Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(239,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.p (of order \(4\), 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: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + \cdots + 59049 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 281.3 | ||
Root | \(-1.01577 + 1.40293i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.281 |
Dual form | 546.2.p.c.239.3 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | 0.273767 | + | 1.71028i | 0.158059 | + | 0.987430i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −1.75112 | + | 1.75112i | −0.783124 | + | 0.783124i | −0.980357 | − | 0.197233i | \(-0.936804\pi\) |
0.197233 | + | 0.980357i | \(0.436804\pi\) | |||||||
\(6\) | −1.40293 | − | 1.01577i | −0.572744 | − | 0.414685i | ||||
\(7\) | 0.707107 | − | 0.707107i | 0.267261 | − | 0.267261i | ||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | −2.85010 | + | 0.936434i | −0.950035 | + | 0.312145i | ||||
\(10\) | − | 2.47645i | − | 0.783124i | ||||||
\(11\) | −2.12300 | − | 2.12300i | −0.640108 | − | 0.640108i | 0.310474 | − | 0.950582i | \(-0.399512\pi\) |
−0.950582 | + | 0.310474i | \(0.899512\pi\) | |||||||
\(12\) | 1.71028 | − | 0.273767i | 0.493715 | − | 0.0790296i | ||||
\(13\) | −3.47808 | − | 0.950237i | −0.964646 | − | 0.263548i | ||||
\(14\) | 1.00000i | 0.267261i | ||||||||
\(15\) | −3.47430 | − | 2.51550i | −0.897059 | − | 0.649499i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −3.03575 | −0.736277 | −0.368138 | − | 0.929771i | \(-0.620005\pi\) | ||||
−0.368138 | + | 0.929771i | \(0.620005\pi\) | |||||||
\(18\) | 1.35317 | − | 2.67749i | 0.318945 | − | 0.631090i | ||||
\(19\) | 2.63603 | + | 2.63603i | 0.604747 | + | 0.604747i | 0.941568 | − | 0.336822i | \(-0.109352\pi\) |
−0.336822 | + | 0.941568i | \(0.609352\pi\) | |||||||
\(20\) | 1.75112 | + | 1.75112i | 0.391562 | + | 0.391562i | ||||
\(21\) | 1.40293 | + | 1.01577i | 0.306145 | + | 0.221659i | ||||
\(22\) | 3.00237 | 0.640108 | ||||||||
\(23\) | −0.478247 | −0.0997215 | −0.0498607 | − | 0.998756i | \(-0.515878\pi\) | ||||
−0.0498607 | + | 0.998756i | \(0.515878\pi\) | |||||||
\(24\) | −1.01577 | + | 1.40293i | −0.207343 | + | 0.286372i | ||||
\(25\) | − | 1.13282i | − | 0.226565i | ||||||
\(26\) | 3.13129 | − | 1.78746i | 0.614097 | − | 0.350549i | ||||
\(27\) | −2.38183 | − | 4.61811i | −0.458383 | − | 0.888755i | ||||
\(28\) | −0.707107 | − | 0.707107i | −0.133631 | − | 0.133631i | ||||
\(29\) | − | 6.03691i | − | 1.12103i | −0.828145 | − | 0.560513i | \(-0.810604\pi\) | ||
0.828145 | − | 0.560513i | \(-0.189396\pi\) | |||||||
\(30\) | 4.23543 | − | 0.677971i | 0.773279 | − | 0.123780i | ||||
\(31\) | −2.07156 | − | 2.07156i | −0.372064 | − | 0.372064i | 0.496165 | − | 0.868228i | \(-0.334741\pi\) |
−0.868228 | + | 0.496165i | \(0.834741\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 3.04971 | − | 4.21213i | 0.530887 | − | 0.733237i | ||||
\(34\) | 2.14660 | − | 2.14660i | 0.368138 | − | 0.368138i | ||||
\(35\) | 2.47645i | 0.418597i | ||||||||
\(36\) | 0.936434 | + | 2.85010i | 0.156072 | + | 0.475017i | ||||
\(37\) | −4.21400 | + | 4.21400i | −0.692778 | + | 0.692778i | −0.962842 | − | 0.270064i | \(-0.912955\pi\) |
0.270064 | + | 0.962842i | \(0.412955\pi\) | |||||||
\(38\) | −3.72791 | −0.604747 | ||||||||
\(39\) | 0.672986 | − | 6.20863i | 0.107764 | − | 0.994176i | ||||
\(40\) | −2.47645 | −0.391562 | ||||||||
\(41\) | −4.84049 | + | 4.84049i | −0.755957 | + | 0.755957i | −0.975584 | − | 0.219627i | \(-0.929516\pi\) |
0.219627 | + | 0.975584i | \(0.429516\pi\) | |||||||
\(42\) | −1.71028 | + | 0.273767i | −0.263902 | + | 0.0422431i | ||||
\(43\) | − | 4.59522i | − | 0.700764i | −0.936607 | − | 0.350382i | \(-0.886052\pi\) | ||
0.936607 | − | 0.350382i | \(-0.113948\pi\) | |||||||
\(44\) | −2.12300 | + | 2.12300i | −0.320054 | + | 0.320054i | ||||
\(45\) | 3.35106 | − | 6.63067i | 0.499546 | − | 0.988442i | ||||
\(46\) | 0.338172 | − | 0.338172i | 0.0498607 | − | 0.0498607i | ||||
\(47\) | 6.97225 | + | 6.97225i | 1.01701 | + | 1.01701i | 0.999853 | + | 0.0171544i | \(0.00546067\pi\) |
0.0171544 | + | 0.999853i | \(0.494539\pi\) | |||||||
\(48\) | −0.273767 | − | 1.71028i | −0.0395148 | − | 0.246857i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0.801028 | + | 0.801028i | 0.113282 | + | 0.113282i | ||||
\(51\) | −0.831086 | − | 5.19197i | −0.116375 | − | 0.727021i | ||||
\(52\) | −0.950237 | + | 3.47808i | −0.131774 | + | 0.482323i | ||||
\(53\) | − | 5.90009i | − | 0.810440i | −0.914219 | − | 0.405220i | \(-0.867195\pi\) | ||
0.914219 | − | 0.405220i | \(-0.132805\pi\) | |||||||
\(54\) | 4.94970 | + | 1.58129i | 0.673569 | + | 0.215186i | ||||
\(55\) | 7.43524 | 1.00257 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −3.78669 | + | 5.23000i | −0.501559 | + | 0.692730i | ||||
\(58\) | 4.26874 | + | 4.26874i | 0.560513 | + | 0.560513i | ||||
\(59\) | −3.76763 | − | 3.76763i | −0.490504 | − | 0.490504i | 0.417961 | − | 0.908465i | \(-0.362745\pi\) |
−0.908465 | + | 0.417961i | \(0.862745\pi\) | |||||||
\(60\) | −2.51550 | + | 3.47430i | −0.324750 | + | 0.448530i | ||||
\(61\) | 13.2619 | 1.69801 | 0.849007 | − | 0.528382i | \(-0.177201\pi\) | ||||
0.849007 | + | 0.528382i | \(0.177201\pi\) | |||||||
\(62\) | 2.92963 | 0.372064 | ||||||||
\(63\) | −1.35317 | + | 2.67749i | −0.170483 | + | 0.337332i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 7.75451 | − | 4.42655i | 0.961828 | − | 0.549046i | ||||
\(66\) | 0.821950 | + | 5.13490i | 0.101175 | + | 0.632062i | ||||
\(67\) | −6.61080 | − | 6.61080i | −0.807638 | − | 0.807638i | 0.176638 | − | 0.984276i | \(-0.443478\pi\) |
−0.984276 | + | 0.176638i | \(0.943478\pi\) | |||||||
\(68\) | 3.03575i | 0.368138i | ||||||||
\(69\) | −0.130928 | − | 0.817936i | −0.0157619 | − | 0.0984680i | ||||
\(70\) | −1.75112 | − | 1.75112i | −0.209299 | − | 0.209299i | ||||
\(71\) | −7.36537 | + | 7.36537i | −0.874109 | + | 0.874109i | −0.992917 | − | 0.118808i | \(-0.962093\pi\) |
0.118808 | + | 0.992917i | \(0.462093\pi\) | |||||||
\(72\) | −2.67749 | − | 1.35317i | −0.315545 | − | 0.159472i | ||||
\(73\) | −8.06119 | + | 8.06119i | −0.943491 | + | 0.943491i | −0.998487 | − | 0.0549955i | \(-0.982486\pi\) |
0.0549955 | + | 0.998487i | \(0.482486\pi\) | |||||||
\(74\) | − | 5.95950i | − | 0.692778i | ||||||
\(75\) | 1.93745 | − | 0.310130i | 0.223717 | − | 0.0358107i | ||||
\(76\) | 2.63603 | − | 2.63603i | 0.302373 | − | 0.302373i | ||||
\(77\) | −3.00237 | −0.342152 | ||||||||
\(78\) | 3.91429 | + | 4.86604i | 0.443206 | + | 0.550970i | ||||
\(79\) | −11.6022 | −1.30535 | −0.652673 | − | 0.757640i | \(-0.726353\pi\) | ||||
−0.652673 | + | 0.757640i | \(0.726353\pi\) | |||||||
\(80\) | 1.75112 | − | 1.75112i | 0.195781 | − | 0.195781i | ||||
\(81\) | 7.24618 | − | 5.33787i | 0.805131 | − | 0.593097i | ||||
\(82\) | − | 6.84548i | − | 0.755957i | ||||||
\(83\) | −9.96904 | + | 9.96904i | −1.09424 | + | 1.09424i | −0.0991748 | + | 0.995070i | \(0.531620\pi\) |
−0.995070 | + | 0.0991748i | \(0.968380\pi\) | |||||||
\(84\) | 1.01577 | − | 1.40293i | 0.110829 | − | 0.153072i | ||||
\(85\) | 5.31595 | − | 5.31595i | 0.576596 | − | 0.576596i | ||||
\(86\) | 3.24931 | + | 3.24931i | 0.350382 | + | 0.350382i | ||||
\(87\) | 10.3248 | − | 1.65271i | 1.10694 | − | 0.177189i | ||||
\(88\) | − | 3.00237i | − | 0.320054i | ||||||
\(89\) | −10.9270 | − | 10.9270i | −1.15826 | − | 1.15826i | −0.984849 | − | 0.173415i | \(-0.944520\pi\) |
−0.173415 | − | 0.984849i | \(-0.555480\pi\) | |||||||
\(90\) | 2.31904 | + | 7.05815i | 0.244448 | + | 0.743994i | ||||
\(91\) | −3.13129 | + | 1.78746i | −0.328249 | + | 0.187376i | ||||
\(92\) | 0.478247i | 0.0498607i | ||||||||
\(93\) | 2.97582 | − | 4.11007i | 0.308579 | − | 0.426195i | ||||
\(94\) | −9.86025 | −1.01701 | ||||||||
\(95\) | −9.23199 | −0.947182 | ||||||||
\(96\) | 1.40293 | + | 1.01577i | 0.143186 | + | 0.103671i | ||||
\(97\) | 10.7186 | + | 10.7186i | 1.08831 | + | 1.08831i | 0.995703 | + | 0.0926043i | \(0.0295192\pi\) |
0.0926043 | + | 0.995703i | \(0.470481\pi\) | |||||||
\(98\) | 0.707107 | + | 0.707107i | 0.0714286 | + | 0.0714286i | ||||
\(99\) | 8.03882 | + | 4.06272i | 0.807932 | + | 0.408319i | ||||
\(100\) | −1.13282 | −0.113282 | ||||||||
\(101\) | 5.04608 | 0.502103 | 0.251052 | − | 0.967974i | \(-0.419224\pi\) | ||||
0.251052 | + | 0.967974i | \(0.419224\pi\) | |||||||
\(102\) | 4.25894 | + | 3.08361i | 0.421698 | + | 0.305323i | ||||
\(103\) | 17.3260i | 1.70718i | 0.520944 | + | 0.853591i | \(0.325580\pi\) | ||||
−0.520944 | + | 0.853591i | \(0.674420\pi\) | |||||||
\(104\) | −1.78746 | − | 3.13129i | −0.175274 | − | 0.307049i | ||||
\(105\) | −4.23543 | + | 0.677971i | −0.413335 | + | 0.0661632i | ||||
\(106\) | 4.17199 | + | 4.17199i | 0.405220 | + | 0.405220i | ||||
\(107\) | 7.64785i | 0.739345i | 0.929162 | + | 0.369673i | \(0.120530\pi\) | ||||
−0.929162 | + | 0.369673i | \(0.879470\pi\) | |||||||
\(108\) | −4.61811 | + | 2.38183i | −0.444377 | + | 0.229191i | ||||
\(109\) | 2.94969 | + | 2.94969i | 0.282529 | + | 0.282529i | 0.834117 | − | 0.551588i | \(-0.185978\pi\) |
−0.551588 | + | 0.834117i | \(0.685978\pi\) | |||||||
\(110\) | −5.25751 | + | 5.25751i | −0.501284 | + | 0.501284i | ||||
\(111\) | −8.36077 | − | 6.05346i | −0.793569 | − | 0.574569i | ||||
\(112\) | −0.707107 | + | 0.707107i | −0.0668153 | + | 0.0668153i | ||||
\(113\) | 4.99755i | 0.470130i | 0.971980 | + | 0.235065i | \(0.0755303\pi\) | ||||
−0.971980 | + | 0.235065i | \(0.924470\pi\) | |||||||
\(114\) | −1.02058 | − | 6.37576i | −0.0955858 | − | 0.597145i | ||||
