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: | \( x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + 1065 x^{12} - 2080 x^{11} + 3712 x^{10} - 6240 x^{9} + 9585 x^{8} - 14364 x^{7} + \cdots + 59049 \) |
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 | 239.8 | ||
Root | \(-1.01577 - 1.40293i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.239 |
Dual form | 546.2.p.d.281.8 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | \(-0.0631956\pi\) |
−0.197233 | + | 0.980357i | \(0.563196\pi\) | |||||||
\(6\) | −1.01577 | + | 1.40293i | −0.414685 | + | 0.572744i | ||||
\(7\) | 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 | \(-0.600488\pi\) |
0.950582 | + | 0.310474i | \(0.100488\pi\) | |||||||
\(12\) | −1.71028 | + | 0.273767i | −0.493715 | + | 0.0790296i | ||||
\(13\) | −3.47808 | + | 0.950237i | −0.964646 | + | 0.263548i | ||||
\(14\) | 1.00000i | 0.267261i | ||||||||
\(15\) | −2.51550 | + | 3.47430i | −0.649499 | + | 0.897059i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.03575 | 0.736277 | 0.368138 | − | 0.929771i | \(-0.379995\pi\) | ||||
0.368138 | + | 0.929771i | \(0.379995\pi\) | |||||||
\(18\) | −2.67749 | − | 1.35317i | −0.631090 | − | 0.318945i | ||||
\(19\) | 2.63603 | − | 2.63603i | 0.604747 | − | 0.604747i | −0.336822 | − | 0.941568i | \(-0.609352\pi\) |
0.941568 | + | 0.336822i | \(0.109352\pi\) | |||||||
\(20\) | −1.75112 | + | 1.75112i | −0.391562 | + | 0.391562i | ||||
\(21\) | −1.01577 | + | 1.40293i | −0.221659 | + | 0.306145i | ||||
\(22\) | 3.00237 | 0.640108 | ||||||||
\(23\) | 0.478247 | 0.0997215 | 0.0498607 | − | 0.998756i | \(-0.484122\pi\) | ||||
0.0498607 | + | 0.998756i | \(0.484122\pi\) | |||||||
\(24\) | −1.40293 | − | 1.01577i | −0.286372 | − | 0.207343i | ||||
\(25\) | 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 | −0.868228 | − | 0.496165i | \(-0.834741\pi\) |
0.496165 | + | 0.868228i | \(0.334741\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 4.21213 | + | 3.04971i | 0.733237 | + | 0.530887i | ||||
\(34\) | 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 | 0.270064 | − | 0.962842i | \(-0.412955\pi\) |
−0.962842 | + | 0.270064i | \(0.912955\pi\) | |||||||
\(38\) | 3.72791 | 0.604747 | ||||||||
\(39\) | −2.57735 | − | 5.68834i | −0.412707 | − | 0.910864i | ||||
\(40\) | −2.47645 | −0.391562 | ||||||||
\(41\) | 4.84049 | + | 4.84049i | 0.755957 | + | 0.755957i | 0.975584 | − | 0.219627i | \(-0.0704840\pi\) |
−0.219627 | + | 0.975584i | \(0.570484\pi\) | |||||||
\(42\) | −1.71028 | + | 0.273767i | −0.263902 | + | 0.0422431i | ||||
\(43\) | 4.59522i | 0.700764i | 0.936607 | + | 0.350382i | \(0.113948\pi\) | ||||
−0.936607 | + | 0.350382i | \(0.886052\pi\) | |||||||
\(44\) | 2.12300 | + | 2.12300i | 0.320054 | + | 0.320054i | ||||
\(45\) | −6.63067 | − | 3.35106i | −0.988442 | − | 0.499546i | ||||
\(46\) | 0.338172 | + | 0.338172i | 0.0498607 | + | 0.0498607i | ||||
\(47\) | −6.97225 | + | 6.97225i | −1.01701 | + | 1.01701i | −0.0171544 | + | 0.999853i | \(0.505461\pi\) |
−0.999853 | + | 0.0171544i | \(0.994539\pi\) | |||||||
\(48\) | −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 | \(-0.132805\pi\) | |||||||
\(54\) | 1.58129 | − | 4.94970i | 0.215186 | − | 0.673569i | ||||
\(55\) | 7.43524 | 1.00257 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 5.23000 | + | 3.78669i | 0.692730 | + | 0.501559i | ||||
\(58\) | 4.26874 | − | 4.26874i | 0.560513 | − | 0.560513i | ||||
\(59\) | 3.76763 | − | 3.76763i | 0.490504 | − | 0.490504i | −0.417961 | − | 0.908465i | \(-0.637255\pi\) |
0.908465 | + | 0.417961i | \(0.137255\pi\) | |||||||
\(60\) | −3.47430 | − | 2.51550i | −0.448530 | − | 0.324750i | ||||
\(61\) | 13.2619 | 1.69801 | 0.849007 | − | 0.528382i | \(-0.177201\pi\) | ||||
0.849007 | + | 0.528382i | \(0.177201\pi\) | |||||||
\(62\) | −2.92963 | −0.372064 | ||||||||
\(63\) | −2.67749 | − | 1.35317i | −0.337332 | − | 0.170483i | ||||
\(64\) | − | 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 | −0.984276 | − | 0.176638i | \(-0.943478\pi\) |
0.176638 | + | 0.984276i | \(0.443478\pi\) | |||||||
\(68\) | 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 | \(-0.0379073\pi\) |
−0.118808 | + | 0.992917i | \(0.537907\pi\) | |||||||
\(72\) | 1.35317 | − | 2.67749i | 0.159472 | − | 0.315545i | ||||
\(73\) | −8.06119 | − | 8.06119i | −0.943491 | − | 0.943491i | 0.0549955 | − | 0.998487i | \(-0.482486\pi\) |
−0.998487 | + | 0.0549955i | \(0.982486\pi\) | |||||||
\(74\) | − | 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 | ||||||||
\(78\) | 2.19980 | − | 5.84473i | 0.249079 | − | 0.661785i | ||||
\(79\) | −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 | 0.995070 | + | 0.0991748i | \(0.0316203\pi\) |
0.0991748 | + | 0.995070i | \(0.468380\pi\) | |||||||
\(84\) | −1.40293 | − | 1.01577i | −0.153072 | − | 0.110829i | ||||
\(85\) | 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 | 0.173415 | − | 0.984849i | \(-0.444520\pi\) |
0.984849 | − | 0.173415i | \(-0.0554803\pi\) | |||||||
\(90\) | −2.31904 | − | 7.05815i | −0.244448 | − | 0.743994i | ||||
\(91\) | −3.13129 | − | 1.78746i | −0.328249 | − | 0.187376i | ||||
\(92\) | 0.478247i | 0.0498607i | ||||||||
\(93\) | −4.11007 | − | 2.97582i | −0.426195 | − | 0.308579i | ||||
