | \(0.805296\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | −1.75877 | + | 3.04628i | −0.126599 | + | 0.219276i | −0.922357 | − | 0.386339i | \(-0.873740\pi\) |
0.795758 | + | 0.605615i | \(0.207073\pi\) | |||||||
\(194\) | −4.92513 | + | 8.53057i | −0.353604 | + | 0.612460i | ||||
\(195\) | −11.3089 | + | 5.66624i | −0.809845 | + | 0.405768i | ||||
\(196\) | 6.90136 | − | 1.17099i | 0.492954 | − | 0.0836418i | ||||
\(197\) | 1.15702 | + | 2.00402i | 0.0824345 | + | 0.142781i | 0.904295 | − | 0.426908i | \(-0.140397\pi\) |
−0.821861 | + | 0.569689i | \(0.807064\pi\) | |||||||
\(198\) | −6.40782 | −0.455384 | ||||||||
\(199\) | 5.69467 | 0.403684 | 0.201842 | − | 0.979418i | \(-0.435307\pi\) | ||||
0.201842 | + | 0.979418i | \(0.435307\pi\) | |||||||
\(200\) | −3.65372 | − | 6.32843i | −0.258357 | − | 0.447488i | ||||
\(201\) | −3.64461 | − | 6.31265i | −0.257071 | − | 0.445260i | ||||
\(202\) | −6.91016 | + | 11.9687i | −0.486197 | + | 0.842118i | ||||
\(203\) | 3.71691 | + | 5.34495i | 0.260876 | + | 0.375142i | ||||
\(204\) | −2.33890 | + | 4.05110i | −0.163756 | + | 0.283634i | ||||
\(205\) | 35.7345 | 2.49581 | ||||||||
\(206\) | −6.56658 | + | 11.3737i | −0.457515 | + | 0.792440i | ||||
\(207\) | 1.08480 | + | 1.87894i | 0.0753991 | + | 0.130595i | ||||
\(208\) | −0.213022 | + | 3.59925i | −0.0147704 | + | 0.249563i | ||||
\(209\) | −33.5655 | −2.32178 | ||||||||
\(210\) | −5.29925 | − | 7.62037i | −0.365683 | − | 0.525856i | ||||
\(211\) | 0.291966 | + | 0.505700i | 0.0200998 | + | 0.0348139i | 0.875900 | − | 0.482492i | \(-0.160268\pi\) |
−0.855801 | + | 0.517306i | \(0.826935\pi\) | |||||||
\(212\) | −1.05395 | − | 1.82549i | −0.0723853 | − | 0.125375i | ||||
\(213\) | 2.79339 | + | 4.83829i | 0.191400 | + | 0.331514i | ||||
\(214\) | −9.76463 | −0.667496 | ||||||||
\(215\) | 4.18660 | + | 7.25141i | 0.285524 | + | 0.494542i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −13.4750 | − | 19.3772i | −0.914743 | − | 1.31541i | ||||
\(218\) | 1.14786 | + | 1.98816i | 0.0777430 | + | 0.134655i | ||||
\(219\) | −8.46350 | −0.571911 | ||||||||
\(220\) | −11.2399 | − | 19.4682i | −0.757797 | − | 1.31254i | ||||
\(221\) | −0.996476 | + | 16.8366i | −0.0670302 | + | 1.13255i | ||||
\(222\) | −1.94981 | + | 3.37717i | −0.130863 | + | 0.226661i | ||||
\(223\) | −7.25749 | − | 12.5703i | −0.485998 | − | 0.841773i | 0.513873 | − | 0.857866i | \(-0.328210\pi\) |
−0.999870 | + | 0.0160938i | \(0.994877\pi\) | |||||||
\(224\) | −2.63641 | + | 0.222079i | −0.176153 | + | 0.0148383i | ||||
\(225\) | −3.65372 | + | 6.32843i | −0.243582 | + | 0.421896i | ||||
\(226\) | 1.96268 | − | 3.39947i | 0.130556 | − | 0.226129i | ||||
\(227\) | 20.2464 | 1.34380 | 0.671899 | − | 0.740643i | \(-0.265479\pi\) | ||||
0.671899 | + | 0.740643i | \(0.265479\pi\) | |||||||
\(228\) | 5.23821 | 0.346909 | ||||||||
\(229\) | −0.668929 | + | 1.15862i | −0.0442041 | + | 0.0765637i | −0.887281 | − | 0.461229i | \(-0.847409\pi\) |
0.843077 | + | 0.537793i | \(0.180742\pi\) | |||||||
\(230\) | −3.80571 | + | 6.59168i | −0.250941 | + | 0.434643i | ||||
\(231\) | −9.67923 | − | 13.9188i | −0.636846 | − | 0.915792i | ||||
\(232\) | −1.23033 | − | 2.13099i | −0.0807752 | − | 0.139907i | ||||
\(233\) | 6.97568 | − | 12.0822i | 0.456992 | − | 0.791534i | −0.541808 | − | 0.840502i | \(-0.682260\pi\) |
0.998800 | + | 0.0489686i | \(0.0155934\pi\) | |||||||
\(234\) | 3.22356 | − | 1.61514i | 0.210730 | − | 0.105585i | ||||
\(235\) | 8.56246 | + | 14.8306i | 0.558553 | + | 0.967443i | ||||
\(236\) | −11.7946 | −0.767761 | ||||||||
\(237\) | 0.893764 | + | 1.54804i | 0.0580562 | + | 0.100556i | ||||
\(238\) | −12.3326 | + | 1.03884i | −0.799406 | + | 0.0673382i | ||||
\(239\) | 9.05495 | 0.585716 | 0.292858 | − | 0.956156i | \(-0.405394\pi\) | ||||
0.292858 | + | 0.956156i | \(0.405394\pi\) | |||||||
\(240\) | 1.75410 | + | 3.03819i | 0.113227 | + | 0.196114i | ||||
\(241\) | 20.1102 | 1.29541 | 0.647705 | − | 0.761891i | \(-0.275729\pi\) | ||||
0.647705 | + | 0.761891i | \(0.275729\pi\) | |||||||
\(242\) | −15.0301 | − | 26.0329i | −0.966171 | − | 1.67346i | ||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −4.67781 | − | 8.10220i | −0.299466 | − | 0.518690i | ||||
\(245\) | 8.54799 | − | 23.0217i | 0.546111 | − | 1.47080i | ||||
\(246\) | −10.1860 | −0.649436 | ||||||||
\(247\) | 16.8857 | − | 8.46047i | 1.07441 | − | 0.538327i | ||||
\(248\) | 4.46035 | + | 7.72555i | 0.283232 | + | 0.490573i | ||||
\(249\) | 1.29609 | − | 2.24489i | 0.0821363 | − | 0.142264i | ||||
\(250\) | −8.09497 | −0.511971 | ||||||||
\(251\) | 4.09035 | − | 7.08469i | 0.258181 | − | 0.447182i | −0.707574 | − | 0.706639i | \(-0.750210\pi\) |
0.965755 | + | 0.259457i | \(0.0835437\pi\) | |||||||
\(252\) | 1.51053 | + | 2.17216i | 0.0951547 | + | 0.136833i | ||||
\(253\) | −6.95123 | + | 12.0399i | −0.437020 | + | 0.756941i | ||||
\(254\) | 3.51196 | + | 6.08289i | 0.220360 | + | 0.381674i | ||||
\(255\) | 8.20533 | + | 14.2121i | 0.513838 | + | 0.889993i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.75393 | 0.608433 | 0.304217 | − | 0.952603i | \(-0.401605\pi\) | ||||
0.304217 | + | 0.952603i | \(0.401605\pi\) | |||||||
\(258\) | −1.19338 | − | 2.06699i | −0.0742964 | − | 0.128685i | ||||
\(259\) | −10.2810 | + | 0.866025i | −0.638832 | + | 0.0538122i | ||||
\(260\) | 10.5615 | + | 6.96065i | 0.654999 | + | 0.431681i | ||||
\(261\) | −1.23033 | + | 2.13099i | −0.0761555 | + | 0.131905i | ||||
\(262\) | −4.56251 | + | 7.90250i | −0.281873 | + | 0.488218i | ||||
\(263\) | 1.47358 | − | 2.55232i | 0.0908648 | − | 0.157383i | −0.817010 | − | 0.576623i | \(-0.804370\pi\) |
0.907875 | + | 0.419240i | \(0.137704\pi\) | |||||||
\(264\) | 3.20391 | + | 5.54934i | 0.197187 | + | 0.341538i | ||||
\(265\) | −7.39490 | −0.454265 | ||||||||
\(266\) | 7.91249 | + | 11.3782i | 0.485146 | + | 0.697645i | ||||
\(267\) | −3.50376 | + | 6.06869i | −0.214427 | + | 0.371398i | ||||
\(268\) | −3.64461 | + | 6.31265i | −0.222630 | + | 0.385607i | ||||
\(269\) | −23.9353 | −1.45936 | −0.729679 | − | 0.683790i | \(-0.760331\pi\) | ||||
−0.729679 | + | 0.683790i | \(0.760331\pi\) | |||||||
\(270\) | 1.75410 | − | 3.03819i | 0.106751 | − | 0.184898i | ||||
\(271\) | 19.3667 | 1.17644 | 0.588222 | − | 0.808700i | \(-0.299828\pi\) | ||||
0.588222 | + | 0.808700i | \(0.299828\pi\) | |||||||
\(272\) | 4.67781 | 0.283634 | ||||||||
\(273\) | 8.37764 | + | 4.56236i | 0.507038 | + | 0.276126i | ||||
\(274\) | 15.0674 | 0.910255 | ||||||||
\(275\) | −46.8248 | −2.82364 | ||||||||
\(276\) | 1.08480 | − | 1.87894i | 0.0652976 | − | 0.113099i | ||||
\(277\) | 2.43419 | 0.146256 | 0.0731282 | − | 0.997323i | \(-0.476702\pi\) | ||||
0.0731282 | + | 0.997323i | \(0.476702\pi\) | |||||||
\(278\) | 7.02519 | − | 12.1680i | 0.421343 | − | 0.729787i | ||||
\(279\) | 4.46035 | − | 7.72555i | 0.267034 | − | 0.462516i | ||||
\(280\) | −3.94981 | + | 8.39947i | −0.236046 | + | 0.501964i | ||||
\(281\) | −2.80329 | −0.167230 | −0.0836152 | − | 0.996498i | \(-0.526647\pi\) | ||||
−0.0836152 | + | 0.996498i | \(0.526647\pi\) | |||||||
\(282\) | −2.44070 | − | 4.22742i | −0.145342 | − | 0.251739i | ||||
\(283\) | 8.47705 | − | 14.6827i | 0.503909 | − | 0.872795i | −0.496081 | − | 0.868276i | \(-0.665228\pi\) |
0.999990 | − | 0.00451916i | \(-0.00143850\pi\) | |||||||
\(284\) | 2.79339 | − | 4.83829i | 0.165757 | − | 0.287100i | ||||
\(285\) | 9.18834 | − | 15.9147i | 0.544270 | − | 0.942704i | ||||
\(286\) | 19.2910 | + | 12.7138i | 1.14070 | + | 0.751784i | ||||
\(287\) | −15.3863 | − | 22.1257i | −0.908224 | − | 1.30604i | ||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | 4.88187 | 0.287169 | ||||||||
\(290\) | −8.63248 | −0.506917 | ||||||||
\(291\) | −4.92513 | − | 8.53057i | −0.288716 | − | 0.500071i | ||||