\(115\) | 0.837467 | − | 0.837467i | 0.0780942 | − | 0.0780942i | ||||
\(116\) | −6.03691 | −0.560513 | ||||||||
\(117\) | 10.8027 | − | 0.548722i | 0.998712 | − | 0.0507294i | ||||
\(118\) | 5.32824 | 0.490504 | ||||||||
\(119\) | −2.14660 | + | 2.14660i | −0.196778 | + | 0.196778i | ||||
\(120\) | −0.677971 | − | 4.23543i | −0.0618900 | − | 0.386640i | ||||
\(121\) | − | 1.98575i | − | 0.180522i | ||||||
\(122\) | −9.37758 | + | 9.37758i | −0.849007 | + | 0.849007i | ||||
\(123\) | −9.60374 | − | 6.95342i | −0.865940 | − | 0.626968i | ||||
\(124\) | −2.07156 | + | 2.07156i | −0.186032 | + | 0.186032i | ||||
\(125\) | −6.77188 | − | 6.77188i | −0.605695 | − | 0.605695i | ||||
\(126\) | −0.936434 | − | 2.85010i | −0.0834242 | − | 0.253907i | ||||
\(127\) | − | 0.521751i | − | 0.0462979i | −0.999732 | − | 0.0231490i | \(-0.992631\pi\) | ||
0.999732 | − | 0.0231490i | \(-0.00736920\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 7.85910 | − | 1.25802i | 0.691956 | − | 0.110762i | ||||
\(130\) | −2.35322 | + | 8.61331i | −0.206391 | + | 0.755437i | ||||
\(131\) | 10.1350i | 0.885497i | 0.896646 | + | 0.442748i | \(0.145997\pi\) | ||||
−0.896646 | + | 0.442748i | \(0.854003\pi\) | |||||||
\(132\) | −4.21213 | − | 3.04971i | −0.366619 | − | 0.265443i | ||||
\(133\) | 3.72791 | 0.323251 | ||||||||
\(134\) | 9.34908 | 0.807638 | ||||||||
\(135\) | 12.2577 | + | 3.91599i | 1.05498 | + | 0.337034i | ||||
\(136\) | −2.14660 | − | 2.14660i | −0.184069 | − | 0.184069i | ||||
\(137\) | 4.06995 | + | 4.06995i | 0.347720 | + | 0.347720i | 0.859259 | − | 0.511540i | \(-0.170925\pi\) |
−0.511540 | + | 0.859259i | \(0.670925\pi\) | |||||||
\(138\) | 0.670949 | + | 0.485788i | 0.0571149 | + | 0.0413530i | ||||
\(139\) | 0.173766 | 0.0147387 | 0.00736933 | − | 0.999973i | \(-0.497654\pi\) | ||||
0.00736933 | + | 0.999973i | \(0.497654\pi\) | |||||||
\(140\) | 2.47645 | 0.209299 | ||||||||
\(141\) | −10.0157 | + | 13.8333i | −0.843476 | + | 1.16497i | ||||
\(142\) | − | 10.4162i | − | 0.874109i | ||||||
\(143\) | 5.36661 | + | 9.40132i | 0.448779 | + | 0.786178i | ||||
\(144\) | 2.85010 | − | 0.936434i | 0.237509 | − | 0.0780362i | ||||
\(145\) | 10.5713 | + | 10.5713i | 0.877903 | + | 0.877903i | ||||
\(146\) | − | 11.4002i | − | 0.943491i | ||||||
\(147\) | 1.71028 | − | 0.273767i | 0.141061 | − | 0.0225799i | ||||
\(148\) | 4.21400 | + | 4.21400i | 0.346389 | + | 0.346389i | ||||
\(149\) | −4.13899 | + | 4.13899i | −0.339079 | + | 0.339079i | −0.856021 | − | 0.516941i | \(-0.827071\pi\) |
0.516941 | + | 0.856021i | \(0.327071\pi\) | |||||||
\(150\) | −1.15069 | + | 1.58928i | −0.0939531 | + | 0.129764i | ||||
\(151\) | −6.75083 | + | 6.75083i | −0.549375 | + | 0.549375i | −0.926260 | − | 0.376885i | \(-0.876995\pi\) |
0.376885 | + | 0.926260i | \(0.376995\pi\) | |||||||
\(152\) | 3.72791i | 0.302373i | ||||||||
\(153\) | 8.65219 | − | 2.84278i | 0.699488 | − | 0.229825i | ||||
\(154\) | 2.12300 | − | 2.12300i | 0.171076 | − | 0.171076i | ||||
\(155\) | 7.25510 | 0.582744 | ||||||||
\(156\) | −6.20863 | − | 0.672986i | −0.497088 | − | 0.0538820i | ||||
\(157\) | −4.14765 | −0.331018 | −0.165509 | − | 0.986208i | \(-0.552927\pi\) | ||||
−0.165509 | + | 0.986208i | \(0.552927\pi\) | |||||||
\(158\) | 8.20397 | − | 8.20397i | 0.652673 | − | 0.652673i | ||||
\(159\) | 10.0908 | − | 1.61525i | 0.800252 | − | 0.128098i | ||||
\(160\) | 2.47645i | 0.195781i | ||||||||
\(161\) | −0.338172 | + | 0.338172i | −0.0266517 | + | 0.0266517i | ||||
\(162\) | −1.34938 | + | 8.89827i | −0.106017 | + | 0.699114i | ||||
\(163\) | −13.3414 | + | 13.3414i | −1.04498 | + | 1.04498i | −0.0460395 | + | 0.998940i | \(0.514660\pi\) |
−0.998940 | + | 0.0460395i | \(0.985340\pi\) | |||||||
\(164\) | 4.84049 | + | 4.84049i | 0.377979 | + | 0.377979i | ||||
\(165\) | 2.03552 | + | 12.7163i | 0.158465 | + | 0.989965i | ||||
\(166\) | − | 14.0984i | − | 1.09424i | ||||||
\(167\) | 6.44717 | + | 6.44717i | 0.498897 | + | 0.498897i | 0.911095 | − | 0.412197i | \(-0.135239\pi\) |
−0.412197 | + | 0.911095i | \(0.635239\pi\) | |||||||
\(168\) | 0.273767 | + | 1.71028i | 0.0211216 | + | 0.131951i | ||||
\(169\) | 11.1941 | + | 6.61000i | 0.861085 | + | 0.508462i | ||||
\(170\) | 7.51789i | 0.576596i | ||||||||
\(171\) | −9.98142 | − | 5.04449i | −0.763299 | − | 0.385762i | ||||
\(172\) | −4.59522 | −0.350382 | ||||||||
\(173\) | −2.65682 | −0.201994 | −0.100997 | − | 0.994887i | \(-0.532203\pi\) | ||||
−0.100997 | + | 0.994887i | \(0.532203\pi\) | |||||||
\(174\) | −6.13210 | + | 8.46938i | −0.464873 | + | 0.642062i | ||||
\(175\) | −0.801028 | − | 0.801028i | −0.0605520 | − | 0.0605520i | ||||
\(176\) | 2.12300 | + | 2.12300i | 0.160027 | + | 0.160027i | ||||
\(177\) | 5.41225 | − | 7.47515i | 0.406809 | − | 0.561867i | ||||
\(178\) | 15.4532 | 1.15826 | ||||||||
\(179\) | −3.64878 | −0.272723 | −0.136361 | − | 0.990659i | \(-0.543541\pi\) | ||||
−0.136361 | + | 0.990659i | \(0.543541\pi\) | |||||||
\(180\) | −6.63067 | − | 3.35106i | −0.494221 | − | 0.249773i | ||||
\(181\) | − | 19.5037i | − | 1.44970i | −0.688909 | − | 0.724848i | \(-0.741910\pi\) | ||
0.688909 | − | 0.724848i | \(-0.258090\pi\) | |||||||
\(182\) | 0.950237 | − | 3.47808i | 0.0704362 | − | 0.257813i | ||||
\(183\) | 3.63067 | + | 22.6815i | 0.268387 | + | 1.67667i | ||||
\(184\) | −0.338172 | − | 0.338172i | −0.0249304 | − | 0.0249304i | ||||
\(185\) | − | 14.7584i | − | 1.08506i | ||||||
\(186\) | 0.802036 | + | 5.01049i | 0.0588081 | + | 0.367387i | ||||
\(187\) | 6.44489 | + | 6.44489i | 0.471297 | + | 0.471297i | ||||
\(188\) | 6.97225 | − | 6.97225i | 0.508504 | − | 0.508504i | ||||
\(189\) | −4.94970 | − | 1.58129i | −0.360038 | − | 0.115022i | ||||
\(190\) | 6.52800 | − | 6.52800i | 0.473591 | − | 0.473591i | ||||
\(191\) | − | 0.854794i | − | 0.0618508i | −0.999522 | − | 0.0309254i | \(-0.990155\pi\) | ||
0.999522 | − | 0.0309254i | \(-0.00984542\pi\) | |||||||
\(192\) | −1.71028 | + | 0.273767i | −0.123429 | + | 0.0197574i | ||||
\(193\) | −16.3246 | + | 16.3246i | −1.17507 | + | 1.17507i | −0.194083 | + | 0.980985i | \(0.562173\pi\) |
−0.980985 | + | 0.194083i | \(0.937827\pi\) | |||||||
\(194\) | −15.1584 | −1.08831 | ||||||||
\(195\) | 9.69356 | + | 12.0505i | 0.694170 | + | 0.862956i | ||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | 7.45721 | − | 7.45721i | 0.531304 | − | 0.531304i | −0.389656 | − | 0.920960i | \(-0.627406\pi\) |
0.920960 | + | 0.389656i | \(0.127406\pi\) | |||||||
\(198\) | −8.55708 | + | 2.81153i | −0.608125 | + | 0.199807i | ||||
\(199\) | 0.778109i | 0.0551587i | 0.999620 | + | 0.0275793i | \(0.00877989\pi\) | ||||
−0.999620 | + | 0.0275793i | \(0.991220\pi\) | |||||||
\(200\) | 0.801028 | − | 0.801028i | 0.0566412 | − | 0.0566412i | ||||
\(201\) | 9.49649 | − | 13.1161i | 0.669831 | − | 0.925140i | ||||
\(202\) | −3.56811 | + | 3.56811i | −0.251052 | + | 0.251052i | ||||
\(203\) | −4.26874 | − | 4.26874i | −0.299607 | − | 0.299607i | ||||
\(204\) | −5.19197 | + | 0.831086i | −0.363511 | + | 0.0581877i | ||||
\(205\) | − | 16.9525i | − | 1.18402i | ||||||
\(206\) | −12.2513 | − | 12.2513i | −0.853591 | − | 0.853591i | ||||
\(207\) | 1.36305 | − | 0.447847i | 0.0947389 | − | 0.0311275i | ||||
\(208\) | 3.47808 | + | 0.950237i | 0.241162 | + | 0.0658871i | ||||
\(209\) | − | 11.1926i | − | 0.774207i | ||||||
\(210\) | 2.51550 | − | 3.47430i | 0.173586 | − | 0.239749i | ||||
\(211\) | −4.51239 | −0.310646 | −0.155323 | − | 0.987864i | \(-0.549642\pi\) | ||||
−0.155323 | + | 0.987864i | \(0.549642\pi\) | |||||||
\(212\) | −5.90009 | −0.405220 | ||||||||
\(213\) | −14.6132 | − | 10.5804i | −1.00128 | − | 0.724960i | ||||
\(214\) | −5.40784 | − | 5.40784i | −0.369673 | − | 0.369673i | ||||
\(215\) | 8.04677 | + | 8.04677i | 0.548785 | + | 0.548785i | ||||
\(216\) | 1.58129 | − | 4.94970i | 0.107593 | − | 0.336784i | ||||
\(217\) | −2.92963 | −0.198876 | ||||||||
\(218\) | −4.17149 | −0.282529 | ||||||||
\(219\) | −15.9938 | − | 11.5800i | −1.08076 | − | 0.782504i | ||||
\(220\) | − | 7.43524i | − | 0.501284i | ||||||
\(221\) | 10.5586 | + | 2.88468i | 0.710246 | + | 0.194044i | ||||
\(222\) | 10.1924 | − | 1.63151i | 0.684069 | − | 0.109500i | ||||
\(223\) | −3.08394 | − | 3.08394i | −0.206516 | − | 0.206516i | 0.596269 | − | 0.802785i | \(-0.296649\pi\) |
−0.802785 | + | 0.596269i | \(0.796649\pi\) | |||||||
\(224\) | − | 1.00000i | − | 0.0668153i | ||||||
\(225\) | 1.06082 | + | 3.22867i | 0.0707211 | + | 0.215245i | ||||
\(226\) | −3.53380 | − | 3.53380i | −0.235065 | − | 0.235065i | ||||
\(227\) | 18.9348 | − | 18.9348i | 1.25675 | − | 1.25675i | 0.304109 | − | 0.952637i | \(-0.401641\pi\) |
0.952637 | − | 0.304109i | \(-0.0983588\pi\) | |||||||
\(228\) | 5.23000 | + | 3.78669i | 0.346365 | + | 0.250779i | ||||
\(229\) | 12.2479 | − | 12.2479i | 0.809366 | − | 0.809366i | −0.175172 | − | 0.984538i | \(-0.556048\pi\) |
0.984538 | + | 0.175172i | \(0.0560482\pi\) | |||||||
\(230\) | 1.18436i | 0.0780942i | ||||||||
\(231\) | −0.821950 | − | 5.13490i | −0.0540804 | − | 0.337851i | ||||
\(232\) | 4.26874 | − | 4.26874i | 0.280257 | − | 0.280257i | ||||
\(233\) | 15.4793 | 1.01408 | 0.507041 | − | 0.861922i | \(-0.330739\pi\) | ||||
0.507041 | + | 0.861922i | \(0.330739\pi\) | |||||||
\(234\) | −7.25068 | + | 8.02669i | −0.473992 | + | 0.524721i | ||||
\(235\) | −24.4185 | −1.59288 | ||||||||
\(236\) | −3.76763 | + | 3.76763i | −0.245252 | + | 0.245252i | ||||
\(237\) | −3.17629 | − | 19.8429i | −0.206322 | − | 1.28894i | ||||
\(238\) | − | 3.03575i | − | 0.196778i | ||||||
\(239\) | 11.2898 | − | 11.2898i | 0.730278 | − | 0.730278i | −0.240397 | − | 0.970675i | \(-0.577278\pi\) |
