Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [65,2,Mod(16,65)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(65, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("65.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 65 = 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 65.e (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: | \(0.519027613138\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 4x^{2} + 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 16.1 | ||
Root | \(-0.651388 - 1.12824i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 65.16 |
Dual form | 65.2.e.b.61.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(41\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.651388 | − | 1.12824i | −0.460601 | − | 0.797784i | 0.538390 | − | 0.842696i | \(-0.319033\pi\) |
−0.998991 | + | 0.0449118i | \(0.985699\pi\) | |||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | 0.684819 | − | 0.728714i | \(-0.259881\pi\) |
−0.973494 | + | 0.228714i | \(0.926548\pi\) | |||||||
\(4\) | 0.151388 | − | 0.262211i | 0.0756939 | − | 0.131106i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.651388 | + | 1.12824i | −0.265928 | + | 0.460601i | ||||
\(7\) | 0.500000 | − | 0.866025i | 0.188982 | − | 0.327327i | −0.755929 | − | 0.654654i | \(-0.772814\pi\) |
0.944911 | + | 0.327327i | \(0.106148\pi\) | |||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | 1.00000 | − | 1.73205i | 0.333333 | − | 0.577350i | ||||
\(10\) | 0.651388 | + | 1.12824i | 0.205987 | + | 0.356780i | ||||
\(11\) | 2.80278 | + | 4.85455i | 0.845069 | + | 1.46370i | 0.885562 | + | 0.464522i | \(0.153774\pi\) |
−0.0404929 | + | 0.999180i | \(0.512893\pi\) | |||||||
\(12\) | −0.302776 | −0.0874038 | ||||||||
\(13\) | 3.60555 | 1.00000 | ||||||||
\(14\) | −1.30278 | −0.348181 | ||||||||
\(15\) | 0.500000 | + | 0.866025i | 0.129099 | + | 0.223607i | ||||
\(16\) | 1.65139 | + | 2.86029i | 0.412847 | + | 0.715072i | ||||
\(17\) | −0.197224 | + | 0.341603i | −0.0478339 | + | 0.0828508i | −0.888951 | − | 0.458002i | \(-0.848565\pi\) |
0.841117 | + | 0.540853i | \(0.181898\pi\) | |||||||
\(18\) | −2.60555 | −0.614134 | ||||||||
\(19\) | −0.802776 | + | 1.39045i | −0.184169 | + | 0.318991i | −0.943296 | − | 0.331952i | \(-0.892293\pi\) |
0.759127 | + | 0.650943i | \(0.225626\pi\) | |||||||
\(20\) | −0.151388 | + | 0.262211i | −0.0338513 | + | 0.0586323i | ||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 3.65139 | − | 6.32439i | 0.778478 | − | 1.34836i | ||||
\(23\) | 1.50000 | + | 2.59808i | 0.312772 | + | 0.541736i | 0.978961 | − | 0.204046i | \(-0.0654092\pi\) |
−0.666190 | + | 0.745782i | \(0.732076\pi\) | |||||||
\(24\) | 1.50000 | + | 2.59808i | 0.306186 | + | 0.530330i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.34861 | − | 4.06792i | −0.460601 | − | 0.797784i | ||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | −0.151388 | − | 0.262211i | −0.0286096 | − | 0.0495533i | ||||
\(29\) | −4.10555 | − | 7.11102i | −0.762382 | − | 1.32048i | −0.941620 | − | 0.336678i | \(-0.890697\pi\) |
0.179238 | − | 0.983806i | \(-0.442637\pi\) | |||||||
\(30\) | 0.651388 | − | 1.12824i | 0.118927 | − | 0.205987i | ||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | −0.848612 | + | 1.46984i | −0.150015 | + | 0.259833i | ||||
\(33\) | 2.80278 | − | 4.85455i | 0.487901 | − | 0.845069i | ||||
\(34\) | 0.513878 | 0.0881294 | ||||||||
\(35\) | −0.500000 | + | 0.866025i | −0.0845154 | + | 0.146385i | ||||
\(36\) | −0.302776 | − | 0.524423i | −0.0504626 | − | 0.0874038i | ||||
\(37\) | 1.80278 | + | 3.12250i | 0.296374 | + | 0.513336i | 0.975304 | − | 0.220868i | \(-0.0708890\pi\) |
−0.678929 | + | 0.734204i | \(0.737556\pi\) | |||||||
\(38\) | 2.09167 | 0.339314 | ||||||||
\(39\) | −1.80278 | − | 3.12250i | −0.288675 | − | 0.500000i | ||||
\(40\) | 3.00000 | 0.474342 | ||||||||
\(41\) | −1.50000 | − | 2.59808i | −0.234261 | − | 0.405751i | 0.724797 | − | 0.688963i | \(-0.241934\pi\) |
−0.959058 | + | 0.283211i | \(0.908600\pi\) | |||||||
\(42\) | 0.651388 | + | 1.12824i | 0.100511 | + | 0.174091i | ||||
\(43\) | −2.10555 | + | 3.64692i | −0.321094 | + | 0.556150i | −0.980714 | − | 0.195449i | \(-0.937384\pi\) |
0.659620 | + | 0.751599i | \(0.270717\pi\) | |||||||
\(44\) | 1.69722 | 0.255866 | ||||||||
\(45\) | −1.00000 | + | 1.73205i | −0.149071 | + | 0.258199i | ||||
\(46\) | 1.95416 | − | 3.38471i | 0.288126 | − | 0.499048i | ||||
\(47\) | −5.21110 | −0.760117 | −0.380059 | − | 0.924962i | \(-0.624096\pi\) | ||||
−0.380059 | + | 0.924962i | \(0.624096\pi\) | |||||||
\(48\) | 1.65139 | − | 2.86029i | 0.238357 | − | 0.412847i | ||||
\(49\) | 3.00000 | + | 5.19615i | 0.428571 | + | 0.742307i | ||||
\(50\) | −0.651388 | − | 1.12824i | −0.0921201 | − | 0.159557i | ||||
\(51\) | 0.394449 | 0.0552339 | ||||||||
\(52\) | 0.545837 | − | 0.945417i | 0.0756939 | − | 0.131106i | ||||
\(53\) | 11.2111 | 1.53996 | 0.769982 | − | 0.638066i | \(-0.220265\pi\) | ||||
0.769982 | + | 0.638066i | \(0.220265\pi\) | |||||||
\(54\) | 3.25694 | + | 5.64118i | 0.443213 | + | 0.767668i | ||||
\(55\) | −2.80278 | − | 4.85455i | −0.377926 | − | 0.654587i | ||||
\(56\) | −1.50000 | + | 2.59808i | −0.200446 | + | 0.347183i | ||||
\(57\) | 1.60555 | 0.212660 | ||||||||
\(58\) | −5.34861 | + | 9.26407i | −0.702307 | + | 1.21643i | ||||
\(59\) | −5.40833 | + | 9.36750i | −0.704104 | + | 1.21954i | 0.262910 | + | 0.964820i | \(0.415318\pi\) |
−0.967014 | + | 0.254724i | \(0.918015\pi\) | |||||||
\(60\) | 0.302776 | 0.0390882 | ||||||||
\(61\) | 0.500000 | − | 0.866025i | 0.0640184 | − | 0.110883i | −0.832240 | − | 0.554416i | \(-0.812942\pi\) |
0.896258 | + | 0.443533i | \(0.146275\pi\) | |||||||
\(62\) | 2.60555 | + | 4.51295i | 0.330905 | + | 0.573145i | ||||
\(63\) | −1.00000 | − | 1.73205i | −0.125988 | − | 0.218218i | ||||
\(64\) | 8.81665 | 1.10208 | ||||||||
\(65\) | −3.60555 | −0.447214 | ||||||||
\(66\) | −7.30278 | −0.898910 | ||||||||
\(67\) | 3.50000 | + | 6.06218i | 0.427593 | + | 0.740613i | 0.996659 | − | 0.0816792i | \(-0.0260283\pi\) |
−0.569066 | + | 0.822292i | \(0.692695\pi\) | |||||||
\(68\) | 0.0597147 | + | 0.103429i | 0.00724147 | + | 0.0125426i | ||||
\(69\) | 1.50000 | − | 2.59808i | 0.180579 | − | 0.312772i | ||||
\(70\) | 1.30278 | 0.155711 | ||||||||
\(71\) | 8.40833 | − | 14.5636i | 0.997885 | − | 1.72839i | 0.442645 | − | 0.896697i | \(-0.354040\pi\) |
0.555240 | − | 0.831690i | \(-0.312626\pi\) | |||||||
\(72\) | −3.00000 | + | 5.19615i | −0.353553 | + | 0.612372i | ||||
\(73\) | −15.2111 | −1.78032 | −0.890162 | − | 0.455643i | \(-0.849409\pi\) | ||||
−0.890162 | + | 0.455643i | \(0.849409\pi\) | |||||||
\(74\) | 2.34861 | − | 4.06792i | 0.273021 | − | 0.472886i | ||||
\(75\) | −0.500000 | − | 0.866025i | −0.0577350 | − | 0.100000i | ||||
\(76\) | 0.243061 | + | 0.420994i | 0.0278810 | + | 0.0482913i | ||||
\(77\) | 5.60555 | 0.638812 | ||||||||
\(78\) | −2.34861 | + | 4.06792i | −0.265928 | + | 0.460601i | ||||
\(79\) | −9.21110 | −1.03633 | −0.518165 | − | 0.855281i | \(-0.673385\pi\) | ||||
−0.518165 | + | 0.855281i | \(0.673385\pi\) | |||||||
\(80\) | −1.65139 | − | 2.86029i | −0.184631 | − | 0.319790i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −1.95416 | + | 3.38471i | −0.215801 | + | 0.373779i | ||||
\(83\) | 5.21110 | 0.571993 | 0.285996 | − | 0.958231i | \(-0.407675\pi\) | ||||
0.285996 | + | 0.958231i | \(0.407675\pi\) | |||||||
\(84\) | −0.151388 | + | 0.262211i | −0.0165178 | + | 0.0286096i | ||||
\(85\) | 0.197224 | − | 0.341603i | 0.0213920 | − | 0.0370520i | ||||
\(86\) | 5.48612 | 0.591584 | ||||||||
\(87\) | −4.10555 | + | 7.11102i | −0.440161 | + | 0.762382i | ||||
\(88\) | −8.40833 | − | 14.5636i | −0.896331 | − | 1.55249i | ||||
\(89\) | −4.10555 | − | 7.11102i | −0.435188 | − | 0.753767i | 0.562123 | − | 0.827053i | \(-0.309985\pi\) |
−0.997311 | + | 0.0732864i | \(0.976651\pi\) | |||||||
\(90\) | 2.60555 | 0.274649 | ||||||||
\(91\) | 1.80278 | − | 3.12250i | 0.188982 | − | 0.327327i | ||||
\(92\) | 0.908327 | 0.0946996 | ||||||||
\(93\) | 2.00000 | + | 3.46410i | 0.207390 | + | 0.359211i | ||||
\(94\) | 3.39445 | + | 5.87936i | 0.350111 | + | 0.606409i | ||||
\(95\) | 0.802776 | − | 1.39045i | 0.0823630 | − | 0.142657i | ||||
\(96\) | 1.69722 | 0.173222 | ||||||||
\(97\) | 7.80278 | − | 13.5148i | 0.792252 | − | 1.37222i | −0.132318 | − | 0.991207i | \(-0.542242\pi\) |
0.924570 | − | 0.381013i | \(-0.124425\pi\) | |||||||
\(98\) | 3.90833 | − | 6.76942i | 0.394801 | − | 0.683815i | ||||
\(99\) | 11.2111 | 1.12676 | ||||||||
\(100\) | 0.151388 | − | 0.262211i | 0.0151388 | − | 0.0262211i | ||||
\(101\) | 4.50000 | + | 7.79423i | 0.447767 | + | 0.775555i | 0.998240 | − | 0.0592978i | \(-0.0188862\pi\) |
−0.550474 | + | 0.834853i | \(0.685553\pi\) | |||||||
\(102\) | −0.256939 | − | 0.445032i | −0.0254408 | − | 0.0440647i | ||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | −10.8167 | −1.06066 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | −7.30278 | − | 12.6488i | −0.709308 | − | 1.22856i | ||||
\(107\) | 4.10555 | + | 7.11102i | 0.396899 | + | 0.687449i | 0.993342 | − | 0.115207i | \(-0.0367531\pi\) |
−0.596443 | + | 0.802656i | \(0.703420\pi\) | |||||||
\(108\) | −0.756939 | + | 1.31106i | −0.0728365 | + | 0.126157i | ||||
\(109\) | −4.78890 | −0.458693 | −0.229347 | − | 0.973345i | \(-0.573659\pi\) | ||||
−0.229347 | + | 0.973345i | \(0.573659\pi\) | |||||||
\(110\) | −3.65139 | + | 6.32439i | −0.348146 | + | 0.603007i | ||||
\(111\) | 1.80278 | − | 3.12250i | 0.171112 | − | 0.296374i | ||||
\(112\) | 3.30278 | 0.312083 | ||||||||
\(113\) | −2.80278 | + | 4.85455i | −0.263663 | + | 0.456678i | −0.967212 | − | 0.253969i | \(-0.918264\pi\) |
0.703550 | + | 0.710646i | \(0.251597\pi\) | |||||||