\(292\) | 4.23175 | + | 7.32961i | 0.247645 | + | 0.428933i | ||||
\(293\) | 2.84568 | − | 4.92886i | 0.166246 | − | 0.287947i | −0.770851 | − | 0.637016i | \(-0.780169\pi\) |
0.937097 | + | 0.349069i | \(0.113502\pi\) | |||||||
\(294\) | −2.43658 | + | 6.56225i | −0.142104 | + | 0.382718i | ||||
\(295\) | −20.6888 | + | 35.8341i | −1.20455 | + | 2.08634i | ||||
\(296\) | 3.89962 | 0.226661 | ||||||||
\(297\) | 3.20391 | − | 5.54934i | 0.185910 | − | 0.322005i | ||||
\(298\) | −0.614668 | − | 1.06464i | −0.0356067 | − | 0.0616727i | ||||
\(299\) | 0.462175 | − | 7.80897i | 0.0267283 | − | 0.451605i | ||||
\(300\) | 7.30745 | 0.421896 | ||||||||
\(301\) | 2.68720 | − | 5.71447i | 0.154888 | − | 0.329376i | ||||
\(302\) | 8.17245 | + | 14.1551i | 0.470272 | + | 0.814535i | ||||
\(303\) | −6.91016 | − | 11.9687i | −0.396978 | − | 0.687586i | ||||
\(304\) | −2.61911 | − | 4.53642i | −0.150216 | − | 0.260182i | ||||
\(305\) | −32.8213 | −1.87934 | ||||||||
\(306\) | −2.33890 | − | 4.05110i | −0.133706 | − | 0.231586i | ||||
\(307\) | 3.48603 | 0.198958 | 0.0994791 | − | 0.995040i | \(-0.468282\pi\) | ||||
0.0994791 | + | 0.995040i | \(0.468282\pi\) | |||||||
\(308\) | −7.21444 | + | 15.3419i | −0.411081 | + | 0.874184i | ||||
\(309\) | −6.56658 | − | 11.3737i | −0.373560 | − | 0.647025i | ||||
\(310\) | 31.2955 | 1.77747 | ||||||||
\(311\) | 12.0016 | + | 20.7873i | 0.680546 | + | 1.17874i | 0.974814 | + | 0.223018i | \(0.0715908\pi\) |
−0.294268 | + | 0.955723i | \(0.595076\pi\) | |||||||
\(312\) | −3.01053 | − | 1.98411i | −0.170438 | − | 0.112328i | ||||
\(313\) | −8.77758 | + | 15.2032i | −0.496138 | + | 0.859337i | −0.999990 | − | 0.00445337i | \(-0.998582\pi\) |
0.503852 | + | 0.863790i | \(0.331916\pi\) | |||||||
\(314\) | −7.98494 | − | 13.8303i | −0.450616 | − | 0.780490i | ||||
\(315\) | 9.24906 | − | 0.779098i | 0.521126 | − | 0.0438972i | ||||
\(316\) | 0.893764 | − | 1.54804i | 0.0502781 | − | 0.0870843i | ||||
\(317\) | −1.42018 | + | 2.45983i | −0.0797655 | + | 0.138158i | −0.903149 | − | 0.429328i | \(-0.858750\pi\) |
0.823383 | + | 0.567486i | \(0.192084\pi\) | |||||||
\(318\) | 2.10789 | 0.118205 | ||||||||
\(319\) | −15.7675 | −0.882809 | ||||||||
\(320\) | 1.75410 | − | 3.03819i | 0.0980571 | − | 0.169840i | ||||
\(321\) | 4.88232 | − | 8.45642i | 0.272504 | − | 0.471991i | ||||
\(322\) | 5.71999 | − | 0.481825i | 0.318763 | − | 0.0268511i | ||||
\(323\) | −12.2517 | − | 21.2205i | −0.681701 | − | 1.18074i | ||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 23.5560 | − | 11.8026i | 1.30665 | − | 0.654689i | ||||
\(326\) | −3.89316 | − | 6.74316i | −0.215622 | − | 0.373469i | ||||
\(327\) | −2.29572 | −0.126954 | ||||||||
\(328\) | 5.09300 | + | 8.82134i | 0.281214 | + | 0.487077i | ||||
\(329\) | 5.49588 | − | 11.6873i | 0.302998 | − | 0.644339i | ||||
\(330\) | 22.4799 | 1.23748 | ||||||||
\(331\) | 9.43745 | + | 16.3461i | 0.518729 | + | 0.898465i | 0.999763 | + | 0.0217633i | \(0.00692802\pi\) |
−0.481034 | + | 0.876702i | \(0.659739\pi\) | |||||||
\(332\) | −2.59218 | −0.142264 | ||||||||
\(333\) | −1.94981 | − | 3.37717i | −0.106849 | − | 0.185068i | ||||
\(334\) | 3.32333 | + | 5.75618i | 0.181845 | + | 0.314964i | ||||
\(335\) | 12.7860 | + | 22.1460i | 0.698575 | + | 1.20997i | ||||
\(336\) | 1.12588 | − | 2.39424i | 0.0614218 | − | 0.130617i | ||||
\(337\) | 10.9560 | 0.596813 | 0.298407 | − | 0.954439i | \(-0.403545\pi\) | ||||
0.298407 | + | 0.954439i | \(0.403545\pi\) | |||||||
\(338\) | −12.9092 | − | 1.53344i | −0.702170 | − | 0.0834082i | ||||
\(339\) | 1.96268 | + | 3.39947i | 0.106598 | + | 0.184634i | ||||
\(340\) | 8.20533 | − | 14.2121i | 0.444997 | − | 0.770757i | ||||
\(341\) | 57.1622 | 3.09551 | ||||||||
\(342\) | −2.61911 | + | 4.53642i | −0.141625 | + | 0.245302i | ||||
\(343\) | −17.9348 | + | 4.61985i | −0.968388 | + | 0.249449i | ||||
\(344\) | −1.19338 | + | 2.06699i | −0.0643426 | + | 0.111445i | ||||
\(345\) | −3.80571 | − | 6.59168i | −0.204892 | − | 0.354884i | ||||
\(346\) | 7.30337 | + | 12.6498i | 0.392632 | + | 0.680058i | ||||
\(347\) | −32.1029 | −1.72338 | −0.861688 | − | 0.507438i | \(-0.830592\pi\) | ||||
−0.861688 | + | 0.507438i | \(0.830592\pi\) | |||||||
\(348\) | 2.46066 | 0.131905 | ||||||||
\(349\) | −9.04373 | − | 15.6642i | −0.484100 | − | 0.838485i | 0.515734 | − | 0.856749i | \(-0.327519\pi\) |
−0.999833 | + | 0.0182638i | \(0.994186\pi\) | |||||||
\(350\) | 11.0381 | + | 15.8730i | 0.590013 | + | 0.848445i | ||||
\(351\) | −0.213022 | + | 3.59925i | −0.0113703 | + | 0.192114i | ||||
\(352\) | 3.20391 | − | 5.54934i | 0.170769 | − | 0.295781i | ||||
\(353\) | 13.7323 | − | 23.7850i | 0.730894 | − | 1.26595i | −0.225607 | − | 0.974218i | \(-0.572436\pi\) |
0.956501 | − | 0.291728i | \(-0.0942302\pi\) | |||||||
\(354\) | 5.89729 | − | 10.2144i | 0.313437 | − | 0.542889i | ||||
\(355\) | −9.79976 | − | 16.9737i | −0.520117 | − | 0.900869i | ||||
\(356\) | 7.00752 | 0.371398 | ||||||||
\(357\) | 5.26665 | − | 11.1998i | 0.278741 | − | 0.592756i | ||||
\(358\) | 7.06425 | − | 12.2356i | 0.373357 | − | 0.646673i | ||||
\(359\) | −10.8390 | + | 18.7738i | −0.572063 | + | 0.990842i | 0.424291 | + | 0.905526i | \(0.360523\pi\) |
−0.996354 | + | 0.0853162i | \(0.972810\pi\) | |||||||
\(360\) | −3.50820 | −0.184898 | ||||||||
\(361\) | −4.21943 | + | 7.30827i | −0.222075 | + | 0.384646i | ||||
\(362\) | −13.6453 | −0.717181 | ||||||||
\(363\) | 30.0602 | 1.57775 | ||||||||
\(364\) | −0.237705 | − | 9.53643i | −0.0124591 | − | 0.499845i | ||||
\(365\) | 29.6916 | 1.55413 | ||||||||
\(366\) | 9.35561 | 0.489026 | ||||||||
\(367\) | −7.66086 | + | 13.2690i | −0.399894 | + | 0.692636i | −0.993712 | − | 0.111963i | \(-0.964286\pi\) |
0.593819 | + | 0.804599i | \(0.297620\pi\) | |||||||
\(368\) | −2.16961 | −0.113099 | ||||||||
\(369\) | 5.09300 | − | 8.82134i | 0.265131 | − | 0.459220i | ||||
\(370\) | 6.84033 | − | 11.8478i | 0.355612 | − | 0.615937i | ||||
\(371\) | 3.18404 | + | 4.57868i | 0.165307 | + | 0.237713i | ||||
\(372\) | −8.92069 | −0.462516 | ||||||||
\(373\) | 16.6792 | + | 28.8893i | 0.863618 | + | 1.49583i | 0.868413 | + | 0.495841i | \(0.165140\pi\) |
−0.00479550 | + | 0.999989i | \(0.501526\pi\) | |||||||
\(374\) | 14.9873 | − | 25.9587i | 0.774973 | − | 1.34229i | ||||
\(375\) | 4.04749 | − | 7.01045i | 0.209011 | − | 0.362018i | ||||
\(376\) | −2.44070 | + | 4.22742i | −0.125870 | + | 0.218012i | ||||
\(377\) | 7.93208 | − | 3.97432i | 0.408523 | − | 0.204688i | ||||
\(378\) | −2.63641 | + | 0.222079i | −0.135603 | + | 0.0114225i | ||||
\(379\) | 8.43868 | + | 14.6162i | 0.433466 | + | 0.750785i | 0.997169 | − | 0.0751926i | \(-0.0239571\pi\) |
−0.563703 | + | 0.825977i | \(0.690624\pi\) | |||||||
\(380\) | −18.3767 | −0.942704 | ||||||||
\(381\) | −7.02391 | −0.359846 | ||||||||
\(382\) | 1.21572 | + | 2.10569i | 0.0622018 | + | 0.107737i | ||||
\(383\) | −10.7933 | − | 18.6945i | −0.551512 | − | 0.955246i | −0.998166 | − | 0.0605395i | \(-0.980718\pi\) |
0.446654 | − | 0.894707i | \(-0.352615\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | 33.9566 | + | 48.8300i | 1.73059 | + | 2.48861i | ||||
\(386\) | −1.75877 | + | 3.04628i | −0.0895191 | + | 0.155052i | ||||
\(387\) | 2.38675 | 0.121326 | ||||||||
\(388\) | −4.92513 | + | 8.53057i | −0.250036 | + | 0.433074i | ||||
\(389\) | 8.68908 | + | 15.0499i | 0.440554 | + | 0.763062i | 0.997731 | − | 0.0673322i | \(-0.0214487\pi\) |
−0.557177 | + | 0.830394i | \(0.688115\pi\) | |||||||
\(390\) | −11.3089 | + | 5.66624i | −0.572647 | + | 0.286921i | ||||
\(391\) | −10.1490 | −0.513258 | ||||||||
\(392\) | 6.90136 | − | 1.17099i | 0.348571 | − | 0.0591437i | ||||
\(393\) | −4.56251 | − | 7.90250i | −0.230148 | − | 0.398628i | ||||