0.970675 | + | 0.240397i | \(0.0772776\pi\) | |||||||
\(240\) | 3.47430 | + | 2.51550i | 0.224265 | + | 0.162375i | ||||
\(241\) | −3.14172 | + | 3.14172i | −0.202376 | + | 0.202376i | −0.801017 | − | 0.598641i | \(-0.795707\pi\) |
0.598641 | + | 0.801017i | \(0.295707\pi\) | |||||||
\(242\) | 1.40413 | + | 1.40413i | 0.0902612 | + | 0.0902612i | ||||
\(243\) | 11.1130 | + | 10.9317i | 0.712900 | + | 0.701266i | ||||
\(244\) | − | 13.2619i | − | 0.849007i | ||||||
\(245\) | 1.75112 | + | 1.75112i | 0.111875 | + | 0.111875i | ||||
\(246\) | 11.7077 | − | 1.87406i | 0.746454 | − | 0.119486i | ||||
\(247\) | −6.66347 | − | 11.6732i | −0.423987 | − | 0.742746i | ||||
\(248\) | − | 2.92963i | − | 0.186032i | ||||||
\(249\) | −19.7790 | − | 14.3206i | −1.25345 | − | 0.907534i | ||||
\(250\) | 9.57688 | 0.605695 | ||||||||
\(251\) | −18.4294 | −1.16326 | −0.581628 | − | 0.813455i | \(-0.697584\pi\) | ||||
−0.581628 | + | 0.813455i | \(0.697584\pi\) | |||||||
\(252\) | 2.67749 | + | 1.35317i | 0.168666 | + | 0.0852416i | ||||
\(253\) | 1.01532 | + | 1.01532i | 0.0638326 | + | 0.0638326i | ||||
\(254\) | 0.368934 | + | 0.368934i | 0.0231490 | + | 0.0231490i | ||||
\(255\) | 10.5471 | + | 7.63642i | 0.660484 | + | 0.478211i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.35687 | 0.271774 | 0.135887 | − | 0.990724i | \(-0.456612\pi\) | ||||
0.135887 | + | 0.990724i | \(0.456612\pi\) | |||||||
\(258\) | −4.66767 | + | 6.44678i | −0.290597 | + | 0.401359i | ||||
\(259\) | 5.95950i | 0.370305i | ||||||||
\(260\) | −4.42655 | − | 7.75451i | −0.274523 | − | 0.480914i | ||||
\(261\) | 5.65317 | + | 17.2058i | 0.349923 | + | 1.06501i | ||||
\(262\) | −7.16651 | − | 7.16651i | −0.442748 | − | 0.442748i | ||||
\(263\) | − | 1.49647i | − | 0.0922762i | −0.998935 | − | 0.0461381i | \(-0.985309\pi\) | ||
0.998935 | − | 0.0461381i | \(-0.0146914\pi\) | |||||||
\(264\) | 5.13490 | − | 0.821950i | 0.316031 | − | 0.0505875i | ||||
\(265\) | 10.3318 | + | 10.3318i | 0.634674 | + | 0.634674i | ||||
\(266\) | −2.63603 | + | 2.63603i | −0.161625 | + | 0.161625i | ||||
\(267\) | 15.6968 | − | 21.6797i | 0.960630 | − | 1.32678i | ||||
\(268\) | −6.61080 | + | 6.61080i | −0.403819 | + | 0.403819i | ||||
\(269\) | − | 11.0765i | − | 0.675349i | −0.941263 | − | 0.337674i | \(-0.890360\pi\) | ||
0.941263 | − | 0.337674i | \(-0.109640\pi\) | |||||||
\(270\) | −11.4365 | + | 5.89849i | −0.696005 | + | 0.358970i | ||||
\(271\) | −9.41699 | + | 9.41699i | −0.572042 | + | 0.572042i | −0.932699 | − | 0.360657i | \(-0.882553\pi\) |
0.360657 | + | 0.932699i | \(0.382553\pi\) | |||||||
\(272\) | 3.03575 | 0.184069 | ||||||||
\(273\) | −3.91429 | − | 4.86604i | −0.236904 | − | 0.294506i | ||||
\(274\) | −5.75578 | −0.347720 | ||||||||
\(275\) | −2.40499 | + | 2.40499i | −0.145026 | + | 0.145026i | ||||
\(276\) | −0.817936 | + | 0.130928i | −0.0492340 | + | 0.00788095i | ||||
\(277\) | − | 20.3743i | − | 1.22417i | −0.790792 | − | 0.612085i | \(-0.790331\pi\) | ||
0.790792 | − | 0.612085i | \(-0.209669\pi\) | |||||||
\(278\) | −0.122871 | + | 0.122871i | −0.00736933 | + | 0.00736933i | ||||
\(279\) | 7.84405 | + | 3.96429i | 0.469611 | + | 0.237336i | ||||
\(280\) | −1.75112 | + | 1.75112i | −0.104649 | + | 0.104649i | ||||
\(281\) | −14.5729 | − | 14.5729i | −0.869346 | − | 0.869346i | 0.123054 | − | 0.992400i | \(-0.460731\pi\) |
−0.992400 | + | 0.123054i | \(0.960731\pi\) | |||||||
\(282\) | −2.69941 | − | 16.8638i | −0.160747 | − | 1.00422i | ||||
\(283\) | − | 17.5244i | − | 1.04171i | −0.853644 | − | 0.520857i | \(-0.825612\pi\) | ||
0.853644 | − | 0.520857i | \(-0.174388\pi\) | |||||||
\(284\) | 7.36537 | + | 7.36537i | 0.437055 | + | 0.437055i | ||||
\(285\) | −2.52741 | − | 15.7893i | −0.149711 | − | 0.935276i | ||||
\(286\) | −10.4425 | − | 2.85297i | −0.617478 | − | 0.168699i | ||||
\(287\) | 6.84548i | 0.404076i | ||||||||
\(288\) | −1.35317 | + | 2.67749i | −0.0797362 | + | 0.157772i | ||||
\(289\) | −7.78425 | −0.457897 | ||||||||
\(290\) | −14.9501 | −0.877903 | ||||||||
\(291\) | −15.3974 | + | 21.2662i | −0.902610 | + | 1.24664i | ||||
\(292\) | 8.06119 | + | 8.06119i | 0.471746 | + | 0.471746i | ||||
\(293\) | 22.5588 | + | 22.5588i | 1.31790 | + | 1.31790i | 0.915435 | + | 0.402466i | \(0.131847\pi\) |
0.402466 | + | 0.915435i | \(0.368153\pi\) | |||||||
\(294\) | −1.01577 | + | 1.40293i | −0.0592407 | + | 0.0818206i | ||||
\(295\) | 13.1951 | 0.768250 | ||||||||
\(296\) | −5.95950 | −0.346389 | ||||||||
\(297\) | −4.74762 | + | 14.8609i | −0.275485 | + | 0.862314i | ||||
\(298\) | − | 5.85342i | − | 0.339079i | ||||||
\(299\) | 1.66338 | + | 0.454448i | 0.0961960 | + | 0.0262814i | ||||
\(300\) | −0.310130 | − | 1.93745i | −0.0179053 | − | 0.111858i | ||||
\(301\) | −3.24931 | − | 3.24931i | −0.187287 | − | 0.187287i | ||||
\(302\) | − | 9.54712i | − | 0.549375i | ||||||
\(303\) | 1.38145 | + | 8.63019i | 0.0793621 | + | 0.495792i | ||||
\(304\) | −2.63603 | − | 2.63603i | −0.151187 | − | 0.151187i | ||||
\(305\) | −23.2232 | + | 23.2232i | −1.32975 | + | 1.32975i | ||||
\(306\) | −4.10788 | + | 8.12817i | −0.234832 | + | 0.464657i | ||||
\(307\) | 15.0145 | − | 15.0145i | 0.856921 | − | 0.856921i | −0.134053 | − | 0.990974i | \(-0.542799\pi\) |
0.990974 | + | 0.134053i | \(0.0427992\pi\) | |||||||
\(308\) | 3.00237i | 0.171076i | ||||||||
\(309\) | −29.6323 | + | 4.74328i | −1.68572 | + | 0.269836i | ||||
\(310\) | −5.13013 | + | 5.13013i | −0.291372 | + | 0.291372i | ||||
\(311\) | 10.7272 | 0.608283 | 0.304142 | − | 0.952627i | \(-0.401630\pi\) | ||||
0.304142 | + | 0.952627i | \(0.401630\pi\) | |||||||
\(312\) | 4.86604 | − | 3.91429i | 0.275485 | − | 0.221603i | ||||
\(313\) | −17.3350 | −0.979834 | −0.489917 | − | 0.871769i | \(-0.662973\pi\) | ||||
−0.489917 | + | 0.871769i | \(0.662973\pi\) | |||||||
\(314\) | 2.93283 | − | 2.93283i | 0.165509 | − | 0.165509i | ||||
\(315\) | −2.31904 | − | 7.05815i | −0.130663 | − | 0.397682i | ||||
\(316\) | 11.6022i | 0.652673i | ||||||||
\(317\) | 19.6716 | − | 19.6716i | 1.10487 | − | 1.10487i | 0.111055 | − | 0.993814i | \(-0.464577\pi\) |
0.993814 | − | 0.111055i | \(-0.0354229\pi\) | |||||||
\(318\) | −5.99312 | + | 8.27742i | −0.336077 | + | 0.464175i | ||||
\(319\) | −12.8164 | + | 12.8164i | −0.717579 | + | 0.717579i | ||||
\(320\) | −1.75112 | − | 1.75112i | −0.0978904 | − | 0.0978904i | ||||
\(321\) | −13.0799 | + | 2.09373i | −0.730051 | + | 0.116860i | ||||
\(322\) | − | 0.478247i | − | 0.0266517i | ||||||
\(323\) | −8.00231 | − | 8.00231i | −0.445261 | − | 0.445261i | ||||
\(324\) | −5.33787 | − | 7.24618i | −0.296548 | − | 0.402566i | ||||
\(325\) | −1.07645 | + | 3.94006i | −0.0597108 | + | 0.218555i | ||||
\(326\) | − | 18.8676i | − | 1.04498i | ||||||
\(327\) | −4.23726 | + | 5.85232i | −0.234321 | + | 0.323634i | ||||
\(328\) | −6.84548 | −0.377979 | ||||||||
\(329\) | 9.86025 | 0.543613 | ||||||||
\(330\) | −10.4311 | − | 7.55248i | −0.574215 | − | 0.415750i | ||||
\(331\) | 4.17896 | + | 4.17896i | 0.229697 | + | 0.229697i | 0.812566 | − | 0.582869i | \(-0.198070\pi\) |
−0.582869 | + | 0.812566i | \(0.698070\pi\) | |||||||
\(332\) | 9.96904 | + | 9.96904i | 0.547122 | + | 0.547122i | ||||
\(333\) | 8.06421 | − | 15.9565i | 0.441916 | − | 0.874410i | ||||
\(334\) | −9.11768 | −0.498897 | ||||||||
\(335\) | 23.1526 | 1.26496 | ||||||||
\(336\) | −1.40293 | − | 1.01577i | −0.0765362 | − | 0.0554146i | ||||
\(337\) | 7.79284i | 0.424503i | 0.977215 | + | 0.212251i | \(0.0680796\pi\) | ||||
−0.977215 | + | 0.212251i | \(0.931920\pi\) | |||||||
\(338\) | −12.5894 | + | 3.24145i | −0.684773 | + | 0.176311i | ||||
\(339\) | −8.54720 | + | 1.36816i | −0.464220 | + | 0.0743084i | ||||
\(340\) | −5.31595 | − | 5.31595i | −0.288298 | − | 0.288298i | ||||
\(341\) | 8.79586i | 0.476322i | ||||||||
\(342\) | 10.6249 | − | 3.49094i | 0.574530 | − | 0.188768i | ||||
\(343\) | −0.707107 | − | 0.707107i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | 3.24931 | − | 3.24931i | 0.175191 | − | 0.175191i | ||||
\(345\) | 1.66157 | + | 1.20303i | 0.0894561 | + | 0.0647691i | ||||
\(346\) | 1.87865 | − | 1.87865i | 0.100997 | − | 0.100997i | ||||
\(347\) | 10.9288i | 0.586690i | 0.956007 | + | 0.293345i | \(0.0947684\pi\) | ||||
−0.956007 | + | 0.293345i | \(0.905232\pi\) | |||||||
\(348\) | −1.65271 | − | 10.3248i | −0.0885944 | − | 0.553468i | ||||
\(349\) | −23.3039 | + | 23.3039i | −1.24743 | + | 1.24743i | −0.290581 | + | 0.956850i | \(0.593849\pi\) |
−0.956850 | + | 0.290581i | \(0.906151\pi\) | |||||||
\(350\) | 1.13282 | 0.0605520 | ||||||||
\(351\) | 3.89589 | + | 18.3254i | 0.207947 | + | 0.978140i | ||||
\(352\) | −3.00237 | −0.160027 | ||||||||
\(353\) | 17.4264 | − | 17.4264i | 0.927516 | − | 0.927516i | −0.0700290 | − | 0.997545i | \(-0.522309\pi\) |
0.997545 | + | 0.0700290i | \(0.0223092\pi\) | |||||||
\(354\) | 1.45869 | + | 9.11277i | 0.0775287 | + | 0.484338i | ||||
\(355\) | − | 25.7953i | − | 1.36907i | ||||||
\(356\) | −10.9270 | + | 10.9270i | −0.579132 | + | 0.579132i | ||||
\(357\) | −4.25894 | − | 3.08361i | −0.225407 | − | 0.163202i | ||||
\(358\) | 2.58008 | − | 2.58008i | 0.136361 | − | 0.136361i | ||||
\(359\) | 13.3523 | + | 13.3523i | 0.704707 | + | 0.704707i | 0.965417 | − | 0.260710i | \(-0.0839568\pi\) |
−0.260710 | + | 0.965417i | \(0.583957\pi\) | |||||||
\(360\) | 7.05815 | − | 2.31904i | 0.371997 | − | 0.122224i | ||||
\(361\) | − | 5.10270i | − | 0.268563i | ||||||
\(362\) | 13.7912 | + | 13.7912i | 0.724848 | + | 0.724848i | ||||
\(363\) | 3.39618 | − | 0.543631i | 0.178253 | − | 0.0285332i | ||||
\(364\) | 1.78746 | + | 3.13129i | 0.0936882 | + | 0.164124i | ||||