\(94\) | −9.86025 | −1.01701 | ||||||||
\(95\) | 9.23199 | 0.947182 | ||||||||
\(96\) | 1.01577 | − | 1.40293i | 0.103671 | − | 0.143186i | ||||
\(97\) | 10.7186 | − | 10.7186i | 1.08831 | − | 1.08831i | 0.0926043 | − | 0.995703i | \(-0.470481\pi\) |
0.995703 | − | 0.0926043i | \(-0.0295192\pi\) | |||||||
\(98\) | −0.707107 | + | 0.707107i | −0.0714286 | + | 0.0714286i | ||||
\(99\) | −4.06272 | + | 8.03882i | −0.408319 | + | 0.807932i | ||||
\(100\) | −1.13282 | −0.113282 | ||||||||
\(101\) | −5.04608 | −0.502103 | −0.251052 | − | 0.967974i | \(-0.580776\pi\) | ||||
−0.251052 | + | 0.967974i | \(0.580776\pi\) | |||||||
\(102\) | −3.08361 | + | 4.25894i | −0.305323 | + | 0.421698i | ||||
\(103\) | − | 17.3260i | − | 1.70718i | −0.520944 | − | 0.853591i | \(-0.674420\pi\) | ||
0.520944 | − | 0.853591i | \(-0.325580\pi\) | |||||||
\(104\) | 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 | −0.551588 | − | 0.834117i | \(-0.685978\pi\) |
0.834117 | + | 0.551588i | \(0.185978\pi\) | |||||||
\(110\) | 5.25751 | + | 5.25751i | 0.501284 | + | 0.501284i | ||||
\(111\) | 6.05346 | − | 8.36077i | 0.574569 | − | 0.793569i | ||||
\(112\) | −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 | ||||||||
\(117\) | 9.02306 | − | 5.96527i | 0.834182 | − | 0.551489i | ||||
\(118\) | 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 | ||||
\(123\) | −6.95342 | + | 9.60374i | −0.626968 | + | 0.865940i | ||||
\(124\) | −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 | \(0.00736920\pi\) | ||||
−0.999732 | + | 0.0231490i | \(0.992631\pi\) | |||||||
\(128\) | 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 | \(0.854003\pi\) | |||||||
\(132\) | −3.04971 | + | 4.21213i | −0.265443 | + | 0.366619i | ||||
\(133\) | 3.72791 | 0.323251 | ||||||||
\(134\) | −9.34908 | −0.807638 | ||||||||
\(135\) | 3.91599 | − | 12.2577i | 0.337034 | − | 1.05498i | ||||
\(136\) | −2.14660 | + | 2.14660i | −0.184069 | + | 0.184069i | ||||
\(137\) | −4.06995 | + | 4.06995i | −0.347720 | + | 0.347720i | −0.859259 | − | 0.511540i | \(-0.829075\pi\) |
0.511540 | + | 0.859259i | \(0.329075\pi\) | |||||||
\(138\) | −0.485788 | + | 0.670949i | −0.0413530 | + | 0.0571149i | ||||
\(139\) | 0.173766 | 0.0147387 | 0.00736933 | − | 0.999973i | \(-0.497654\pi\) | ||||
0.00736933 | + | 0.999973i | \(0.497654\pi\) | |||||||
\(140\) | −2.47645 | −0.209299 | ||||||||
\(141\) | −13.8333 | − | 10.0157i | −1.16497 | − | 0.843476i | ||||
\(142\) | 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 | \(-0.172929\pi\) |
−0.516941 | + | 0.856021i | \(0.672929\pi\) | |||||||
\(150\) | −1.58928 | − | 1.15069i | −0.129764 | − | 0.0939531i | ||||
\(151\) | −6.75083 | − | 6.75083i | −0.549375 | − | 0.549375i | 0.376885 | − | 0.926260i | \(-0.376995\pi\) |
−0.926260 | + | 0.376885i | \(0.876995\pi\) | |||||||
\(152\) | 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 | ||||||||
\(156\) | 5.68834 | − | 2.57735i | 0.455432 | − | 0.206353i | ||||
\(157\) | −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 | ||||
\(162\) | 8.89827 | + | 1.34938i | 0.699114 | + | 0.106017i | ||||
\(163\) | −13.3414 | − | 13.3414i | −1.04498 | − | 1.04498i | −0.998940 | − | 0.0460395i | \(-0.985340\pi\) |
−0.0460395 | − | 0.998940i | \(-0.514660\pi\) | |||||||
\(164\) | −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 | \(-0.864761\pi\) |
0.412197 | + | 0.911095i | \(0.364761\pi\) | |||||||
\(168\) | −0.273767 | − | 1.71028i | −0.0211216 | − | 0.131951i | ||||
\(169\) | 11.1941 | − | 6.61000i | 0.861085 | − | 0.508462i | ||||
\(170\) | 7.51789i | 0.576596i | ||||||||
\(171\) | −5.04449 | + | 9.98142i | −0.385762 | + | 0.763299i | ||||
\(172\) | −4.59522 | −0.350382 | ||||||||
\(173\) | 2.65682 | 0.201994 | 0.100997 | − | 0.994887i | \(-0.467797\pi\) | ||||
0.100997 | + | 0.994887i | \(0.467797\pi\) | |||||||
\(174\) | 8.46938 | + | 6.13210i | 0.642062 | + | 0.464873i | ||||
\(175\) | −0.801028 | + | 0.801028i | −0.0605520 | + | 0.0605520i | ||||
\(176\) | −2.12300 | + | 2.12300i | −0.160027 | + | 0.160027i | ||||
\(177\) | 7.47515 | + | 5.41225i | 0.561867 | + | 0.406809i | ||||
\(178\) | 15.4532 | 1.15826 | ||||||||
\(179\) | 3.64878 | 0.272723 | 0.136361 | − | 0.990659i | \(-0.456459\pi\) | ||||
0.136361 | + | 0.990659i | \(0.456459\pi\) | |||||||
\(180\) | 3.35106 | − | 6.63067i | 0.249773 | − | 0.494221i | ||||
\(181\) | 19.5037i | 1.44970i | 0.688909 | + | 0.724848i | \(0.258090\pi\) | ||||
−0.688909 | + | 0.724848i | \(0.741910\pi\) | |||||||
\(182\) | −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 | ||||
\(189\) | 1.58129 | − | 4.94970i | 0.115022 | − | 0.360038i | ||||
\(190\) | 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 | −0.980985 | − | 0.194083i | \(-0.937827\pi\) |
−0.194083 | − | 0.980985i | \(-0.562173\pi\) | |||||||
\(194\) | 15.1584 | 1.08831 | ||||||||
\(195\) | 5.44771 | − | 14.4742i | 0.390119 | − | 1.03652i | ||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | −7.45721 | − | 7.45721i | −0.531304 | − | 0.531304i | 0.389656 | − | 0.920960i | \(-0.372594\pi\) |
−0.920960 | + | 0.389656i | \(0.872594\pi\) | |||||||
\(198\) | −8.55708 | + | 2.81153i | −0.608125 | + | 0.199807i | ||||