\(394\) | 1.15702 | + | 2.00402i | 0.0582900 | + | 0.100961i | ||||
\(395\) | −3.13550 | − | 5.43084i | −0.157764 | − | 0.273255i | ||||
\(396\) | −6.40782 | −0.322005 | ||||||||
\(397\) | −2.93718 | − | 5.08734i | −0.147413 | − | 0.255326i | 0.782858 | − | 0.622201i | \(-0.213761\pi\) |
−0.930270 | + | 0.366874i | \(0.880428\pi\) | |||||||
\(398\) | 5.69467 | 0.285448 | ||||||||
\(399\) | −13.8101 | + | 1.16330i | −0.691370 | + | 0.0582377i | ||||
\(400\) | −3.65372 | − | 6.32843i | −0.182686 | − | 0.316422i | ||||
\(401\) | −13.9771 | −0.697983 | −0.348992 | − | 0.937126i | \(-0.613476\pi\) | ||||
−0.348992 | + | 0.937126i | \(0.613476\pi\) | |||||||
\(402\) | −3.64461 | − | 6.31265i | −0.181777 | − | 0.314846i | ||||
\(403\) | −28.7563 | + | 14.4082i | −1.43246 | + | 0.717724i | ||||
\(404\) | −6.91016 | + | 11.9687i | −0.343793 | + | 0.595467i | ||||
\(405\) | 1.75410 | + | 3.03819i | 0.0871619 | + | 0.150969i | ||||
\(406\) | 3.71691 | + | 5.34495i | 0.184467 | + | 0.265266i | ||||
\(407\) | 12.4940 | − | 21.6403i | 0.619307 | − | 1.07267i | ||||
\(408\) | −2.33890 | + | 4.05110i | −0.115793 | + | 0.200559i | ||||
\(409\) | −37.4897 | −1.85375 | −0.926873 | − | 0.375375i | \(-0.877514\pi\) | ||||
−0.926873 | + | 0.375375i | \(0.877514\pi\) | |||||||
\(410\) | 35.7345 | 1.76480 | ||||||||
\(411\) | −7.53370 | + | 13.0488i | −0.371610 | + | 0.643648i | ||||
\(412\) | −6.56658 | + | 11.3737i | −0.323512 | + | 0.560340i | ||||
\(413\) | 31.0954 | − | 2.61933i | 1.53010 | − | 0.128889i | ||||
\(414\) | 1.08480 | + | 1.87894i | 0.0533152 | + | 0.0923447i | ||||
\(415\) | −4.54694 | + | 7.87553i | −0.223200 | + | 0.386594i | ||||
\(416\) | −0.213022 | + | 3.59925i | −0.0104443 | + | 0.176468i | ||||
\(417\) | 7.02519 | + | 12.1680i | 0.344025 | + | 0.595869i | ||||
\(418\) | −33.5655 | −1.64174 | ||||||||
\(419\) | −16.9548 | − | 29.3665i | −0.828294 | − | 1.43465i | −0.899375 | − | 0.437177i | \(-0.855978\pi\) |
0.0710814 | − | 0.997471i | \(-0.477355\pi\) | |||||||
\(420\) | −5.29925 | − | 7.62037i | −0.258577 | − | 0.371836i | ||||
\(421\) | −10.5503 | −0.514192 | −0.257096 | − | 0.966386i | \(-0.582766\pi\) | ||||
−0.257096 | + | 0.966386i | \(0.582766\pi\) | |||||||
\(422\) | 0.291966 | + | 0.505700i | 0.0142127 | + | 0.0246171i | ||||
\(423\) | 4.88140 | 0.237342 | ||||||||
\(424\) | −1.05395 | − | 1.82549i | −0.0511842 | − | 0.0886536i | ||||
\(425\) | −17.0914 | − | 29.6032i | −0.829055 | − | 1.43597i | ||||
\(426\) | 2.79339 | + | 4.83829i | 0.135340 | + | 0.234416i | ||||
\(427\) | 14.1320 | + | 20.3219i | 0.683894 | + | 0.983446i | ||||
\(428\) | −9.76463 | −0.471991 | ||||||||
\(429\) | −20.6560 | + | 10.3496i | −0.997280 | + | 0.499681i | ||||
\(430\) | 4.18660 | + | 7.25141i | 0.201896 | + | 0.349694i | ||||
\(431\) | 12.8043 | − | 22.1777i | 0.616761 | − | 1.06826i | −0.373312 | − | 0.927706i | \(-0.621778\pi\) |
0.990073 | − | 0.140555i | \(-0.0448887\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 3.68968 | − | 6.39071i | 0.177315 | − | 0.307118i | −0.763645 | − | 0.645636i | \(-0.776592\pi\) |
0.940960 | + | 0.338518i | \(0.109926\pi\) | |||||||
\(434\) | −13.4750 | − | 19.3772i | −0.646821 | − | 0.930135i | ||||
\(435\) | 4.31624 | − | 7.47595i | 0.206948 | − | 0.358444i | ||||
\(436\) | 1.14786 | + | 1.98816i | 0.0549726 | + | 0.0952154i | ||||
\(437\) | 5.68244 | + | 9.84227i | 0.271828 | + | 0.470820i | ||||
\(438\) | −8.46350 | −0.404402 | ||||||||
\(439\) | −23.0510 | −1.10016 | −0.550082 | − | 0.835110i | \(-0.685404\pi\) | ||||
−0.550082 | + | 0.835110i | \(0.685404\pi\) | |||||||
\(440\) | −11.2399 | − | 19.4682i | −0.535844 | − | 0.928108i | ||||
\(441\) | −4.46478 | − | 5.39126i | −0.212609 | − | 0.256727i | ||||
\(442\) | −0.996476 | + | 16.8366i | −0.0473975 | + | 0.800836i | ||||
\(443\) | 9.05605 | − | 15.6855i | 0.430266 | − | 0.745242i | −0.566630 | − | 0.823972i | \(-0.691753\pi\) |
0.996896 | + | 0.0787300i | \(0.0250865\pi\) | |||||||
\(444\) | −1.94981 | + | 3.37717i | −0.0925340 | + | 0.160274i | ||||
\(445\) | 12.2919 | − | 21.2902i | 0.582691 | − | 1.00925i | ||||
\(446\) | −7.25749 | − | 12.5703i | −0.343652 | − | 0.595223i | ||||
\(447\) | 1.22934 | 0.0581456 | ||||||||
\(448\) | −2.63641 | + | 0.222079i | −0.124559 | + | 0.0104923i | ||||
\(449\) | −9.23084 | + | 15.9883i | −0.435630 | + | 0.754534i | −0.997347 | − | 0.0727961i | \(-0.976808\pi\) |
0.561717 | + | 0.827330i | \(0.310141\pi\) | |||||||
\(450\) | −3.65372 | + | 6.32843i | −0.172238 | + | 0.298325i | ||||
\(451\) | 65.2701 | 3.07345 | ||||||||
\(452\) | 1.96268 | − | 3.39947i | 0.0923168 | − | 0.159897i | ||||
\(453\) | −16.3449 | −0.767951 | ||||||||
\(454\) | 20.2464 | 0.950209 | ||||||||
\(455\) | −29.3904 | − | 16.0056i | −1.37784 | − | 0.750356i | ||||
\(456\) | 5.23821 | 0.245302 | ||||||||
\(457\) | −17.8047 | −0.832866 | −0.416433 | − | 0.909166i | \(-0.636720\pi\) | ||||
−0.416433 | + | 0.909166i | \(0.636720\pi\) | |||||||
\(458\) | −0.668929 | + | 1.15862i | −0.0312570 | + | 0.0541387i | ||||
\(459\) | 4.67781 | 0.218341 | ||||||||
\(460\) | −3.80571 | + | 6.59168i | −0.177442 | + | 0.307339i | ||||
\(461\) | −2.51030 | + | 4.34797i | −0.116916 | + | 0.202505i | −0.918544 | − | 0.395318i | \(-0.870634\pi\) |
0.801628 | + | 0.597823i | \(0.203968\pi\) | |||||||
\(462\) | −9.67923 | − | 13.9188i | −0.450318 | − | 0.647562i | ||||
\(463\) | −25.0075 | −1.16220 | −0.581099 | − | 0.813833i | \(-0.697377\pi\) | ||||
−0.581099 | + | 0.813833i | \(0.697377\pi\) | |||||||
\(464\) | −1.23033 | − | 2.13099i | −0.0571167 | − | 0.0989290i | ||||
\(465\) | −15.6478 | + | 27.1027i | −0.725648 | + | 1.25686i | ||||
\(466\) | 6.97568 | − | 12.0822i | 0.323142 | − | 0.559699i | ||||
\(467\) | 12.9128 | − | 22.3656i | 0.597532 | − | 1.03496i | −0.395653 | − | 0.918400i | \(-0.629482\pi\) |
0.993184 | − | 0.116555i | \(-0.0371851\pi\) | |||||||
\(468\) | 3.22356 | − | 1.61514i | 0.149009 | − | 0.0746601i | ||||
\(469\) | 8.20680 | − | 17.4522i | 0.378955 | − | 0.805866i | ||||
\(470\) | 8.56246 | + | 14.8306i | 0.394957 | + | 0.684085i | ||||
\(471\) | 15.9699 | 0.735853 | ||||||||
\(472\) | −11.7946 | −0.542889 | ||||||||
\(473\) | 7.64695 | + | 13.2449i | 0.351607 | + | 0.609001i | ||||
\(474\) | 0.893764 | + | 1.54804i | 0.0410519 | + | 0.0711040i | ||||
\(475\) | −19.1390 | + | 33.1497i | −0.878156 | + | 1.52101i | ||||
\(476\) | −12.3326 | + | 1.03884i | −0.565265 | + | 0.0476153i | ||||
\(477\) | −1.05395 | + | 1.82549i | −0.0482569 | + | 0.0835834i | ||||
\(478\) | 9.05495 | 0.414164 | ||||||||
\(479\) | −11.5569 | + | 20.0171i | −0.528047 | + | 0.914604i | 0.471418 | + | 0.881910i | \(0.343742\pi\) |
−0.999465 | + | 0.0326944i | \(0.989591\pi\) | |||||||
\(480\) | 1.75410 | + | 3.03819i | 0.0800633 | + | 0.138674i | ||||
\(481\) | −0.830706 | + | 14.0357i | −0.0378769 | + | 0.639974i | ||||
\(482\) | 20.1102 | 0.915993 | ||||||||
\(483\) | −2.44272 | + | 5.19457i | −0.111148 | + | 0.236361i | ||||
\(484\) | −15.0301 | − | 26.0329i | −0.683186 | − | 1.18331i | ||||
\(485\) | 17.2783 | + | 29.9269i | 0.784568 | + | 1.35891i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | −16.2740 | −0.737447 | −0.368723 | − | 0.929539i | \(-0.620205\pi\) | ||||
−0.368723 | + | 0.929539i | \(0.620205\pi\) | |||||||
\(488\) | −4.67781 | − | 8.10220i | −0.211754 | − | 0.366769i | ||||
\(489\) | 7.78633 | 0.352110 | ||||||||
\(490\) | 8.54799 | − | 23.0217i | 0.386159 | − | 1.04001i | ||||
\(491\) | −19.0299 | − | 32.9608i | −0.858809 | − | 1.48750i | −0.873065 | − | 0.487603i | \(-0.837871\pi\) |
0.0142561 | − | 0.999898i | \(-0.495462\pi\) | |||||||
\(492\) | −10.1860 | −0.459220 | ||||||||
\(493\) | −5.75525 | − | 9.96838i | −0.259203 | − | 0.448953i | ||||