\(365\) | − | 28.2322i | − | 1.47774i | ||||||
\(366\) | −18.6055 | − | 13.4710i | −0.972528 | − | 0.704141i | ||||
\(367\) | 23.3338 | 1.21801 | 0.609006 | − | 0.793165i | \(-0.291568\pi\) | ||||
0.609006 | + | 0.793165i | \(0.291568\pi\) | |||||||
\(368\) | 0.478247 | 0.0249304 | ||||||||
\(369\) | 9.26309 | − | 18.3287i | 0.482217 | − | 0.954153i | ||||
\(370\) | 10.4358 | + | 10.4358i | 0.542531 | + | 0.542531i | ||||
\(371\) | −4.17199 | − | 4.17199i | −0.216599 | − | 0.216599i | ||||
\(372\) | −4.11007 | − | 2.97582i | −0.213097 | − | 0.154289i | ||||
\(373\) | 6.26271 | 0.324271 | 0.162135 | − | 0.986769i | \(-0.448162\pi\) | ||||
0.162135 | + | 0.986769i | \(0.448162\pi\) | |||||||
\(374\) | −9.11445 | −0.471297 | ||||||||
\(375\) | 9.72788 | − | 13.4357i | 0.502346 | − | 0.693817i | ||||
\(376\) | 9.86025i | 0.508504i | ||||||||
\(377\) | −5.73650 | + | 20.9969i | −0.295445 | + | 1.08139i | ||||
\(378\) | 4.61811 | − | 2.38183i | 0.237530 | − | 0.122508i | ||||
\(379\) | −23.9024 | − | 23.9024i | −1.22779 | − | 1.22779i | −0.964800 | − | 0.262986i | \(-0.915293\pi\) |
−0.262986 | − | 0.964800i | \(-0.584707\pi\) | |||||||
\(380\) | 9.23199i | 0.473591i | ||||||||
\(381\) | 0.892340 | − | 0.142838i | 0.0457160 | − | 0.00731782i | ||||
\(382\) | 0.604431 | + | 0.604431i | 0.0309254 | + | 0.0309254i | ||||
\(383\) | −6.96614 | + | 6.96614i | −0.355953 | + | 0.355953i | −0.862319 | − | 0.506366i | \(-0.830989\pi\) |
0.506366 | + | 0.862319i | \(0.330989\pi\) | |||||||
\(384\) | 1.01577 | − | 1.40293i | 0.0518356 | − | 0.0715931i | ||||
\(385\) | 5.25751 | − | 5.25751i | 0.267948 | − | 0.267948i | ||||
\(386\) | − | 23.0864i | − | 1.17507i | ||||||
\(387\) | 4.30312 | + | 13.0969i | 0.218740 | + | 0.665750i | ||||
\(388\) | 10.7186 | − | 10.7186i | 0.544154 | − | 0.544154i | ||||
\(389\) | 33.8785 | 1.71771 | 0.858854 | − | 0.512220i | \(-0.171177\pi\) | ||||
0.858854 | + | 0.512220i | \(0.171177\pi\) | |||||||
\(390\) | −15.3754 | − | 1.66662i | −0.778563 | − | 0.0843926i | ||||
\(391\) | 1.45184 | 0.0734226 | ||||||||
\(392\) | 0.707107 | − | 0.707107i | 0.0357143 | − | 0.0357143i | ||||
\(393\) | −17.3336 | + | 2.77462i | −0.874366 | + | 0.139961i | ||||
\(394\) | 10.5461i | 0.531304i | ||||||||
\(395\) | 20.3168 | − | 20.3168i | 1.02225 | − | 1.02225i | ||||
\(396\) | 4.06272 | − | 8.03882i | 0.204159 | − | 0.403966i | ||||
\(397\) | 1.28835 | − | 1.28835i | 0.0646606 | − | 0.0646606i | −0.674037 | − | 0.738698i | \(-0.735441\pi\) |
0.738698 | + | 0.674037i | \(0.235441\pi\) | |||||||
\(398\) | −0.550206 | − | 0.550206i | −0.0275793 | − | 0.0275793i | ||||
\(399\) | 1.02058 | + | 6.37576i | 0.0510928 | + | 0.319187i | ||||
\(400\) | 1.13282i | 0.0566412i | ||||||||
\(401\) | −17.5817 | − | 17.5817i | −0.877988 | − | 0.877988i | 0.115339 | − | 0.993326i | \(-0.463205\pi\) |
−0.993326 | + | 0.115339i | \(0.963205\pi\) | |||||||
\(402\) | 2.55947 | + | 15.9895i | 0.127655 | + | 0.797486i | ||||
\(403\) | 5.23659 | + | 9.17354i | 0.260853 | + | 0.456967i | ||||
\(404\) | − | 5.04608i | − | 0.251052i | ||||||
\(405\) | −3.34168 | + | 22.0362i | −0.166049 | + | 1.09499i | ||||
\(406\) | 6.03691 | 0.299607 | ||||||||
\(407\) | 17.8927 | 0.886906 | ||||||||
\(408\) | 3.08361 | − | 4.25894i | 0.152661 | − | 0.210849i | ||||
\(409\) | 21.1765 | + | 21.1765i | 1.04711 | + | 1.04711i | 0.998834 | + | 0.0482783i | \(0.0153735\pi\) |
0.0482783 | + | 0.998834i | \(0.484627\pi\) | |||||||
\(410\) | 11.9872 | + | 11.9872i | 0.592008 | + | 0.592008i | ||||
\(411\) | −5.84653 | + | 8.07497i | −0.288388 | + | 0.398309i | ||||
\(412\) | 17.3260 | 0.853591 | ||||||||
\(413\) | −5.32824 | −0.262185 | ||||||||
\(414\) | −0.647149 | + | 1.28050i | −0.0318057 | + | 0.0629332i | ||||
\(415\) | − | 34.9139i | − | 1.71386i | ||||||
\(416\) | −3.13129 | + | 1.78746i | −0.153524 | + | 0.0876372i | ||||
\(417\) | 0.0475714 | + | 0.297189i | 0.00232958 | + | 0.0145534i | ||||
\(418\) | 7.91435 | + | 7.91435i | 0.387103 | + | 0.387103i | ||||
\(419\) | 31.9709i | 1.56188i | 0.624607 | + | 0.780939i | \(0.285259\pi\) | ||||
−0.624607 | + | 0.780939i | \(0.714741\pi\) | |||||||
\(420\) | 0.677971 | + | 4.23543i | 0.0330816 | + | 0.206668i | ||||
\(421\) | 11.0977 | + | 11.0977i | 0.540869 | + | 0.540869i | 0.923784 | − | 0.382915i | \(-0.125080\pi\) |
−0.382915 | + | 0.923784i | \(0.625080\pi\) | |||||||
\(422\) | 3.19074 | − | 3.19074i | 0.155323 | − | 0.155323i | ||||
\(423\) | −26.4007 | − | 13.3426i | −1.28365 | − | 0.648738i | ||||
\(424\) | 4.17199 | − | 4.17199i | 0.202610 | − | 0.202610i | ||||
\(425\) | 3.43897i | 0.166814i | ||||||||
\(426\) | 17.8146 | − | 2.85161i | 0.863121 | − | 0.138161i | ||||
\(427\) | 9.37758 | − | 9.37758i | 0.453813 | − | 0.453813i | ||||
\(428\) | 7.64785 | 0.369673 | ||||||||
\(429\) | −14.6097 | + | 11.7522i | −0.705361 | + | 0.567400i | ||||
\(430\) | −11.3798 | −0.548785 | ||||||||
\(431\) | −0.127561 | + | 0.127561i | −0.00614442 | + | 0.00614442i | −0.710172 | − | 0.704028i | \(-0.751383\pi\) |
0.704028 | + | 0.710172i | \(0.251383\pi\) | |||||||
\(432\) | 2.38183 | + | 4.61811i | 0.114596 | + | 0.222189i | ||||
\(433\) | − | 10.1128i | − | 0.485988i | −0.970028 | − | 0.242994i | \(-0.921870\pi\) | ||
0.970028 | − | 0.242994i | \(-0.0781296\pi\) | |||||||
\(434\) | 2.07156 | − | 2.07156i | 0.0994382 | − | 0.0994382i | ||||
\(435\) | −15.1859 | + | 20.9740i | −0.728106 | + | 1.00563i | ||||
\(436\) | 2.94969 | − | 2.94969i | 0.141265 | − | 0.141265i | ||||
\(437\) | −1.26067 | − | 1.26067i | −0.0603062 | − | 0.0603062i | ||||
\(438\) | 19.4976 | − | 3.12101i | 0.931631 | − | 0.149128i | ||||
\(439\) | 22.8399i | 1.09009i | 0.838408 | + | 0.545043i | \(0.183487\pi\) | ||||
−0.838408 | + | 0.545043i | \(0.816513\pi\) | |||||||
\(440\) | 5.25751 | + | 5.25751i | 0.250642 | + | 0.250642i | ||||
\(441\) | 0.936434 | + | 2.85010i | 0.0445921 | + | 0.135719i | ||||
\(442\) | −9.50581 | + | 5.42626i | −0.452145 | + | 0.258101i | ||||
\(443\) | − | 8.91535i | − | 0.423581i | −0.977315 | − | 0.211791i | \(-0.932071\pi\) | ||
0.977315 | − | 0.211791i | \(-0.0679295\pi\) | |||||||
\(444\) | −6.05346 | + | 8.36077i | −0.287285 | + | 0.396785i | ||||
\(445\) | 38.2691 | 1.81413 | ||||||||
\(446\) | 4.36135 | 0.206516 | ||||||||
\(447\) | −8.21195 | − | 5.94571i | −0.388412 | − | 0.281222i | ||||
\(448\) | 0.707107 | + | 0.707107i | 0.0334077 | + | 0.0334077i | ||||
\(449\) | −19.3368 | − | 19.3368i | −0.912558 | − | 0.912558i | 0.0839148 | − | 0.996473i | \(-0.473258\pi\) |
−0.996473 | + | 0.0839148i | \(0.973258\pi\) | |||||||
\(450\) | −3.03312 | − | 1.53290i | −0.142983 | − | 0.0722617i | ||||
\(451\) | 20.5527 | 0.967789 | ||||||||
\(452\) | 4.99755 | 0.235065 | ||||||||
\(453\) | −13.3940 | − | 9.69765i | −0.629303 | − | 0.455635i | ||||
\(454\) | 26.7778i | 1.25675i | ||||||||
\(455\) | 2.35322 | − | 8.61331i | 0.110321 | − | 0.403798i | ||||
\(456\) | −6.37576 | + | 1.02058i | −0.298572 | + | 0.0477929i | ||||
\(457\) | 6.87890 | + | 6.87890i | 0.321781 | + | 0.321781i | 0.849450 | − | 0.527669i | \(-0.176934\pi\) |
−0.527669 | + | 0.849450i | \(0.676934\pi\) | |||||||
\(458\) | 17.3212i | 0.809366i | ||||||||
\(459\) | 7.23062 | + | 14.0194i | 0.337497 | + | 0.654369i | ||||
\(460\) | −0.837467 | − | 0.837467i | −0.0390471 | − | 0.0390471i | ||||
\(461\) | 5.37847 | − | 5.37847i | 0.250500 | − | 0.250500i | −0.570675 | − | 0.821176i | \(-0.693319\pi\) |
0.821176 | + | 0.570675i | \(0.193319\pi\) | |||||||
\(462\) | 4.21213 | + | 3.04971i | 0.195966 | + | 0.141886i | ||||
\(463\) | −1.71052 | + | 1.71052i | −0.0794944 | + | 0.0794944i | −0.745736 | − | 0.666242i | \(-0.767902\pi\) |
0.666242 | + | 0.745736i | \(0.267902\pi\) | |||||||
\(464\) | 6.03691i | 0.280257i | ||||||||
\(465\) | 1.98621 | + | 12.4082i | 0.0921081 | + | 0.575418i | ||||
\(466\) | −10.9455 | + | 10.9455i | −0.507041 | + | 0.507041i | ||||
\(467\) | −12.1098 | −0.560375 | −0.280188 | − | 0.959945i | \(-0.590397\pi\) | ||||
−0.280188 | + | 0.959945i | \(0.590397\pi\) | |||||||
\(468\) | −0.548722 | − | 10.8027i | −0.0253647 | − | 0.499356i | ||||
\(469\) | −9.34908 | −0.431701 | ||||||||
\(470\) | 17.2665 | − | 17.2665i | 0.796442 | − | 0.796442i | ||||
\(471\) | −1.13549 | − | 7.09363i | −0.0523205 | − | 0.326857i | ||||
\(472\) | − | 5.32824i | − | 0.245252i | ||||||
\(473\) | −9.75565 | + | 9.75565i | −0.448565 | + | 0.448565i | ||||
\(474\) | 16.2771 | + | 11.7851i | 0.747630 | + | 0.541308i | ||||
\(475\) | 2.98616 | − | 2.98616i | 0.137014 | − | 0.137014i | ||||
\(476\) | 2.14660 | + | 2.14660i | 0.0983891 | + | 0.0983891i | ||||
\(477\) | 5.52505 | + | 16.8159i | 0.252975 | + | 0.769946i | ||||
\(478\) | 15.9662i | 0.730278i | ||||||||
\(479\) | −0.535810 | − | 0.535810i | −0.0244818 | − | 0.0244818i | 0.694760 | − | 0.719242i | \(-0.255511\pi\) |
−0.719242 | + | 0.694760i | \(0.755511\pi\) | |||||||
\(480\) | −4.23543 | + | 0.677971i | −0.193320 | + | 0.0309450i | ||||
\(481\) | 18.6609 | − | 10.6523i | 0.850866 | − | 0.485705i | ||||
\(482\) | − | 4.44306i | − | 0.202376i | ||||||
\(483\) | −0.670949 | − | 0.485788i | −0.0305292 | − | 0.0221041i | ||||
\(484\) | −1.98575 | −0.0902612 | ||||||||
\(485\) | −37.5390 | −1.70456 | ||||||||
\(486\) | −15.5879 | + | 0.128235i | −0.707083 | + | 0.00581687i | ||||
\(487\) | 5.52429 | + | 5.52429i | 0.250329 | + | 0.250329i | 0.821106 | − | 0.570776i | \(-0.193358\pi\) |
−0.570776 | + | 0.821106i | \(0.693358\pi\) | |||||||
\(488\) | 9.37758 | + | 9.37758i | 0.424503 | + | 0.424503i | ||||
\(489\) | −26.4699 | − | 19.1651i | −1.19701 | − | 0.866675i | ||||
\(490\) | −2.47645 | −0.111875 | ||||||||