\(114\) | −1.04584 | − | 1.81144i | −0.0979516 | − | 0.169657i | ||||
\(115\) | −1.50000 | − | 2.59808i | −0.139876 | − | 0.242272i | ||||
\(116\) | −2.48612 | −0.230831 | ||||||||
\(117\) | 3.60555 | − | 6.24500i | 0.333333 | − | 0.577350i | ||||
\(118\) | 14.0917 | 1.29724 | ||||||||
\(119\) | 0.197224 | + | 0.341603i | 0.0180795 | + | 0.0313147i | ||||
\(120\) | −1.50000 | − | 2.59808i | −0.136931 | − | 0.237171i | ||||
\(121\) | −10.2111 | + | 17.6861i | −0.928282 | + | 1.60783i | ||||
\(122\) | −1.30278 | −0.117948 | ||||||||
\(123\) | −1.50000 | + | 2.59808i | −0.135250 | + | 0.234261i | ||||
\(124\) | −0.605551 | + | 1.04885i | −0.0543801 | + | 0.0941891i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −1.30278 | + | 2.25647i | −0.116060 | + | 0.201023i | ||||
\(127\) | −5.10555 | − | 8.84307i | −0.453044 | − | 0.784696i | 0.545529 | − | 0.838092i | \(-0.316329\pi\) |
−0.998573 | + | 0.0533960i | \(0.982995\pi\) | |||||||
\(128\) | −4.04584 | − | 7.00759i | −0.357605 | − | 0.619390i | ||||
\(129\) | 4.21110 | 0.370767 | ||||||||
\(130\) | 2.34861 | + | 4.06792i | 0.205987 | + | 0.356780i | ||||
\(131\) | −6.78890 | −0.593149 | −0.296574 | − | 0.955010i | \(-0.595844\pi\) | ||||
−0.296574 | + | 0.955010i | \(0.595844\pi\) | |||||||
\(132\) | −0.848612 | − | 1.46984i | −0.0738622 | − | 0.127933i | ||||
\(133\) | 0.802776 | + | 1.39045i | 0.0696095 | + | 0.120567i | ||||
\(134\) | 4.55971 | − | 7.89766i | 0.393899 | − | 0.682254i | ||||
\(135\) | 5.00000 | 0.430331 | ||||||||
\(136\) | 0.591673 | − | 1.02481i | 0.0507355 | − | 0.0878765i | ||||
\(137\) | −2.80278 | + | 4.85455i | −0.239457 | + | 0.414752i | −0.960559 | − | 0.278077i | \(-0.910303\pi\) |
0.721101 | + | 0.692830i | \(0.243636\pi\) | |||||||
\(138\) | −3.90833 | −0.332699 | ||||||||
\(139\) | −6.80278 | + | 11.7828i | −0.577004 | + | 0.999400i | 0.418817 | + | 0.908071i | \(0.362445\pi\) |
−0.995821 | + | 0.0913293i | \(0.970888\pi\) | |||||||
\(140\) | 0.151388 | + | 0.262211i | 0.0127946 | + | 0.0221609i | ||||
\(141\) | 2.60555 | + | 4.51295i | 0.219427 | + | 0.380059i | ||||
\(142\) | −21.9083 | −1.83851 | ||||||||
\(143\) | 10.1056 | + | 17.5033i | 0.845069 | + | 1.46370i | ||||
\(144\) | 6.60555 | 0.550463 | ||||||||
\(145\) | 4.10555 | + | 7.11102i | 0.340947 | + | 0.590538i | ||||
\(146\) | 9.90833 | + | 17.1617i | 0.820019 | + | 1.42031i | ||||
\(147\) | 3.00000 | − | 5.19615i | 0.247436 | − | 0.428571i | ||||
\(148\) | 1.09167 | 0.0897350 | ||||||||
\(149\) | −1.50000 | + | 2.59808i | −0.122885 | + | 0.212843i | −0.920904 | − | 0.389789i | \(-0.872548\pi\) |
0.798019 | + | 0.602632i | \(0.205881\pi\) | |||||||
\(150\) | −0.651388 | + | 1.12824i | −0.0531856 | + | 0.0921201i | ||||
\(151\) | 13.2111 | 1.07510 | 0.537552 | − | 0.843231i | \(-0.319349\pi\) | ||||
0.537552 | + | 0.843231i | \(0.319349\pi\) | |||||||
\(152\) | 2.40833 | − | 4.17134i | 0.195341 | − | 0.338341i | ||||
\(153\) | 0.394449 | + | 0.683205i | 0.0318893 | + | 0.0552339i | ||||
\(154\) | −3.65139 | − | 6.32439i | −0.294237 | − | 0.509634i | ||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | −1.09167 | −0.0874038 | ||||||||
\(157\) | −3.21110 | −0.256274 | −0.128137 | − | 0.991756i | \(-0.540900\pi\) | ||||
−0.128137 | + | 0.991756i | \(0.540900\pi\) | |||||||
\(158\) | 6.00000 | + | 10.3923i | 0.477334 | + | 0.826767i | ||||
\(159\) | −5.60555 | − | 9.70910i | −0.444549 | − | 0.769982i | ||||
\(160\) | 0.848612 | − | 1.46984i | 0.0670887 | − | 0.116201i | ||||
\(161\) | 3.00000 | 0.236433 | ||||||||
\(162\) | −0.651388 | + | 1.12824i | −0.0511779 | + | 0.0886427i | ||||
\(163\) | 9.10555 | − | 15.7713i | 0.713202 | − | 1.23530i | −0.250447 | − | 0.968130i | \(-0.580578\pi\) |
0.963649 | − | 0.267172i | \(-0.0860890\pi\) | |||||||
\(164\) | −0.908327 | −0.0709284 | ||||||||
\(165\) | −2.80278 | + | 4.85455i | −0.218196 | + | 0.377926i | ||||
\(166\) | −3.39445 | − | 5.87936i | −0.263460 | − | 0.456327i | ||||
\(167\) | −4.50000 | − | 7.79423i | −0.348220 | − | 0.603136i | 0.637713 | − | 0.770274i | \(-0.279881\pi\) |
−0.985933 | + | 0.167139i | \(0.946547\pi\) | |||||||
\(168\) | 3.00000 | 0.231455 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | −0.513878 | −0.0394127 | ||||||||
\(171\) | 1.60555 | + | 2.78090i | 0.122780 | + | 0.212660i | ||||
\(172\) | 0.637510 | + | 1.10420i | 0.0486097 | + | 0.0841944i | ||||
\(173\) | 8.40833 | − | 14.5636i | 0.639273 | − | 1.10725i | −0.346319 | − | 0.938117i | \(-0.612569\pi\) |
0.985593 | − | 0.169137i | \(-0.0540981\pi\) | |||||||
\(174\) | 10.6972 | 0.810954 | ||||||||
\(175\) | 0.500000 | − | 0.866025i | 0.0377964 | − | 0.0654654i | ||||
\(176\) | −9.25694 | + | 16.0335i | −0.697768 | + | 1.20857i | ||||
\(177\) | 10.8167 | 0.813029 | ||||||||
\(178\) | −5.34861 | + | 9.26407i | −0.400895 | + | 0.694371i | ||||
\(179\) | −0.591673 | − | 1.02481i | −0.0442237 | − | 0.0765977i | 0.843066 | − | 0.537810i | \(-0.180748\pi\) |
−0.887290 | + | 0.461212i | \(0.847415\pi\) | |||||||
\(180\) | 0.302776 | + | 0.524423i | 0.0225676 | + | 0.0390882i | ||||
\(181\) | −25.6333 | −1.90531 | −0.952654 | − | 0.304055i | \(-0.901659\pi\) | ||||
−0.952654 | + | 0.304055i | \(0.901659\pi\) | |||||||
\(182\) | −4.69722 | −0.348181 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | −4.50000 | − | 7.79423i | −0.331744 | − | 0.574598i | ||||
\(185\) | −1.80278 | − | 3.12250i | −0.132543 | − | 0.229571i | ||||
\(186\) | 2.60555 | − | 4.51295i | 0.191048 | − | 0.330905i | ||||
\(187\) | −2.21110 | −0.161692 | ||||||||
\(188\) | −0.788897 | + | 1.36641i | −0.0575363 | + | 0.0996557i | ||||
\(189\) | −2.50000 | + | 4.33013i | −0.181848 | + | 0.314970i | ||||
\(190\) | −2.09167 | −0.151746 | ||||||||
\(191\) | 2.40833 | − | 4.17134i | 0.174260 | − | 0.301828i | −0.765645 | − | 0.643264i | \(-0.777580\pi\) |
0.939905 | + | 0.341436i | \(0.110913\pi\) | |||||||
\(192\) | −4.40833 | − | 7.63545i | −0.318144 | − | 0.551041i | ||||
\(193\) | −4.19722 | − | 7.26981i | −0.302123 | − | 0.523292i | 0.674494 | − | 0.738281i | \(-0.264362\pi\) |
−0.976617 | + | 0.214988i | \(0.931029\pi\) | |||||||
\(194\) | −20.3305 | −1.45965 | ||||||||
\(195\) | 1.80278 | + | 3.12250i | 0.129099 | + | 0.223607i | ||||
\(196\) | 1.81665 | 0.129761 | ||||||||
\(197\) | −11.4083 | − | 19.7598i | −0.812810 | − | 1.40783i | −0.910890 | − | 0.412649i | \(-0.864604\pi\) |
0.0980804 | − | 0.995178i | \(-0.468730\pi\) | |||||||
\(198\) | −7.30278 | − | 12.6488i | −0.518986 | − | 0.898910i | ||||
\(199\) | 4.40833 | − | 7.63545i | 0.312498 | − | 0.541262i | −0.666404 | − | 0.745590i | \(-0.732168\pi\) |
0.978902 | + | 0.204328i | \(0.0655009\pi\) | |||||||
\(200\) | −3.00000 | −0.212132 | ||||||||
\(201\) | 3.50000 | − | 6.06218i | 0.246871 | − | 0.427593i | ||||
\(202\) | 5.86249 | − | 10.1541i | 0.412483 | − | 0.714442i | ||||
\(203\) | −8.21110 | −0.576306 | ||||||||
\(204\) | 0.0597147 | − | 0.103429i | 0.00418087 | − | 0.00724147i | ||||
\(205\) | 1.50000 | + | 2.59808i | 0.104765 | + | 0.181458i | ||||
\(206\) | 2.60555 | + | 4.51295i | 0.181537 | + | 0.314432i | ||||
\(207\) | 6.00000 | 0.417029 | ||||||||
\(208\) | 5.95416 | + | 10.3129i | 0.412847 | + | 0.715072i | ||||
\(209\) | −9.00000 | −0.622543 | ||||||||
\(210\) | −0.651388 | − | 1.12824i | −0.0449500 | − | 0.0778557i | ||||
\(211\) | 8.19722 | + | 14.1980i | 0.564320 | + | 0.977431i | 0.997113 | + | 0.0759376i | \(0.0241950\pi\) |
−0.432792 | + | 0.901494i | \(0.642472\pi\) | |||||||
\(212\) | 1.69722 | − | 2.93968i | 0.116566 | − | 0.201898i | ||||
\(213\) | −16.8167 | −1.15226 | ||||||||
\(214\) | 5.34861 | − | 9.26407i | 0.365624 | − | 0.633279i | ||||
\(215\) | 2.10555 | − | 3.64692i | 0.143597 | − | 0.248718i | ||||
\(216\) | 15.0000 | 1.02062 | ||||||||
\(217\) | −2.00000 | + | 3.46410i | −0.135769 | + | 0.235159i | ||||
\(218\) | 3.11943 | + | 5.40301i | 0.211274 | + | 0.365938i | ||||
\(219\) | 7.60555 | + | 13.1732i | 0.513936 | + | 0.890162i | ||||
\(220\) | −1.69722 | −0.114427 | ||||||||
\(221\) | −0.711103 | + | 1.23167i | −0.0478339 | + | 0.0828508i | ||||
\(222\) | −4.69722 | −0.315257 | ||||||||
\(223\) | −5.10555 | − | 8.84307i | −0.341893 | − | 0.592176i | 0.642891 | − | 0.765957i | \(-0.277735\pi\) |
−0.984784 | + | 0.173781i | \(0.944401\pi\) | |||||||
\(224\) | 0.848612 | + | 1.46984i | 0.0567003 | + | 0.0982078i | ||||
\(225\) | 1.00000 | − | 1.73205i | 0.0666667 | − | 0.115470i | ||||
\(226\) | 7.30278 | 0.485773 | ||||||||
\(227\) | −0.711103 | + | 1.23167i | −0.0471975 | + | 0.0817485i | −0.888659 | − | 0.458569i | \(-0.848362\pi\) |
0.841462 | + | 0.540317i | \(0.181696\pi\) | |||||||
\(228\) | 0.243061 | − | 0.420994i | 0.0160971 | − | 0.0278810i | ||||
\(229\) | 14.0000 | 0.925146 | 0.462573 | − | 0.886581i | \(-0.346926\pi\) | ||||
0.462573 | + | 0.886581i | \(0.346926\pi\) | |||||||
\(230\) | −1.95416 | + | 3.38471i | −0.128854 | + | 0.223181i | ||||
\(231\) | −2.80278 | − | 4.85455i | −0.184409 | − | 0.319406i | ||||
\(232\) | 12.3167 | + | 21.3331i | 0.808628 | + | 1.40058i | ||||
\(233\) | 0.788897 | 0.0516824 | 0.0258412 | − | 0.999666i | \(-0.491774\pi\) | ||||
0.0258412 | + | 0.999666i | \(0.491774\pi\) | |||||||
\(234\) | −9.39445 | −0.614134 | ||||||||
\(235\) | 5.21110 | 0.339935 | ||||||||
\(236\) | 1.63751 | + | 2.83625i | 0.106593 | + | 0.184624i | ||||
\(237\) | 4.60555 | + | 7.97705i | 0.299163 | + | 0.518165i | ||||
\(238\) | 0.256939 | − | 0.445032i | 0.0166549 | − | 0.0288471i | ||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | −1.65139 | + | 2.86029i | −0.106597 | + | 0.184631i | ||||
\(241\) | −8.10555 | + | 14.0392i | −0.522124 | + | 0.904346i | 0.477544 | + | 0.878608i | \(0.341527\pi\) |
−0.999669 | + | 0.0257384i | \(0.991806\pi\) | |||||||