\(199\) | − | 0.778109i | − | 0.0551587i | −0.999620 | − | 0.0275793i | \(-0.991220\pi\) | ||
0.999620 | − | 0.0275793i | \(-0.00877989\pi\) | |||||||
\(200\) | −0.801028 | − | 0.801028i | −0.0566412 | − | 0.0566412i | ||||
\(201\) | −13.1161 | − | 9.49649i | −0.925140 | − | 0.669831i | ||||
\(202\) | −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 | ||||||
\(210\) | −3.47430 | − | 2.51550i | −0.239749 | − | 0.173586i | ||||
\(211\) | −4.51239 | −0.310646 | −0.155323 | − | 0.987864i | \(-0.549642\pi\) | ||||
−0.155323 | + | 0.987864i | \(0.549642\pi\) | |||||||
\(212\) | 5.90009 | 0.405220 | ||||||||
\(213\) | −10.5804 | + | 14.6132i | −0.724960 | + | 1.00128i | ||||
\(214\) | −5.40784 | + | 5.40784i | −0.369673 | + | 0.369673i | ||||
\(215\) | −8.04677 | + | 8.04677i | −0.548785 | + | 0.548785i | ||||
\(216\) | 4.94970 | + | 1.58129i | 0.336784 | + | 0.107593i | ||||
\(217\) | −2.92963 | −0.198876 | ||||||||
\(218\) | 4.17149 | 0.282529 | ||||||||
\(219\) | 11.5800 | − | 15.9938i | 0.782504 | − | 1.08076i | ||||
\(220\) | 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 | −0.802785 | − | 0.596269i | \(-0.796649\pi\) |
0.596269 | + | 0.802785i | \(0.296649\pi\) | |||||||
\(224\) | − | 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 | −0.952637 | − | 0.304109i | \(-0.901641\pi\) |
−0.304109 | − | 0.952637i | \(-0.598359\pi\) | |||||||
\(228\) | −3.78669 | + | 5.23000i | −0.250779 | + | 0.346365i | ||||
\(229\) | 12.2479 | + | 12.2479i | 0.809366 | + | 0.809366i | 0.984538 | − | 0.175172i | \(-0.0560482\pi\) |
−0.175172 | + | 0.984538i | \(0.556048\pi\) | |||||||
\(230\) | 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 | \(-0.669261\pi\) | ||||
−0.507041 | + | 0.861922i | \(0.669261\pi\) | |||||||
\(234\) | 10.5983 | + | 2.16218i | 0.692836 | + | 0.141346i | ||||
\(235\) | −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 | \(-0.422722\pi\) |
−0.970675 | + | 0.240397i | \(0.922722\pi\) | |||||||
\(240\) | 2.51550 | − | 3.47430i | 0.162375 | − | 0.224265i | ||||
\(241\) | −3.14172 | − | 3.14172i | −0.202376 | − | 0.202376i | 0.598641 | − | 0.801017i | \(-0.295707\pi\) |
−0.801017 | + | 0.598641i | \(0.795707\pi\) | |||||||
\(242\) | −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 | ||||||
\(249\) | −14.3206 | + | 19.7790i | −0.907534 | + | 1.25345i | ||||
\(250\) | 9.57688 | 0.605695 | ||||||||
\(251\) | 18.4294 | 1.16326 | 0.581628 | − | 0.813455i | \(-0.302416\pi\) | ||||
0.581628 | + | 0.813455i | \(0.302416\pi\) | |||||||
\(252\) | 1.35317 | − | 2.67749i | 0.0852416 | − | 0.168666i | ||||
\(253\) | 1.01532 | − | 1.01532i | 0.0638326 | − | 0.0638326i | ||||
\(254\) | −0.368934 | + | 0.368934i | −0.0231490 | + | 0.0231490i | ||||
\(255\) | −7.63642 | + | 10.5471i | −0.478211 | + | 0.660484i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.35687 | −0.271774 | −0.135887 | − | 0.990724i | \(-0.543388\pi\) | ||||
−0.135887 | + | 0.990724i | \(0.543388\pi\) | |||||||
\(258\) | −6.44678 | − | 4.66767i | −0.401359 | − | 0.290597i | ||||
\(259\) | − | 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 | ||||
\(267\) | 21.6797 | + | 15.6968i | 1.32678 | + | 0.960630i | ||||
\(268\) | −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 | 0.360657 | − | 0.932699i | \(-0.382553\pi\) |
−0.932699 | + | 0.360657i | \(0.882553\pi\) | |||||||
\(272\) | −3.03575 | −0.184069 | ||||||||
\(273\) | 2.19980 | − | 5.84473i | 0.133138 | − | 0.353739i | ||||
\(274\) | −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 | \(0.209669\pi\) | ||||
−0.790792 | + | 0.612085i | \(0.790331\pi\) | |||||||
\(278\) | 0.122871 | + | 0.122871i | 0.00736933 | + | 0.00736933i | ||||
\(279\) | 3.96429 | − | 7.84405i | 0.237336 | − | 0.469611i | ||||
\(280\) | −1.75112 | − | 1.75112i | −0.104649 | − | 0.104649i | ||||
\(281\) | 14.5729 | − | 14.5729i | 0.869346 | − | 0.869346i | −0.123054 | − | 0.992400i | \(-0.539269\pi\) |
0.992400 | + | 0.123054i | \(0.0392690\pi\) | |||||||
\(282\) | −2.69941 | − | 16.8638i | −0.160747 | − | 1.00422i | ||||
\(283\) | 17.5244i | 1.04171i | 0.853644 | + | 0.520857i | \(0.174388\pi\) | ||||
−0.853644 | + | 0.520857i | \(0.825612\pi\) | |||||||
\(284\) | −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 | ||||||||
\(288\) | 2.67749 | + | 1.35317i | 0.157772 | + | 0.0797362i | ||||
\(289\) | −7.78425 | −0.457897 | ||||||||
\(290\) | 14.9501 | 0.877903 | ||||||||
\(291\) | 21.2662 | + | 15.3974i | 1.24664 | + | 0.902610i | ||||
\(292\) | 8.06119 | − | 8.06119i | 0.471746 | − | 0.471746i | ||||
\(293\) | −22.5588 | + | 22.5588i | −1.31790 | + | 1.31790i | −0.402466 | + | 0.915435i | \(0.631847\pi\) |
−0.915435 | + | 0.402466i | \(0.868153\pi\) | |||||||
\(294\) | −1.40293 | − | 1.01577i | −0.0818206 | − | 0.0592407i | ||||
\(295\) | 13.1951 | 0.768250 | ||||||||
\(296\) | 5.95950 | 0.346389 | ||||||||
\(297\) | −14.8609 | − | 4.74762i | −0.862314 | − | 0.275485i | ||||
\(298\) | 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 | ||||
\(306\) | −8.12817 | − | 4.10788i | −0.464657 | − | 0.234832i | ||||
\(307\) | 15.0145 | + | 15.0145i | 0.856921 | + | 0.856921i | 0.990974 | − | 0.134053i | \(-0.0427992\pi\) |
−0.134053 | + | 0.990974i | \(0.542799\pi\) | |||||||