\(491\) | −32.2992 | −1.45764 | −0.728821 | − | 0.684704i | \(-0.759932\pi\) | ||||
−0.728821 | + | 0.684704i | \(0.759932\pi\) | |||||||
\(492\) | −6.95342 | + | 9.60374i | −0.313484 | + | 0.432970i | ||||
\(493\) | 18.3265i | 0.825386i | ||||||||
\(494\) | 12.9660 | + | 3.54240i | 0.583366 | + | 0.159380i | ||||
\(495\) | −21.1912 | + | 6.96262i | −0.952474 | + | 0.312946i | ||||
\(496\) | 2.07156 | + | 2.07156i | 0.0930159 | + | 0.0930159i | ||||
\(497\) | 10.4162i | 0.467231i | ||||||||
\(498\) | 24.1121 | − | 3.85966i | 1.08049 | − | 0.172956i | ||||
\(499\) | 24.5090 | + | 24.5090i | 1.09717 | + | 1.09717i | 0.994740 | + | 0.102433i | \(0.0326627\pi\) |
0.102433 | + | 0.994740i | \(0.467337\pi\) | |||||||
\(500\) | −6.77188 | + | 6.77188i | −0.302848 | + | 0.302848i | ||||
\(501\) | −9.26144 | + | 12.7915i | −0.413771 | + | 0.571481i | ||||
\(502\) | 13.0316 | − | 13.0316i | 0.581628 | − | 0.581628i | ||||
\(503\) | 22.3557i | 0.996792i | 0.866949 | + | 0.498396i | \(0.166077\pi\) | ||||
−0.866949 | + | 0.498396i | \(0.833923\pi\) | |||||||
\(504\) | −2.85010 | + | 0.936434i | −0.126954 | + | 0.0417121i | ||||
\(505\) | −8.83627 | + | 8.83627i | −0.393209 | + | 0.393209i | ||||
\(506\) | −1.43588 | −0.0638326 | ||||||||
\(507\) | −8.24037 | + | 20.9546i | −0.365968 | + | 0.930628i | ||||
\(508\) | −0.521751 | −0.0231490 | ||||||||
\(509\) | 2.91721 | − | 2.91721i | 0.129303 | − | 0.129303i | −0.639493 | − | 0.768797i | \(-0.720856\pi\) |
0.768797 | + | 0.639493i | \(0.220856\pi\) | |||||||
\(510\) | −12.8577 | + | 2.05815i | −0.569347 | + | 0.0911363i | ||||
\(511\) | 11.4002i | 0.504317i | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 5.89490 | − | 18.4520i | 0.260266 | − | 0.814677i | ||||
\(514\) | −3.08077 | + | 3.08077i | −0.135887 | + | 0.135887i | ||||
\(515\) | −30.3399 | − | 30.3399i | −1.33693 | − | 1.33693i | ||||
\(516\) | −1.25802 | − | 7.85910i | −0.0553812 | − | 0.345978i | ||||
\(517\) | − | 29.6042i | − | 1.30199i | ||||||
\(518\) | −4.21400 | − | 4.21400i | −0.185153 | − | 0.185153i | ||||
\(519\) | −0.727347 | − | 4.54389i | −0.0319270 | − | 0.199455i | ||||
\(520\) | 8.61331 | + | 2.35322i | 0.377719 | + | 0.103195i | ||||
\(521\) | 20.6947i | 0.906651i | 0.891345 | + | 0.453325i | \(0.149762\pi\) | ||||
−0.891345 | + | 0.453325i | \(0.850238\pi\) | |||||||
\(522\) | −16.1638 | − | 8.16896i | −0.707469 | − | 0.357546i | ||||
\(523\) | −22.5537 | −0.986202 | −0.493101 | − | 0.869972i | \(-0.664137\pi\) | ||||
−0.493101 | + | 0.869972i | \(0.664137\pi\) | |||||||
\(524\) | 10.1350 | 0.442748 | ||||||||
\(525\) | 1.15069 | − | 1.58928i | 0.0502201 | − | 0.0693617i | ||||
\(526\) | 1.05816 | + | 1.05816i | 0.0461381 | + | 0.0461381i | ||||
\(527\) | 6.28874 | + | 6.28874i | 0.273942 | + | 0.273942i | ||||
\(528\) | −3.04971 | + | 4.21213i | −0.132722 | + | 0.183309i | ||||
\(529\) | −22.7713 | −0.990056 | ||||||||
\(530\) | −14.6113 | −0.634674 | ||||||||
\(531\) | 14.2663 | + | 7.21000i | 0.619104 | + | 0.312887i | ||||
\(532\) | − | 3.72791i | − | 0.161625i | ||||||
\(533\) | 21.4352 | − | 12.2360i | 0.928462 | − | 0.530000i | ||||
\(534\) | 4.23056 | + | 26.4292i | 0.183074 | + | 1.14370i | ||||
\(535\) | −13.3923 | − | 13.3923i | −0.578999 | − | 0.578999i | ||||
\(536\) | − | 9.34908i | − | 0.403819i | ||||||
\(537\) | −0.998915 | − | 6.24043i | −0.0431063 | − | 0.269294i | ||||
\(538\) | 7.83230 | + | 7.83230i | 0.337674 | + | 0.337674i | ||||
\(539\) | −2.12300 | + | 2.12300i | −0.0914441 | + | 0.0914441i | ||||
\(540\) | 3.91599 | − | 12.2577i | 0.168517 | − | 0.527488i | ||||
\(541\) | −0.860954 | + | 0.860954i | −0.0370153 | + | 0.0370153i | −0.725372 | − | 0.688357i | \(-0.758332\pi\) |
0.688357 | + | 0.725372i | \(0.258332\pi\) | |||||||
\(542\) | − | 13.3176i | − | 0.572042i | ||||||
\(543\) | 33.3567 | − | 5.33945i | 1.43147 | − | 0.229138i | ||||
\(544\) | −2.14660 | + | 2.14660i | −0.0920346 | + | 0.0920346i | ||||
\(545\) | −10.3305 | −0.442510 | ||||||||
\(546\) | 6.20863 | + | 0.672986i | 0.265705 | + | 0.0288012i | ||||
\(547\) | 38.4468 | 1.64387 | 0.821934 | − | 0.569582i | \(-0.192895\pi\) | ||||
0.821934 | + | 0.569582i | \(0.192895\pi\) | |||||||
\(548\) | 4.06995 | − | 4.06995i | 0.173860 | − | 0.173860i | ||||
\(549\) | −37.7978 | + | 12.4189i | −1.61317 | + | 0.530026i | ||||
\(550\) | − | 3.40116i | − | 0.145026i | ||||||
\(551\) | 15.9135 | − | 15.9135i | 0.677937 | − | 0.677937i | ||||
\(552\) | 0.485788 | − | 0.670949i | 0.0206765 | − | 0.0285575i | ||||
\(553\) | −8.20397 | + | 8.20397i | −0.348868 | + | 0.348868i | ||||
\(554\) | 14.4068 | + | 14.4068i | 0.612085 | + | 0.612085i | ||||
\(555\) | 25.2410 | − | 4.04037i | 1.07142 | − | 0.171504i | ||||
\(556\) | − | 0.173766i | − | 0.00736933i | ||||||
\(557\) | −0.845111 | − | 0.845111i | −0.0358085 | − | 0.0358085i | 0.688976 | − | 0.724784i | \(-0.258061\pi\) |
−0.724784 | + | 0.688976i | \(0.758061\pi\) | |||||||
\(558\) | −8.34976 | + | 2.74341i | −0.353473 | + | 0.116138i | ||||
\(559\) | −4.36655 | + | 15.9825i | −0.184685 | + | 0.675990i | ||||
\(560\) | − | 2.47645i | − | 0.104649i | ||||||
\(561\) | −9.25816 | + | 12.7869i | −0.390880 | + | 0.539865i | ||||
\(562\) | 20.6092 | 0.869346 | ||||||||
\(563\) | −42.4619 | −1.78955 | −0.894777 | − | 0.446513i | \(-0.852666\pi\) | ||||
−0.894777 | + | 0.446513i | \(0.852666\pi\) | |||||||
\(564\) | 13.8333 | + | 10.0157i | 0.582485 | + | 0.421738i | ||||
\(565\) | −8.75130 | − | 8.75130i | −0.368170 | − | 0.368170i | ||||
\(566\) | 12.3916 | + | 12.3916i | 0.520857 | + | 0.520857i | ||||
\(567\) | 1.34938 | − | 8.89827i | 0.0566686 | − | 0.373692i | ||||
\(568\) | −10.4162 | −0.437055 | ||||||||
\(569\) | 13.1702 | 0.552122 | 0.276061 | − | 0.961140i | \(-0.410971\pi\) | ||||
0.276061 | + | 0.961140i | \(0.410971\pi\) | |||||||
\(570\) | 12.9519 | + | 9.37755i | 0.542493 | + | 0.392783i | ||||
\(571\) | 22.7843i | 0.953494i | 0.879041 | + | 0.476747i | \(0.158184\pi\) | ||||
−0.879041 | + | 0.476747i | \(0.841816\pi\) | |||||||
\(572\) | 9.40132 | − | 5.36661i | 0.393089 | − | 0.224389i | ||||
\(573\) | 1.46194 | − | 0.234014i | 0.0610733 | − | 0.00977609i | ||||
\(574\) | −4.84049 | − | 4.84049i | −0.202038 | − | 0.202038i | ||||
\(575\) | 0.541771i | 0.0225934i | ||||||||
\(576\) | −0.936434 | − | 2.85010i | −0.0390181 | − | 0.118754i | ||||
\(577\) | 17.2984 | + | 17.2984i | 0.720142 | + | 0.720142i | 0.968634 | − | 0.248492i | \(-0.0799350\pi\) |
−0.248492 | + | 0.968634i | \(0.579935\pi\) | |||||||
\(578\) | 5.50429 | − | 5.50429i | 0.228948 | − | 0.228948i | ||||
\(579\) | −32.3887 | − | 23.4504i | −1.34603 | − | 0.974567i | ||||
\(580\) | 10.5713 | − | 10.5713i | 0.438951 | − | 0.438951i | ||||
\(581\) | 14.0984i | 0.584898i | ||||||||
\(582\) | −4.14986 | − | 25.9250i | −0.172017 | − | 1.07463i | ||||
\(583\) | −12.5259 | + | 12.5259i | −0.518769 | + | 0.518769i | ||||
\(584\) | −11.4002 | −0.471746 | ||||||||
\(585\) | −17.9560 | + | 19.8777i | −0.742388 | + | 0.821843i | ||||
\(586\) | −31.9030 | −1.31790 | ||||||||
\(587\) | −21.3846 | + | 21.3846i | −0.882638 | + | 0.882638i | −0.993802 | − | 0.111164i | \(-0.964542\pi\) |
0.111164 | + | 0.993802i | \(0.464542\pi\) | |||||||
\(588\) | −0.273767 | − | 1.71028i | −0.0112899 | − | 0.0705307i | ||||
\(589\) | − | 10.9214i | − | 0.450009i | ||||||
\(590\) | −9.33037 | + | 9.33037i | −0.384125 | + | 0.384125i | ||||
\(591\) | 14.7954 | + | 10.7124i | 0.608603 | + | 0.440648i | ||||
\(592\) | 4.21400 | − | 4.21400i | 0.173194 | − | 0.173194i | ||||
\(593\) | −0.343278 | − | 0.343278i | −0.0140968 | − | 0.0140968i | 0.700023 | − | 0.714120i | \(-0.253173\pi\) |
−0.714120 | + | 0.700023i | \(0.753173\pi\) | |||||||
\(594\) | −7.15114 | − | 13.8653i | −0.293415 | − | 0.568900i | ||||
\(595\) | − | 7.51789i | − | 0.308203i | ||||||
\(596\) | 4.13899 | + | 4.13899i | 0.169540 | + | 0.169540i | ||||
\(597\) | −1.33078 | + | 0.213020i | −0.0544653 | + | 0.00871834i | ||||
\(598\) | −1.49753 | + | 0.854846i | −0.0612387 | + | 0.0349573i | ||||
\(599\) | − | 36.3142i | − | 1.48376i | −0.670534 | − | 0.741879i | \(-0.733935\pi\) | ||
0.670534 | − | 0.741879i | \(-0.266065\pi\) | |||||||
\(600\) | 1.58928 | + | 1.15069i | 0.0648819 | + | 0.0469766i | ||||
\(601\) | −21.1337 | −0.862061 | −0.431031 | − | 0.902337i | \(-0.641850\pi\) | ||||
−0.431031 | + | 0.902337i | \(0.641850\pi\) | |||||||
\(602\) | 4.59522 | 0.187287 | ||||||||
\(603\) | 25.0320 | + | 12.6509i | 1.01938 | + | 0.515184i | ||||
\(604\) | 6.75083 | + | 6.75083i | 0.274687 | + | 0.274687i | ||||
\(605\) | 3.47727 | + | 3.47727i | 0.141371 | + | 0.141371i | ||||
\(606\) | −7.07930 | − | 5.12564i | −0.287577 | − | 0.208215i | ||||
\(607\) | −5.09736 | −0.206896 | −0.103448 | − | 0.994635i | \(-0.532987\pi\) | ||||
−0.103448 | + | 0.994635i | \(0.532987\pi\) | |||||||
\(608\) | 3.72791 | 0.151187 | ||||||||
\(609\) | 6.13210 | − | 8.46938i | 0.248485 | − | 0.343197i | ||||
\(610\) | − | 32.8425i | − | 1.32975i | ||||||
\(611\) | −17.6248 | − | 30.8753i | −0.713022 | − | 1.24908i | ||||
\(612\) | −2.84278 | − | 8.65219i | −0.114912 | − | 0.349744i | ||||
\(613\) | 28.8407 | + | 28.8407i | 1.16486 | + | 1.16486i | 0.983397 | + | 0.181467i | \(0.0580845\pi\) |
0.181467 | + | 0.983397i | \(0.441915\pi\) | |||||||
\(614\) | 21.2337i | 0.856921i | ||||||||
\(615\) | 28.9935 | − | 4.64104i | 1.16913 | − | 0.187145i | ||||
\(616\) | −2.12300 | − | 2.12300i | −0.0855381 | − | 0.0855381i | ||||
\(617\) | −29.3917 | + | 29.3917i | −1.18327 | + | 1.18327i | −0.204373 | + | 0.978893i | \(0.565515\pi\) |
−0.978893 | + | 0.204373i | \(0.934485\pi\) | |||||||
\(618\) | 17.5992 | − | 24.3072i | 0.707943 | − | 0.977779i | ||||