\(242\) | 26.6056 | 1.71027 | ||||||||
\(243\) | −8.00000 | + | 13.8564i | −0.513200 | + | 0.888889i | ||||
\(244\) | −0.151388 | − | 0.262211i | −0.00969161 | − | 0.0167864i | ||||
\(245\) | −3.00000 | − | 5.19615i | −0.191663 | − | 0.331970i | ||||
\(246\) | 3.90833 | 0.249186 | ||||||||
\(247\) | −2.89445 | + | 5.01333i | −0.184169 | + | 0.318991i | ||||
\(248\) | 12.0000 | 0.762001 | ||||||||
\(249\) | −2.60555 | − | 4.51295i | −0.165120 | − | 0.285996i | ||||
\(250\) | 0.651388 | + | 1.12824i | 0.0411974 | + | 0.0713560i | ||||
\(251\) | 14.4083 | − | 24.9560i | 0.909446 | − | 1.57521i | 0.0946094 | − | 0.995514i | \(-0.469840\pi\) |
0.814836 | − | 0.579691i | \(-0.196827\pi\) | |||||||
\(252\) | −0.605551 | −0.0381461 | ||||||||
\(253\) | −8.40833 | + | 14.5636i | −0.528627 | + | 0.915609i | ||||
\(254\) | −6.65139 | + | 11.5205i | −0.417345 | + | 0.722863i | ||||
\(255\) | −0.394449 | −0.0247013 | ||||||||
\(256\) | 3.54584 | − | 6.14157i | 0.221615 | − | 0.383848i | ||||
\(257\) | 11.8028 | + | 20.4430i | 0.736237 | + | 1.27520i | 0.954179 | + | 0.299238i | \(0.0967324\pi\) |
−0.217942 | + | 0.975962i | \(0.569934\pi\) | |||||||
\(258\) | −2.74306 | − | 4.75112i | −0.170776 | − | 0.295792i | ||||
\(259\) | 3.60555 | 0.224038 | ||||||||
\(260\) | −0.545837 | + | 0.945417i | −0.0338513 | + | 0.0586323i | ||||
\(261\) | −16.4222 | −1.01651 | ||||||||
\(262\) | 4.42221 | + | 7.65948i | 0.273205 | + | 0.473204i | ||||
\(263\) | −13.1056 | − | 22.6995i | −0.808123 | − | 1.39971i | −0.914162 | − | 0.405348i | \(-0.867150\pi\) |
0.106040 | − | 0.994362i | \(-0.466183\pi\) | |||||||
\(264\) | −8.40833 | + | 14.5636i | −0.517497 | + | 0.896331i | ||||
\(265\) | −11.2111 | −0.688693 | ||||||||
\(266\) | 1.04584 | − | 1.81144i | 0.0641244 | − | 0.111067i | ||||
\(267\) | −4.10555 | + | 7.11102i | −0.251256 | + | 0.435188i | ||||
\(268\) | 2.11943 | 0.129465 | ||||||||
\(269\) | 4.50000 | − | 7.79423i | 0.274370 | − | 0.475223i | −0.695606 | − | 0.718423i | \(-0.744864\pi\) |
0.969976 | + | 0.243201i | \(0.0781974\pi\) | |||||||
\(270\) | −3.25694 | − | 5.64118i | −0.198211 | − | 0.343312i | ||||
\(271\) | −0.408327 | − | 0.707243i | −0.0248041 | − | 0.0429620i | 0.853357 | − | 0.521327i | \(-0.174563\pi\) |
−0.878161 | + | 0.478365i | \(0.841230\pi\) | |||||||
\(272\) | −1.30278 | −0.0789924 | ||||||||
\(273\) | −3.60555 | −0.218218 | ||||||||
\(274\) | 7.30278 | 0.441177 | ||||||||
\(275\) | 2.80278 | + | 4.85455i | 0.169014 | + | 0.292740i | ||||
\(276\) | −0.454163 | − | 0.786634i | −0.0273374 | − | 0.0473498i | ||||
\(277\) | −10.1972 | + | 17.6621i | −0.612692 | + | 1.06121i | 0.378093 | + | 0.925768i | \(0.376580\pi\) |
−0.990785 | + | 0.135446i | \(0.956753\pi\) | |||||||
\(278\) | 17.7250 | 1.06307 | ||||||||
\(279\) | −4.00000 | + | 6.92820i | −0.239474 | + | 0.414781i | ||||
\(280\) | 1.50000 | − | 2.59808i | 0.0896421 | − | 0.155265i | ||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 3.39445 | − | 5.87936i | 0.202136 | − | 0.350111i | ||||
\(283\) | −2.50000 | − | 4.33013i | −0.148610 | − | 0.257399i | 0.782104 | − | 0.623148i | \(-0.214146\pi\) |
−0.930714 | + | 0.365748i | \(0.880813\pi\) | |||||||
\(284\) | −2.54584 | − | 4.40952i | −0.151068 | − | 0.261657i | ||||
\(285\) | −1.60555 | −0.0951046 | ||||||||
\(286\) | 13.1653 | − | 22.8029i | 0.778478 | − | 1.34836i | ||||
\(287\) | −3.00000 | −0.177084 | ||||||||
\(288\) | 1.69722 | + | 2.93968i | 0.100010 | + | 0.173222i | ||||
\(289\) | 8.42221 | + | 14.5877i | 0.495424 | + | 0.858099i | ||||
\(290\) | 5.34861 | − | 9.26407i | 0.314081 | − | 0.544005i | ||||
\(291\) | −15.6056 | −0.914814 | ||||||||
\(292\) | −2.30278 | + | 3.98852i | −0.134760 | + | 0.233411i | ||||
\(293\) | −8.80278 | + | 15.2469i | −0.514264 | + | 0.890731i | 0.485599 | + | 0.874181i | \(0.338601\pi\) |
−0.999863 | + | 0.0165493i | \(0.994732\pi\) | |||||||
\(294\) | −7.81665 | −0.455877 | ||||||||
\(295\) | 5.40833 | − | 9.36750i | 0.314885 | − | 0.545397i | ||||
\(296\) | −5.40833 | − | 9.36750i | −0.314353 | − | 0.544475i | ||||
\(297\) | −14.0139 | − | 24.2727i | −0.813168 | − | 1.40845i | ||||
\(298\) | 3.90833 | 0.226403 | ||||||||
\(299\) | 5.40833 | + | 9.36750i | 0.312772 | + | 0.541736i | ||||
\(300\) | −0.302776 | −0.0174808 | ||||||||
\(301\) | 2.10555 | + | 3.64692i | 0.121362 | + | 0.210205i | ||||
\(302\) | −8.60555 | − | 14.9053i | −0.495194 | − | 0.857701i | ||||
\(303\) | 4.50000 | − | 7.79423i | 0.258518 | − | 0.447767i | ||||
\(304\) | −5.30278 | −0.304135 | ||||||||
\(305\) | −0.500000 | + | 0.866025i | −0.0286299 | + | 0.0495885i | ||||
\(306\) | 0.513878 | − | 0.890063i | 0.0293765 | − | 0.0508815i | ||||
\(307\) | −16.0000 | −0.913168 | −0.456584 | − | 0.889680i | \(-0.650927\pi\) | ||||
−0.456584 | + | 0.889680i | \(0.650927\pi\) | |||||||
\(308\) | 0.848612 | − | 1.46984i | 0.0483542 | − | 0.0837519i | ||||
\(309\) | 2.00000 | + | 3.46410i | 0.113776 | + | 0.197066i | ||||
\(310\) | −2.60555 | − | 4.51295i | −0.147985 | − | 0.256318i | ||||
\(311\) | 5.21110 | 0.295495 | 0.147747 | − | 0.989025i | \(-0.452798\pi\) | ||||
0.147747 | + | 0.989025i | \(0.452798\pi\) | |||||||
\(312\) | 5.40833 | + | 9.36750i | 0.306186 | + | 0.530330i | ||||
\(313\) | 14.0000 | 0.791327 | 0.395663 | − | 0.918396i | \(-0.370515\pi\) | ||||
0.395663 | + | 0.918396i | \(0.370515\pi\) | |||||||
\(314\) | 2.09167 | + | 3.62288i | 0.118040 | + | 0.204451i | ||||
\(315\) | 1.00000 | + | 1.73205i | 0.0563436 | + | 0.0975900i | ||||
\(316\) | −1.39445 | + | 2.41526i | −0.0784439 | + | 0.135869i | ||||
\(317\) | 6.00000 | 0.336994 | 0.168497 | − | 0.985702i | \(-0.446109\pi\) | ||||
0.168497 | + | 0.985702i | \(0.446109\pi\) | |||||||
\(318\) | −7.30278 | + | 12.6488i | −0.409519 | + | 0.709308i | ||||
\(319\) | 23.0139 | − | 39.8612i | 1.28853 | − | 2.23180i | ||||
\(320\) | −8.81665 | −0.492866 | ||||||||
\(321\) | 4.10555 | − | 7.11102i | 0.229150 | − | 0.396899i | ||||
\(322\) | −1.95416 | − | 3.38471i | −0.108901 | − | 0.188623i | ||||
\(323\) | −0.316654 | − | 0.548461i | −0.0176191 | − | 0.0305172i | ||||
\(324\) | −0.302776 | −0.0168209 | ||||||||
\(325\) | 3.60555 | 0.200000 | ||||||||
\(326\) | −23.7250 | −1.31401 | ||||||||
\(327\) | 2.39445 | + | 4.14731i | 0.132413 | + | 0.229347i | ||||
\(328\) | 4.50000 | + | 7.79423i | 0.248471 | + | 0.430364i | ||||
\(329\) | −2.60555 | + | 4.51295i | −0.143649 | + | 0.248807i | ||||
\(330\) | 7.30278 | 0.402005 | ||||||||
\(331\) | 13.0139 | − | 22.5407i | 0.715307 | − | 1.23895i | −0.247533 | − | 0.968879i | \(-0.579620\pi\) |
0.962841 | − | 0.270069i | \(-0.0870467\pi\) | |||||||
\(332\) | 0.788897 | − | 1.36641i | 0.0432964 | − | 0.0749915i | ||||
\(333\) | 7.21110 | 0.395166 | ||||||||
\(334\) | −5.86249 | + | 10.1541i | −0.320781 | + | 0.555609i | ||||
\(335\) | −3.50000 | − | 6.06218i | −0.191225 | − | 0.331212i | ||||
\(336\) | −1.65139 | − | 2.86029i | −0.0900906 | − | 0.156041i | ||||
\(337\) | 17.6333 | 0.960547 | 0.480274 | − | 0.877119i | \(-0.340537\pi\) | ||||
0.480274 | + | 0.877119i | \(0.340537\pi\) | |||||||
\(338\) | −8.46804 | − | 14.6671i | −0.460601 | − | 0.797784i | ||||
\(339\) | 5.60555 | 0.304452 | ||||||||
\(340\) | −0.0597147 | − | 0.103429i | −0.00323849 | − | 0.00560922i | ||||
\(341\) | −11.2111 | − | 19.4182i | −0.607115 | − | 1.05155i | ||||
\(342\) | 2.09167 | − | 3.62288i | 0.113105 | − | 0.195903i | ||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | 6.31665 | − | 10.9408i | 0.340571 | − | 0.589887i | ||||
\(345\) | −1.50000 | + | 2.59808i | −0.0807573 | + | 0.139876i | ||||
\(346\) | −21.9083 | −1.17780 | ||||||||
\(347\) | −10.1056 | + | 17.5033i | −0.542494 | + | 0.939628i | 0.456266 | + | 0.889844i | \(0.349187\pi\) |
−0.998760 | + | 0.0497842i | \(0.984147\pi\) | |||||||
\(348\) | 1.24306 | + | 2.15304i | 0.0666351 | + | 0.115415i | ||||
\(349\) | 9.10555 | + | 15.7713i | 0.487409 | + | 0.844217i | 0.999895 | − | 0.0144783i | \(-0.00460876\pi\) |
−0.512486 | + | 0.858695i | \(0.671275\pi\) | |||||||
\(350\) | −1.30278 | −0.0696363 | ||||||||
\(351\) | −18.0278 | −0.962250 | ||||||||
\(352\) | −9.51388 | −0.507091 | ||||||||
\(353\) | 2.40833 | + | 4.17134i | 0.128182 | + | 0.222018i | 0.922972 | − | 0.384866i | \(-0.125752\pi\) |
−0.794790 | + | 0.606884i | \(0.792419\pi\) | |||||||
\(354\) | −7.04584 | − | 12.2037i | −0.374482 | − | 0.648622i | ||||
\(355\) | −8.40833 | + | 14.5636i | −0.446268 | + | 0.772958i | ||||
\(356\) | −2.48612 | −0.131764 | ||||||||
\(357\) | 0.197224 | − | 0.341603i | 0.0104382 | − | 0.0180795i | ||||
\(358\) | −0.770817 | + | 1.33509i | −0.0407390 | + | 0.0705619i | ||||
\(359\) | −10.4222 | −0.550063 | −0.275031 | − | 0.961435i | \(-0.588688\pi\) | ||||
−0.275031 | + | 0.961435i | \(0.588688\pi\) | |||||||
\(360\) | 3.00000 | − | 5.19615i | 0.158114 | − | 0.273861i | ||||
\(361\) | 8.21110 | + | 14.2220i | 0.432163 | + | 0.748529i | ||||
\(362\) | 16.6972 | + | 28.9204i | 0.877587 | + | 1.52002i | ||||
\(363\) | 20.4222 | 1.07189 | ||||||||
\(364\) | −0.545837 | − | 0.945417i | −0.0286096 | − | 0.0495533i | ||||
\(365\) | 15.2111 | 0.796185 | ||||||||
\(366\) | 0.651388 | + | 1.12824i | 0.0340486 | + | 0.0589739i | ||||
\(367\) | 8.71110 | + | 15.0881i | 0.454716 | + | 0.787591i | 0.998672 | − | 0.0515228i | \(-0.0164075\pi\) |
−0.543956 | + | 0.839114i | \(0.683074\pi\) | |||||||
\(368\) | −4.95416 | + | 8.58086i | −0.258254 | + | 0.447308i | ||||
\(369\) | −6.00000 | −0.312348 | ||||||||
\(370\) | −2.34861 | + | 4.06792i | −0.122099 | + | 0.211481i | ||||
\(371\) | 5.60555 | − | 9.70910i | 0.291026 | − | 0.504071i | ||||
\(372\) | 1.21110 | 0.0627927 | ||||||||
\(373\) | 13.8028 | − | 23.9071i | 0.714681 | − | 1.23786i | −0.248402 | − | 0.968657i | \(-0.579905\pi\) |