\(308\) | 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 | \(-0.598370\pi\) | ||||
−0.304142 | + | 0.952627i | \(0.598370\pi\) | |||||||
\(312\) | 5.84473 | + | 2.19980i | 0.330893 | + | 0.124539i | ||||
\(313\) | −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 | −0.993814 | − | 0.111055i | \(-0.964577\pi\) |
−0.111055 | − | 0.993814i | \(-0.535423\pi\) | |||||||
\(318\) | 8.27742 | + | 5.99312i | 0.464175 | + | 0.336077i | ||||
\(319\) | −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 | ||||||
\(327\) | 5.85232 | + | 4.23726i | 0.323634 | + | 0.234321i | ||||
\(328\) | −6.84548 | −0.377979 | ||||||||
\(329\) | −9.86025 | −0.543613 | ||||||||
\(330\) | −7.55248 | + | 10.4311i | −0.415750 | + | 0.574215i | ||||
\(331\) | 4.17896 | − | 4.17896i | 0.229697 | − | 0.229697i | −0.582869 | − | 0.812566i | \(-0.698070\pi\) |
0.812566 | + | 0.582869i | \(0.198070\pi\) | |||||||
\(332\) | −9.96904 | + | 9.96904i | −0.547122 | + | 0.547122i | ||||
\(333\) | 15.9565 | + | 8.06421i | 0.874410 | + | 0.441916i | ||||
\(334\) | −9.11768 | −0.498897 | ||||||||
\(335\) | −23.1526 | −1.26496 | ||||||||
\(336\) | 1.01577 | − | 1.40293i | 0.0554146 | − | 0.0765362i | ||||
\(337\) | − | 7.79284i | − | 0.424503i | −0.977215 | − | 0.212251i | \(-0.931920\pi\) | ||
0.977215 | − | 0.212251i | \(-0.0680796\pi\) | |||||||
\(338\) | 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 | ||||
\(345\) | −1.20303 | + | 1.66157i | −0.0647691 | + | 0.0894561i | ||||
\(346\) | 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 | −0.956850 | − | 0.290581i | \(-0.906151\pi\) |
−0.290581 | − | 0.956850i | \(-0.593849\pi\) | |||||||
\(350\) | −1.13282 | −0.0605520 | ||||||||
\(351\) | 12.6725 | + | 13.7988i | 0.676407 | + | 0.736528i | ||||
\(352\) | −3.00237 | −0.160027 | ||||||||
\(353\) | −17.4264 | − | 17.4264i | −0.927516 | − | 0.927516i | 0.0700290 | − | 0.997545i | \(-0.477691\pi\) |
−0.997545 | + | 0.0700290i | \(0.977691\pi\) | |||||||
\(354\) | 1.45869 | + | 9.11277i | 0.0775287 | + | 0.484338i | ||||
\(355\) | 25.7953i | 1.36907i | ||||||||
\(356\) | 10.9270 | + | 10.9270i | 0.579132 | + | 0.579132i | ||||
\(357\) | −3.08361 | + | 4.25894i | −0.163202 | + | 0.225407i | ||||
\(358\) | 2.58008 | + | 2.58008i | 0.136361 | + | 0.136361i | ||||
\(359\) | −13.3523 | + | 13.3523i | −0.704707 | + | 0.704707i | −0.965417 | − | 0.260710i | \(-0.916043\pi\) |
0.260710 | + | 0.965417i | \(0.416043\pi\) | |||||||
\(360\) | 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 | ||||||
\(366\) | −13.4710 | + | 18.6055i | −0.704141 | + | 0.972528i | ||||
\(367\) | 23.3338 | 1.21801 | 0.609006 | − | 0.793165i | \(-0.291568\pi\) | ||||
0.609006 | + | 0.793165i | \(0.291568\pi\) | |||||||
\(368\) | −0.478247 | −0.0249304 | ||||||||
\(369\) | −18.3287 | − | 9.26309i | −0.954153 | − | 0.482217i | ||||
\(370\) | 10.4358 | − | 10.4358i | 0.542531 | − | 0.542531i | ||||
\(371\) | 4.17199 | − | 4.17199i | 0.216599 | − | 0.216599i | ||||
\(372\) | 2.97582 | − | 4.11007i | 0.154289 | − | 0.213097i | ||||
\(373\) | 6.26271 | 0.324271 | 0.162135 | − | 0.986769i | \(-0.448162\pi\) | ||||
0.162135 | + | 0.986769i | \(0.448162\pi\) | |||||||
\(374\) | 9.11445 | 0.471297 | ||||||||
\(375\) | 13.4357 | + | 9.72788i | 0.693817 | + | 0.502346i | ||||
\(376\) | − | 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 | −0.262986 | + | 0.964800i | \(0.584707\pi\) |
−0.964800 | + | 0.262986i | \(0.915293\pi\) | |||||||
\(380\) | 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 | \(-0.169011\pi\) |
−0.506366 | + | 0.862319i | \(0.669011\pi\) | |||||||
\(384\) | 1.40293 | + | 1.01577i | 0.0715931 | + | 0.0518356i | ||||
\(385\) | 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 | \(-0.828823\pi\) | ||||
−0.858854 | + | 0.512220i | \(0.828823\pi\) | |||||||
\(390\) | 14.0869 | − | 6.38269i | 0.713319 | − | 0.323200i | ||||
\(391\) | 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 | ||||
\(396\) | −8.03882 | − | 4.06272i | −0.403966 | − | 0.204159i | ||||
\(397\) | 1.28835 | + | 1.28835i | 0.0646606 | + | 0.0646606i | 0.738698 | − | 0.674037i | \(-0.235441\pi\) |
−0.674037 | + | 0.738698i | \(0.735441\pi\) | |||||||
\(398\) | 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 | \(-0.536795\pi\) |
0.993326 | + | 0.115339i | \(0.0367953\pi\) | |||||||
\(402\) | −2.55947 | − | 15.9895i | −0.127655 | − | 0.797486i | ||||
\(403\) | 5.23659 | − | 9.17354i | 0.260853 | − | 0.456967i | ||||
\(404\) | − | 5.04608i | − | 0.251052i | ||||||
\(405\) | 22.0362 | + | 3.34168i | 1.09499 | + | 0.166049i | ||||
\(406\) | 6.03691 | 0.299607 | ||||||||
\(407\) | −17.8927 | −0.886906 | ||||||||
\(408\) | −4.25894 | − | 3.08361i | −0.210849 | − | 0.152661i | ||||
\(409\) | 21.1765 | − | 21.1765i | 1.04711 | − | 1.04711i | 0.0482783 | − | 0.998834i | \(-0.484627\pi\) |
0.998834 | − | 0.0482783i | \(-0.0153735\pi\) | |||||||
\(410\) | −11.9872 | + | 11.9872i | −0.592008 | + | 0.592008i | ||||
\(411\) | −8.07497 | − | 5.84653i | −0.398309 | − | 0.288388i | ||||
\(412\) | 17.3260 | 0.853591 | ||||||||
\(413\) | 5.32824 | 0.262185 | ||||||||
\(414\) | −1.28050 | − | 0.647149i | −0.0629332 | − | 0.0318057i | ||||
\(415\) | 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 | −0.382915 | − | 0.923784i | \(-0.625080\pi\) |