\(619\) | −2.81364 | + | 2.81364i | −0.113090 | + | 0.113090i | −0.761387 | − | 0.648298i | \(-0.775481\pi\) |
0.648298 | + | 0.761387i | \(0.275481\pi\) | |||||||
\(620\) | − | 7.25510i | − | 0.291372i | ||||||
\(621\) | 1.13910 | + | 2.20860i | 0.0457106 | + | 0.0886280i | ||||
\(622\) | −7.58527 | + | 7.58527i | −0.304142 | + | 0.304142i | ||||
\(623\) | −15.4532 | −0.619118 | ||||||||
\(624\) | −0.672986 | + | 6.20863i | −0.0269410 | + | 0.248544i | ||||
\(625\) | 29.3808 | 1.17523 | ||||||||
\(626\) | 12.2577 | − | 12.2577i | 0.489917 | − | 0.489917i | ||||
\(627\) | 19.1424 | − | 3.06415i | 0.764475 | − | 0.122371i | ||||
\(628\) | 4.14765i | 0.165509i | ||||||||
\(629\) | 12.7926 | − | 12.7926i | 0.510076 | − | 0.510076i | ||||
\(630\) | 6.63067 | + | 3.35106i | 0.264172 | + | 0.133509i | ||||
\(631\) | −22.1341 | + | 22.1341i | −0.881143 | + | 0.881143i | −0.993651 | − | 0.112507i | \(-0.964112\pi\) |
0.112507 | + | 0.993651i | \(0.464112\pi\) | |||||||
\(632\) | −8.20397 | − | 8.20397i | −0.326337 | − | 0.326337i | ||||
\(633\) | −1.23534 | − | 7.71744i | −0.0491004 | − | 0.306741i | ||||
\(634\) | 27.8199i | 1.10487i | ||||||||
\(635\) | 0.913648 | + | 0.913648i | 0.0362570 | + | 0.0362570i | ||||
\(636\) | −1.61525 | − | 10.0908i | −0.0640488 | − | 0.400126i | ||||
\(637\) | −0.950237 | + | 3.47808i | −0.0376498 | + | 0.137807i | ||||
\(638\) | − | 18.1251i | − | 0.717579i | ||||||
\(639\) | 14.0949 | − | 27.8893i | 0.557585 | − | 1.10328i | ||||
\(640\) | 2.47645 | 0.0978904 | ||||||||
\(641\) | 22.5807 | 0.891885 | 0.445943 | − | 0.895062i | \(-0.352869\pi\) | ||||
0.445943 | + | 0.895062i | \(0.352869\pi\) | |||||||
\(642\) | 7.76843 | − | 10.7294i | 0.306595 | − | 0.423456i | ||||
\(643\) | −11.9697 | − | 11.9697i | −0.472039 | − | 0.472039i | 0.430535 | − | 0.902574i | \(-0.358325\pi\) |
−0.902574 | + | 0.430535i | \(0.858325\pi\) | |||||||
\(644\) | 0.338172 | + | 0.338172i | 0.0133258 | + | 0.0133258i | ||||
\(645\) | −11.5593 | + | 15.9652i | −0.455146 | + | 0.628627i | ||||
\(646\) | 11.3170 | 0.445261 | ||||||||
\(647\) | 49.1692 | 1.93304 | 0.966521 | − | 0.256586i | \(-0.0825978\pi\) | ||||
0.966521 | + | 0.256586i | \(0.0825978\pi\) | |||||||
\(648\) | 8.89827 | + | 1.34938i | 0.349557 | + | 0.0530086i | ||||
\(649\) | 15.9974i | 0.627951i | ||||||||
\(650\) | −2.02487 | − | 3.54721i | −0.0794221 | − | 0.139133i | ||||
\(651\) | −0.802036 | − | 5.01049i | −0.0314343 | − | 0.196376i | ||||
\(652\) | 13.3414 | + | 13.3414i | 0.522490 | + | 0.522490i | ||||
\(653\) | 34.8066i | 1.36209i | 0.732242 | + | 0.681044i | \(0.238474\pi\) | ||||
−0.732242 | + | 0.681044i | \(0.761526\pi\) | |||||||
\(654\) | −1.14202 | − | 7.13441i | −0.0446563 | − | 0.278978i | ||||
\(655\) | −17.7475 | − | 17.7475i | −0.693453 | − | 0.693453i | ||||
\(656\) | 4.84049 | − | 4.84049i | 0.188989 | − | 0.188989i | ||||
\(657\) | 15.4265 | − | 30.5240i | 0.601843 | − | 1.19085i | ||||
\(658\) | −6.97225 | + | 6.97225i | −0.271807 | + | 0.271807i | ||||
\(659\) | − | 12.0404i | − | 0.469029i | −0.972113 | − | 0.234514i | \(-0.924650\pi\) | ||
0.972113 | − | 0.234514i | \(-0.0753500\pi\) | |||||||
\(660\) | 12.7163 | − | 2.03552i | 0.494983 | − | 0.0792326i | ||||
\(661\) | 27.1053 | − | 27.1053i | 1.05427 | − | 1.05427i | 0.0558331 | − | 0.998440i | \(-0.482219\pi\) |
0.998440 | − | 0.0558331i | \(-0.0177815\pi\) | |||||||
\(662\) | −5.90994 | −0.229697 | ||||||||
\(663\) | −2.04302 | + | 18.8478i | −0.0793442 | + | 0.731989i | ||||
\(664\) | −14.0984 | −0.547122 | ||||||||
\(665\) | −6.52800 | + | 6.52800i | −0.253145 | + | 0.253145i | ||||
\(666\) | 5.58068 | + | 16.9852i | 0.216247 | + | 0.658163i | ||||
\(667\) | 2.88714i | 0.111790i | ||||||||
\(668\) | 6.44717 | − | 6.44717i | 0.249449 | − | 0.249449i | ||||
\(669\) | 4.43011 | − | 6.11867i | 0.171278 | − | 0.236561i | ||||
\(670\) | −16.3713 | + | 16.3713i | −0.632480 | + | 0.632480i | ||||
\(671\) | −28.1550 | − | 28.1550i | −1.08691 | − | 1.08691i | ||||
\(672\) | 1.71028 | − | 0.273767i | 0.0659754 | − | 0.0105608i | ||||
\(673\) | − | 17.0132i | − | 0.655809i | −0.944711 | − | 0.327905i | \(-0.893658\pi\) | ||
0.944711 | − | 0.327905i | \(-0.106342\pi\) | |||||||
\(674\) | −5.51037 | − | 5.51037i | −0.212251 | − | 0.212251i | ||||
\(675\) | −5.23150 | + | 2.69819i | −0.201361 | + | 0.103853i | ||||
\(676\) | 6.61000 | − | 11.1941i | 0.254231 | − | 0.430542i | ||||
\(677\) | − | 2.58605i | − | 0.0993901i | −0.998764 | − | 0.0496950i | \(-0.984175\pi\) | ||
0.998764 | − | 0.0496950i | \(-0.0158249\pi\) | |||||||
\(678\) | 5.07635 | − | 7.01122i | 0.194956 | − | 0.269264i | ||||
\(679\) | 15.1584 | 0.581725 | ||||||||
\(680\) | 7.51789 | 0.288298 | ||||||||
\(681\) | 37.5675 | + | 27.2001i | 1.43959 | + | 1.04231i | ||||
\(682\) | −6.21961 | − | 6.21961i | −0.238161 | − | 0.238161i | ||||
\(683\) | −25.9379 | − | 25.9379i | −0.992486 | − | 0.992486i | 0.00748557 | − | 0.999972i | \(-0.497617\pi\) |
−0.999972 | + | 0.00748557i | \(0.997617\pi\) | |||||||
\(684\) | −5.04449 | + | 9.98142i | −0.192881 | + | 0.381649i | ||||
\(685\) | −14.2539 | −0.544615 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 24.3004 | + | 17.5943i | 0.927119 | + | 0.671264i | ||||
\(688\) | 4.59522i | 0.175191i | ||||||||
\(689\) | −5.60648 | + | 20.5210i | −0.213590 | + | 0.781788i | ||||
\(690\) | −2.02558 | + | 0.324238i | −0.0771126 | + | 0.0123435i | ||||
\(691\) | −35.6892 | − | 35.6892i | −1.35768 | − | 1.35768i | −0.876768 | − | 0.480914i | \(-0.840305\pi\) |
−0.480914 | − | 0.876768i | \(-0.659695\pi\) | |||||||
\(692\) | 2.65682i | 0.100997i | ||||||||
\(693\) | 8.55708 | − | 2.81153i | 0.325057 | − | 0.106801i | ||||
\(694\) | −7.72784 | − | 7.72784i | −0.293345 | − | 0.293345i | ||||
\(695\) | −0.304285 | + | 0.304285i | −0.0115422 | + | 0.0115422i | ||||
\(696\) | 8.46938 | + | 6.13210i | 0.321031 | + | 0.232437i | ||||
\(697\) | 14.6945 | − | 14.6945i | 0.556593 | − | 0.556593i | ||||
\(698\) | − | 32.9568i | − | 1.24743i | ||||||
\(699\) | 4.23771 | + | 26.4739i | 0.160285 | + | 1.00133i | ||||
\(700\) | −0.801028 | + | 0.801028i | −0.0302760 | + | 0.0302760i | ||||
\(701\) | 28.4715 | 1.07535 | 0.537676 | − | 0.843151i | \(-0.319302\pi\) | ||||
0.537676 | + | 0.843151i | \(0.319302\pi\) | |||||||
\(702\) | −15.7129 | − | 10.2032i | −0.593044 | − | 0.385096i | ||||
\(703\) | −22.2165 | −0.837910 | ||||||||
\(704\) | 2.12300 | − | 2.12300i | 0.0800136 | − | 0.0800136i | ||||
\(705\) | −6.68496 | − | 41.7624i | −0.251770 | − | 1.57286i | ||||
\(706\) | 24.6447i | 0.927516i | ||||||||
\(707\) | 3.56811 | − | 3.56811i | 0.134193 | − | 0.134193i | ||||
\(708\) | −7.47515 | − | 5.41225i | −0.280933 | − | 0.203405i | ||||
\(709\) | 34.7099 | − | 34.7099i | 1.30356 | − | 1.30356i | 0.377584 | − | 0.925975i | \(-0.376755\pi\) |
0.925975 | − | 0.377584i | \(-0.123245\pi\) | |||||||
\(710\) | 18.2400 | + | 18.2400i | 0.684535 | + | 0.684535i | ||||
\(711\) | 33.0674 | − | 10.8647i | 1.24012 | − | 0.407457i | ||||
\(712\) | − | 15.4532i | − | 0.579132i | ||||||
\(713\) | 0.990720 | + | 0.990720i | 0.0371028 | + | 0.0371028i | ||||
\(714\) | 5.19197 | − | 0.831086i | 0.194305 | − | 0.0311026i | ||||
\(715\) | −25.8604 | − | 7.06524i | −0.967123 | − | 0.264225i | ||||
\(716\) | 3.64878i | 0.136361i | ||||||||
\(717\) | 22.3995 | + | 16.2180i | 0.836525 | + | 0.605671i | ||||
\(718\) | −18.8830 | −0.704707 | ||||||||
\(719\) | 3.99422 | 0.148959 | 0.0744797 | − | 0.997223i | \(-0.476270\pi\) | ||||
0.0744797 | + | 0.997223i | \(0.476270\pi\) | |||||||
\(720\) | −3.35106 | + | 6.63067i | −0.124887 | + | 0.247111i | ||||
\(721\) | 12.2513 | + | 12.2513i | 0.456263 | + | 0.456263i | ||||
\(722\) | 3.60816 | + | 3.60816i | 0.134282 | + | 0.134282i | ||||
\(723\) | −6.23331 | − | 4.51311i | −0.231819 | − | 0.167844i | ||||
\(724\) | −19.5037 | −0.724848 | ||||||||
\(725\) | −6.83877 | −0.253985 | ||||||||
\(726\) | −2.01705 | + | 2.78587i | −0.0748599 | + | 0.103393i | ||||
\(727\) | − | 31.5807i | − | 1.17126i | −0.810577 | − | 0.585632i | \(-0.800846\pi\) | ||
0.810577 | − | 0.585632i | \(-0.199154\pi\) | |||||||
\(728\) | −3.47808 | − | 0.950237i | −0.128906 | − | 0.0352181i | ||||
\(729\) | −15.6538 | + | 21.9991i | −0.579770 | + | 0.814780i | ||||
\(730\) | 19.9632 | + | 19.9632i | 0.738870 | + | 0.738870i | ||||
\(731\) | 13.9499i | 0.515956i | ||||||||
\(732\) | 22.6815 | − | 3.63067i | 0.838334 | − | 0.134193i | ||||
\(733\) | −3.05349 | − | 3.05349i | −0.112783 | − | 0.112783i | 0.648463 | − | 0.761246i | \(-0.275412\pi\) |
−0.761246 | + | 0.648463i | \(0.775412\pi\) | |||||||
\(734\) | −16.4995 | + | 16.4995i | −0.609006 | + | 0.609006i | ||||
\(735\) | −2.51550 | + | 3.47430i | −0.0927856 | + | 0.128151i | ||||
\(736\) | −0.338172 | + | 0.338172i | −0.0124652 | + | 0.0124652i | ||||
\(737\) | 28.0695i | 1.03395i | ||||||||
\(738\) | 6.41035 | + | 19.5103i | 0.235968 | + | 0.718185i | ||||
\(739\) | 5.30152 | − | 5.30152i | 0.195020 | − | 0.195020i | −0.602841 | − | 0.797861i | \(-0.705965\pi\) |
0.797861 | + | 0.602841i | \(0.205965\pi\) | |||||||
\(740\) | −14.7584 | −0.542531 | ||||||||
\(741\) | 18.1401 | − | 14.5921i | 0.666395 | − | 0.536055i | ||||
\(742\) | 5.90009 | 0.216599 | ||||||||
\(743\) | −21.0757 | + | 21.0757i | −0.773191 | + | 0.773191i | −0.978663 | − | 0.205472i | \(-0.934127\pi\) |
0.205472 | + | 0.978663i | \(0.434127\pi\) | |||||||
\(744\) | 5.01049 | − | 0.802036i | 0.183693 | − | 0.0294041i | ||||
\(745\) | − | 14.4957i | − | 0.531082i | ||||||
\(746\) | −4.42841 | + | 4.42841i | −0.162135 | + | 0.162135i | ||||