\(494\) | 16.8857 | − | 8.46047i | 0.759722 | − | 0.380654i | ||||
\(495\) | −11.2399 | + | 19.4682i | −0.505198 | + | 0.875029i | ||||
\(496\) | 4.46035 | + | 7.72555i | 0.200275 | + | 0.346887i | ||||
\(497\) | −6.29005 | + | 13.3761i | −0.282147 | + | 0.600000i | ||||
\(498\) | 1.29609 | − | 2.24489i | 0.0580792 | − | 0.100596i | ||||
\(499\) | 17.1178 | − | 29.6489i | 0.766297 | − | 1.32727i | −0.173261 | − | 0.984876i | \(-0.555430\pi\) |
0.939558 | − | 0.342389i | \(-0.111236\pi\) | |||||||
\(500\) | −8.09497 | −0.362018 | ||||||||
\(501\) | −6.64666 | −0.296951 | ||||||||
\(502\) | 4.09035 | − | 7.08469i | 0.182561 | − | 0.316205i | ||||
\(503\) | −1.12053 | + | 1.94081i | −0.0499619 | + | 0.0865365i | −0.889925 | − | 0.456107i | \(-0.849243\pi\) |
0.839963 | + | 0.542644i | \(0.182577\pi\) | |||||||
\(504\) | 1.51053 | + | 2.17216i | 0.0672845 | + | 0.0967558i | ||||
\(505\) | 24.2422 | + | 41.9887i | 1.07876 | + | 1.86847i | ||||
\(506\) | −6.95123 | + | 12.0399i | −0.309020 | + | 0.535238i | ||||
\(507\) | 7.78262 | − | 10.4130i | 0.345638 | − | 0.462458i | ||||
\(508\) | 3.51196 | + | 6.08289i | 0.155818 | + | 0.269884i | ||||
\(509\) | −25.8328 | −1.14502 | −0.572509 | − | 0.819899i | \(-0.694030\pi\) | ||||
−0.572509 | + | 0.819899i | \(0.694030\pi\) | |||||||
\(510\) | 8.20533 | + | 14.2121i | 0.363338 | + | 0.629320i | ||||
\(511\) | −12.7844 | − | 18.3841i | −0.565549 | − | 0.813265i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.61911 | − | 4.53642i | −0.115636 | − | 0.200288i | ||||
\(514\) | 9.75393 | 0.430227 | ||||||||
\(515\) | 23.0369 | + | 39.9010i | 1.01513 | + | 1.75825i | ||||
\(516\) | −1.19338 | − | 2.06699i | −0.0525355 | − | 0.0909942i | ||||
\(517\) | 15.6396 | + | 27.0885i | 0.687828 | + | 1.19135i | ||||
\(518\) | −10.2810 | + | 0.866025i | −0.451722 | + | 0.0380510i | ||||
\(519\) | −14.6067 | −0.641165 | ||||||||
\(520\) | 10.5615 | + | 6.96065i | 0.463154 | + | 0.305244i | ||||
\(521\) | −12.1715 | − | 21.0817i | −0.533245 | − | 0.923607i | −0.999246 | − | 0.0388230i | \(-0.987639\pi\) |
0.466001 | − | 0.884784i | \(-0.345694\pi\) | |||||||
\(522\) | −1.23033 | + | 2.13099i | −0.0538501 | + | 0.0932711i | ||||
\(523\) | 8.88709 | 0.388605 | 0.194303 | − | 0.980942i | \(-0.437756\pi\) | ||||
0.194303 | + | 0.980942i | \(0.437756\pi\) | |||||||
\(524\) | −4.56251 | + | 7.90250i | −0.199314 | + | 0.345222i | ||||
\(525\) | −19.2655 | + | 1.62283i | −0.840813 | + | 0.0708262i | ||||
\(526\) | 1.47358 | − | 2.55232i | 0.0642511 | − | 0.111286i | ||||
\(527\) | 20.8646 | + | 36.1386i | 0.908878 | + | 1.57422i | ||||
\(528\) | 3.20391 | + | 5.54934i | 0.139432 | + | 0.241504i | ||||
\(529\) | −18.2928 | −0.795339 | ||||||||
\(530\) | −7.39490 | −0.321214 | ||||||||
\(531\) | 5.89729 | + | 10.2144i | 0.255920 | + | 0.443267i | ||||
\(532\) | 7.91249 | + | 11.3782i | 0.343050 | + | 0.493310i | ||||
\(533\) | −32.8351 | + | 16.4519i | −1.42225 | + | 0.712609i | ||||
\(534\) | −3.50376 | + | 6.06869i | −0.151622 | + | 0.262618i | ||||
\(535\) | −17.1281 | + | 29.6668i | −0.740513 | + | 1.28261i | ||||
\(536\) | −3.64461 | + | 6.31265i | −0.157423 | + | 0.272665i | ||||
\(537\) | 7.06425 | + | 12.2356i | 0.304845 | + | 0.528006i | ||||
\(538\) | −23.9353 | −1.03192 | ||||||||
\(539\) | 15.6132 | − | 42.0497i | 0.672506 | − | 1.81121i | ||||
\(540\) | 1.75410 | − | 3.03819i | 0.0754844 | − | 0.130743i | ||||
\(541\) | 8.01702 | − | 13.8859i | 0.344679 | − | 0.597001i | −0.640617 | − | 0.767861i | \(-0.721321\pi\) |
0.985295 | + | 0.170860i | \(0.0546545\pi\) | |||||||
\(542\) | 19.3667 | 0.831871 | ||||||||
\(543\) | 6.82265 | − | 11.8172i | 0.292788 | − | 0.507124i | ||||
\(544\) | 4.67781 | 0.200559 | ||||||||
\(545\) | 8.05385 | 0.344989 | ||||||||
\(546\) | 8.37764 | + | 4.56236i | 0.358530 | + | 0.195251i | ||||
\(547\) | −10.3955 | −0.444481 | −0.222240 | − | 0.974992i | \(-0.571337\pi\) | ||||
−0.222240 | + | 0.974992i | \(0.571337\pi\) | |||||||
\(548\) | 15.0674 | 0.643648 | ||||||||
\(549\) | −4.67781 | + | 8.10220i | −0.199644 | + | 0.345793i | ||||
\(550\) | −46.8248 | −1.99662 | ||||||||
\(551\) | −6.44473 | + | 11.1626i | −0.274555 | + | 0.475543i | ||||
\(552\) | 1.08480 | − | 1.87894i | 0.0461724 | − | 0.0799729i | ||||
\(553\) | −2.01254 | + | 4.27977i | −0.0855821 | + | 0.181994i | ||||
\(554\) | 2.43419 | 0.103419 | ||||||||
\(555\) | 6.84033 | + | 11.8478i | 0.290356 | + | 0.502911i | ||||
\(556\) | 7.02519 | − | 12.1680i | 0.297934 | − | 0.516038i | ||||
\(557\) | −16.1951 | + | 28.0508i | −0.686209 | + | 1.18855i | 0.286846 | + | 0.957977i | \(0.407393\pi\) |
−0.973055 | + | 0.230572i | \(0.925940\pi\) | |||||||
\(558\) | 4.46035 | − | 7.72555i | 0.188821 | − | 0.327048i | ||||
\(559\) | −7.18540 | − | 4.73558i | −0.303910 | − | 0.200294i | ||||
\(560\) | −3.94981 | + | 8.39947i | −0.166910 | + | 0.354942i | ||||
\(561\) | 14.9873 | + | 25.9587i | 0.632763 | + | 1.09598i | ||||
\(562\) | −2.80329 | −0.118250 | ||||||||
\(563\) | −2.43309 | −0.102543 | −0.0512713 | − | 0.998685i | \(-0.516327\pi\) | ||||
−0.0512713 | + | 0.998685i | \(0.516327\pi\) | |||||||
\(564\) | −2.44070 | − | 4.22742i | −0.102772 | − | 0.178006i | ||||
\(565\) | −6.88548 | − | 11.9260i | −0.289674 | − | 0.501730i | ||||
\(566\) | 8.47705 | − | 14.6827i | 0.356317 | − | 0.617159i | ||||
\(567\) | 1.12588 | − | 2.39424i | 0.0472826 | − | 0.100549i | ||||
\(568\) | 2.79339 | − | 4.83829i | 0.117208 | − | 0.203010i | ||||
\(569\) | −7.94066 | −0.332890 | −0.166445 | − | 0.986051i | \(-0.553229\pi\) | ||||
−0.166445 | + | 0.986051i | \(0.553229\pi\) | |||||||
\(570\) | 9.18834 | − | 15.9147i | 0.384857 | − | 0.666592i | ||||
\(571\) | 18.0463 | + | 31.2571i | 0.755214 | + | 1.30807i | 0.945268 | + | 0.326295i | \(0.105800\pi\) |
−0.190054 | + | 0.981774i | \(0.560866\pi\) | |||||||
\(572\) | 19.2910 | + | 12.7138i | 0.806596 | + | 0.531591i | ||||
\(573\) | −2.43145 | −0.101575 | ||||||||
\(574\) | −15.3863 | − | 22.1257i | −0.642212 | − | 0.923507i | ||||
\(575\) | 7.92715 | + | 13.7302i | 0.330585 | + | 0.572590i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −16.3980 | − | 28.4021i | −0.682657 | − | 1.18240i | −0.974167 | − | 0.225829i | \(-0.927491\pi\) |
0.291510 | − | 0.956568i | \(-0.405842\pi\) | |||||||
\(578\) | 4.88187 | 0.203059 | ||||||||
\(579\) | −1.75877 | − | 3.04628i | −0.0730920 | − | 0.126599i | ||||
\(580\) | −8.63248 | −0.358444 | ||||||||
\(581\) | 6.83406 | − | 0.575669i | 0.283524 | − | 0.0238828i | ||||
\(582\) | −4.92513 | − | 8.53057i | −0.204153 | − | 0.353604i | ||||
\(583\) | −13.5070 | −0.559403 | ||||||||
\(584\) | 4.23175 | + | 7.32961i | 0.175111 | + | 0.303301i | ||||
\(585\) | 0.747323 | − | 12.6269i | 0.0308980 | − | 0.522058i | ||||
\(586\) | 2.84568 | − | 4.92886i | 0.117554 | − | 0.203609i | ||||
\(587\) | 10.9482 | + | 18.9629i | 0.451881 | + | 0.782681i | 0.998503 | − | 0.0546984i | \(-0.0174197\pi\) |
−0.546622 | + | 0.837380i | \(0.684086\pi\) | |||||||
\(588\) | −2.43658 | + | 6.56225i | −0.100483 | + | 0.270623i | ||||
\(589\) | 23.3642 | − | 40.4680i | 0.962707 | − | 1.66746i | ||||
\(590\) | −20.6888 | + | 35.8341i | −0.851746 | + | 1.47527i | ||||
\(591\) | −2.31405 | −0.0951871 | ||||||||
\(592\) | 3.89962 | 0.160274 | ||||||||
\(593\) | 3.25002 | − | 5.62921i | 0.133463 | − | 0.231164i | −0.791547 | − | 0.611109i | \(-0.790724\pi\) |
0.925009 | + | 0.379945i | \(0.124057\pi\) | |||||||
\(594\) | 3.20391 | − | 5.54934i | 0.131458 | − | 0.227692i | ||||
\(595\) | −18.4765 | + | 39.2911i | −0.757461 | + | 1.61078i | ||||
\(596\) | −0.614668 | − | 1.06464i | −0.0251778 | − | 0.0436092i | ||||
\(597\) | −2.84733 | + | 4.93173i | −0.116534 | + | 0.201842i | ||||
\(598\) | 0.462175 | − | 7.80897i | 0.0188997 | − | 0.319333i | ||||