0.923784 | + | 0.382915i | \(0.125080\pi\) | |||||||
\(422\) | −3.19074 | − | 3.19074i | −0.155323 | − | 0.155323i | ||||
\(423\) | 13.3426 | − | 26.4007i | 0.648738 | − | 1.28365i | ||||
\(424\) | 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 | ||||||||
\(429\) | −17.5481 | − | 6.60463i | −0.847229 | − | 0.318875i | ||||
\(430\) | −11.3798 | −0.548785 | ||||||||
\(431\) | 0.127561 | + | 0.127561i | 0.00614442 | + | 0.00614442i | 0.710172 | − | 0.704028i | \(-0.248617\pi\) |
−0.704028 | + | 0.710172i | \(0.748617\pi\) | |||||||
\(432\) | 2.38183 | + | 4.61811i | 0.114596 | + | 0.222189i | ||||
\(433\) | 10.1128i | 0.485988i | 0.970028 | + | 0.242994i | \(0.0781296\pi\) | ||||
−0.970028 | + | 0.242994i | \(0.921870\pi\) | |||||||
\(434\) | −2.07156 | − | 2.07156i | −0.0994382 | − | 0.0994382i | ||||
\(435\) | 20.9740 | + | 15.1859i | 1.00563 | + | 0.728106i | ||||
\(436\) | 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 | \(-0.816513\pi\) | ||
0.838408 | − | 0.545043i | \(-0.183487\pi\) | |||||||
\(440\) | −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 | \(-0.0679295\pi\) | |||||||
\(444\) | 8.36077 | + | 6.05346i | 0.396785 | + | 0.287285i | ||||
\(445\) | 38.2691 | 1.81413 | ||||||||
\(446\) | −4.36135 | −0.206516 | ||||||||
\(447\) | −5.94571 | + | 8.21195i | −0.281222 | + | 0.388412i | ||||
\(448\) | 0.707107 | − | 0.707107i | 0.0334077 | − | 0.0334077i | ||||
\(449\) | 19.3368 | − | 19.3368i | 0.912558 | − | 0.912558i | −0.0839148 | − | 0.996473i | \(-0.526742\pi\) |
0.996473 | + | 0.0839148i | \(0.0267424\pi\) | |||||||
\(450\) | 1.53290 | − | 3.03312i | 0.0722617 | − | 0.142983i | ||||
\(451\) | 20.5527 | 0.967789 | ||||||||
\(452\) | −4.99755 | −0.235065 | ||||||||
\(453\) | 9.69765 | − | 13.3940i | 0.455635 | − | 0.629303i | ||||
\(454\) | − | 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 | −0.527669 | − | 0.849450i | \(-0.676934\pi\) |
0.849450 | + | 0.527669i | \(0.176934\pi\) | |||||||
\(458\) | 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 | \(-0.306681\pi\) |
−0.821176 | + | 0.570675i | \(0.806681\pi\) | |||||||
\(462\) | −3.04971 | + | 4.21213i | −0.141886 | + | 0.195966i | ||||
\(463\) | −1.71052 | − | 1.71052i | −0.0794944 | − | 0.0794944i | 0.666242 | − | 0.745736i | \(-0.267902\pi\) |
−0.745736 | + | 0.666242i | \(0.767902\pi\) | |||||||
\(464\) | 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 | \(-0.409603\pi\) | ||||
0.280188 | + | 0.959945i | \(0.409603\pi\) | |||||||
\(468\) | 5.96527 | + | 9.02306i | 0.275745 | + | 0.417091i | ||||
\(469\) | −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 | ||||
\(474\) | 11.7851 | − | 16.2771i | 0.541308 | − | 0.747630i | ||||
\(475\) | 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 | \(-0.744489\pi\) |
0.719242 | + | 0.694760i | \(0.244489\pi\) | |||||||
\(480\) | 4.23543 | − | 0.677971i | 0.193320 | − | 0.0309450i | ||||
\(481\) | 18.6609 | + | 10.6523i | 0.850866 | + | 0.485705i | ||||
\(482\) | − | 4.44306i | − | 0.202376i | ||||||
\(483\) | −0.485788 | + | 0.670949i | −0.0221041 | + | 0.0305292i | ||||
\(484\) | −1.98575 | −0.0902612 | ||||||||
\(485\) | 37.5390 | 1.70456 | ||||||||
\(486\) | 0.128235 | + | 15.5879i | 0.00581687 | + | 0.707083i | ||||
\(487\) | 5.52429 | − | 5.52429i | 0.250329 | − | 0.250329i | −0.570776 | − | 0.821106i | \(-0.693358\pi\) |
0.821106 | + | 0.570776i | \(0.193358\pi\) | |||||||
\(488\) | −9.37758 | + | 9.37758i | −0.424503 | + | 0.424503i | ||||
\(489\) | 19.1651 | − | 26.4699i | 0.866675 | − | 1.19701i | ||||
\(490\) | −2.47645 | −0.111875 | ||||||||
\(491\) | 32.2992 | 1.45764 | 0.728821 | − | 0.684704i | \(-0.240068\pi\) | ||||
0.728821 | + | 0.684704i | \(0.240068\pi\) | |||||||
\(492\) | −9.60374 | − | 6.95342i | −0.432970 | − | 0.313484i | ||||
\(493\) | − | 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 | 0.102433 | − | 0.994740i | \(-0.467337\pi\) |
0.994740 | − | 0.102433i | \(-0.0326627\pi\) | |||||||
\(500\) | 6.77188 | + | 6.77188i | 0.302848 | + | 0.302848i | ||||
\(501\) | −12.7915 | − | 9.26144i | −0.571481 | − | 0.413771i | ||||
\(502\) | 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 | ||||||||
\(507\) | 14.3695 | + | 17.3354i | 0.638173 | + | 0.769893i | ||||
\(508\) | −0.521751 | −0.0231490 | ||||||||
\(509\) | −2.91721 | − | 2.91721i | −0.129303 | − | 0.129303i | 0.639493 | − | 0.768797i | \(-0.279144\pi\) |
−0.768797 | + | 0.639493i | \(0.779144\pi\) | |||||||
\(510\) | −12.8577 | + | 2.05815i | −0.569347 | + | 0.0911363i | ||||
\(511\) | − | 11.4002i | − | 0.504317i | ||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −18.4520 | − | 5.89490i | −0.814677 | − | 0.260266i | ||||
\(514\) | −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 | \(0.850238\pi\) | |||||||
\(522\) | −8.16896 | + | 16.1638i | −0.357546 | + | 0.707469i | ||||
\(523\) | −22.5537 | −0.986202 | −0.493101 | − | 0.869972i | \(-0.664137\pi\) | ||||
−0.493101 | + | 0.869972i | \(0.664137\pi\) | |||||||
\(524\) | −10.1350 | −0.442748 | ||||||||
\(525\) | −1.58928 | − | 1.15069i | −0.0693617 | − | 0.0502201i | ||||
\(526\) | 1.05816 | − | 1.05816i | 0.0461381 | − | 0.0461381i | ||||
\(527\) | −6.28874 | + | 6.28874i | −0.273942 | + | 0.273942i | ||||