\(747\) | 19.0775 | − | 37.7482i | 0.698007 | − | 1.38113i | ||||
\(748\) | 6.44489 | − | 6.44489i | 0.235648 | − | 0.235648i | ||||
\(749\) | 5.40784 | + | 5.40784i | 0.197598 | + | 0.197598i | ||||
\(750\) | 2.62183 | + | 16.3791i | 0.0957357 | + | 0.598081i | ||||
\(751\) | − | 52.4292i | − | 1.91317i | −0.291454 | − | 0.956585i | \(-0.594139\pi\) | ||
0.291454 | − | 0.956585i | \(-0.405861\pi\) | |||||||
\(752\) | −6.97225 | − | 6.97225i | −0.254252 | − | 0.254252i | ||||
\(753\) | −5.04536 | − | 31.5195i | −0.183863 | − | 1.14863i | ||||
\(754\) | −10.7907 | − | 18.9034i | −0.392975 | − | 0.688420i | ||||
\(755\) | − | 23.6430i | − | 0.860457i | ||||||
\(756\) | −1.58129 | + | 4.94970i | −0.0575109 | + | 0.180019i | ||||
\(757\) | −37.6352 | −1.36787 | −0.683937 | − | 0.729541i | \(-0.739734\pi\) | ||||
−0.683937 | + | 0.729541i | \(0.739734\pi\) | |||||||
\(758\) | 33.8031 | 1.22779 | ||||||||
\(759\) | −1.45852 | + | 2.01444i | −0.0529408 | + | 0.0731195i | ||||
\(760\) | −6.52800 | − | 6.52800i | −0.236796 | − | 0.236796i | ||||
\(761\) | −4.70073 | − | 4.70073i | −0.170401 | − | 0.170401i | 0.616754 | − | 0.787156i | \(-0.288447\pi\) |
−0.787156 | + | 0.616754i | \(0.788447\pi\) | |||||||
\(762\) | −0.529978 | + | 0.731981i | −0.0191991 | + | 0.0265169i | ||||
\(763\) | 4.17149 | 0.151018 | ||||||||
\(764\) | −0.854794 | −0.0309254 | ||||||||
\(765\) | −10.1730 | + | 20.1290i | −0.367804 | + | 0.727767i | ||||
\(766\) | − | 9.85161i | − | 0.355953i | ||||||
\(767\) | 9.52399 | + | 16.6843i | 0.343891 | + | 0.602434i | ||||
\(768\) | 0.273767 | + | 1.71028i | 0.00987870 | + | 0.0617144i | ||||
\(769\) | −11.5981 | − | 11.5981i | −0.418239 | − | 0.418239i | 0.466358 | − | 0.884596i | \(-0.345566\pi\) |
−0.884596 | + | 0.466358i | \(0.845566\pi\) | |||||||
\(770\) | 7.43524i | 0.267948i | ||||||||
\(771\) | 1.19277 | + | 7.45146i | 0.0429564 | + | 0.268358i | ||||
\(772\) | 16.3246 | + | 16.3246i | 0.587534 | + | 0.587534i | ||||
\(773\) | −21.5154 | + | 21.5154i | −0.773854 | + | 0.773854i | −0.978778 | − | 0.204924i | \(-0.934305\pi\) |
0.204924 | + | 0.978778i | \(0.434305\pi\) | |||||||
\(774\) | −12.3036 | − | 6.21811i | −0.442245 | − | 0.223505i | ||||
\(775\) | −2.34672 | + | 2.34672i | −0.0842966 | + | 0.0842966i | ||||
\(776\) | 15.1584i | 0.544154i | ||||||||
\(777\) | −10.1924 | + | 1.63151i | −0.365650 | + | 0.0585302i | ||||
\(778\) | −23.9557 | + | 23.9557i | −0.858854 | + | 0.858854i | ||||
\(779\) | −25.5193 | −0.914325 | ||||||||
\(780\) | 12.0505 | − | 9.69356i | 0.431478 | − | 0.347085i | ||||
\(781\) | 31.2734 | 1.11905 | ||||||||
\(782\) | −1.02660 | + | 1.02660i | −0.0367113 | + | 0.0367113i | ||||
\(783\) | −27.8791 | + | 14.3789i | −0.996318 | + | 0.513859i | ||||
\(784\) | 1.00000i | 0.0357143i | ||||||||
\(785\) | 7.26302 | − | 7.26302i | 0.259228 | − | 0.259228i | ||||
\(786\) | 10.2948 | − | 14.2187i | 0.367202 | − | 0.507163i | ||||
\(787\) | −16.1871 | + | 16.1871i | −0.577009 | + | 0.577009i | −0.934078 | − | 0.357069i | \(-0.883776\pi\) |
0.357069 | + | 0.934078i | \(0.383776\pi\) | |||||||
\(788\) | −7.45721 | − | 7.45721i | −0.265652 | − | 0.265652i | ||||
\(789\) | 2.55938 | − | 0.409683i | 0.0911163 | − | 0.0145851i | ||||
\(790\) | 28.7322i | 1.02225i | ||||||||
\(791\) | 3.53380 | + | 3.53380i | 0.125648 | + | 0.125648i | ||||
\(792\) | 2.81153 | + | 8.55708i | 0.0999033 | + | 0.304063i | ||||
\(793\) | −46.1260 | − | 12.6020i | −1.63798 | − | 0.447508i | ||||
\(794\) | 1.82201i | 0.0646606i | ||||||||
\(795\) | −14.8417 | + | 20.4987i | −0.526380 | + | 0.727013i | ||||
\(796\) | 0.778109 | 0.0275793 | ||||||||
\(797\) | −39.4250 | −1.39651 | −0.698253 | − | 0.715851i | \(-0.746039\pi\) | ||||
−0.698253 | + | 0.715851i | \(0.746039\pi\) | |||||||
\(798\) | −5.23000 | − | 3.78669i | −0.185140 | − | 0.134047i | ||||
\(799\) | −21.1660 | − | 21.1660i | −0.748799 | − | 0.748799i | ||||
\(800\) | −0.801028 | − | 0.801028i | −0.0283206 | − | 0.0283206i | ||||
\(801\) | 41.3757 | + | 20.9107i | 1.46194 | + | 0.738845i | ||||
\(802\) | 24.8643 | 0.877988 | ||||||||
\(803\) | 34.2278 | 1.20787 | ||||||||
\(804\) | −13.1161 | − | 9.49649i | −0.462570 | − | 0.334915i | ||||
\(805\) | − | 1.18436i | − | 0.0417431i | ||||||
\(806\) | −10.1895 | − | 2.78385i | −0.358910 | − | 0.0980568i | ||||
\(807\) | 18.9440 | − | 3.03239i | 0.666860 | − | 0.106745i | ||||
\(808\) | 3.56811 | + | 3.56811i | 0.125526 | + | 0.125526i | ||||
\(809\) | − | 0.405681i | − | 0.0142630i | −0.999975 | − | 0.00713149i | \(-0.997730\pi\) | ||
0.999975 | − | 0.00713149i | \(-0.00227004\pi\) | |||||||
\(810\) | −13.2190 | − | 17.9448i | −0.464468 | − | 0.630517i | ||||
\(811\) | −26.4050 | − | 26.4050i | −0.927206 | − | 0.927206i | 0.0703186 | − | 0.997525i | \(-0.477598\pi\) |
−0.997525 | + | 0.0703186i | \(0.977598\pi\) | |||||||
\(812\) | −4.26874 | + | 4.26874i | −0.149804 | + | 0.149804i | ||||
\(813\) | −18.6837 | − | 13.5276i | −0.655267 | − | 0.474434i | ||||
\(814\) | −12.6520 | + | 12.6520i | −0.443453 | + | 0.443453i | ||||
\(815\) | − | 46.7247i | − | 1.63670i | ||||||
\(816\) | 0.831086 | + | 5.19197i | 0.0290938 | + | 0.181755i | ||||
\(817\) | 12.1131 | − | 12.1131i | 0.423785 | − | 0.423785i | ||||
\(818\) | −29.9481 | −1.04711 | ||||||||
\(819\) | 7.25068 | − | 8.02669i | 0.253359 | − | 0.280475i | ||||
\(820\) | −16.9525 | −0.592008 | ||||||||
\(821\) | −31.8342 | + | 31.8342i | −1.11102 | + | 1.11102i | −0.118010 | + | 0.993012i | \(0.537651\pi\) |
−0.993012 | + | 0.118010i | \(0.962349\pi\) | |||||||
\(822\) | −1.57574 | − | 9.84399i | −0.0549603 | − | 0.343349i | ||||
\(823\) | − | 29.9746i | − | 1.04485i | −0.852685 | − | 0.522425i | \(-0.825027\pi\) | ||
0.852685 | − | 0.522425i | \(-0.174973\pi\) | |||||||
\(824\) | −12.2513 | + | 12.2513i | −0.426795 | + | 0.426795i | ||||
\(825\) | −4.77160 | − | 3.45479i | −0.166126 | − | 0.120280i | ||||
\(826\) | 3.76763 | − | 3.76763i | 0.131093 | − | 0.131093i | ||||
\(827\) | 22.1847 | + | 22.1847i | 0.771436 | + | 0.771436i | 0.978358 | − | 0.206921i | \(-0.0663444\pi\) |
−0.206921 | + | 0.978358i | \(0.566344\pi\) | |||||||
\(828\) | −0.447847 | − | 1.36305i | −0.0155638 | − | 0.0473694i | ||||
\(829\) | − | 25.2640i | − | 0.877455i | −0.898620 | − | 0.438728i | \(-0.855429\pi\) | ||
0.898620 | − | 0.438728i | \(-0.144571\pi\) | |||||||
\(830\) | 24.6879 | + | 24.6879i | 0.856929 | + | 0.856929i | ||||
\(831\) | 34.8457 | − | 5.57779i | 1.20878 | − | 0.193492i | ||||
\(832\) | 0.950237 | − | 3.47808i | 0.0329435 | − | 0.120581i | ||||
\(833\) | 3.03575i | 0.105182i | ||||||||
\(834\) | −0.243782 | − | 0.176506i | −0.00844148 | − | 0.00611190i | ||||
\(835\) | −22.5795 | −0.781396 | ||||||||
\(836\) | −11.1926 | −0.387103 | ||||||||
\(837\) | −4.63259 | + | 14.5008i | −0.160126 | + | 0.501221i | ||||
\(838\) | −22.6068 | − | 22.6068i | −0.780939 | − | 0.780939i | ||||
\(839\) | 21.9032 | + | 21.9032i | 0.756182 | + | 0.756182i | 0.975625 | − | 0.219443i | \(-0.0704240\pi\) |
−0.219443 | + | 0.975625i | \(0.570424\pi\) | |||||||
\(840\) | −3.47430 | − | 2.51550i | −0.119875 | − | 0.0867930i | ||||
\(841\) | −7.44434 | −0.256701 | ||||||||
\(842\) | −15.6945 | −0.540869 | ||||||||
\(843\) | 20.9341 | − | 28.9133i | 0.721009 | − | 0.995826i | ||||
\(844\) | 4.51239i | 0.155323i | ||||||||
\(845\) | −31.1771 | + | 8.02730i | −1.07252 | + | 0.276147i | ||||
\(846\) | 28.1027 | − | 9.23348i | 0.966192 | − | 0.317454i | ||||
\(847\) | −1.40413 | − | 1.40413i | −0.0482466 | − | 0.0482466i | ||||
\(848\) | 5.90009i | 0.202610i | ||||||||
\(849\) | 29.9715 | − | 4.79758i | 1.02862 | − | 0.164653i | ||||
\(850\) | −2.43172 | − | 2.43172i | −0.0834072 | − | 0.0834072i | ||||
\(851\) | 2.01534 | − | 2.01534i | 0.0690848 | − | 0.0690848i | ||||
\(852\) | −10.5804 | + | 14.6132i | −0.362480 | + | 0.500641i | ||||
\(853\) | −26.8634 | + | 26.8634i | −0.919786 | + | 0.919786i | −0.997013 | − | 0.0772278i | \(-0.975393\pi\) |
0.0772278 | + | 0.997013i | \(0.475393\pi\) | |||||||
\(854\) | 13.2619i | 0.453813i | ||||||||
\(855\) | 26.3121 | − | 8.64516i | 0.899856 | − | 0.295658i | ||||
\(856\) | −5.40784 | + | 5.40784i | −0.184836 | + | 0.184836i | ||||
\(857\) | −14.0267 | −0.479144 | −0.239572 | − | 0.970879i | \(-0.577007\pi\) | ||||
−0.239572 | + | 0.970879i | \(0.577007\pi\) | |||||||
\(858\) | 2.02056 | − | 18.6406i | 0.0689807 | − | 0.636381i | ||||
\(859\) | −8.32911 | −0.284185 | −0.142093 | − | 0.989853i | \(-0.545383\pi\) | ||||
−0.142093 | + | 0.989853i | \(0.545383\pi\) | |||||||
\(860\) | 8.04677 | − | 8.04677i | 0.274393 | − | 0.274393i | ||||
\(861\) | −11.7077 | + | 1.87406i | −0.398997 | + | 0.0638680i | ||||
\(862\) | − | 0.180399i | − | 0.00614442i | ||||||
\(863\) | 16.9934 | − | 16.9934i | 0.578463 | − | 0.578463i | −0.356017 | − | 0.934480i | \(-0.615865\pi\) |
0.934480 | + | 0.356017i | \(0.115865\pi\) | |||||||
\(864\) | −4.94970 | − | 1.58129i | −0.168392 | − | 0.0537965i | ||||
\(865\) | 4.65240 | − | 4.65240i | 0.158186 | − | 0.158186i | ||||
\(866\) | 7.15080 | + | 7.15080i | 0.242994 | + | 0.242994i | ||||
\(867\) | −2.13107 | − | 13.3132i | −0.0723748 | − | 0.452141i | ||||
\(868\) | 2.92963i | 0.0994382i | ||||||||
\(869\) | 24.6314 | + | 24.6314i | 0.835563 | + | 0.835563i | ||||
\(870\) | −4.09285 | − | 25.5689i | −0.138761 | − | 0.866867i | ||||
\(871\) | 16.7111 | + | 29.2747i | 0.566233 | + | 0.991936i | ||||
\(872\) | 4.17149i | 0.141265i | ||||||||
\(873\) | −40.5863 | − | 20.5118i | −1.37364 | − | 0.694220i | ||||
\(874\) | 1.78286 | 0.0603062 | ||||||||
\(875\) | −9.57688 | −0.323758 | ||||||||
\(876\) | −11.5800 | + | 15.9938i | −0.391252 | + | 0.540379i | ||||