0.963083 | − | 0.269206i | \(-0.0867613\pi\) | |||||||
\(374\) | 1.44029 | + | 2.49465i | 0.0744754 | + | 0.128995i | ||||
\(375\) | 0.500000 | + | 0.866025i | 0.0258199 | + | 0.0447214i | ||||
\(376\) | 15.6333 | 0.806226 | ||||||||
\(377\) | −14.8028 | − | 25.6392i | −0.762382 | − | 1.32048i | ||||
\(378\) | 6.51388 | 0.335038 | ||||||||
\(379\) | −1.19722 | − | 2.07365i | −0.0614973 | − | 0.106516i | 0.833638 | − | 0.552312i | \(-0.186254\pi\) |
−0.895135 | + | 0.445795i | \(0.852921\pi\) | |||||||
\(380\) | −0.243061 | − | 0.420994i | −0.0124688 | − | 0.0215965i | ||||
\(381\) | −5.10555 | + | 8.84307i | −0.261565 | + | 0.453044i | ||||
\(382\) | −6.27502 | −0.321058 | ||||||||
\(383\) | −9.31665 | + | 16.1369i | −0.476059 | + | 0.824558i | −0.999624 | − | 0.0274277i | \(-0.991268\pi\) |
0.523565 | + | 0.851986i | \(0.324602\pi\) | |||||||
\(384\) | −4.04584 | + | 7.00759i | −0.206463 | + | 0.357605i | ||||
\(385\) | −5.60555 | −0.285685 | ||||||||
\(386\) | −5.46804 | + | 9.47093i | −0.278316 | + | 0.482057i | ||||
\(387\) | 4.21110 | + | 7.29384i | 0.214062 | + | 0.370767i | ||||
\(388\) | −2.36249 | − | 4.09195i | −0.119937 | − | 0.207737i | ||||
\(389\) | −0.788897 | −0.0399987 | −0.0199993 | − | 0.999800i | \(-0.506366\pi\) | ||||
−0.0199993 | + | 0.999800i | \(0.506366\pi\) | |||||||
\(390\) | 2.34861 | − | 4.06792i | 0.118927 | − | 0.205987i | ||||
\(391\) | −1.18335 | −0.0598444 | ||||||||
\(392\) | −9.00000 | − | 15.5885i | −0.454569 | − | 0.787336i | ||||
\(393\) | 3.39445 | + | 5.87936i | 0.171227 | + | 0.296574i | ||||
\(394\) | −14.8625 | + | 25.7426i | −0.748761 | + | 1.29689i | ||||
\(395\) | 9.21110 | 0.463461 | ||||||||
\(396\) | 1.69722 | − | 2.93968i | 0.0852887 | − | 0.147724i | ||||
\(397\) | 7.01388 | − | 12.1484i | 0.352016 | − | 0.609710i | −0.634586 | − | 0.772852i | \(-0.718829\pi\) |
0.986603 | + | 0.163142i | \(0.0521628\pi\) | |||||||
\(398\) | −11.4861 | −0.575747 | ||||||||
\(399\) | 0.802776 | − | 1.39045i | 0.0401890 | − | 0.0696095i | ||||
\(400\) | 1.65139 | + | 2.86029i | 0.0825694 | + | 0.143014i | ||||
\(401\) | 1.10555 | + | 1.91487i | 0.0552086 | + | 0.0956241i | 0.892309 | − | 0.451425i | \(-0.149084\pi\) |
−0.837100 | + | 0.547049i | \(0.815751\pi\) | |||||||
\(402\) | −9.11943 | −0.454836 | ||||||||
\(403\) | −14.4222 | −0.718421 | ||||||||
\(404\) | 2.72498 | 0.135573 | ||||||||
\(405\) | 0.500000 | + | 0.866025i | 0.0248452 | + | 0.0430331i | ||||
\(406\) | 5.34861 | + | 9.26407i | 0.265447 | + | 0.459768i | ||||
\(407\) | −10.1056 | + | 17.5033i | −0.500914 | + | 0.867608i | ||||
\(408\) | −1.18335 | −0.0585844 | ||||||||
\(409\) | 3.10555 | − | 5.37897i | 0.153560 | − | 0.265973i | −0.778974 | − | 0.627056i | \(-0.784260\pi\) |
0.932534 | + | 0.361083i | \(0.117593\pi\) | |||||||
\(410\) | 1.95416 | − | 3.38471i | 0.0965093 | − | 0.167159i | ||||
\(411\) | 5.60555 | 0.276501 | ||||||||
\(412\) | −0.605551 | + | 1.04885i | −0.0298334 | + | 0.0516729i | ||||
\(413\) | 5.40833 | + | 9.36750i | 0.266126 | + | 0.460944i | ||||
\(414\) | −3.90833 | − | 6.76942i | −0.192084 | − | 0.332699i | ||||
\(415\) | −5.21110 | −0.255803 | ||||||||
\(416\) | −3.05971 | + | 5.29958i | −0.150015 | + | 0.259833i | ||||
\(417\) | 13.6056 | 0.666267 | ||||||||
\(418\) | 5.86249 | + | 10.1541i | 0.286744 | + | 0.496655i | ||||
\(419\) | 16.6194 | + | 28.7857i | 0.811912 | + | 1.40627i | 0.911524 | + | 0.411247i | \(0.134907\pi\) |
−0.0996117 | + | 0.995026i | \(0.531760\pi\) | |||||||
\(420\) | 0.151388 | − | 0.262211i | 0.00738697 | − | 0.0127946i | ||||
\(421\) | 3.57779 | 0.174371 | 0.0871855 | − | 0.996192i | \(-0.472213\pi\) | ||||
0.0871855 | + | 0.996192i | \(0.472213\pi\) | |||||||
\(422\) | 10.6791 | − | 18.4968i | 0.519853 | − | 0.900411i | ||||
\(423\) | −5.21110 | + | 9.02589i | −0.253372 | + | 0.438854i | ||||
\(424\) | −33.6333 | −1.63338 | ||||||||
\(425\) | −0.197224 | + | 0.341603i | −0.00956679 | + | 0.0165702i | ||||
\(426\) | 10.9542 | + | 18.9732i | 0.530731 | + | 0.919253i | ||||
\(427\) | −0.500000 | − | 0.866025i | −0.0241967 | − | 0.0419099i | ||||
\(428\) | 2.48612 | 0.120171 | ||||||||
\(429\) | 10.1056 | − | 17.5033i | 0.487901 | − | 0.845069i | ||||
\(430\) | −5.48612 | −0.264564 | ||||||||
\(431\) | 10.6194 | + | 18.3934i | 0.511520 | + | 0.885978i | 0.999911 | + | 0.0133535i | \(0.00425069\pi\) |
−0.488391 | + | 0.872625i | \(0.662416\pi\) | |||||||
\(432\) | −8.25694 | − | 14.3014i | −0.397262 | − | 0.688078i | ||||
\(433\) | 1.80278 | − | 3.12250i | 0.0866359 | − | 0.150058i | −0.819451 | − | 0.573149i | \(-0.805722\pi\) |
0.906087 | + | 0.423091i | \(0.139055\pi\) | |||||||
\(434\) | 5.21110 | 0.250141 | ||||||||
\(435\) | 4.10555 | − | 7.11102i | 0.196846 | − | 0.340947i | ||||
\(436\) | −0.724981 | + | 1.25570i | −0.0347203 | + | 0.0601373i | ||||
\(437\) | −4.81665 | −0.230412 | ||||||||
\(438\) | 9.90833 | − | 17.1617i | 0.473438 | − | 0.820019i | ||||
\(439\) | −11.6194 | − | 20.1254i | −0.554565 | − | 0.960535i | −0.997937 | − | 0.0641973i | \(-0.979551\pi\) |
0.443372 | − | 0.896338i | \(-0.353782\pi\) | |||||||
\(440\) | 8.40833 | + | 14.5636i | 0.400851 | + | 0.694295i | ||||
\(441\) | 12.0000 | 0.571429 | ||||||||
\(442\) | 1.85281 | 0.0881294 | ||||||||
\(443\) | −22.4222 | −1.06531 | −0.532656 | − | 0.846332i | \(-0.678806\pi\) | ||||
−0.532656 | + | 0.846332i | \(0.678806\pi\) | |||||||
\(444\) | −0.545837 | − | 0.945417i | −0.0259043 | − | 0.0448675i | ||||
\(445\) | 4.10555 | + | 7.11102i | 0.194622 | + | 0.337095i | ||||
\(446\) | −6.65139 | + | 11.5205i | −0.314952 | + | 0.545513i | ||||
\(447\) | 3.00000 | 0.141895 | ||||||||
\(448\) | 4.40833 | − | 7.63545i | 0.208274 | − | 0.360741i | ||||
\(449\) | 6.31665 | − | 10.9408i | 0.298101 | − | 0.516327i | −0.677600 | − | 0.735430i | \(-0.736980\pi\) |
0.975702 | + | 0.219104i | \(0.0703133\pi\) | |||||||
\(450\) | −2.60555 | −0.122827 | ||||||||
\(451\) | 8.40833 | − | 14.5636i | 0.395933 | − | 0.685775i | ||||
\(452\) | 0.848612 | + | 1.46984i | 0.0399154 | + | 0.0691354i | ||||
\(453\) | −6.60555 | − | 11.4412i | −0.310356 | − | 0.537552i | ||||
\(454\) | 1.85281 | 0.0869569 | ||||||||
\(455\) | −1.80278 | + | 3.12250i | −0.0845154 | + | 0.146385i | ||||
\(456\) | −4.81665 | −0.225560 | ||||||||
\(457\) | 2.59167 | + | 4.48891i | 0.121233 | + | 0.209982i | 0.920254 | − | 0.391321i | \(-0.127982\pi\) |
−0.799021 | + | 0.601303i | \(0.794648\pi\) | |||||||
\(458\) | −9.11943 | − | 15.7953i | −0.426123 | − | 0.738067i | ||||
\(459\) | 0.986122 | − | 1.70801i | 0.0460282 | − | 0.0797232i | ||||
\(460\) | −0.908327 | −0.0423510 | ||||||||
\(461\) | −10.8944 | + | 18.8697i | −0.507405 | + | 0.878851i | 0.492558 | + | 0.870280i | \(0.336062\pi\) |
−0.999963 | + | 0.00857184i | \(0.997271\pi\) | |||||||
\(462\) | −3.65139 | + | 6.32439i | −0.169878 | + | 0.294237i | ||||
\(463\) | −5.57779 | −0.259222 | −0.129611 | − | 0.991565i | \(-0.541373\pi\) | ||||
−0.129611 | + | 0.991565i | \(0.541373\pi\) | |||||||
\(464\) | 13.5597 | − | 23.4861i | 0.629494 | − | 1.09032i | ||||
\(465\) | −2.00000 | − | 3.46410i | −0.0927478 | − | 0.160644i | ||||
\(466\) | −0.513878 | − | 0.890063i | −0.0238049 | − | 0.0412314i | ||||
\(467\) | 17.2111 | 0.796435 | 0.398217 | − | 0.917291i | \(-0.369629\pi\) | ||||
0.398217 | + | 0.917291i | \(0.369629\pi\) | |||||||
\(468\) | −1.09167 | − | 1.89083i | −0.0504626 | − | 0.0874038i | ||||
\(469\) | 7.00000 | 0.323230 | ||||||||
\(470\) | −3.39445 | − | 5.87936i | −0.156574 | − | 0.271195i | ||||
\(471\) | 1.60555 | + | 2.78090i | 0.0739799 | + | 0.128137i | ||||
\(472\) | 16.2250 | − | 28.1025i | 0.746815 | − | 1.29352i | ||||
\(473\) | −23.6056 | −1.08538 | ||||||||
\(474\) | 6.00000 | − | 10.3923i | 0.275589 | − | 0.477334i | ||||
\(475\) | −0.802776 | + | 1.39045i | −0.0368339 | + | 0.0637981i | ||||
\(476\) | 0.119429 | 0.00547404 | ||||||||
\(477\) | 11.2111 | − | 19.4182i | 0.513321 | − | 0.889098i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.59167 | + | 6.22096i | 0.164108 | + | 0.284243i | 0.936338 | − | 0.351100i | \(-0.114192\pi\) |
−0.772230 | + | 0.635343i | \(0.780859\pi\) | |||||||
\(480\) | −1.69722 | −0.0774673 | ||||||||
\(481\) | 6.50000 | + | 11.2583i | 0.296374 | + | 0.513336i | ||||
\(482\) | 21.1194 | 0.961964 | ||||||||
\(483\) | −1.50000 | − | 2.59808i | −0.0682524 | − | 0.118217i | ||||
\(484\) | 3.09167 | + | 5.35493i | 0.140531 | + | 0.243406i | ||||
\(485\) | −7.80278 | + | 13.5148i | −0.354306 | + | 0.613676i | ||||
\(486\) | 20.8444 | 0.945522 | ||||||||
\(487\) | 0.500000 | − | 0.866025i | 0.0226572 | − | 0.0392434i | −0.854475 | − | 0.519493i | \(-0.826121\pi\) |
0.877132 | + | 0.480250i | \(0.159454\pi\) | |||||||
\(488\) | −1.50000 | + | 2.59808i | −0.0679018 | + | 0.117609i | ||||
\(489\) | −18.2111 | −0.823535 | ||||||||
\(490\) | −3.90833 | + | 6.76942i | −0.176560 | + | 0.305811i | ||||
\(491\) | −2.40833 | − | 4.17134i | −0.108686 | − | 0.188250i | 0.806552 | − | 0.591163i | \(-0.201331\pi\) |
−0.915238 | + | 0.402913i | \(0.867998\pi\) | |||||||
\(492\) | 0.454163 | + | 0.786634i | 0.0204753 | + | 0.0354642i | ||||
\(493\) | 3.23886 | 0.145871 | ||||||||
\(494\) | 7.54163 | 0.339314 | ||||||||
\(495\) | −11.2111 | −0.503902 | ||||||||
\(496\) | −6.60555 | − | 11.4412i | −0.296598 | − | 0.513723i | ||||
\(497\) | −8.40833 | − | 14.5636i | −0.377165 | − | 0.653269i | ||||
\(498\) | −3.39445 | + | 5.87936i | −0.152109 | + | 0.263460i | ||||
\(499\) | −26.4222 | −1.18282 | −0.591410 | − | 0.806371i | \(-0.701429\pi\) | ||||
−0.591410 | + | 0.806371i | \(0.701429\pi\) | |||||||
\(500\) | −0.151388 | + | 0.262211i | −0.00677027 | + | 0.0117265i | ||||
\(501\) | −4.50000 | + | 7.79423i | −0.201045 | + | 0.348220i | ||||