\(528\) | −4.21213 | − | 3.04971i | −0.183309 | − | 0.132722i | ||||
\(529\) | −22.7713 | −0.990056 | ||||||||
\(530\) | 14.6113 | 0.634674 | ||||||||
\(531\) | −7.21000 | + | 14.2663i | −0.312887 | + | 0.619104i | ||||
\(532\) | 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 | ||||
\(540\) | 12.2577 | + | 3.91599i | 0.527488 | + | 0.168517i | ||||
\(541\) | −0.860954 | − | 0.860954i | −0.0370153 | − | 0.0370153i | 0.688357 | − | 0.725372i | \(-0.258332\pi\) |
−0.725372 | + | 0.688357i | \(0.758332\pi\) | |||||||
\(542\) | − | 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 | ||||||||
\(546\) | 5.68834 | − | 2.57735i | 0.243439 | − | 0.110300i | ||||
\(547\) | 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 | ||||
\(552\) | −0.670949 | − | 0.485788i | −0.0285575 | − | 0.0206765i | ||||
\(553\) | −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 | \(-0.741939\pi\) |
0.724784 | + | 0.688976i | \(0.241939\pi\) | |||||||
\(558\) | 8.34976 | − | 2.74341i | 0.353473 | − | 0.116138i | ||||
\(559\) | −4.36655 | − | 15.9825i | −0.184685 | − | 0.675990i | ||||
\(560\) | − | 2.47645i | − | 0.104649i | ||||||
\(561\) | 12.7869 | + | 9.25816i | 0.539865 | + | 0.390880i | ||||
\(562\) | 20.6092 | 0.869346 | ||||||||
\(563\) | 42.4619 | 1.78955 | 0.894777 | − | 0.446513i | \(-0.147334\pi\) | ||||
0.894777 | + | 0.446513i | \(0.147334\pi\) | |||||||
\(564\) | 10.0157 | − | 13.8333i | 0.421738 | − | 0.582485i | ||||
\(565\) | −8.75130 | + | 8.75130i | −0.368170 | + | 0.368170i | ||||
\(566\) | −12.3916 | + | 12.3916i | −0.520857 | + | 0.520857i | ||||
\(567\) | 8.89827 | + | 1.34938i | 0.373692 | + | 0.0566686i | ||||
\(568\) | −10.4162 | −0.437055 | ||||||||
\(569\) | −13.1702 | −0.552122 | −0.276061 | − | 0.961140i | \(-0.589029\pi\) | ||||
−0.276061 | + | 0.961140i | \(0.589029\pi\) | |||||||
\(570\) | −9.37755 | + | 12.9519i | −0.392783 | + | 0.542493i | ||||
\(571\) | − | 22.7843i | − | 0.953494i | −0.879041 | − | 0.476747i | \(-0.841816\pi\) | ||
0.879041 | − | 0.476747i | \(-0.158184\pi\) | |||||||
\(572\) | −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 | −0.248492 | − | 0.968634i | \(-0.579935\pi\) |
0.968634 | + | 0.248492i | \(0.0799350\pi\) | |||||||
\(578\) | −5.50429 | − | 5.50429i | −0.228948 | − | 0.228948i | ||||
\(579\) | 23.4504 | − | 32.3887i | 0.974567 | − | 1.34603i | ||||
\(580\) | 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 | ||||||||
\(585\) | 26.2463 | + | 5.35455i | 1.08515 | + | 0.221383i | ||||
\(586\) | −31.9030 | −1.31790 | ||||||||
\(587\) | 21.3846 | + | 21.3846i | 0.882638 | + | 0.882638i | 0.993802 | − | 0.111164i | \(-0.0354580\pi\) |
−0.111164 | + | 0.993802i | \(0.535458\pi\) | |||||||
\(588\) | −0.273767 | − | 1.71028i | −0.0112899 | − | 0.0705307i | ||||
\(589\) | 10.9214i | 0.450009i | ||||||||
\(590\) | 9.33037 | + | 9.33037i | 0.384125 | + | 0.384125i | ||||
\(591\) | 10.7124 | − | 14.7954i | 0.440648 | − | 0.608603i | ||||
\(592\) | 4.21400 | + | 4.21400i | 0.173194 | + | 0.173194i | ||||
\(593\) | 0.343278 | − | 0.343278i | 0.0140968 | − | 0.0140968i | −0.700023 | − | 0.714120i | \(-0.746827\pi\) |
0.714120 | + | 0.700023i | \(0.246827\pi\) | |||||||
\(594\) | −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 | \(-0.266065\pi\) | |||||||
\(600\) | 1.15069 | − | 1.58928i | 0.0469766 | − | 0.0648819i | ||||
\(601\) | −21.1337 | −0.862061 | −0.431031 | − | 0.902337i | \(-0.641850\pi\) | ||||
−0.431031 | + | 0.902337i | \(0.641850\pi\) | |||||||
\(602\) | −4.59522 | −0.187287 | ||||||||
\(603\) | 12.6509 | − | 25.0320i | 0.515184 | − | 1.01938i | ||||
\(604\) | 6.75083 | − | 6.75083i | 0.274687 | − | 0.274687i | ||||
\(605\) | −3.47727 | + | 3.47727i | −0.141371 | + | 0.141371i | ||||
\(606\) | 5.12564 | − | 7.07930i | 0.208215 | − | 0.287577i | ||||
\(607\) | −5.09736 | −0.206896 | −0.103448 | − | 0.994635i | \(-0.532987\pi\) | ||||
−0.103448 | + | 0.994635i | \(0.532987\pi\) | |||||||
\(608\) | −3.72791 | −0.151187 | ||||||||
\(609\) | 8.46938 | + | 6.13210i | 0.343197 | + | 0.248485i | ||||
\(610\) | 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 | 0.181467 | − | 0.983397i | \(-0.441915\pi\) |
0.983397 | − | 0.181467i | \(-0.0580845\pi\) | |||||||
\(614\) | 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 | 0.978893 | + | 0.204373i | \(0.0655155\pi\) |
0.204373 | + | 0.978893i | \(0.434485\pi\) | |||||||
\(618\) | 24.3072 | + | 17.5992i | 0.977779 | + | 0.707943i | ||||
\(619\) | −2.81364 | − | 2.81364i | −0.113090 | − | 0.113090i | 0.648298 | − | 0.761387i | \(-0.275481\pi\) |
−0.761387 | + | 0.648298i | \(0.775481\pi\) | |||||||
\(620\) | − | 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 | ||||||||
\(624\) | 2.57735 | + | 5.68834i | 0.103177 | + | 0.227716i | ||||
\(625\) | 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 | ||||
\(630\) | 3.35106 | − | 6.63067i | 0.133509 | − | 0.264172i | ||||
\(631\) | −22.1341 | − | 22.1341i | −0.881143 | − | 0.881143i | 0.112507 | − | 0.993651i | \(-0.464112\pi\) |
−0.993651 | + | 0.112507i | \(0.964112\pi\) | |||||||
\(632\) | 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 | ||||||
\(639\) | −27.8893 | − | 14.0949i | −1.10328 | − | 0.557585i | ||||