\(877\) | −11.7092 | − | 11.7092i | −0.395392 | − | 0.395392i | 0.481212 | − | 0.876604i | \(-0.340197\pi\) |
−0.876604 | + | 0.481212i | \(0.840197\pi\) | |||||||
\(878\) | −16.1502 | − | 16.1502i | −0.545043 | − | 0.545043i | ||||
\(879\) | −32.4060 | + | 44.7577i | −1.09303 | + | 1.50964i | ||||
\(880\) | −7.43524 | −0.250642 | ||||||||
\(881\) | −34.9545 | −1.17765 | −0.588824 | − | 0.808261i | \(-0.700409\pi\) | ||||
−0.588824 | + | 0.808261i | \(0.700409\pi\) | |||||||
\(882\) | −2.67749 | − | 1.35317i | −0.0901557 | − | 0.0455636i | ||||
\(883\) | 38.3261i | 1.28978i | 0.764277 | + | 0.644888i | \(0.223096\pi\) | ||||
−0.764277 | + | 0.644888i | \(0.776904\pi\) | |||||||
\(884\) | 2.88468 | − | 10.5586i | 0.0970222 | − | 0.355123i | ||||
\(885\) | 3.61239 | + | 22.5673i | 0.121429 | + | 0.758593i | ||||
\(886\) | 6.30410 | + | 6.30410i | 0.211791 | + | 0.211791i | ||||
\(887\) | 35.4423i | 1.19004i | 0.803712 | + | 0.595018i | \(0.202855\pi\) | ||||
−0.803712 | + | 0.595018i | \(0.797145\pi\) | |||||||
\(888\) | −1.63151 | − | 10.1924i | −0.0547500 | − | 0.342035i | ||||
\(889\) | −0.368934 | − | 0.368934i | −0.0123736 | − | 0.0123736i | ||||
\(890\) | −27.0603 | + | 27.0603i | −0.907064 | + | 0.907064i | ||||
\(891\) | −26.7159 | − | 4.05134i | −0.895018 | − | 0.135725i | ||||
\(892\) | −3.08394 | + | 3.08394i | −0.103258 | + | 0.103258i | ||||
\(893\) | 36.7581i | 1.23006i | ||||||||
\(894\) | 10.0110 | − | 1.60247i | 0.334817 | − | 0.0535947i | ||||
\(895\) | 6.38944 | − | 6.38944i | 0.213576 | − | 0.213576i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −0.321854 | + | 2.96926i | −0.0107464 | + | 0.0991408i | ||||
\(898\) | 27.3463 | 0.912558 | ||||||||
\(899\) | −12.5059 | + | 12.5059i | −0.417093 | + | 0.417093i | ||||
\(900\) | 3.22867 | − | 1.06082i | 0.107622 | − | 0.0353605i | ||||
\(901\) | 17.9112i | 0.596708i | ||||||||
\(902\) | −14.5330 | + | 14.5330i | −0.483894 | + | 0.483894i | ||||
\(903\) | 4.66767 | − | 6.44678i | 0.155330 | − | 0.214535i | ||||
\(904\) | −3.53380 | + | 3.53380i | −0.117533 | + | 0.117533i | ||||
\(905\) | 34.1532 | + | 34.1532i | 1.13529 | + | 1.13529i | ||||
\(906\) | 16.3282 | − | 2.61368i | 0.542469 | − | 0.0868338i | ||||
\(907\) | 10.5119i | 0.349043i | 0.984653 | + | 0.174522i | \(0.0558379\pi\) | ||||
−0.984653 | + | 0.174522i | \(0.944162\pi\) | |||||||
\(908\) | −18.9348 | − | 18.9348i | −0.628373 | − | 0.628373i | ||||
\(909\) | −14.3818 | + | 4.72532i | −0.477015 | + | 0.156729i | ||||
\(910\) | 4.42655 | + | 7.75451i | 0.146739 | + | 0.257059i | ||||
\(911\) | − | 47.2476i | − | 1.56538i | −0.622410 | − | 0.782691i | \(-0.713846\pi\) | ||
0.622410 | − | 0.782691i | \(-0.286154\pi\) | |||||||
\(912\) | 3.78669 | − | 5.23000i | 0.125390 | − | 0.173183i | ||||
\(913\) | 42.3286 | 1.40087 | ||||||||
\(914\) | −9.72824 | −0.321781 | ||||||||
\(915\) | −46.0758 | − | 33.3603i | −1.52322 | − | 1.10286i | ||||
\(916\) | −12.2479 | − | 12.2479i | −0.404683 | − | 0.404683i | ||||
\(917\) | 7.16651 | + | 7.16651i | 0.236659 | + | 0.236659i | ||||
\(918\) | −15.0260 | − | 4.80039i | −0.495933 | − | 0.158436i | ||||
\(919\) | −55.3266 | −1.82506 | −0.912529 | − | 0.409013i | \(-0.865873\pi\) | ||||
−0.912529 | + | 0.409013i | \(0.865873\pi\) | |||||||
\(920\) | 1.18436 | 0.0390471 | ||||||||
\(921\) | 29.7894 | + | 21.5685i | 0.981594 | + | 0.710705i | ||||
\(922\) | 7.60631i | 0.250500i | ||||||||
\(923\) | 32.6162 | − | 18.6185i | 1.07358 | − | 0.612836i | ||||
\(924\) | −5.13490 | + | 0.821950i | −0.168926 | + | 0.0270402i | ||||
\(925\) | 4.77373 | + | 4.77373i | 0.156959 | + | 0.156959i | ||||
\(926\) | − | 2.41903i | − | 0.0794944i | ||||||
\(927\) | −16.2247 | − | 49.3809i | −0.532888 | − | 1.62188i | ||||
\(928\) | −4.26874 | − | 4.26874i | −0.140128 | − | 0.140128i | ||||
\(929\) | 15.2981 | − | 15.2981i | 0.501914 | − | 0.501914i | −0.410119 | − | 0.912032i | \(-0.634513\pi\) |
0.912032 | + | 0.410119i | \(0.134513\pi\) | |||||||
\(930\) | −10.1784 | − | 7.36949i | −0.333763 | − | 0.241655i | ||||
\(931\) | 2.63603 | − | 2.63603i | 0.0863924 | − | 0.0863924i | ||||
\(932\) | − | 15.4793i | − | 0.507041i | ||||||
\(933\) | 2.93675 | + | 18.3465i | 0.0961448 | + | 0.600637i | ||||
\(934\) | 8.56293 | − | 8.56293i | 0.280188 | − | 0.280188i | ||||
\(935\) | −22.5715 | −0.738167 | ||||||||
\(936\) | 8.02669 | + | 7.25068i | 0.262360 | + | 0.236996i | ||||
\(937\) | 50.3587 | 1.64515 | 0.822574 | − | 0.568658i | \(-0.192537\pi\) | ||||
0.822574 | + | 0.568658i | \(0.192537\pi\) | |||||||
\(938\) | 6.61080 | − | 6.61080i | 0.215850 | − | 0.215850i | ||||
\(939\) | −4.74576 | − | 29.6477i | −0.154872 | − | 0.967517i | ||||
\(940\) | 24.4185i | 0.796442i | ||||||||
\(941\) | 32.9621 | − | 32.9621i | 1.07453 | − | 1.07453i | 0.0775433 | − | 0.996989i | \(-0.475292\pi\) |
0.996989 | − | 0.0775433i | \(-0.0247076\pi\) | |||||||
\(942\) | 5.81887 | + | 4.21304i | 0.189589 | + | 0.137268i | ||||
\(943\) | 2.31495 | − | 2.31495i | 0.0753852 | − | 0.0753852i | ||||
\(944\) | 3.76763 | + | 3.76763i | 0.122626 | + | 0.122626i | ||||
\(945\) | 11.4365 | − | 5.89849i | 0.372030 | − | 0.191878i | ||||
\(946\) | − | 13.7966i | − | 0.448565i | ||||||
\(947\) | −2.53584 | − | 2.53584i | −0.0824038 | − | 0.0824038i | 0.664703 | − | 0.747107i | \(-0.268558\pi\) |
−0.747107 | + | 0.664703i | \(0.768558\pi\) | |||||||
\(948\) | −19.8429 | + | 3.17629i | −0.644469 | + | 0.103161i | ||||
\(949\) | 35.6975 | − | 20.3774i | 1.15879 | − | 0.661480i | ||||
\(950\) | 4.22307i | 0.137014i | ||||||||
\(951\) | 39.0294 | + | 28.2585i | 1.26562 | + | 0.916346i | ||||
\(952\) | −3.03575 | −0.0983891 | ||||||||
\(953\) | 5.10013 | 0.165209 | 0.0826047 | − | 0.996582i | \(-0.473676\pi\) | ||||
0.0826047 | + | 0.996582i | \(0.473676\pi\) | |||||||
\(954\) | −15.7974 | − | 7.98382i | −0.511460 | − | 0.258486i | ||||
\(955\) | 1.49685 | + | 1.49685i | 0.0484368 | + | 0.0484368i | ||||
\(956\) | −11.2898 | − | 11.2898i | −0.365139 | − | 0.365139i | ||||
\(957\) | −25.4282 | − | 18.4109i | −0.821979 | − | 0.595139i | ||||
\(958\) | 0.757750 | 0.0244818 | ||||||||
\(959\) | 5.75578 | 0.185864 | ||||||||
\(960\) | 2.51550 | − | 3.47430i | 0.0811874 | − | 0.112132i | ||||
\(961\) | − | 22.4173i | − | 0.723137i | ||||||
\(962\) | −5.66294 | + | 20.7276i | −0.182580 | + | 0.668285i | ||||
\(963\) | −7.16171 | − | 21.7972i | −0.230783 | − | 0.702403i | ||||
\(964\) | 3.14172 | + | 3.14172i | 0.101188 | + | 0.101188i | ||||
\(965\) | − | 57.1725i | − | 1.84045i | ||||||
\(966\) | 0.817936 | − | 0.130928i | 0.0263167 | − | 0.00421255i | ||||
\(967\) | −36.9427 | − | 36.9427i | −1.18800 | − | 1.18800i | −0.977621 | − | 0.210376i | \(-0.932531\pi\) |
−0.210376 | − | 0.977621i | \(-0.567469\pi\) | |||||||
\(968\) | 1.40413 | − | 1.40413i | 0.0451306 | − | 0.0451306i | ||||
\(969\) | 11.4954 | − | 15.8770i | 0.369286 | − | 0.510041i | ||||
\(970\) | 26.5441 | − | 26.5441i | 0.852279 | − | 0.852279i | ||||
\(971\) | 57.2866i | 1.83842i | 0.393773 | + | 0.919208i | \(0.371170\pi\) | ||||
−0.393773 | + | 0.919208i | \(0.628830\pi\) | |||||||
\(972\) | 10.9317 | − | 11.1130i | 0.350633 | − | 0.356450i | ||||
\(973\) | 0.122871 | − | 0.122871i | 0.00393907 | − | 0.00393907i | ||||
\(974\) | −7.81252 | −0.250329 | ||||||||
\(975\) | −7.03329 | − | 0.762376i | −0.225246 | − | 0.0244156i | ||||
\(976\) | −13.2619 | −0.424503 | ||||||||
\(977\) | 24.4879 | − | 24.4879i | 0.783437 | − | 0.783437i | −0.196972 | − | 0.980409i | \(-0.563111\pi\) |
0.980409 | + | 0.196972i | \(0.0631107\pi\) | |||||||
\(978\) | 32.2688 | − | 5.16532i | 1.03184 | − | 0.165169i | ||||
\(979\) | 46.3962i | 1.48283i | ||||||||
\(980\) | 1.75112 | − | 1.75112i | 0.0559374 | − | 0.0559374i | ||||
\(981\) | −11.1691 | − | 5.64473i | −0.356602 | − | 0.180222i | ||||
\(982\) | 22.8390 | − | 22.8390i | 0.728821 | − | 0.728821i | ||||
\(983\) | 10.8336 | + | 10.8336i | 0.345537 | + | 0.345537i | 0.858444 | − | 0.512907i | \(-0.171432\pi\) |
−0.512907 | + | 0.858444i | \(0.671432\pi\) | |||||||
\(984\) | −1.87406 | − | 11.7077i | −0.0597430 | − | 0.373227i | ||||
\(985\) | 26.1169i | 0.832154i | ||||||||
\(986\) | −12.9588 | − | 12.9588i | −0.412693 | − | 0.412693i | ||||
\(987\) | 2.69941 | + | 16.8638i | 0.0859231 | + | 0.536780i | ||||
\(988\) | −11.6732 | + | 6.66347i | −0.371373 | + | 0.211993i | ||||
\(989\) | 2.19765i | 0.0698813i | ||||||||
\(990\) | 10.0611 | − | 19.9078i | 0.319764 | − | 0.632710i | ||||
\(991\) | 49.1490 | 1.56127 | 0.780635 | − | 0.624988i | \(-0.214896\pi\) | ||||
0.780635 | + | 0.624988i | \(0.214896\pi\) | |||||||
\(992\) | −2.92963 | −0.0930159 | ||||||||
\(993\) | −6.00313 | + | 8.29125i | −0.190503 | + | 0.263115i | ||||
\(994\) | −7.36537 | − | 7.36537i | −0.233615 | − | 0.233615i | ||||
\(995\) | −1.36256 | − | 1.36256i | −0.0431961 | − | 0.0431961i | ||||
\(996\) | −14.3206 | + | 19.7790i | −0.453767 | + | 0.626723i | ||||
\(997\) | −3.17797 | −0.100647 | −0.0503237 | − | 0.998733i | \(-0.516025\pi\) | ||||
−0.0503237 | + | 0.998733i | \(0.516025\pi\) | |||||||
\(998\) | −34.6609 | −1.09717 | ||||||||
\(999\) | 29.4977 | + | 9.42368i | 0.933267 | + | 0.298152i |
(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.p.c.281.3 | yes | 20 | |
3.2 | odd | 2 | 546.2.p.d.281.8 | yes | 20 | ||
13.5 | odd | 4 | 546.2.p.d.239.8 | yes | 20 | ||
39.5 | even | 4 | inner | 546.2.p.c.239.3 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.p.c.239.3 | ✓ | 20 | 39.5 | even | 4 | inner | |
546.2.p.c.281.3 | yes | 20 | 1.1 | even | 1 | trivial | |
546.2.p.d.239.8 | yes | 20 | 13.5 | odd | 4 | ||
546.2.p.d.281.8 | yes | 20 | 3.2 | odd | 2 |