\(599\) | 1.40105 | + | 2.42668i | 0.0572452 | + | 0.0991516i | 0.893228 | − | 0.449604i | \(-0.148435\pi\) |
−0.835983 | + | 0.548756i | \(0.815102\pi\) | |||||||
\(600\) | 7.30745 | 0.298325 | ||||||||
\(601\) | −11.8591 | − | 20.5405i | −0.483741 | − | 0.837864i | 0.516085 | − | 0.856538i | \(-0.327389\pi\) |
−0.999826 | + | 0.0186737i | \(0.994056\pi\) | |||||||
\(602\) | 2.68720 | − | 5.71447i | 0.109522 | − | 0.232904i | ||||
\(603\) | 7.28922 | 0.296840 | ||||||||
\(604\) | 8.17245 | + | 14.1551i | 0.332532 | + | 0.575963i | ||||
\(605\) | −105.457 | −4.28744 | ||||||||
\(606\) | −6.91016 | − | 11.9687i | −0.280706 | − | 0.486197i | ||||
\(607\) | 5.92151 | + | 10.2564i | 0.240347 | + | 0.416293i | 0.960813 | − | 0.277197i | \(-0.0894055\pi\) |
−0.720466 | + | 0.693490i | \(0.756072\pi\) | |||||||
\(608\) | −2.61911 | − | 4.53642i | −0.106219 | − | 0.183976i | ||||
\(609\) | −6.48732 | + | 0.546462i | −0.262880 | + | 0.0221437i | ||||
\(610\) | −32.8213 | −1.32890 | ||||||||
\(611\) | −14.6956 | − | 9.68523i | −0.594521 | − | 0.391823i | ||||
\(612\) | −2.33890 | − | 4.05110i | −0.0945446 | − | 0.163756i | ||||
\(613\) | 8.09895 | − | 14.0278i | 0.327114 | − | 0.566577i | −0.654824 | − | 0.755781i | \(-0.727257\pi\) |
0.981938 | + | 0.189204i | \(0.0605907\pi\) | |||||||
\(614\) | 3.48603 | 0.140685 | ||||||||
\(615\) | −17.8673 | + | 30.9470i | −0.720477 | + | 1.24790i | ||||
\(616\) | −7.21444 | + | 15.3419i | −0.290678 | + | 0.618142i | ||||
\(617\) | −22.0973 | + | 38.2737i | −0.889606 | + | 1.54084i | −0.0492637 | + | 0.998786i | \(0.515687\pi\) |
−0.840342 | + | 0.542057i | \(0.817646\pi\) | |||||||
\(618\) | −6.56658 | − | 11.3737i | −0.264147 | − | 0.457515i | ||||
\(619\) | −17.0272 | − | 29.4920i | −0.684383 | − | 1.18539i | −0.973630 | − | 0.228131i | \(-0.926738\pi\) |
0.289248 | − | 0.957254i | \(-0.406595\pi\) | |||||||
\(620\) | 31.2955 | 1.25686 | ||||||||
\(621\) | −2.16961 | −0.0870634 | ||||||||
\(622\) | 12.0016 | + | 20.7873i | 0.481219 | + | 0.833496i | ||||
\(623\) | −18.4747 | + | 1.55622i | −0.740174 | + | 0.0623488i | ||||
\(624\) | −3.01053 | − | 1.98411i | −0.120518 | − | 0.0794279i | ||||
\(625\) | 4.06923 | − | 7.04812i | 0.162769 | − | 0.281925i | ||||
\(626\) | −8.77758 | + | 15.2032i | −0.350823 | + | 0.607643i | ||||
\(627\) | 16.7828 | − | 29.0686i | 0.670239 | − | 1.16089i | ||||
\(628\) | −7.98494 | − | 13.8303i | −0.318634 | − | 0.551890i | ||||
\(629\) | 18.2417 | 0.727344 | ||||||||
\(630\) | 9.24906 | − | 0.779098i | 0.368491 | − | 0.0310400i | ||||
\(631\) | −0.712707 | + | 1.23444i | −0.0283724 | + | 0.0491424i | −0.879863 | − | 0.475227i | \(-0.842366\pi\) |
0.851491 | + | 0.524370i | \(0.175699\pi\) | |||||||
\(632\) | 0.893764 | − | 1.54804i | 0.0355520 | − | 0.0615779i | ||||
\(633\) | −0.583933 | −0.0232092 | ||||||||
\(634\) | −1.42018 | + | 2.45983i | −0.0564027 | + | 0.0976923i | ||||
\(635\) | 24.6413 | 0.977859 | ||||||||
\(636\) | 2.10789 | 0.0835834 | ||||||||
\(637\) | 2.74453 | + | 25.0892i | 0.108742 | + | 0.994070i | ||||
\(638\) | −15.7675 | −0.624240 | ||||||||
\(639\) | −5.58678 | −0.221009 | ||||||||
\(640\) | 1.75410 | − | 3.03819i | 0.0693368 | − | 0.120095i | ||||
\(641\) | −23.2001 | −0.916350 | −0.458175 | − | 0.888862i | \(-0.651497\pi\) | ||||
−0.458175 | + | 0.888862i | \(0.651497\pi\) | |||||||
\(642\) | 4.88232 | − | 8.45642i | 0.192690 | − | 0.333748i | ||||
\(643\) | 3.41821 | − | 5.92052i | 0.134801 | − | 0.233482i | −0.790720 | − | 0.612178i | \(-0.790294\pi\) |
0.925521 | + | 0.378695i | \(0.123627\pi\) | |||||||
\(644\) | 5.71999 | − | 0.481825i | 0.225399 | − | 0.0189866i | ||||
\(645\) | −8.37320 | −0.329695 | ||||||||
\(646\) | −12.2517 | − | 21.2205i | −0.482036 | − | 0.834910i | ||||
\(647\) | 21.2982 | − | 36.8896i | 0.837320 | − | 1.45028i | −0.0548069 | − | 0.998497i | \(-0.517454\pi\) |
0.892127 | − | 0.451784i | \(-0.149212\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | −37.7888 | + | 65.4521i | −1.48334 | + | 2.56922i | ||||
\(650\) | 23.5560 | − | 11.8026i | 0.923941 | − | 0.462935i | ||||
\(651\) | 23.5186 | − | 1.98110i | 0.921768 | − | 0.0776454i | ||||
\(652\) | −3.89316 | − | 6.74316i | −0.152468 | − | 0.264082i | ||||
\(653\) | −39.4447 | −1.54359 | −0.771794 | − | 0.635872i | \(-0.780640\pi\) | ||||
−0.771794 | + | 0.635872i | \(0.780640\pi\) | |||||||
\(654\) | −2.29572 | −0.0897699 | ||||||||
\(655\) | 16.0062 | + | 27.7235i | 0.625413 | + | 1.08325i | ||||
\(656\) | 5.09300 | + | 8.82134i | 0.198848 | + | 0.344415i | ||||
\(657\) | 4.23175 | − | 7.32961i | 0.165096 | − | 0.285955i | ||||
\(658\) | 5.49588 | − | 11.6873i | 0.214252 | − | 0.455617i | ||||
\(659\) | 0.667872 | − | 1.15679i | 0.0260166 | − | 0.0450621i | −0.852724 | − | 0.522362i | \(-0.825051\pi\) |
0.878741 | + | 0.477300i | \(0.158384\pi\) | |||||||
\(660\) | 22.4799 | 0.875029 | ||||||||
\(661\) | 6.44661 | − | 11.1659i | 0.250744 | − | 0.434301i | −0.712987 | − | 0.701177i | \(-0.752658\pi\) |
0.963731 | + | 0.266876i | \(0.0859914\pi\) | |||||||
\(662\) | 9.43745 | + | 16.3461i | 0.366797 | + | 0.635311i | ||||
\(663\) | −14.0827 | − | 9.28128i | −0.546926 | − | 0.360455i | ||||
\(664\) | −2.59218 | −0.100596 | ||||||||
\(665\) | 48.4485 | − | 4.08108i | 1.87875 | − | 0.158257i | ||||
\(666\) | −1.94981 | − | 3.37717i | −0.0755537 | − | 0.130863i | ||||
\(667\) | 2.66934 | + | 4.62343i | 0.103357 | + | 0.179020i | ||||
\(668\) | 3.32333 | + | 5.75618i | 0.128584 | + | 0.222713i | ||||
\(669\) | 14.5150 | 0.561182 | ||||||||
\(670\) | 12.7860 | + | 22.1460i | 0.493967 | + | 0.855576i | ||||
\(671\) | −59.9491 | −2.31431 | ||||||||
\(672\) | 1.12588 | − | 2.39424i | 0.0434318 | − | 0.0923599i | ||||
\(673\) | −13.8759 | − | 24.0338i | −0.534877 | − | 0.926434i | −0.999169 | − | 0.0407519i | \(-0.987025\pi\) |
0.464292 | − | 0.885682i | \(-0.346309\pi\) | |||||||
\(674\) | 10.9560 | 0.422011 | ||||||||
\(675\) | −3.65372 | − | 6.32843i | −0.140632 | − | 0.243582i | ||||
\(676\) | −12.9092 | − | 1.53344i | −0.496509 | − | 0.0589785i | ||||
\(677\) | −1.50219 | + | 2.60188i | −0.0577340 | + | 0.0999982i | −0.893448 | − | 0.449167i | \(-0.851721\pi\) |
0.835714 | + | 0.549165i | \(0.185054\pi\) | |||||||
\(678\) | 1.96268 | + | 3.39947i | 0.0753764 | + | 0.130556i | ||||
\(679\) | 11.0902 | − | 23.5839i | 0.425604 | − | 0.905067i | ||||
\(680\) | 8.20533 | − | 14.2121i | 0.314660 | − | 0.545007i | ||||
\(681\) | −10.1232 | + | 17.5339i | −0.387921 | + | 0.671899i | ||||
\(682\) | 57.1622 | 2.18885 | ||||||||
\(683\) | −14.8693 | −0.568959 | −0.284480 | − | 0.958682i | \(-0.591821\pi\) | ||||
−0.284480 | + | 0.958682i | \(0.591821\pi\) | |||||||
\(684\) | −2.61911 | + | 4.53642i | −0.100144 | + | 0.173455i | ||||
\(685\) | 26.4297 | − | 45.7776i | 1.00983 | − | 1.74907i | ||||
\(686\) | −17.9348 | + | 4.61985i | −0.684754 | + | 0.176387i | ||||
\(687\) | −0.668929 | − | 1.15862i | −0.0255212 | − | 0.0442041i | ||||
\(688\) | −1.19338 | + | 2.06699i | −0.0454971 | + | 0.0788033i | ||||
\(689\) | 6.79491 | − | 3.40455i | 0.258865 | − | 0.129703i | ||||
\(690\) | −3.80571 | − | 6.59168i | −0.144881 | − | 0.250941i | ||||
\(691\) | 8.38107 | 0.318831 | 0.159415 | − | 0.987212i | \(-0.449039\pi\) | ||||
0.159415 | + | 0.987212i | \(0.449039\pi\) | |||||||
\(692\) | 7.30337 | + | 12.6498i | 0.277633 | + | 0.480874i | ||||
\(693\) | 16.8937 | − | 1.42304i | 0.641738 | − | 0.0540570i | ||||
\(694\) | −32.1029 | −1.21861 | ||||||||
\(695\) | −24.6457 | − | 42.6877i | −0.934867 | − | 1.61924i | ||||
\(696\) | 2.46066 | 0.0932711 | ||||||||
\(697\) | 23.8241 | + | 41.2645i | 0.902401 | + | 1.56300i | ||||
\(698\) | −9.04373 | − | 15.6642i | −0.342310 | − | 0.592899i | ||||
\(699\) | 6.97568 | + | 12.0822i | 0.263845 | + | 0.456992i | ||||