\(640\) | 2.47645 | 0.0978904 | ||||||||
\(641\) | −22.5807 | −0.891885 | −0.445943 | − | 0.895062i | \(-0.647131\pi\) | ||||
−0.445943 | + | 0.895062i | \(0.647131\pi\) | |||||||
\(642\) | −10.7294 | − | 7.76843i | −0.423456 | − | 0.306595i | ||||
\(643\) | −11.9697 | + | 11.9697i | −0.472039 | + | 0.472039i | −0.902574 | − | 0.430535i | \(-0.858325\pi\) |
0.430535 | + | 0.902574i | \(0.358325\pi\) | |||||||
\(644\) | −0.338172 | + | 0.338172i | −0.0133258 | + | 0.0133258i | ||||
\(645\) | −15.9652 | − | 11.5593i | −0.628627 | − | 0.455146i | ||||
\(646\) | 11.3170 | 0.445261 | ||||||||
\(647\) | −49.1692 | −1.93304 | −0.966521 | − | 0.256586i | \(-0.917402\pi\) | ||||
−0.966521 | + | 0.256586i | \(0.917402\pi\) | |||||||
\(648\) | −1.34938 | + | 8.89827i | −0.0530086 | + | 0.349557i | ||||
\(649\) | − | 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 | ||||
\(657\) | 30.5240 | + | 15.4265i | 1.19085 | + | 0.601843i | ||||
\(658\) | −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 | 0.998440 | + | 0.0558331i | \(0.0177815\pi\) |
0.0558331 | + | 0.998440i | \(0.482219\pi\) | |||||||
\(662\) | 5.90994 | 0.229697 | ||||||||
\(663\) | −7.82419 | − | 17.2684i | −0.303866 | − | 0.670648i | ||||
\(664\) | −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 | ||||
\(669\) | −6.11867 | − | 4.43011i | −0.236561 | − | 0.171278i | ||||
\(670\) | −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 | \(0.106342\pi\) | ||||
−0.944711 | + | 0.327905i | \(0.893658\pi\) | |||||||
\(674\) | 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 | \(-0.0158249\pi\) | |||||||
\(678\) | −7.01122 | − | 5.07635i | −0.269264 | − | 0.194956i | ||||
\(679\) | 15.1584 | 0.581725 | ||||||||
\(680\) | −7.51789 | −0.288298 | ||||||||
\(681\) | 27.2001 | − | 37.5675i | 1.04231 | − | 1.43959i | ||||
\(682\) | −6.21961 | + | 6.21961i | −0.238161 | + | 0.238161i | ||||
\(683\) | 25.9379 | − | 25.9379i | 0.992486 | − | 0.992486i | −0.00748557 | − | 0.999972i | \(-0.502383\pi\) |
0.999972 | + | 0.00748557i | \(0.00238275\pi\) | |||||||
\(684\) | −9.98142 | − | 5.04449i | −0.381649 | − | 0.192881i | ||||
\(685\) | −14.2539 | −0.544615 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −17.5943 | + | 24.3004i | −0.671264 | + | 0.927119i | ||||
\(688\) | − | 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 | −0.480914 | + | 0.876768i | \(0.659695\pi\) |
−0.876768 | + | 0.480914i | \(0.840305\pi\) | |||||||
\(692\) | 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 | ||||
\(696\) | −6.13210 | + | 8.46938i | −0.232437 | + | 0.321031i | ||||
\(697\) | 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 | \(-0.680698\pi\) | ||||
−0.537676 | + | 0.843151i | \(0.680698\pi\) | |||||||
\(702\) | −0.796461 | + | 18.7181i | −0.0300605 | + | 0.706468i | ||||
\(703\) | −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 | ||||
\(708\) | −5.41225 | + | 7.47515i | −0.203405 | + | 0.280933i | ||||
\(709\) | 34.7099 | + | 34.7099i | 1.30356 | + | 1.30356i | 0.925975 | + | 0.377584i | \(0.123245\pi\) |
0.377584 | + | 0.925975i | \(0.376755\pi\) | |||||||
\(710\) | −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 | ||||||||
\(717\) | 16.2180 | − | 22.3995i | 0.605671 | − | 0.836525i | ||||
\(718\) | −18.8830 | −0.704707 | ||||||||
\(719\) | −3.99422 | −0.148959 | −0.0744797 | − | 0.997223i | \(-0.523730\pi\) | ||||
−0.0744797 | + | 0.997223i | \(0.523730\pi\) | |||||||
\(720\) | 6.63067 | + | 3.35106i | 0.247111 | + | 0.124887i | ||||
\(721\) | 12.2513 | − | 12.2513i | 0.456263 | − | 0.456263i | ||||
\(722\) | −3.60816 | + | 3.60816i | −0.134282 | + | 0.134282i | ||||
\(723\) | 4.51311 | − | 6.23331i | 0.167844 | − | 0.231819i | ||||
\(724\) | −19.5037 | −0.724848 | ||||||||
\(725\) | 6.83877 | 0.253985 | ||||||||
\(726\) | −2.78587 | − | 2.01705i | −0.103393 | − | 0.0748599i | ||||
\(727\) | 31.5807i | 1.17126i | 0.810577 | + | 0.585632i | \(0.199154\pi\) | ||||
−0.810577 | + | 0.585632i | \(0.800846\pi\) | |||||||
\(728\) | 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 | −0.761246 | − | 0.648463i | \(-0.775412\pi\) |
0.648463 | + | 0.761246i | \(0.275412\pi\) | |||||||
\(734\) | 16.4995 | + | 16.4995i | 0.609006 | + | 0.609006i | ||||
\(735\) | −3.47430 | − | 2.51550i | −0.128151 | − | 0.0927856i | ||||
\(736\) | −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 | 0.797861 | − | 0.602841i | \(-0.205965\pi\) |
−0.602841 | + | 0.797861i | \(0.705965\pi\) | |||||||
\(740\) | 14.7584 | 0.542531 | ||||||||
\(741\) | −21.7886 | − | 8.20066i | −0.800425 | − | 0.301259i | ||||
\(742\) | 5.90009 | 0.216599 | ||||||||
\(743\) | 21.0757 | + | 21.0757i | 0.773191 | + | 0.773191i | 0.978663 | − | 0.205472i | \(-0.0658728\pi\) |
−0.205472 | + | 0.978663i | \(0.565873\pi\) | |||||||
\(744\) | 5.01049 | − | 0.802036i | 0.183693 | − | 0.0294041i | ||||
\(745\) | 14.4957i | 0.531082i | ||||||||
\(746\) | 4.42841 | + | 4.42841i | 0.162135 | + | 0.162135i | ||||
\(747\) | −37.7482 | − | 19.0775i | −1.38113 | − | 0.698007i | ||||
\(748\) | 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 | \(0.405861\pi\) | ||||
−0.291454 | + | 0.956585i | \(0.594139\pi\) | |||||||
\(752\) | 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 | ||||||