\(502\) | −37.5416 | −1.67557 | ||||||||
\(503\) | −1.50000 | + | 2.59808i | −0.0668817 | + | 0.115842i | −0.897527 | − | 0.440959i | \(-0.854638\pi\) |
0.830645 | + | 0.556802i | \(0.187972\pi\) | |||||||
\(504\) | 3.00000 | + | 5.19615i | 0.133631 | + | 0.231455i | ||||
\(505\) | −4.50000 | − | 7.79423i | −0.200247 | − | 0.346839i | ||||
\(506\) | 21.9083 | 0.973944 | ||||||||
\(507\) | −6.50000 | − | 11.2583i | −0.288675 | − | 0.500000i | ||||
\(508\) | −3.09167 | −0.137171 | ||||||||
\(509\) | −1.50000 | − | 2.59808i | −0.0664863 | − | 0.115158i | 0.830866 | − | 0.556473i | \(-0.187846\pi\) |
−0.897352 | + | 0.441315i | \(0.854512\pi\) | |||||||
\(510\) | 0.256939 | + | 0.445032i | 0.0113775 | + | 0.0197063i | ||||
\(511\) | −7.60555 | + | 13.1732i | −0.336450 | + | 0.582748i | ||||
\(512\) | −25.4222 | −1.12351 | ||||||||
\(513\) | 4.01388 | − | 6.95224i | 0.177217 | − | 0.306949i | ||||
\(514\) | 15.3764 | − | 26.6327i | 0.678223 | − | 1.17472i | ||||
\(515\) | 4.00000 | 0.176261 | ||||||||
\(516\) | 0.637510 | − | 1.10420i | 0.0280648 | − | 0.0486097i | ||||
\(517\) | −14.6056 | − | 25.2976i | −0.642351 | − | 1.11259i | ||||
\(518\) | −2.34861 | − | 4.06792i | −0.103192 | − | 0.178734i | ||||
\(519\) | −16.8167 | −0.738169 | ||||||||
\(520\) | 10.8167 | 0.474342 | ||||||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | 10.6972 | + | 18.5281i | 0.468205 | + | 0.810954i | ||||
\(523\) | −13.7111 | − | 23.7483i | −0.599545 | − | 1.03844i | −0.992888 | − | 0.119050i | \(-0.962015\pi\) |
0.393344 | − | 0.919392i | \(-0.371318\pi\) | |||||||
\(524\) | −1.02776 | + | 1.78013i | −0.0448977 | + | 0.0777652i | ||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | −17.0736 | + | 29.5723i | −0.744444 | + | 1.28941i | ||||
\(527\) | 0.788897 | − | 1.36641i | 0.0343649 | − | 0.0595218i | ||||
\(528\) | 18.5139 | 0.805713 | ||||||||
\(529\) | 7.00000 | − | 12.1244i | 0.304348 | − | 0.527146i | ||||
\(530\) | 7.30278 | + | 12.6488i | 0.317212 | + | 0.549428i | ||||
\(531\) | 10.8167 | + | 18.7350i | 0.469403 | + | 0.813029i | ||||
\(532\) | 0.486122 | 0.0210761 | ||||||||
\(533\) | −5.40833 | − | 9.36750i | −0.234261 | − | 0.405751i | ||||
\(534\) | 10.6972 | 0.462914 | ||||||||
\(535\) | −4.10555 | − | 7.11102i | −0.177498 | − | 0.307436i | ||||
\(536\) | −10.5000 | − | 18.1865i | −0.453531 | − | 0.785539i | ||||
\(537\) | −0.591673 | + | 1.02481i | −0.0255326 | + | 0.0442237i | ||||
\(538\) | −11.7250 | −0.505500 | ||||||||
\(539\) | −16.8167 | + | 29.1273i | −0.724345 | + | 1.25460i | ||||
\(540\) | 0.756939 | − | 1.31106i | 0.0325735 | − | 0.0564189i | ||||
\(541\) | 17.6333 | 0.758115 | 0.379058 | − | 0.925373i | \(-0.376248\pi\) | ||||
0.379058 | + | 0.925373i | \(0.376248\pi\) | |||||||
\(542\) | −0.531958 | + | 0.921379i | −0.0228496 | + | 0.0395766i | ||||
\(543\) | 12.8167 | + | 22.1991i | 0.550015 | + | 0.952654i | ||||
\(544\) | −0.334734 | − | 0.579776i | −0.0143516 | − | 0.0248577i | ||||
\(545\) | 4.78890 | 0.205134 | ||||||||
\(546\) | 2.34861 | + | 4.06792i | 0.100511 | + | 0.174091i | ||||
\(547\) | −24.8444 | −1.06227 | −0.531135 | − | 0.847287i | \(-0.678234\pi\) | ||||
−0.531135 | + | 0.847287i | \(0.678234\pi\) | |||||||
\(548\) | 0.848612 | + | 1.46984i | 0.0362509 | + | 0.0627884i | ||||
\(549\) | −1.00000 | − | 1.73205i | −0.0426790 | − | 0.0739221i | ||||
\(550\) | 3.65139 | − | 6.32439i | 0.155696 | − | 0.269673i | ||||
\(551\) | 13.1833 | 0.561629 | ||||||||
\(552\) | −4.50000 | + | 7.79423i | −0.191533 | + | 0.331744i | ||||
\(553\) | −4.60555 | + | 7.97705i | −0.195848 | + | 0.339219i | ||||
\(554\) | 26.5694 | 1.12883 | ||||||||
\(555\) | −1.80278 | + | 3.12250i | −0.0765236 | + | 0.132543i | ||||
\(556\) | 2.05971 | + | 3.56753i | 0.0873514 | + | 0.151297i | ||||
\(557\) | −2.80278 | − | 4.85455i | −0.118757 | − | 0.205694i | 0.800518 | − | 0.599309i | \(-0.204558\pi\) |
−0.919276 | + | 0.393615i | \(0.871224\pi\) | |||||||
\(558\) | 10.4222 | 0.441207 | ||||||||
\(559\) | −7.59167 | + | 13.1492i | −0.321094 | + | 0.556150i | ||||
\(560\) | −3.30278 | −0.139568 | ||||||||
\(561\) | 1.10555 | + | 1.91487i | 0.0466764 | + | 0.0808459i | ||||
\(562\) | 3.90833 | + | 6.76942i | 0.164863 | + | 0.285551i | ||||
\(563\) | 9.71110 | − | 16.8201i | 0.409274 | − | 0.708884i | −0.585534 | − | 0.810648i | \(-0.699115\pi\) |
0.994809 | + | 0.101764i | \(0.0324486\pi\) | |||||||
\(564\) | 1.57779 | 0.0664372 | ||||||||
\(565\) | 2.80278 | − | 4.85455i | 0.117914 | − | 0.204232i | ||||
\(566\) | −3.25694 | + | 5.64118i | −0.136899 | + | 0.237117i | ||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −25.2250 | + | 43.6909i | −1.05842 | + | 1.83323i | ||||
\(569\) | −0.711103 | − | 1.23167i | −0.0298110 | − | 0.0516341i | 0.850735 | − | 0.525595i | \(-0.176157\pi\) |
−0.880546 | + | 0.473961i | \(0.842824\pi\) | |||||||
\(570\) | 1.04584 | + | 1.81144i | 0.0438053 | + | 0.0758730i | ||||
\(571\) | −36.8444 | −1.54189 | −0.770945 | − | 0.636901i | \(-0.780216\pi\) | ||||
−0.770945 | + | 0.636901i | \(0.780216\pi\) | |||||||
\(572\) | 6.11943 | 0.255866 | ||||||||
\(573\) | −4.81665 | −0.201219 | ||||||||
\(574\) | 1.95416 | + | 3.38471i | 0.0815652 | + | 0.141275i | ||||
\(575\) | 1.50000 | + | 2.59808i | 0.0625543 | + | 0.108347i | ||||
\(576\) | 8.81665 | − | 15.2709i | 0.367361 | − | 0.636287i | ||||
\(577\) | 29.6333 | 1.23365 | 0.616825 | − | 0.787100i | \(-0.288418\pi\) | ||||
0.616825 | + | 0.787100i | \(0.288418\pi\) | |||||||
\(578\) | 10.9722 | − | 19.0045i | 0.456385 | − | 0.790482i | ||||
\(579\) | −4.19722 | + | 7.26981i | −0.174431 | + | 0.302123i | ||||
\(580\) | 2.48612 | 0.103231 | ||||||||
\(581\) | 2.60555 | − | 4.51295i | 0.108096 | − | 0.187229i | ||||
\(582\) | 10.1653 | + | 17.6068i | 0.421364 | + | 0.729824i | ||||
\(583\) | 31.4222 | + | 54.4249i | 1.30137 | + | 2.25405i | ||||
\(584\) | 45.6333 | 1.88832 | ||||||||
\(585\) | −3.60555 | + | 6.24500i | −0.149071 | + | 0.258199i | ||||
\(586\) | 22.9361 | 0.947481 | ||||||||
\(587\) | 2.28890 | + | 3.96449i | 0.0944729 | + | 0.163632i | 0.909389 | − | 0.415948i | \(-0.136550\pi\) |
−0.814916 | + | 0.579580i | \(0.803217\pi\) | |||||||
\(588\) | −0.908327 | − | 1.57327i | −0.0374588 | − | 0.0648805i | ||||
\(589\) | 3.21110 | − | 5.56179i | 0.132311 | − | 0.229170i | ||||
\(590\) | −14.0917 | −0.580145 | ||||||||
\(591\) | −11.4083 | + | 19.7598i | −0.469276 | + | 0.812810i | ||||
\(592\) | −5.95416 | + | 10.3129i | −0.244715 | + | 0.423858i | ||||
\(593\) | 35.2111 | 1.44595 | 0.722973 | − | 0.690876i | \(-0.242775\pi\) | ||||
0.722973 | + | 0.690876i | \(0.242775\pi\) | |||||||
\(594\) | −18.2569 | + | 31.6219i | −0.749091 | + | 1.29746i | ||||
\(595\) | −0.197224 | − | 0.341603i | −0.00808541 | − | 0.0140043i | ||||
\(596\) | 0.454163 | + | 0.786634i | 0.0186033 | + | 0.0322218i | ||||
\(597\) | −8.81665 | −0.360842 | ||||||||
\(598\) | 7.04584 | − | 12.2037i | 0.288126 | − | 0.499048i | ||||
\(599\) | −6.78890 | −0.277387 | −0.138693 | − | 0.990335i | \(-0.544290\pi\) | ||||
−0.138693 | + | 0.990335i | \(0.544290\pi\) | |||||||
\(600\) | 1.50000 | + | 2.59808i | 0.0612372 | + | 0.106066i | ||||
\(601\) | −14.1056 | − | 24.4315i | −0.575377 | − | 0.996583i | −0.996001 | − | 0.0893475i | \(-0.971522\pi\) |
0.420623 | − | 0.907235i | \(-0.361811\pi\) | |||||||
\(602\) | 2.74306 | − | 4.75112i | 0.111799 | − | 0.193641i | ||||
\(603\) | 14.0000 | 0.570124 | ||||||||
\(604\) | 2.00000 | − | 3.46410i | 0.0813788 | − | 0.140952i | ||||
\(605\) | 10.2111 | − | 17.6861i | 0.415140 | − | 0.719044i | ||||
\(606\) | −11.7250 | −0.476295 | ||||||||
\(607\) | 9.89445 | − | 17.1377i | 0.401603 | − | 0.695597i | −0.592316 | − | 0.805706i | \(-0.701786\pi\) |
0.993920 | + | 0.110108i | \(0.0351197\pi\) | |||||||
\(608\) | −1.36249 | − | 2.35990i | −0.0552563 | − | 0.0957067i | ||||
\(609\) | 4.10555 | + | 7.11102i | 0.166365 | + | 0.288153i | ||||
\(610\) | 1.30278 | 0.0527478 | ||||||||
\(611\) | −18.7889 | −0.760117 | ||||||||
\(612\) | 0.238859 | 0.00965530 | ||||||||
\(613\) | −0.802776 | − | 1.39045i | −0.0324238 | − | 0.0561597i | 0.849358 | − | 0.527817i | \(-0.176989\pi\) |
−0.881782 | + | 0.471657i | \(0.843656\pi\) | |||||||
\(614\) | 10.4222 | + | 18.0518i | 0.420606 | + | 0.728511i | ||||
\(615\) | 1.50000 | − | 2.59808i | 0.0604858 | − | 0.104765i | ||||
\(616\) | −16.8167 | −0.677562 | ||||||||
\(617\) | −13.2250 | + | 22.9063i | −0.532418 | + | 0.922174i | 0.466866 | + | 0.884328i | \(0.345383\pi\) |
−0.999284 | + | 0.0378463i | \(0.987950\pi\) | |||||||
\(618\) | 2.60555 | − | 4.51295i | 0.104811 | − | 0.181537i | ||||
\(619\) | −14.4222 | −0.579677 | −0.289839 | − | 0.957076i | \(-0.593602\pi\) | ||||
−0.289839 | + | 0.957076i | \(0.593602\pi\) | |||||||
\(620\) | 0.605551 | − | 1.04885i | 0.0243195 | − | 0.0421227i | ||||
\(621\) | −7.50000 | − | 12.9904i | −0.300965 | − | 0.521286i | ||||
\(622\) | −3.39445 | − | 5.87936i | −0.136105 | − | 0.235741i | ||||
\(623\) | −8.21110 | −0.328971 | ||||||||
\(624\) | 5.95416 | − | 10.3129i | 0.238357 | − | 0.412847i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −9.11943 | − | 15.7953i | −0.364486 | − | 0.631308i | ||||
\(627\) | 4.50000 | + | 7.79423i | 0.179713 | + | 0.311272i | ||||
\(628\) | −0.486122 | + | 0.841988i | −0.0193984 | + | 0.0335990i | ||||
\(629\) | −1.42221 | −0.0567070 | ||||||||
\(630\) | 1.30278 | − | 2.25647i | 0.0519038 | − | 0.0899001i | ||||
\(631\) | −0.0138782 | + | 0.0240377i | −0.000552482 | + | 0.000956927i | −0.866302 | − | 0.499521i | \(-0.833509\pi\) |
0.865749 | + | 0.500478i | \(0.166843\pi\) | |||||||
\(632\) | 27.6333 | 1.09919 | ||||||||
\(633\) | 8.19722 | − | 14.1980i | 0.325810 | − | 0.564320i | ||||
\(634\) | −3.90833 | − | 6.76942i | −0.155219 | − | 0.268848i | ||||