\(700\) | 11.0381 | + | 15.8730i | 0.417203 | + | 0.599941i | ||||
\(701\) | 39.2809 | 1.48362 | 0.741809 | − | 0.670611i | \(-0.233968\pi\) | ||||
0.741809 | + | 0.670611i | \(0.233968\pi\) | |||||||
\(702\) | −0.213022 | + | 3.59925i | −0.00804000 | + | 0.135845i | ||||
\(703\) | −10.2135 | − | 17.6904i | −0.385211 | − | 0.667204i | ||||
\(704\) | 3.20391 | − | 5.54934i | 0.120752 | − | 0.209148i | ||||
\(705\) | −17.1249 | −0.644962 | ||||||||
\(706\) | 13.7323 | − | 23.7850i | 0.516820 | − | 0.895159i | ||||
\(707\) | 15.5600 | − | 33.0892i | 0.585195 | − | 1.24445i | ||||
\(708\) | 5.89729 | − | 10.2144i | 0.221634 | − | 0.383881i | ||||
\(709\) | −9.66018 | − | 16.7319i | −0.362796 | − | 0.628381i | 0.625624 | − | 0.780125i | \(-0.284844\pi\) |
−0.988420 | + | 0.151744i | \(0.951511\pi\) | |||||||
\(710\) | −9.79976 | − | 16.9737i | −0.367778 | − | 0.637011i | ||||
\(711\) | −1.78753 | −0.0670375 | ||||||||
\(712\) | 7.00752 | 0.262618 | ||||||||
\(713\) | −9.67721 | − | 16.7614i | −0.362414 | − | 0.627720i | ||||
\(714\) | 5.26665 | − | 11.1998i | 0.197100 | − | 0.419142i | ||||
\(715\) | 72.4652 | − | 36.3083i | 2.71004 | − | 1.35785i | ||||
\(716\) | 7.06425 | − | 12.2356i | 0.264003 | − | 0.457267i | ||||
\(717\) | −4.52748 | + | 7.84182i | −0.169082 | + | 0.292858i | ||||
\(718\) | −10.8390 | + | 18.7738i | −0.404510 | + | 0.700631i | ||||
\(719\) | 14.2205 | + | 24.6306i | 0.530335 | + | 0.918567i | 0.999374 | + | 0.0353892i | \(0.0112671\pi\) |
−0.469039 | + | 0.883178i | \(0.655400\pi\) | |||||||
\(720\) | −3.50820 | −0.130743 | ||||||||
\(721\) | 14.7864 | − | 31.4440i | 0.550674 | − | 1.17103i | ||||
\(722\) | −4.21943 | + | 7.30827i | −0.157031 | + | 0.271986i | ||||
\(723\) | −10.0551 | + | 17.4159i | −0.373953 | + | 0.647705i | ||||
\(724\) | −13.6453 | −0.507124 | ||||||||
\(725\) | −8.99057 | + | 15.5721i | −0.333902 | + | 0.578334i | ||||
\(726\) | 30.0602 | 1.11564 | ||||||||
\(727\) | −48.4057 | −1.79527 | −0.897634 | − | 0.440741i | \(-0.854716\pi\) | ||||
−0.897634 | + | 0.440741i | \(0.854716\pi\) | |||||||
\(728\) | −0.237705 | − | 9.53643i | −0.00880992 | − | 0.353444i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 29.6916 | 1.09894 | ||||||||
\(731\) | −5.58239 | + | 9.66898i | −0.206472 | + | 0.357620i | ||||
\(732\) | 9.35561 | 0.345793 | ||||||||
\(733\) | −3.69118 | + | 6.39332i | −0.136337 | + | 0.236143i | −0.926107 | − | 0.377260i | \(-0.876866\pi\) |
0.789770 | + | 0.613403i | \(0.210200\pi\) | |||||||
\(734\) | −7.66086 | + | 13.2690i | −0.282768 | + | 0.489768i | ||||
\(735\) | 15.6633 | + | 18.9136i | 0.577751 | + | 0.697639i | ||||
\(736\) | −2.16961 | −0.0799729 | ||||||||
\(737\) | 23.3540 | + | 40.4503i | 0.860256 | + | 1.49001i | ||||
\(738\) | 5.09300 | − | 8.82134i | 0.187476 | − | 0.324718i | ||||
\(739\) | −2.41213 | + | 4.17793i | −0.0887316 | + | 0.153688i | −0.906975 | − | 0.421184i | \(-0.861615\pi\) |
0.818244 | + | 0.574872i | \(0.194948\pi\) | |||||||
\(740\) | 6.84033 | − | 11.8478i | 0.251455 | − | 0.435533i | ||||
\(741\) | −1.11585 | + | 18.8536i | −0.0409920 | + | 0.692606i | ||||
\(742\) | 3.18404 | + | 4.57868i | 0.116890 | + | 0.168089i | ||||
\(743\) | 17.8556 | + | 30.9268i | 0.655059 | + | 1.13460i | 0.981879 | + | 0.189509i | \(0.0606895\pi\) |
−0.326820 | + | 0.945087i | \(0.605977\pi\) | |||||||
\(744\) | −8.92069 | −0.327048 | ||||||||
\(745\) | −4.31275 | −0.158007 | ||||||||
\(746\) | 16.6792 | + | 28.8893i | 0.610670 | + | 1.05771i | ||||
\(747\) | 1.29609 | + | 2.24489i | 0.0474214 | + | 0.0821363i | ||||
\(748\) | 14.9873 | − | 25.9587i | 0.547989 | − | 0.949145i | ||||
\(749\) | 25.7436 | − | 2.16852i | 0.940651 | − | 0.0792361i | ||||
\(750\) | 4.04749 | − | 7.01045i | 0.147793 | − | 0.255986i | ||||
\(751\) | 13.0969 | 0.477913 | 0.238956 | − | 0.971030i | \(-0.423195\pi\) | ||||
0.238956 | + | 0.971030i | \(0.423195\pi\) | |||||||
\(752\) | −2.44070 | + | 4.22742i | −0.0890032 | + | 0.154158i | ||||
\(753\) | 4.09035 | + | 7.08469i | 0.149061 | + | 0.258181i | ||||
\(754\) | 7.93208 | − | 3.97432i | 0.288869 | − | 0.144736i | ||||
\(755\) | 57.3411 | 2.08686 | ||||||||
\(756\) | −2.63641 | + | 0.222079i | −0.0958855 | + | 0.00807694i | ||||
\(757\) | −22.0344 | − | 38.1646i | −0.800852 | − | 1.38712i | −0.919056 | − | 0.394127i | \(-0.871047\pi\) |
0.118204 | − | 0.992989i | \(-0.462286\pi\) | |||||||
\(758\) | 8.43868 | + | 14.6162i | 0.306507 | + | 0.530885i | ||||
\(759\) | −6.95123 | − | 12.0399i | −0.252314 | − | 0.437020i | ||||
\(760\) | −18.3767 | −0.666592 | ||||||||
\(761\) | 4.30571 | + | 7.45771i | 0.156082 | + | 0.270342i | 0.933452 | − | 0.358701i | \(-0.116780\pi\) |
−0.777371 | + | 0.629043i | \(0.783447\pi\) | |||||||
\(762\) | −7.02391 | −0.254449 | ||||||||
\(763\) | −3.46777 | − | 4.98669i | −0.125542 | − | 0.180530i | ||||
\(764\) | 1.21572 | + | 2.10569i | 0.0439833 | + | 0.0761814i | ||||
\(765\) | −16.4107 | −0.593329 | ||||||||
\(766\) | −10.7933 | − | 18.6945i | −0.389978 | − | 0.675461i | ||||
\(767\) | 2.51251 | − | 42.4517i | 0.0907213 | − | 1.53284i | ||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | −3.20391 | − | 5.54934i | −0.115536 | − | 0.200114i | 0.802458 | − | 0.596709i | \(-0.203525\pi\) |
−0.917994 | + | 0.396595i | \(0.870192\pi\) | |||||||
\(770\) | 33.9566 | + | 48.8300i | 1.22371 | + | 1.75971i | ||||
\(771\) | −4.87696 | + | 8.44715i | −0.175640 | + | 0.304217i | ||||
\(772\) | −1.75877 | + | 3.04628i | −0.0632996 | + | 0.109638i | ||||
\(773\) | 12.5816 | 0.452530 | 0.226265 | − | 0.974066i | \(-0.427348\pi\) | ||||
0.226265 | + | 0.974066i | \(0.427348\pi\) | |||||||
\(774\) | 2.38675 | 0.0857901 | ||||||||
\(775\) | 32.5937 | − | 56.4540i | 1.17080 | − | 2.02789i | ||||
\(776\) | −4.92513 | + | 8.53057i | −0.176802 | + | 0.306230i | ||||
\(777\) | 4.39051 | − | 9.33664i | 0.157509 | − | 0.334950i | ||||
\(778\) | 8.68908 | + | 15.0499i | 0.311519 | + | 0.539566i | ||||
\(779\) | 26.6782 | − | 46.2080i | 0.955846 | − | 1.65557i | ||||
\(780\) | −11.3089 | + | 5.66624i | −0.404922 | + | 0.202884i | ||||
\(781\) | −17.8995 | − | 31.0029i | −0.640496 | − | 1.10937i | ||||
\(782\) | −10.1490 | −0.362928 | ||||||||
\(783\) | −1.23033 | − | 2.13099i | −0.0439684 | − | 0.0761555i | ||||
\(784\) | 6.90136 | − | 1.17099i | 0.246477 | − | 0.0418209i | ||||
\(785\) | −56.0255 | −1.99963 | ||||||||
\(786\) | −4.56251 | − | 7.90250i | −0.162739 | − | 0.281873i | ||||
\(787\) | −19.2139 | −0.684900 | −0.342450 | − | 0.939536i | \(-0.611257\pi\) | ||||
−0.342450 | + | 0.939536i | \(0.611257\pi\) | |||||||
\(788\) | 1.15702 | + | 2.00402i | 0.0412172 | + | 0.0713904i | ||||
\(789\) | 1.47358 | + | 2.55232i | 0.0524608 | + | 0.0908648i | ||||
\(790\) | −3.13550 | − | 5.43084i | −0.111556 | − | 0.193221i | ||||
\(791\) | −4.41949 | + | 9.39827i | −0.157139 | + | 0.334164i | ||||
\(792\) | −6.40782 | −0.227692 | ||||||||
\(793\) | 30.1583 | − | 15.1107i | 1.07095 | − | 0.536595i | ||||
\(794\) | −2.93718 | − | 5.08734i | −0.104237 | − | 0.180543i | ||||
\(795\) | 3.69745 | − | 6.40417i | 0.131135 | − | 0.227133i | ||||
\(796\) | 5.69467 | 0.201842 | ||||||||
\(797\) | −8.43333 | + | 14.6070i | −0.298724 | + | 0.517405i | −0.975844 | − | 0.218467i | \(-0.929894\pi\) |
0.677120 | + | 0.735872i | \(0.263228\pi\) | |||||||
\(798\) | −13.8101 | + | 1.16330i | −0.488872 | + | 0.0411803i | ||||
\(799\) | −11.4171 | + | 19.7750i | −0.403909 | + | 0.699591i | ||||
\(800\) | −3.65372 | − | 6.32843i | −0.129179 | − | 0.223744i | ||||
\(801\) | −3.50376 | − | 6.06869i | −0.123799 | − | 0.214427i | ||||
\(802\) | −13.9771 | −0.493549 | ||||||||
\(803\) | 54.2326 | 1.91383 | ||||||||
\(804\) | −3.64461 | − | 6.31265i | −0.128536 | − | 0.222630i | ||||