\(635\) | 5.10555 | + | 8.84307i | 0.202608 | + | 0.350927i | ||||
\(636\) | −3.39445 | −0.134599 | ||||||||
\(637\) | 10.8167 | + | 18.7350i | 0.428571 | + | 0.742307i | ||||
\(638\) | −59.9638 | −2.37399 | ||||||||
\(639\) | −16.8167 | − | 29.1273i | −0.665257 | − | 1.15226i | ||||
\(640\) | 4.04584 | + | 7.00759i | 0.159926 | + | 0.276999i | ||||
\(641\) | 9.71110 | − | 16.8201i | 0.383565 | − | 0.664355i | −0.608004 | − | 0.793934i | \(-0.708029\pi\) |
0.991569 | + | 0.129579i | \(0.0413627\pi\) | |||||||
\(642\) | −10.6972 | −0.422186 | ||||||||
\(643\) | 20.3167 | − | 35.1895i | 0.801211 | − | 1.38774i | −0.117609 | − | 0.993060i | \(-0.537523\pi\) |
0.918820 | − | 0.394678i | \(-0.129144\pi\) | |||||||
\(644\) | 0.454163 | − | 0.786634i | 0.0178965 | − | 0.0309977i | ||||
\(645\) | −4.21110 | −0.165812 | ||||||||
\(646\) | −0.412529 | + | 0.714521i | −0.0162307 | + | 0.0281125i | ||||
\(647\) | −5.28890 | − | 9.16064i | −0.207928 | − | 0.360142i | 0.743134 | − | 0.669143i | \(-0.233339\pi\) |
−0.951062 | + | 0.309001i | \(0.900005\pi\) | |||||||
\(648\) | 1.50000 | + | 2.59808i | 0.0589256 | + | 0.102062i | ||||
\(649\) | −60.6333 | −2.38007 | ||||||||
\(650\) | −2.34861 | − | 4.06792i | −0.0921201 | − | 0.159557i | ||||
\(651\) | 4.00000 | 0.156772 | ||||||||
\(652\) | −2.75694 | − | 4.77516i | −0.107970 | − | 0.187010i | ||||
\(653\) | 14.4083 | + | 24.9560i | 0.563841 | + | 0.976602i | 0.997156 | + | 0.0753594i | \(0.0240104\pi\) |
−0.433315 | + | 0.901243i | \(0.642656\pi\) | |||||||
\(654\) | 3.11943 | − | 5.40301i | 0.121979 | − | 0.211274i | ||||
\(655\) | 6.78890 | 0.265264 | ||||||||
\(656\) | 4.95416 | − | 8.58086i | 0.193428 | − | 0.335026i | ||||
\(657\) | −15.2111 | + | 26.3464i | −0.593442 | + | 1.02787i | ||||
\(658\) | 6.78890 | 0.264659 | ||||||||
\(659\) | 6.59167 | − | 11.4171i | 0.256775 | − | 0.444748i | −0.708601 | − | 0.705609i | \(-0.750673\pi\) |
0.965376 | + | 0.260862i | \(0.0840067\pi\) | |||||||
\(660\) | 0.848612 | + | 1.46984i | 0.0330322 | + | 0.0572134i | ||||
\(661\) | −19.3167 | − | 33.4574i | −0.751331 | − | 1.30134i | −0.947178 | − | 0.320709i | \(-0.896079\pi\) |
0.195847 | − | 0.980634i | \(-0.437254\pi\) | |||||||
\(662\) | −33.9083 | −1.31788 | ||||||||
\(663\) | 1.42221 | 0.0552339 | ||||||||
\(664\) | −15.6333 | −0.606690 | ||||||||
\(665\) | −0.802776 | − | 1.39045i | −0.0311303 | − | 0.0539193i | ||||
\(666\) | −4.69722 | − | 8.13583i | −0.182014 | − | 0.315257i | ||||
\(667\) | 12.3167 | − | 21.3331i | 0.476903 | − | 0.826020i | ||||
\(668\) | −2.72498 | −0.105433 | ||||||||
\(669\) | −5.10555 | + | 8.84307i | −0.197392 | + | 0.341893i | ||||
\(670\) | −4.55971 | + | 7.89766i | −0.176157 | + | 0.305113i | ||||
\(671\) | 5.60555 | 0.216400 | ||||||||
\(672\) | 0.848612 | − | 1.46984i | 0.0327359 | − | 0.0567003i | ||||
\(673\) | 5.19722 | + | 9.00186i | 0.200338 | + | 0.346996i | 0.948637 | − | 0.316365i | \(-0.102463\pi\) |
−0.748299 | + | 0.663361i | \(0.769129\pi\) | |||||||
\(674\) | −11.4861 | − | 19.8945i | −0.442429 | − | 0.766309i | ||||
\(675\) | −5.00000 | −0.192450 | ||||||||
\(676\) | 1.96804 | − | 3.40875i | 0.0756939 | − | 0.131106i | ||||
\(677\) | 33.6333 | 1.29263 | 0.646317 | − | 0.763069i | \(-0.276309\pi\) | ||||
0.646317 | + | 0.763069i | \(0.276309\pi\) | |||||||
\(678\) | −3.65139 | − | 6.32439i | −0.140231 | − | 0.242887i | ||||
\(679\) | −7.80278 | − | 13.5148i | −0.299443 | − | 0.518651i | ||||
\(680\) | −0.591673 | + | 1.02481i | −0.0226896 | + | 0.0392996i | ||||
\(681\) | 1.42221 | 0.0544990 | ||||||||
\(682\) | −14.6056 | + | 25.2976i | −0.559275 | + | 0.968694i | ||||
\(683\) | −10.8944 | + | 18.8697i | −0.416864 | + | 0.722030i | −0.995622 | − | 0.0934691i | \(-0.970204\pi\) |
0.578758 | + | 0.815500i | \(0.303538\pi\) | |||||||
\(684\) | 0.972244 | 0.0371747 | ||||||||
\(685\) | 2.80278 | − | 4.85455i | 0.107089 | − | 0.185483i | ||||
\(686\) | −8.46804 | − | 14.6671i | −0.323311 | − | 0.559992i | ||||
\(687\) | −7.00000 | − | 12.1244i | −0.267067 | − | 0.462573i | ||||
\(688\) | −13.9083 | −0.530250 | ||||||||
\(689\) | 40.4222 | 1.53996 | ||||||||
\(690\) | 3.90833 | 0.148787 | ||||||||
\(691\) | −3.01388 | − | 5.22019i | −0.114653 | − | 0.198585i | 0.802988 | − | 0.595995i | \(-0.203242\pi\) |
−0.917641 | + | 0.397410i | \(0.869909\pi\) | |||||||
\(692\) | −2.54584 | − | 4.40952i | −0.0967782 | − | 0.167625i | ||||
\(693\) | 5.60555 | − | 9.70910i | 0.212937 | − | 0.368818i | ||||
\(694\) | 26.3305 | 0.999493 | ||||||||
\(695\) | 6.80278 | − | 11.7828i | 0.258044 | − | 0.446945i | ||||
\(696\) | 12.3167 | − | 21.3331i | 0.466862 | − | 0.808628i | ||||
\(697\) | 1.18335 | 0.0448224 | ||||||||
\(698\) | 11.8625 | − | 20.5464i | 0.449002 | − | 0.777694i | ||||
\(699\) | −0.394449 | − | 0.683205i | −0.0149194 | − | 0.0258412i | ||||
\(700\) | −0.151388 | − | 0.262211i | −0.00572192 | − | 0.00991066i | ||||
\(701\) | −7.57779 | −0.286209 | −0.143105 | − | 0.989708i | \(-0.545709\pi\) | ||||
−0.143105 | + | 0.989708i | \(0.545709\pi\) | |||||||
\(702\) | 11.7431 | + | 20.3396i | 0.443213 | + | 0.767668i | ||||
\(703\) | −5.78890 | −0.218332 | ||||||||
\(704\) | 24.7111 | + | 42.8009i | 0.931335 | + | 1.61312i | ||||
\(705\) | −2.60555 | − | 4.51295i | −0.0981307 | − | 0.169967i | ||||
\(706\) | 3.13751 | − | 5.43433i | 0.118082 | − | 0.204524i | ||||
\(707\) | 9.00000 | 0.338480 | ||||||||
\(708\) | 1.63751 | − | 2.83625i | 0.0615414 | − | 0.106593i | ||||
\(709\) | −21.9222 | + | 37.9704i | −0.823306 | + | 1.42601i | 0.0799016 | + | 0.996803i | \(0.474539\pi\) |
−0.903207 | + | 0.429205i | \(0.858794\pi\) | |||||||
\(710\) | 21.9083 | 0.822205 | ||||||||
\(711\) | −9.21110 | + | 15.9541i | −0.345443 | + | 0.598325i | ||||
\(712\) | 12.3167 | + | 21.3331i | 0.461586 | + | 0.799491i | ||||
\(713\) | −6.00000 | − | 10.3923i | −0.224702 | − | 0.389195i | ||||
\(714\) | −0.513878 | −0.0192314 | ||||||||
\(715\) | −10.1056 | − | 17.5033i | −0.377926 | − | 0.654587i | ||||
\(716\) | −0.358288 | −0.0133899 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.78890 | + | 11.7587i | 0.253359 | + | 0.438831i | ||||
\(719\) | 9.19722 | − | 15.9301i | 0.342999 | − | 0.594091i | −0.641989 | − | 0.766713i | \(-0.721891\pi\) |
0.984988 | + | 0.172622i | \(0.0552241\pi\) | |||||||
\(720\) | −6.60555 | −0.246174 | ||||||||
\(721\) | −2.00000 | + | 3.46410i | −0.0744839 | + | 0.129010i | ||||
\(722\) | 10.6972 | − | 18.5281i | 0.398109 | − | 0.689546i | ||||
\(723\) | 16.2111 | 0.602897 | ||||||||
\(724\) | −3.88057 | + | 6.72135i | −0.144220 | + | 0.249797i | ||||
\(725\) | −4.10555 | − | 7.11102i | −0.152476 | − | 0.264097i | ||||
\(726\) | −13.3028 | − | 23.0411i | −0.493712 | − | 0.855135i | ||||
\(727\) | 42.4222 | 1.57335 | 0.786676 | − | 0.617366i | \(-0.211800\pi\) | ||||
0.786676 | + | 0.617366i | \(0.211800\pi\) | |||||||
\(728\) | −5.40833 | + | 9.36750i | −0.200446 | + | 0.347183i | ||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | −9.90833 | − | 17.1617i | −0.366724 | − | 0.635184i | ||||
\(731\) | −0.830532 | − | 1.43852i | −0.0307183 | − | 0.0532057i | ||||
\(732\) | −0.151388 | + | 0.262211i | −0.00559545 | + | 0.00969161i | ||||
\(733\) | 10.8444 | 0.400547 | 0.200274 | − | 0.979740i | \(-0.435817\pi\) | ||||
0.200274 | + | 0.979740i | \(0.435817\pi\) | |||||||
\(734\) | 11.3486 | − | 19.6564i | 0.418885 | − | 0.725530i | ||||
\(735\) | −3.00000 | + | 5.19615i | −0.110657 | + | 0.191663i | ||||
\(736\) | −5.09167 | −0.187682 | ||||||||
\(737\) | −19.6194 | + | 33.9818i | −0.722691 | + | 1.25174i | ||||
\(738\) | 3.90833 | + | 6.76942i | 0.143868 | + | 0.249186i | ||||
\(739\) | 14.1972 | + | 24.5903i | 0.522253 | + | 0.904569i | 0.999665 | + | 0.0258895i | \(0.00824179\pi\) |
−0.477411 | + | 0.878680i | \(0.658425\pi\) | |||||||
\(740\) | −1.09167 | −0.0401307 | ||||||||
\(741\) | 5.78890 | 0.212660 | ||||||||
\(742\) | −14.6056 | −0.536187 | ||||||||
\(743\) | 3.31665 | + | 5.74461i | 0.121676 | + | 0.210749i | 0.920429 | − | 0.390910i | \(-0.127840\pi\) |
−0.798753 | + | 0.601660i | \(0.794506\pi\) | |||||||
\(744\) | −6.00000 | − | 10.3923i | −0.219971 | − | 0.381000i | ||||
\(745\) | 1.50000 | − | 2.59808i | 0.0549557 | − | 0.0951861i | ||||
\(746\) | −35.9638 | −1.31673 | ||||||||
\(747\) | 5.21110 | − | 9.02589i | 0.190664 | − | 0.330240i | ||||
\(748\) | −0.334734 | + | 0.579776i | −0.0122391 | + | 0.0211987i | ||||
\(749\) | 8.21110 | 0.300027 | ||||||||
\(750\) | 0.651388 | − | 1.12824i | 0.0237853 | − | 0.0411974i | ||||
\(751\) | 9.22498 | + | 15.9781i | 0.336624 | + | 0.583050i | 0.983795 | − | 0.179294i | \(-0.0573814\pi\) |
−0.647171 | + | 0.762345i | \(0.724048\pi\) | |||||||
\(752\) | −8.60555 | − | 14.9053i | −0.313812 | − | 0.543539i | ||||
\(753\) | −28.8167 | −1.05014 | ||||||||
\(754\) | −19.2847 | + | 33.4021i | −0.702307 | + | 1.21643i | ||||
\(755\) | −13.2111 | −0.480801 | ||||||||
\(756\) | 0.756939 | + | 1.31106i | 0.0275296 | + | 0.0476827i | ||||
\(757\) | 10.4083 | + | 18.0278i | 0.378297 | + | 0.655230i | 0.990815 | − | 0.135227i | \(-0.0431764\pi\) |
−0.612518 | + | 0.790457i | \(0.709843\pi\) | |||||||
\(758\) | −1.55971 | + | 2.70151i | −0.0566514 | + | 0.0981231i | ||||
\(759\) | 16.8167 | 0.610406 | ||||||||
\(760\) | −2.40833 | + | 4.17134i | −0.0873592 | + | 0.151311i | ||||
\(761\) | 12.3167 | − | 21.3331i | 0.446478 | − | 0.773323i | −0.551676 | − | 0.834059i | \(-0.686011\pi\) |
0.998154 | + | 0.0607356i | \(0.0193447\pi\) | |||||||
\(762\) | 13.3028 | 0.481909 | ||||||||
\(763\) | −2.39445 | + | 4.14731i | −0.0866849 | + | 0.150143i | ||||
\(764\) | −0.729183 | − | 1.26298i | −0.0263809 | − | 0.0456931i | ||||
\(765\) | −0.394449 | − | 0.683205i | −0.0142613 | − | 0.0247013i | ||||
\(766\) | 24.2750 | 0.877092 | ||||||||
\(767\) | −19.5000 | + | 33.7750i | −0.704104 | + | 1.21954i | ||||
\(768\) | −7.09167 | −0.255899 | ||||||||
\(769\) | −5.50000 | − | 9.52628i | −0.198335 | − | 0.343526i | 0.749654 | − | 0.661830i | \(-0.230220\pi\) |
−0.947989 | + | 0.318304i | \(0.896887\pi\) | |||||||
\(770\) | 3.65139 | + | 6.32439i | 0.131587 | + | 0.227915i | ||||
\(771\) | 11.8028 | − | 20.4430i | 0.425067 | − | 0.736237i | ||||
\(772\) | −2.54163 | −0.0914754 | ||||||||
\(773\) | −14.8028 | + | 25.6392i | −0.532419 | + | 0.922176i | 0.466865 | + | 0.884329i | \(0.345384\pi\) |
−0.999284 | + | 0.0378477i | \(0.987950\pi\) | |||||||
\(774\) | 5.48612 | − | 9.50224i | 0.197195 | − | 0.341551i | ||||
\(775\) | −4.00000 | −0.143684 | ||||||||
\(776\) | −23.4083 | + | 40.5444i | −0.840310 | + | 1.45546i | ||||
\(777\) | −1.80278 | − | 3.12250i | −0.0646742 | − | 0.112019i | ||||
\(778\) | 0.513878 | + | 0.890063i | 0.0184234 | + | 0.0319103i | ||||
\(779\) | 4.81665 | 0.172575 | ||||||||
\(780\) | 1.09167 | 0.0390882 | ||||||||
\(781\) | 94.2666 | 3.37312 | ||||||||
\(782\) | 0.770817 | + | 1.33509i | 0.0275644 | + | 0.0477429i | ||||
\(783\) | 20.5278 | + | 35.5551i | 0.733602 | + | 1.27064i | ||||
\(784\) | −9.90833 | + | 17.1617i | −0.353869 | + | 0.612919i | ||||
\(785\) | 3.21110 | 0.114609 | ||||||||
\(786\) | 4.42221 | − | 7.65948i | 0.157735 | − | 0.273205i | ||||
\(787\) | 14.3167 | − | 24.7972i | 0.510334 | − | 0.883924i | −0.489595 | − | 0.871950i | \(-0.662855\pi\) |
0.999928 | − | 0.0119736i | \(-0.00381140\pi\) | |||||||
\(788\) | −6.90833 | −0.246099 | ||||||||
\(789\) | −13.1056 | + | 22.6995i | −0.466570 | + | 0.808123i | ||||
\(790\) | −6.00000 | − | 10.3923i | −0.213470 | − | 0.369742i | ||||
\(791\) | 2.80278 | + | 4.85455i | 0.0996552 | + | 0.172608i | ||||
\(792\) | −33.6333 | −1.19511 | ||||||||
\(793\) | 1.80278 | − | 3.12250i | 0.0640184 | − | 0.110883i | ||||
\(794\) | −18.2750 | −0.648556 | ||||||||
\(795\) | 5.60555 | + | 9.70910i | 0.198808 | + | 0.344346i | ||||
\(796\) | −1.33473 | − | 2.31183i | −0.0473084 | − | 0.0819405i | ||||
\(797\) | −25.2250 | + | 43.6909i | −0.893515 | + | 1.54761i | −0.0578825 | + | 0.998323i | \(0.518435\pi\) |
−0.835632 | + | 0.549289i | \(0.814898\pi\) | |||||||
\(798\) | −2.09167 | −0.0740444 | ||||||||
\(799\) | 1.02776 | − | 1.78013i | 0.0363594 | − | 0.0629763i | ||||
\(800\) | −0.848612 | + | 1.46984i | −0.0300030 | + | 0.0519667i | ||||
\(801\) | −16.4222 | −0.580250 | ||||||||
\(802\) | 1.44029 | − | 2.49465i | 0.0508582 | − | 0.0880891i | ||||
\(803\) | −42.6333 | − | 73.8431i | −1.50450 | − | 2.60586i | ||||
\(804\) | −1.05971 | − | 1.83548i | −0.0373733 | − | 0.0647324i | ||||
\(805\) | −3.00000 | −0.105736 | ||||||||
\(806\) | 9.39445 | + | 16.2717i | 0.330905 | + | 0.573145i | ||||
\(807\) | −9.00000 | −0.316815 | ||||||||
\(808\) | −13.5000 | − | 23.3827i | −0.474928 | − | 0.822600i | ||||
\(809\) | −8.52776 | − | 14.7705i | −0.299820 | − | 0.519303i | 0.676275 | − | 0.736650i | \(-0.263593\pi\) |
−0.976095 | + | 0.217346i | \(0.930260\pi\) | |||||||
\(810\) | 0.651388 | − | 1.12824i | 0.0228874 | − | 0.0396422i | ||||
\(811\) | −17.5778 | −0.617240 | −0.308620 | − | 0.951185i | \(-0.599867\pi\) | ||||
−0.308620 | + | 0.951185i | \(0.599867\pi\) | |||||||
\(812\) | −1.24306 | + | 2.15304i | −0.0436229 | + | 0.0755571i | ||||
\(813\) | −0.408327 | + | 0.707243i | −0.0143207 | + | 0.0248041i | ||||
\(814\) | 26.3305 | 0.922885 | ||||||||
\(815\) | −9.10555 | + | 15.7713i | −0.318954 | + | 0.552444i | ||||
\(816\) | 0.651388 | + | 1.12824i | 0.0228031 | + | 0.0394962i | ||||
\(817\) | −3.38057 | − | 5.85532i | −0.118271 | − | 0.204852i | ||||
\(818\) | −8.09167 | −0.282919 | ||||||||
\(819\) | −3.60555 | − | 6.24500i | −0.125988 | − | 0.218218i | ||||
\(820\) | 0.908327 | 0.0317202 | ||||||||
\(821\) | 3.71110 | + | 6.42782i | 0.129518 | + | 0.224332i | 0.923490 | − | 0.383622i | \(-0.125324\pi\) |
−0.793972 | + | 0.607955i | \(0.791990\pi\) | |||||||
\(822\) | −3.65139 | − | 6.32439i | −0.127357 | − | 0.220588i | ||||
\(823\) | −13.3167 | + | 23.0651i | −0.464189 | + | 0.804000i | −0.999165 | − | 0.0408682i | \(-0.986988\pi\) |
0.534975 | + | 0.844868i | \(0.320321\pi\) | |||||||
\(824\) | 12.0000 | 0.418040 | ||||||||
\(825\) | 2.80278 | − | 4.85455i | 0.0975801 | − | 0.169014i | ||||
\(826\) | 7.04584 | − | 12.2037i | 0.245156 | − | 0.424623i | ||||
\(827\) | −13.5778 | −0.472146 | −0.236073 | − | 0.971735i | \(-0.575860\pi\) | ||||
−0.236073 | + | 0.971735i | \(0.575860\pi\) | |||||||
\(828\) | 0.908327 | − | 1.57327i | 0.0315665 | − | 0.0546749i | ||||
\(829\) | −0.288897 | − | 0.500385i | −0.0100338 | − | 0.0173791i | 0.860965 | − | 0.508664i | \(-0.169861\pi\) |
−0.870999 | + | 0.491285i | \(0.836527\pi\) | |||||||
\(830\) | 3.39445 | + | 5.87936i | 0.117823 | + | 0.204075i | ||||
\(831\) | 20.3944 | 0.707476 | ||||||||
\(832\) | 31.7889 | 1.10208 | ||||||||
\(833\) | −2.36669 | −0.0820010 | ||||||||
\(834\) | −8.86249 | − | 15.3503i | −0.306883 | − | 0.531537i | ||||
\(835\) | 4.50000 | + | 7.79423i | 0.155729 | + | 0.269730i | ||||
\(836\) | −1.36249 | + | 2.35990i | −0.0471227 | + | 0.0816189i | ||||
\(837\) | 20.0000 | 0.691301 | ||||||||
\(838\) | 21.6514 | − | 37.5013i | 0.747935 | − | 1.29546i | ||||
\(839\) | −8.01388 | + | 13.8804i | −0.276670 | + | 0.479206i | −0.970555 | − | 0.240879i | \(-0.922564\pi\) |
0.693885 | + | 0.720086i | \(0.255897\pi\) | |||||||
\(840\) | −3.00000 | −0.103510 | ||||||||
\(841\) | −19.2111 | + | 33.2746i | −0.662452 | + | 1.14740i | ||||
\(842\) | −2.33053 | − | 4.03660i | −0.0803154 | − | 0.139110i | ||||
\(843\) | 3.00000 | + | 5.19615i | 0.103325 | + | 0.178965i | ||||
\(844\) | 4.96384 | 0.170862 | ||||||||
\(845\) | −13.0000 | −0.447214 | ||||||||
\(846\) | 13.5778 | 0.466814 | ||||||||
\(847\) | 10.2111 | + | 17.6861i | 0.350858 | + | 0.607703i | ||||
\(848\) | 18.5139 | + | 32.0670i | 0.635769 | + | 1.10118i | ||||
\(849\) | −2.50000 | + | 4.33013i | −0.0857998 | + | 0.148610i | ||||
\(850\) | 0.513878 | 0.0176259 | ||||||||
\(851\) | −5.40833 | + | 9.36750i | −0.185395 | + | 0.321114i | ||||
\(852\) | −2.54584 | + | 4.40952i | −0.0872189 | + | 0.151068i | ||||
\(853\) | 32.7889 | 1.12267 | 0.561335 | − | 0.827589i | \(-0.310288\pi\) | ||||
0.561335 | + | 0.827589i | \(0.310288\pi\) | |||||||
\(854\) | −0.651388 | + | 1.12824i | −0.0222900 | + | 0.0386075i | ||||
\(855\) | −1.60555 | − | 2.78090i | −0.0549087 | − | 0.0951046i | ||||
\(856\) | −12.3167 | − | 21.3331i | −0.420975 | − | 0.729149i | ||||
\(857\) | 6.00000 | 0.204956 | 0.102478 | − | 0.994735i | \(-0.467323\pi\) | ||||
0.102478 | + | 0.994735i | \(0.467323\pi\) | |||||||
\(858\) | −26.3305 | −0.898910 | ||||||||
\(859\) | 25.2111 | 0.860192 | 0.430096 | − | 0.902783i | \(-0.358480\pi\) | ||||
0.430096 | + | 0.902783i | \(0.358480\pi\) | |||||||
\(860\) | −0.637510 | − | 1.10420i | −0.0217389 | − | 0.0376529i | ||||
\(861\) | 1.50000 | + | 2.59808i | 0.0511199 | + | 0.0885422i | ||||
\(862\) | 13.8347 | − | 23.9625i | 0.471213 | − | 0.816165i | ||||
\(863\) | 36.0000 | 1.22545 | 0.612727 | − | 0.790295i | \(-0.290072\pi\) | ||||
0.612727 | + | 0.790295i | \(0.290072\pi\) | |||||||
\(864\) | 4.24306 | − | 7.34920i | 0.144352 | − | 0.250025i | ||||
\(865\) | −8.40833 | + | 14.5636i | −0.285892 | + | 0.495179i | ||||
\(866\) | −4.69722 | −0.159618 | ||||||||
\(867\) | 8.42221 | − | 14.5877i | 0.286033 | − | 0.495424i | ||||
\(868\) | 0.605551 | + | 1.04885i | 0.0205537 | + | 0.0356001i | ||||
\(869\) | −25.8167 | − | 44.7158i | −0.875770 | − | 1.51688i | ||||
\(870\) | −10.6972 | −0.362670 | ||||||||
\(871\) | 12.6194 | + | 21.8575i | 0.427593 | + | 0.740613i | ||||
\(872\) | 14.3667 | 0.486518 | ||||||||
\(873\) | −15.6056 | − | 27.0296i | −0.528168 | − | 0.914814i | ||||
\(874\) | 3.13751 | + | 5.43433i | 0.106128 | + | 0.183819i | ||||
\(875\) | −0.500000 | + | 0.866025i | −0.0169031 | + | 0.0292770i | ||||
\(876\) | 4.60555 | 0.155607 | ||||||||
\(877\) | 19.0139 | − | 32.9330i | 0.642053 | − | 1.11207i | −0.342921 | − | 0.939364i | \(-0.611416\pi\) |
0.984974 | − | 0.172704i | \(-0.0552504\pi\) | |||||||
\(878\) | −15.1375 | + | 26.2189i | −0.510866 | + | 0.884846i | ||||
\(879\) | 17.6056 | 0.593821 | ||||||||
\(880\) | 9.25694 | − | 16.0335i | 0.312051 | − | 0.540489i | ||||
\(881\) | −17.9222 | − | 31.0422i | −0.603814 | − | 1.04584i | −0.992238 | − | 0.124356i | \(-0.960313\pi\) |
0.388423 | − | 0.921481i | \(-0.373020\pi\) | |||||||
\(882\) | −7.81665 | − | 13.5388i | −0.263200 | − | 0.455877i | ||||
\(883\) | −31.6333 | −1.06455 | −0.532273 | − | 0.846573i | \(-0.678662\pi\) | ||||
−0.532273 | + | 0.846573i | \(0.678662\pi\) | |||||||
\(884\) | 0.215305 | + | 0.372918i | 0.00724147 | + | 0.0125426i | ||||
\(885\) | −10.8167 | −0.363598 | ||||||||
\(886\) | 14.6056 | + | 25.2976i | 0.490683 | + | 0.849888i | ||||
\(887\) | −17.5278 | − | 30.3590i | −0.588524 | − | 1.01935i | −0.994426 | − | 0.105437i | \(-0.966376\pi\) |
0.405901 | − | 0.913917i | \(-0.366958\pi\) | |||||||
\(888\) | −5.40833 | + | 9.36750i | −0.181492 | + | 0.314353i | ||||
\(889\) | −10.2111 | −0.342469 | ||||||||
\(890\) | 5.34861 | − | 9.26407i | 0.179286 | − | 0.310532i | ||||
\(891\) | 2.80278 | − | 4.85455i | 0.0938965 | − | 0.162634i | ||||
\(892\) | −3.09167 | −0.103517 | ||||||||
\(893\) | 4.18335 | − | 7.24577i | 0.139990 | − | 0.242470i | ||||
\(894\) | −1.95416 | − | 3.38471i | −0.0653570 | − | 0.113202i | ||||
\(895\) | 0.591673 | + | 1.02481i | 0.0197775 | + | 0.0342555i | ||||
\(896\) | −8.09167 | −0.270324 | ||||||||
\(897\) | 5.40833 | − | 9.36750i | 0.180579 | − | 0.312772i | ||||
\(898\) | −16.4584 | −0.549223 | ||||||||