\(805\) | 8.56955 | − | 18.2236i | 0.302037 | − | 0.642296i | ||||
\(806\) | −28.7563 | + | 14.4082i | −1.01290 | + | 0.507507i | ||||
\(807\) | 11.9676 | − | 20.7285i | 0.421280 | − | 0.729679i | ||||
\(808\) | −6.91016 | + | 11.9687i | −0.243099 | + | 0.421059i | ||||
\(809\) | −4.38025 | + | 7.58681i | −0.154001 | + | 0.266738i | −0.932695 | − | 0.360666i | \(-0.882549\pi\) |
0.778694 | + | 0.627404i | \(0.215883\pi\) | |||||||
\(810\) | 1.75410 | + | 3.03819i | 0.0616327 | + | 0.106751i | ||||
\(811\) | −32.7259 | −1.14916 | −0.574581 | − | 0.818448i | \(-0.694835\pi\) | ||||
−0.574581 | + | 0.818448i | \(0.694835\pi\) | |||||||
\(812\) | 3.71691 | + | 5.34495i | 0.130438 | + | 0.187571i | ||||
\(813\) | −9.68335 | + | 16.7721i | −0.339610 | + | 0.588222i | ||||
\(814\) | 12.4940 | − | 21.6403i | 0.437916 | − | 0.758493i | ||||
\(815\) | −27.3160 | −0.956837 | ||||||||
\(816\) | −2.33890 | + | 4.05110i | −0.0818780 | + | 0.141817i | ||||
\(817\) | 12.5023 | 0.437401 | ||||||||
\(818\) | −37.4897 | −1.31080 | ||||||||
\(819\) | −8.13994 | + | 4.97407i | −0.284432 | + | 0.173808i | ||||
\(820\) | 35.7345 | 1.24790 | ||||||||
\(821\) | 14.6951 | 0.512863 | 0.256432 | − | 0.966562i | \(-0.417453\pi\) | ||||
0.256432 | + | 0.966562i | \(0.417453\pi\) | |||||||
\(822\) | −7.53370 | + | 13.0488i | −0.262768 | + | 0.455128i | ||||
\(823\) | 41.3989 | 1.44307 | 0.721537 | − | 0.692376i | \(-0.243436\pi\) | ||||
0.721537 | + | 0.692376i | \(0.243436\pi\) | |||||||
\(824\) | −6.56658 | + | 11.3737i | −0.228758 | + | 0.396220i | ||||
\(825\) | 23.4124 | − | 40.5515i | 0.815115 | − | 1.41182i | ||||
\(826\) | 31.0954 | − | 2.61933i | 1.08195 | − | 0.0911381i | ||||
\(827\) | 37.8157 | 1.31498 | 0.657491 | − | 0.753462i | \(-0.271618\pi\) | ||||
0.657491 | + | 0.753462i | \(0.271618\pi\) | |||||||
\(828\) | 1.08480 | + | 1.87894i | 0.0376996 | + | 0.0652976i | ||||
\(829\) | −17.2120 | + | 29.8120i | −0.597796 | + | 1.03541i | 0.395349 | + | 0.918531i | \(0.370624\pi\) |
−0.993146 | + | 0.116883i | \(0.962710\pi\) | |||||||
\(830\) | −4.54694 | + | 7.87553i | −0.157826 | + | 0.273363i | ||||
\(831\) | −1.21710 | + | 2.10807i | −0.0422206 | + | 0.0731282i | ||||
\(832\) | −0.213022 | + | 3.59925i | −0.00738521 | + | 0.124782i | ||||
\(833\) | 32.2832 | − | 5.47764i | 1.11855 | − | 0.189789i | ||||
\(834\) | 7.02519 | + | 12.1680i | 0.243262 | + | 0.421343i | ||||
\(835\) | 23.3178 | 0.806946 | ||||||||
\(836\) | −33.5655 | −1.16089 | ||||||||
\(837\) | 4.46035 | + | 7.72555i | 0.154172 | + | 0.267034i | ||||
\(838\) | −16.9548 | − | 29.3665i | −0.585692 | − | 1.01445i | ||||
\(839\) | −0.709771 | + | 1.22936i | −0.0245040 | + | 0.0424422i | −0.878017 | − | 0.478629i | \(-0.841134\pi\) |
0.853513 | + | 0.521071i | \(0.174467\pi\) | |||||||
\(840\) | −5.29925 | − | 7.62037i | −0.182841 | − | 0.262928i | ||||
\(841\) | 11.4726 | − | 19.8711i | 0.395606 | − | 0.685210i | ||||
\(842\) | −10.5503 | −0.363588 | ||||||||
\(843\) | 1.40165 | − | 2.42772i | 0.0482752 | − | 0.0836152i | ||||
\(844\) | 0.291966 | + | 0.505700i | 0.0100499 | + | 0.0174069i | ||||
\(845\) | −27.3030 | + | 36.5309i | −0.939251 | + | 1.25670i | ||||
\(846\) | 4.88140 | 0.167826 | ||||||||
\(847\) | 45.4069 | + | 65.2956i | 1.56020 | + | 2.24358i | ||||
\(848\) | −1.05395 | − | 1.82549i | −0.0361927 | − | 0.0626875i | ||||
\(849\) | 8.47705 | + | 14.6827i | 0.290932 | + | 0.503909i | ||||
\(850\) | −17.0914 | − | 29.6032i | −0.586230 | − | 1.01538i | ||||
\(851\) | −8.46066 | −0.290028 | ||||||||
\(852\) | 2.79339 | + | 4.83829i | 0.0956999 | + | 0.165757i | ||||
\(853\) | 36.8892 | 1.26306 | 0.631531 | − | 0.775351i | \(-0.282427\pi\) | ||||
0.631531 | + | 0.775351i | \(0.282427\pi\) | |||||||
\(854\) | 14.1320 | + | 20.3219i | 0.483586 | + | 0.695401i | ||||
\(855\) | 9.18834 | + | 15.9147i | 0.314235 | + | 0.544270i | ||||
\(856\) | −9.76463 | −0.333748 | ||||||||
\(857\) | 13.9245 | + | 24.1180i | 0.475653 | + | 0.823855i | 0.999611 | − | 0.0278890i | \(-0.00887851\pi\) |
−0.523958 | + | 0.851744i | \(0.675545\pi\) | |||||||
\(858\) | −20.6560 | + | 10.3496i | −0.705183 | + | 0.353328i | ||||
\(859\) | −25.2862 | + | 43.7970i | −0.862754 | + | 1.49433i | 0.00650572 | + | 0.999979i | \(0.497929\pi\) |
−0.869260 | + | 0.494355i | \(0.835404\pi\) | |||||||
\(860\) | 4.18660 | + | 7.25141i | 0.142762 | + | 0.247271i | ||||
\(861\) | 26.8545 | − | 2.26210i | 0.915200 | − | 0.0770921i | ||||
\(862\) | 12.8043 | − | 22.1777i | 0.436116 | − | 0.755375i | ||||
\(863\) | 14.5501 | − | 25.2016i | 0.495293 | − | 0.857872i | −0.504693 | − | 0.863299i | \(-0.668394\pi\) |
0.999985 | + | 0.00542701i | \(0.00172748\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 51.2433 | 1.74233 | ||||||||
\(866\) | 3.68968 | − | 6.39071i | 0.125380 | − | 0.217165i | ||||
\(867\) | −2.44094 | + | 4.22782i | −0.0828985 | + | 0.143584i | ||||
\(868\) | −13.4750 | − | 19.3772i | −0.457371 | − | 0.657705i | ||||
\(869\) | −5.72708 | − | 9.91959i | −0.194278 | − | 0.336499i | ||||
\(870\) | 4.31624 | − | 7.47595i | 0.146334 | − | 0.253458i | ||||
\(871\) | −21.9444 | − | 14.4626i | −0.743559 | − | 0.490047i | ||||
\(872\) | 1.14786 | + | 1.98816i | 0.0388715 | + | 0.0673275i | ||||
\(873\) | 9.85026 | 0.333381 | ||||||||
\(874\) | 5.68244 | + | 9.84227i | 0.192211 | + | 0.332920i | ||||
\(875\) | 21.3417 | − | 1.79773i | 0.721481 | − | 0.0607742i | ||||
\(876\) | −8.46350 | −0.285955 | ||||||||
\(877\) | −0.556332 | − | 0.963595i | −0.0187860 | − | 0.0325383i | 0.856480 | − | 0.516181i | \(-0.172647\pi\) |
−0.875266 | + | 0.483643i | \(0.839313\pi\) | |||||||
\(878\) | −23.0510 | −0.777934 | ||||||||
\(879\) | 2.84568 | + | 4.92886i | 0.0959823 | + | 0.166246i | ||||
\(880\) | −11.2399 | − | 19.4682i | −0.378899 | − | 0.656272i | ||||
\(881\) | −8.14254 | − | 14.1033i | −0.274329 | − | 0.475152i | 0.695636 | − | 0.718394i | \(-0.255122\pi\) |
−0.969966 | + | 0.243242i | \(0.921789\pi\) | |||||||
\(882\) | −4.46478 | − | 5.39126i | −0.150337 | − | 0.181533i | ||||
\(883\) | −37.0876 | −1.24810 | −0.624048 | − | 0.781386i | \(-0.714513\pi\) | ||||
−0.624048 | + | 0.781386i | \(0.714513\pi\) | |||||||
\(884\) | −0.996476 | + | 16.8366i | −0.0335151 | + | 0.566276i | ||||
\(885\) | −20.6888 | − | 35.8341i | −0.695448 | − | 1.20455i | ||||
\(886\) | 9.05605 | − | 15.6855i | 0.304244 | − | 0.526966i | ||||
\(887\) | −21.6055 | −0.725443 | −0.362722 | − | 0.931898i | \(-0.618152\pi\) | ||||
−0.362722 | + | 0.931898i | \(0.618152\pi\) | |||||||
\(888\) | −1.94981 | + | 3.37717i | −0.0654314 | + | 0.113331i | ||||
\(889\) | −10.6099 | − | 15.2571i | −0.355843 | − | 0.511706i | ||||
\(890\) | 12.2919 | − | 21.2902i | 0.412025 | − | 0.713647i | ||||
\(891\) | 3.20391 | + | 5.54934i | 0.107335 | + | 0.185910i | ||||
\(892\) | −7.25749 | − | 12.5703i | −0.242999 | − | 0.420886i | ||||
\(893\) | 25.5698 | 0.855661 | ||||||||
\(894\) | 1.22934 | 0.0411151 | ||||||||
\(895\) | −24.7828 | − | 42.9250i | −0.828396 | − | 1.43482i | ||||
\(896\) | −2.63641 | + | 0.222079i | −0.0880764 | + | 0.00741914i | ||||
\(897\) | 6.53168 | + | 4.30474i | 0.218086 | + | 0.143731i | ||||
\(898\) | −9.23084 | + | 15.9883i | −0.308037 | + | 0.533536i | ||||
\(899\) | 10.9754 | − | 19.0099i | 0.366050 | − | 0.634017i | ||||
\(900\) | −3.65372 | + | 6.32843i | −0.121791 | + | 0.210948i | ||||
\(901\) | −4.93016 | − | 8.53928i | −0.164247 | − | 0.284485i | ||||
\(902\) | 65.2701 | 2.17326 | ||||||||
\(903\) | 3.60527 | + | 5.18442i | 0.119976 | + | 0.172527i | ||||
\(904\) | 1.96268 | − | 3.39947i | 0.0652778 | − | 0.113065i | ||||
\(905\) | −23.9352 | + | 41.4570i | −0.795633 | + | 1.37808i | ||||
\(906\) | −16.3449 | −0.543023 | ||||||||
\(907\) | 14.5270 | − | 25.1614i | 0.482360 | − | 0.835472i | −0.517435 | − | 0.855722i | \(-0.673113\pi\) |