\(899\) | 16.4222 | + | 28.4441i | 0.547711 | + | 0.948664i | ||||
\(900\) | −0.302776 | − | 0.524423i | −0.0100925 | − | 0.0174808i | ||||
\(901\) | −2.21110 | + | 3.82974i | −0.0736625 | + | 0.127587i | ||||
\(902\) | −21.9083 | −0.729467 | ||||||||
\(903\) | 2.10555 | − | 3.64692i | 0.0700684 | − | 0.121362i | ||||
\(904\) | 8.40833 | − | 14.5636i | 0.279657 | − | 0.484380i | ||||
\(905\) | 25.6333 | 0.852080 | ||||||||
\(906\) | −8.60555 | + | 14.9053i | −0.285900 | + | 0.495194i | ||||
\(907\) | −24.1333 | − | 41.8001i | −0.801333 | − | 1.38795i | −0.918739 | − | 0.394866i | \(-0.870791\pi\) |
0.117405 | − | 0.993084i | \(-0.462542\pi\) | |||||||
\(908\) | 0.215305 | + | 0.372918i | 0.00714513 | + | 0.0123757i | ||||
\(909\) | 18.0000 | 0.597022 | ||||||||
\(910\) | 4.69722 | 0.155711 | ||||||||
\(911\) | −36.0000 | −1.19273 | −0.596367 | − | 0.802712i | \(-0.703390\pi\) | ||||
−0.596367 | + | 0.802712i | \(0.703390\pi\) | |||||||
\(912\) | 2.65139 | + | 4.59234i | 0.0877962 | + | 0.152068i | ||||
\(913\) | 14.6056 | + | 25.2976i | 0.483373 | + | 0.837227i | ||||
\(914\) | 3.37637 | − | 5.84804i | 0.111680 | − | 0.193436i | ||||
\(915\) | 1.00000 | 0.0330590 | ||||||||
\(916\) | 2.11943 | − | 3.67096i | 0.0700279 | − | 0.121292i | ||||
\(917\) | −3.39445 | + | 5.87936i | −0.112095 | + | 0.194153i | ||||
\(918\) | −2.56939 | −0.0848025 | ||||||||
\(919\) | 8.59167 | − | 14.8812i | 0.283413 | − | 0.490886i | −0.688810 | − | 0.724942i | \(-0.741867\pi\) |
0.972223 | + | 0.234056i | \(0.0751999\pi\) | |||||||
\(920\) | 4.50000 | + | 7.79423i | 0.148361 | + | 0.256968i | ||||
\(921\) | 8.00000 | + | 13.8564i | 0.263609 | + | 0.456584i | ||||
\(922\) | 28.3860 | 0.934845 | ||||||||
\(923\) | 30.3167 | − | 52.5100i | 0.997885 | − | 1.72839i | ||||
\(924\) | −1.69722 | −0.0558346 | ||||||||
\(925\) | 1.80278 | + | 3.12250i | 0.0592749 | + | 0.102667i | ||||
\(926\) | 3.63331 | + | 6.29307i | 0.119398 | + | 0.206803i | ||||
\(927\) | −4.00000 | + | 6.92820i | −0.131377 | + | 0.227552i | ||||
\(928\) | 13.9361 | 0.457474 | ||||||||
\(929\) | −6.71110 | + | 11.6240i | −0.220184 | + | 0.381370i | −0.954864 | − | 0.297044i | \(-0.903999\pi\) |
0.734680 | + | 0.678414i | \(0.237332\pi\) | |||||||
\(930\) | −2.60555 | + | 4.51295i | −0.0854394 | + | 0.147985i | ||||
\(931\) | −9.63331 | −0.315719 | ||||||||
\(932\) | 0.119429 | − | 0.206858i | 0.00391204 | − | 0.00677586i | ||||
\(933\) | −2.60555 | − | 4.51295i | −0.0853019 | − | 0.147747i | ||||
\(934\) | −11.2111 | − | 19.4182i | −0.366838 | − | 0.635383i | ||||
\(935\) | 2.21110 | 0.0723108 | ||||||||
\(936\) | −10.8167 | + | 18.7350i | −0.353553 | + | 0.612372i | ||||
\(937\) | −46.4777 | −1.51836 | −0.759180 | − | 0.650880i | \(-0.774400\pi\) | ||||
−0.759180 | + | 0.650880i | \(0.774400\pi\) | |||||||
\(938\) | −4.55971 | − | 7.89766i | −0.148880 | − | 0.257868i | ||||
\(939\) | −7.00000 | − | 12.1244i | −0.228436 | − | 0.395663i | ||||
\(940\) | 0.788897 | − | 1.36641i | 0.0257310 | − | 0.0445674i | ||||
\(941\) | 33.6333 | 1.09641 | 0.548207 | − | 0.836343i | \(-0.315311\pi\) | ||||
0.548207 | + | 0.836343i | \(0.315311\pi\) | |||||||
\(942\) | 2.09167 | − | 3.62288i | 0.0681504 | − | 0.118040i | ||||
\(943\) | 4.50000 | − | 7.79423i | 0.146540 | − | 0.253815i | ||||
\(944\) | −35.7250 | −1.16275 | ||||||||
\(945\) | 2.50000 | − | 4.33013i | 0.0813250 | − | 0.140859i | ||||
\(946\) | 15.3764 | + | 26.6327i | 0.499929 | + | 0.865902i | ||||
\(947\) | −12.3167 | − | 21.3331i | −0.400237 | − | 0.693232i | 0.593517 | − | 0.804822i | \(-0.297739\pi\) |
−0.993754 | + | 0.111590i | \(0.964406\pi\) | |||||||
\(948\) | 2.78890 | 0.0905792 | ||||||||
\(949\) | −54.8444 | −1.78032 | ||||||||
\(950\) | 2.09167 | 0.0678628 | ||||||||
\(951\) | −3.00000 | − | 5.19615i | −0.0972817 | − | 0.168497i | ||||
\(952\) | −0.591673 | − | 1.02481i | −0.0191762 | − | 0.0332142i | ||||
\(953\) | −25.2250 | + | 43.6909i | −0.817117 | + | 1.41529i | 0.0906803 | + | 0.995880i | \(0.471096\pi\) |
−0.907798 | + | 0.419409i | \(0.862237\pi\) | |||||||
\(954\) | −29.2111 | −0.945744 | ||||||||
\(955\) | −2.40833 | + | 4.17134i | −0.0779316 | + | 0.134982i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −46.0278 | −1.48787 | ||||||||
\(958\) | 4.67914 | − | 8.10452i | 0.151176 | − | 0.261845i | ||||
\(959\) | 2.80278 | + | 4.85455i | 0.0905063 | + | 0.156762i | ||||
\(960\) | 4.40833 | + | 7.63545i | 0.142278 | + | 0.246433i | ||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 8.46804 | − | 14.6671i | 0.273021 | − | 0.472886i | ||||
\(963\) | 16.4222 | 0.529198 | ||||||||
\(964\) | 2.45416 | + | 4.25074i | 0.0790433 | + | 0.136907i | ||||
\(965\) | 4.19722 | + | 7.26981i | 0.135113 | + | 0.234023i | ||||
\(966\) | −1.95416 | + | 3.38471i | −0.0628742 | + | 0.108901i | ||||
\(967\) | 56.4777 | 1.81620 | 0.908100 | − | 0.418752i | \(-0.137532\pi\) | ||||
0.908100 | + | 0.418752i | \(0.137532\pi\) | |||||||
\(968\) | 30.6333 | − | 53.0584i | 0.984592 | − | 1.70536i | ||||
\(969\) | −0.316654 | + | 0.548461i | −0.0101724 | + | 0.0176191i | ||||
\(970\) | 20.3305 | 0.652774 | ||||||||
\(971\) | 3.98612 | − | 6.90417i | 0.127921 | − | 0.221565i | −0.794950 | − | 0.606675i | \(-0.792503\pi\) |
0.922871 | + | 0.385110i | \(0.125836\pi\) | |||||||
\(972\) | 2.42221 | + | 4.19538i | 0.0776923 | + | 0.134567i | ||||
\(973\) | 6.80278 | + | 11.7828i | 0.218087 | + | 0.377738i | ||||
\(974\) | −1.30278 | −0.0417436 | ||||||||
\(975\) | −1.80278 | − | 3.12250i | −0.0577350 | − | 0.100000i | ||||
\(976\) | 3.30278 | 0.105719 | ||||||||
\(977\) | −3.59167 | − | 6.22096i | −0.114908 | − | 0.199026i | 0.802835 | − | 0.596201i | \(-0.203324\pi\) |
−0.917743 | + | 0.397175i | \(0.869991\pi\) | |||||||
\(978\) | 11.8625 | + | 20.5464i | 0.379321 | + | 0.657003i | ||||
\(979\) | 23.0139 | − | 39.8612i | 0.735527 | − | 1.27397i | ||||
\(980\) | −1.81665 | −0.0580309 | ||||||||
\(981\) | −4.78890 | + | 8.29461i | −0.152898 | + | 0.264827i | ||||
\(982\) | −3.13751 | + | 5.43433i | −0.100122 | + | 0.173416i | ||||
\(983\) | −10.4222 | −0.332417 | −0.166208 | − | 0.986091i | \(-0.553152\pi\) | ||||
−0.166208 | + | 0.986091i | \(0.553152\pi\) | |||||||
\(984\) | 4.50000 | − | 7.79423i | 0.143455 | − | 0.248471i | ||||
\(985\) | 11.4083 | + | 19.7598i | 0.363500 | + | 0.629600i | ||||
\(986\) | −2.10975 | − | 3.65420i | −0.0671882 | − | 0.116373i | ||||
\(987\) | 5.21110 | 0.165871 | ||||||||
\(988\) | 0.876369 | + | 1.51791i | 0.0278810 | + | 0.0482913i | ||||
\(989\) | −12.6333 | −0.401716 | ||||||||
\(990\) | 7.30278 | + | 12.6488i | 0.232097 | + | 0.402005i | ||||
\(991\) | −1.98612 | − | 3.44006i | −0.0630912 | − | 0.109277i | 0.832754 | − | 0.553642i | \(-0.186763\pi\) |
−0.895846 | + | 0.444365i | \(0.853429\pi\) | |||||||
\(992\) | 3.39445 | − | 5.87936i | 0.107774 | − | 0.186670i | ||||
\(993\) | −26.0278 | −0.825966 | ||||||||
\(994\) | −10.9542 | + | 18.9732i | −0.347445 | + | 0.601792i | ||||
\(995\) | −4.40833 | + | 7.63545i | −0.139753 | + | 0.242060i | ||||
\(996\) | −1.57779 | −0.0499943 | ||||||||
\(997\) | −23.2250 | + | 40.2268i | −0.735543 | + | 1.27400i | 0.218942 | + | 0.975738i | \(0.429739\pi\) |
−0.954485 | + | 0.298259i | \(0.903594\pi\) | |||||||
\(998\) | 17.2111 | + | 29.8105i | 0.544808 | + | 0.943635i | ||||
\(999\) | −9.01388 | − | 15.6125i | −0.285186 | − | 0.493957i |
(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 | 65.2.e.b.16.1 | ✓ | 4 | |
3.2 | odd | 2 | 585.2.j.d.406.2 | 4 | |||
4.3 | odd | 2 | 1040.2.q.o.81.1 | 4 | |||
5.2 | odd | 4 | 325.2.o.b.224.3 | 8 | |||
5.3 | odd | 4 | 325.2.o.b.224.2 | 8 | |||
5.4 | even | 2 | 325.2.e.a.276.2 | 4 | |||
13.2 | odd | 12 | 845.2.c.d.506.2 | 4 | |||
13.3 | even | 3 | 845.2.a.c.1.2 | 2 | |||
13.4 | even | 6 | 845.2.e.d.191.2 | 4 | |||
13.5 | odd | 4 | 845.2.m.d.361.2 | 8 | |||
13.6 | odd | 12 | 845.2.m.d.316.3 | 8 | |||
13.7 | odd | 12 | 845.2.m.d.316.2 | 8 | |||
13.8 | odd | 4 | 845.2.m.d.361.3 | 8 | |||
13.9 | even | 3 | inner | 65.2.e.b.61.1 | yes | 4 | |
13.10 | even | 6 | 845.2.a.f.1.1 | 2 | |||
13.11 | odd | 12 | 845.2.c.d.506.3 | 4 | |||
13.12 | even | 2 | 845.2.e.d.146.2 | 4 | |||
39.23 | odd | 6 | 7605.2.a.bb.1.2 | 2 | |||
39.29 | odd | 6 | 7605.2.a.bg.1.1 | 2 | |||
39.35 | odd | 6 | 585.2.j.d.451.2 | 4 | |||
52.35 | odd | 6 | 1040.2.q.o.321.1 | 4 | |||
65.9 | even | 6 | 325.2.e.a.126.2 | 4 | |||
65.22 | odd | 12 | 325.2.o.b.74.2 | 8 | |||
65.29 | even | 6 | 4225.2.a.x.1.1 | 2 | |||
65.48 | odd | 12 | 325.2.o.b.74.3 | 8 | |||
65.49 | even | 6 | 4225.2.a.t.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.e.b.16.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
65.2.e.b.61.1 | yes | 4 | 13.9 | even | 3 | inner | |
325.2.e.a.126.2 | 4 | 65.9 | even | 6 | |||
325.2.e.a.276.2 | 4 | 5.4 | even | 2 | |||
325.2.o.b.74.2 | 8 | 65.22 | odd | 12 | |||
325.2.o.b.74.3 | 8 | 65.48 | odd | 12 | |||
325.2.o.b.224.2 | 8 | 5.3 | odd | 4 | |||
325.2.o.b.224.3 | 8 | 5.2 | odd | 4 | |||
585.2.j.d.406.2 | 4 | 3.2 | odd | 2 | |||
585.2.j.d.451.2 | 4 | 39.35 | odd | 6 | |||
845.2.a.c.1.2 | 2 | 13.3 | even | 3 | |||
845.2.a.f.1.1 | 2 | 13.10 | even | 6 | |||
845.2.c.d.506.2 | 4 | 13.2 | odd | 12 | |||
845.2.c.d.506.3 | 4 | 13.11 | odd | 12 | |||
845.2.e.d.146.2 | 4 | 13.12 | even | 2 | |||
845.2.e.d.191.2 | 4 | 13.4 | even | 6 | |||
845.2.m.d.316.2 | 8 | 13.7 | odd | 12 | |||
845.2.m.d.316.3 | 8 | 13.6 | odd | 12 | |||
845.2.m.d.361.2 | 8 | 13.5 | odd | 4 | |||
845.2.m.d.361.3 | 8 | 13.8 | odd | 4 | |||
1040.2.q.o.81.1 | 4 | 4.3 | odd | 2 | |||
1040.2.q.o.321.1 | 4 | 52.35 | odd | 6 | |||
4225.2.a.t.1.2 | 2 | 65.49 | even | 6 | |||
4225.2.a.x.1.1 | 2 | 65.29 | even | 6 | |||
7605.2.a.bb.1.2 | 2 | 39.23 | odd | 6 | |||
7605.2.a.bg.1.1 | 2 | 39.29 | odd | 6 |