0.999795 | + | 0.0202508i | \(0.00644647\pi\) | |||||||
\(908\) | 20.2464 | 0.671899 | ||||||||
\(909\) | 13.8203 | 0.458391 | ||||||||
\(910\) | −29.3904 | − | 16.0056i | −0.974283 | − | 0.530582i | ||||
\(911\) | −22.2791 | −0.738141 | −0.369071 | − | 0.929401i | \(-0.620324\pi\) | ||||
−0.369071 | + | 0.929401i | \(0.620324\pi\) | |||||||
\(912\) | 5.23821 | 0.173455 | ||||||||
\(913\) | −8.30511 | + | 14.3849i | −0.274859 | + | 0.476070i | ||||
\(914\) | −17.8047 | −0.588926 | ||||||||
\(915\) | 16.4107 | − | 28.4241i | 0.542520 | − | 0.939672i | ||||
\(916\) | −0.668929 | + | 1.15862i | −0.0221020 | + | 0.0382819i | ||||
\(917\) | 10.2737 | − | 21.8475i | 0.339267 | − | 0.721468i | ||||
\(918\) | 4.67781 | 0.154391 | ||||||||
\(919\) | 17.5718 | + | 30.4352i | 0.579639 | + | 1.00396i | 0.995521 | + | 0.0945453i | \(0.0301397\pi\) |
−0.415882 | + | 0.909419i | \(0.636527\pi\) | |||||||
\(920\) | −3.80571 | + | 6.59168i | −0.125470 | + | 0.217321i | ||||
\(921\) | −1.74302 | + | 3.01899i | −0.0574343 | + | 0.0994791i | ||||
\(922\) | −2.51030 | + | 4.34797i | −0.0826723 | + | 0.143193i | ||||
\(923\) | 16.8192 | + | 11.0848i | 0.553610 | + | 0.364860i | ||||
\(924\) | −9.67923 | − | 13.9188i | −0.318423 | − | 0.457896i | ||||
\(925\) | −14.2481 | − | 24.6785i | −0.468476 | − | 0.811425i | ||||
\(926\) | −25.0075 | −0.821798 | ||||||||
\(927\) | 13.1332 | 0.431350 | ||||||||
\(928\) | −1.23033 | − | 2.13099i | −0.0403876 | − | 0.0699533i | ||||
\(929\) | 18.3722 | + | 31.8217i | 0.602774 | + | 1.04403i | 0.992399 | + | 0.123061i | \(0.0392711\pi\) |
−0.389625 | + | 0.920973i | \(0.627396\pi\) | |||||||
\(930\) | −15.6478 | + | 27.1027i | −0.513111 | + | 0.888734i | ||||
\(931\) | −23.3875 | − | 28.2406i | −0.766494 | − | 0.925547i | ||||
\(932\) | 6.97568 | − | 12.0822i | 0.228496 | − | 0.395767i | ||||
\(933\) | −24.0031 | −0.785827 | ||||||||
\(934\) | 12.9128 | − | 22.3656i | 0.422519 | − | 0.731824i | ||||
\(935\) | −52.5783 | − | 91.0683i | −1.71949 | − | 2.97825i | ||||
\(936\) | 3.22356 | − | 1.61514i | 0.105365 | − | 0.0527926i | ||||
\(937\) | 18.5284 | 0.605295 | 0.302647 | − | 0.953103i | \(-0.402130\pi\) | ||||
0.302647 | + | 0.953103i | \(0.402130\pi\) | |||||||
\(938\) | 8.20680 | − | 17.4522i | 0.267961 | − | 0.569833i | ||||
\(939\) | −8.77758 | − | 15.2032i | −0.286446 | − | 0.496138i | ||||
\(940\) | 8.56246 | + | 14.8306i | 0.279277 | + | 0.483721i | ||||
\(941\) | 22.5985 | + | 39.1417i | 0.736689 | + | 1.27598i | 0.953979 | + | 0.299875i | \(0.0969450\pi\) |
−0.217290 | + | 0.976107i | \(0.569722\pi\) | |||||||
\(942\) | 15.9699 | 0.520327 | ||||||||
\(943\) | −11.0498 | − | 19.1389i | −0.359832 | − | 0.623247i | ||||
\(944\) | −11.7946 | −0.383881 | ||||||||
\(945\) | −3.94981 | + | 8.39947i | −0.128487 | + | 0.273235i | ||||
\(946\) | 7.64695 | + | 13.2449i | 0.248624 | + | 0.430629i | ||||
\(947\) | 28.8667 | 0.938040 | 0.469020 | − | 0.883187i | \(-0.344607\pi\) | ||||
0.469020 | + | 0.883187i | \(0.344607\pi\) | |||||||
\(948\) | 0.893764 | + | 1.54804i | 0.0290281 | + | 0.0502781i | ||||
\(949\) | −27.2826 | + | 13.6698i | −0.885630 | + | 0.443740i | ||||
\(950\) | −19.1390 | + | 33.1497i | −0.620950 | + | 1.07552i | ||||
\(951\) | −1.42018 | − | 2.45983i | −0.0460526 | − | 0.0797655i | ||||
\(952\) | −12.3326 | + | 1.03884i | −0.399703 | + | 0.0336691i | ||||
\(953\) | 8.36687 | − | 14.4919i | 0.271030 | − | 0.469437i | −0.698096 | − | 0.716004i | \(-0.745969\pi\) |
0.969126 | + | 0.246567i | \(0.0793025\pi\) | |||||||
\(954\) | −1.05395 | + | 1.82549i | −0.0341228 | + | 0.0591024i | ||||
\(955\) | 8.52999 | 0.276024 | ||||||||
\(956\) | 9.05495 | 0.292858 | ||||||||
\(957\) | 7.88374 | − | 13.6550i | 0.254845 | − | 0.441405i | ||||
\(958\) | −11.5569 | + | 20.0171i | −0.373386 | + | 0.646723i | ||||
\(959\) | −39.7239 | + | 3.34616i | −1.28275 | + | 0.108053i | ||||
\(960\) | 1.75410 | + | 3.03819i | 0.0566133 | + | 0.0980571i | ||||
\(961\) | −24.2894 | + | 42.0704i | −0.783528 | + | 1.35711i | ||||
\(962\) | −0.830706 | + | 14.0357i | −0.0267830 | + | 0.452530i | ||||
\(963\) | 4.88232 | + | 8.45642i | 0.157330 | + | 0.272504i | ||||
\(964\) | 20.1102 | 0.647705 | ||||||||
\(965\) | 6.17012 | + | 10.6870i | 0.198623 | + | 0.344025i | ||||
\(966\) | −2.44272 | + | 5.19457i | −0.0785933 | + | 0.167132i | ||||
\(967\) | −3.01759 | −0.0970392 | −0.0485196 | − | 0.998822i | \(-0.515450\pi\) | ||||
−0.0485196 | + | 0.998822i | \(0.515450\pi\) | |||||||
\(968\) | −15.0301 | − | 26.0329i | −0.483085 | − | 0.836728i | ||||
\(969\) | 24.5033 | 0.787161 | ||||||||
\(970\) | 17.2783 | + | 29.9269i | 0.554774 | + | 0.960896i | ||||
\(971\) | −12.8401 | − | 22.2397i | −0.412058 | − | 0.713706i | 0.583057 | − | 0.812432i | \(-0.301857\pi\) |
−0.995115 | + | 0.0987260i | \(0.968523\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | −15.8191 | + | 33.6400i | −0.507136 | + | 1.07845i | ||||
\(974\) | −16.2740 | −0.521453 | ||||||||
\(975\) | −1.55665 | + | 26.3013i | −0.0498526 | + | 0.842317i | ||||
\(976\) | −4.67781 | − | 8.10220i | −0.149733 | − | 0.259345i | ||||
\(977\) | 20.3251 | − | 35.2041i | 0.650258 | − | 1.12628i | −0.332802 | − | 0.942997i | \(-0.607994\pi\) |
0.983060 | − | 0.183283i | \(-0.0586726\pi\) | |||||||
\(978\) | 7.78633 | 0.248979 | ||||||||
\(979\) | 22.4515 | − | 38.8871i | 0.717552 | − | 1.24284i | ||||
\(980\) | 8.54799 | − | 23.0217i | 0.273056 | − | 0.735400i | ||||
\(981\) | 1.14786 | − | 1.98816i | 0.0366484 | − | 0.0634769i | ||||
\(982\) | −19.0299 | − | 32.9608i | −0.607270 | − | 1.05182i | ||||
\(983\) | −2.39794 | − | 4.15335i | −0.0764823 | − | 0.132471i | 0.825248 | − | 0.564771i | \(-0.191036\pi\) |
−0.901730 | + | 0.432300i | \(0.857702\pi\) | |||||||
\(984\) | −10.1860 | −0.324718 | ||||||||
\(985\) | 8.11813 | 0.258665 | ||||||||
\(986\) | −5.75525 | − | 9.96838i | −0.183284 | − | 0.317458i | ||||
\(987\) | 7.37352 | + | 10.6032i | 0.234702 | + | 0.337503i | ||||
\(988\) | 16.8857 | − | 8.46047i | 0.537205 | − | 0.269163i | ||||
\(989\) | 2.58916 | − | 4.48456i | 0.0823306 | − | 0.142601i | ||||
\(990\) | −11.2399 | + | 19.4682i | −0.357229 | + | 0.618739i | ||||
\(991\) | 19.5715 | − | 33.8989i | 0.621710 | − | 1.07683i | −0.367457 | − | 0.930040i | \(-0.619772\pi\) |
0.989167 | − | 0.146793i | \(-0.0468951\pi\) | |||||||
\(992\) | 4.46035 | + | 7.72555i | 0.141616 | + | 0.245286i | ||||
\(993\) | −18.8749 | −0.598977 | ||||||||
\(994\) | −6.29005 | + | 13.3761i | −0.199508 | + | 0.424264i | ||||
\(995\) | 9.98901 | − | 17.3015i | 0.316673 | − | 0.548494i | ||||
\(996\) | 1.29609 | − | 2.24489i | 0.0410682 | − | 0.0711321i | ||||
\(997\) | −57.4491 | −1.81943 | −0.909716 | − | 0.415232i | \(-0.863701\pi\) | ||||
−0.909716 | + | 0.415232i | \(0.863701\pi\) | |||||||
\(998\) | 17.1178 | − | 29.6489i | 0.541854 | − | 0.938518i | ||||
\(999\) | 3.89962 | 0.123379 |
(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 | 546.2.j.c.289.4 | ✓ | 8 | |
3.2 | odd | 2 | 1638.2.m.h.289.1 | 8 | |||
7.4 | even | 3 | 546.2.k.c.445.4 | yes | 8 | ||
13.9 | even | 3 | 546.2.k.c.373.4 | yes | 8 | ||
21.11 | odd | 6 | 1638.2.p.h.991.1 | 8 | |||
39.35 | odd | 6 | 1638.2.p.h.919.1 | 8 | |||
91.74 | even | 3 | inner | 546.2.j.c.529.4 | yes | 8 | |
273.74 | odd | 6 | 1638.2.m.h.1621.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.j.c.289.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
546.2.j.c.529.4 | yes | 8 | 91.74 | even | 3 | inner | |
546.2.k.c.373.4 | yes | 8 | 13.9 | even | 3 | ||
546.2.k.c.445.4 | yes | 8 | 7.4 | even | 3 | ||
1638.2.m.h.289.1 | 8 | 3.2 | odd | 2 | |||
1638.2.m.h.1621.1 | 8 | 273.74 | odd | 6 | |||
1638.2.p.h.919.1 | 8 | 39.35 | odd | 6 | |||
1638.2.p.h.991.1 | 8 | 21.11 | odd | 6 |