\(756\) | 4.94970 | + | 1.58129i | 0.180019 | + | 0.0575109i | ||||
\(757\) | −37.6352 | −1.36787 | −0.683937 | − | 0.729541i | \(-0.739734\pi\) | ||||
−0.683937 | + | 0.729541i | \(0.739734\pi\) | |||||||
\(758\) | −33.8031 | −1.22779 | ||||||||
\(759\) | 2.01444 | + | 1.45852i | 0.0731195 | + | 0.0529408i | ||||
\(760\) | −6.52800 | + | 6.52800i | −0.236796 | + | 0.236796i | ||||
\(761\) | 4.70073 | − | 4.70073i | 0.170401 | − | 0.170401i | −0.616754 | − | 0.787156i | \(-0.711553\pi\) |
0.787156 | + | 0.616754i | \(0.211553\pi\) | |||||||
\(762\) | −0.731981 | − | 0.529978i | −0.0265169 | − | 0.0191991i | ||||
\(763\) | 4.17149 | 0.151018 | ||||||||
\(764\) | 0.854794 | 0.0309254 | ||||||||
\(765\) | −20.1290 | − | 10.1730i | −0.727767 | − | 0.367804i | ||||
\(766\) | 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 | −0.884596 | − | 0.466358i | \(-0.845566\pi\) |
0.466358 | + | 0.884596i | \(0.345566\pi\) | |||||||
\(770\) | 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 | \(-0.0656947\pi\) |
−0.204924 | + | 0.978778i | \(0.565695\pi\) | |||||||
\(774\) | 6.21811 | − | 12.3036i | 0.223505 | − | 0.442245i | ||||
\(775\) | −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 | ||||||||
\(780\) | 14.4742 | + | 5.44771i | 0.518260 | + | 0.195059i | ||||
\(781\) | 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 | ||||
\(786\) | −14.2187 | − | 10.2948i | −0.507163 | − | 0.367202i | ||||
\(787\) | −16.1871 | − | 16.1871i | −0.577009 | − | 0.577009i | 0.357069 | − | 0.934078i | \(-0.383776\pi\) |
−0.934078 | + | 0.357069i | \(0.883776\pi\) | |||||||
\(788\) | 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 | ||||||||
\(795\) | 20.4987 | + | 14.8417i | 0.727013 | + | 0.526380i | ||||
\(796\) | 0.778109 | 0.0275793 | ||||||||
\(797\) | 39.4250 | 1.39651 | 0.698253 | − | 0.715851i | \(-0.253961\pi\) | ||||
0.698253 | + | 0.715851i | \(0.253961\pi\) | |||||||
\(798\) | −3.78669 | + | 5.23000i | −0.134047 | + | 0.185140i | ||||
\(799\) | −21.1660 | + | 21.1660i | −0.748799 | + | 0.748799i | ||||
\(800\) | 0.801028 | − | 0.801028i | 0.0283206 | − | 0.0283206i | ||||
\(801\) | −20.9107 | + | 41.3757i | −0.738845 | + | 1.46194i | ||||
\(802\) | 24.8643 | 0.877988 | ||||||||
\(803\) | −34.2278 | −1.20787 | ||||||||
\(804\) | 9.49649 | − | 13.1161i | 0.334915 | − | 0.462570i | ||||
\(805\) | 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 | −0.997525 | − | 0.0703186i | \(-0.977598\pi\) |
0.0703186 | + | 0.997525i | \(0.477598\pi\) | |||||||
\(812\) | 4.26874 | + | 4.26874i | 0.149804 | + | 0.149804i | ||||
\(813\) | 13.5276 | − | 18.6837i | 0.474434 | − | 0.655267i | ||||
\(814\) | −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 | ||||||||
\(819\) | 10.5983 | + | 2.16218i | 0.370336 | + | 0.0755528i | ||||
\(820\) | −16.9525 | −0.592008 | ||||||||
\(821\) | 31.8342 | + | 31.8342i | 1.11102 | + | 1.11102i | 0.993012 | + | 0.118010i | \(0.0376513\pi\) |
0.118010 | + | 0.993012i | \(0.462349\pi\) | |||||||
\(822\) | −1.57574 | − | 9.84399i | −0.0549603 | − | 0.343349i | ||||
\(823\) | 29.9746i | 1.04485i | 0.852685 | + | 0.522425i | \(0.174973\pi\) | ||||
−0.852685 | + | 0.522425i | \(0.825027\pi\) | |||||||
\(824\) | 12.2513 | + | 12.2513i | 0.426795 | + | 0.426795i | ||||
\(825\) | −3.45479 | + | 4.77160i | −0.120280 | + | 0.166126i | ||||
\(826\) | 3.76763 | + | 3.76763i | 0.131093 | + | 0.131093i | ||||
\(827\) | −22.1847 | + | 22.1847i | −0.771436 | + | 0.771436i | −0.978358 | − | 0.206921i | \(-0.933656\pi\) |
0.206921 | + | 0.978358i | \(0.433656\pi\) | |||||||
\(828\) | −0.447847 | − | 1.36305i | −0.0155638 | − | 0.0473694i | ||||
\(829\) | 25.2640i | 0.877455i | 0.898620 | + | 0.438728i | \(0.144571\pi\) | ||||
−0.898620 | + | 0.438728i | \(0.855429\pi\) | |||||||
\(830\) | −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 | ||||||||
\(834\) | −0.176506 | + | 0.243782i | −0.00611190 | + | 0.00844148i | ||||
\(835\) | −22.5795 | −0.781396 | ||||||||
\(836\) | 11.1926 | 0.387103 | ||||||||
\(837\) | 14.5008 | + | 4.63259i | 0.501221 | + | 0.160126i | ||||
\(838\) | −22.6068 | + | 22.6068i | −0.780939 | + | 0.780939i | ||||
\(839\) | −21.9032 | + | 21.9032i | −0.756182 | + | 0.756182i | −0.975625 | − | 0.219443i | \(-0.929576\pi\) |
0.219443 | + | 0.975625i | \(0.429576\pi\) | |||||||
\(840\) | 2.51550 | − | 3.47430i | 0.0867930 | − | 0.119875i | ||||
\(841\) | −7.44434 | −0.256701 | ||||||||
\(842\) | 15.6945 | 0.540869 | ||||||||
\(843\) | 28.9133 | + | 20.9341i | 0.995826 | + | 0.721009i | ||||
\(844\) | − | 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 | ||||
\(852\) | −14.6132 | − | 10.5804i | −0.500641 | − | 0.362480i | ||||
\(853\) | −26.8634 | − | 26.8634i | −0.919786 | − | 0.919786i | 0.0772278 | − | 0.997013i | \(-0.475393\pi\) |
−0.997013 | + | 0.0772278i | \(0.975393\pi\) | |||||||
\(854\) | 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 | \(-0.422993\pi\) | ||||
0.239572 | + | 0.970879i | \(0.422993\pi\) | |||||||
\(858\) | −7.73818 | − | 17.0785i | −0.264177 | − | 0.583052i | ||||
\(859\) | −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 | \(-0.384135\pi\) |
−0.934480 | + | 0.356017i | \(0.884135\pi\) | |||||||
\(864\) | −1.58129 | + | 4.94970i | −0.0537965 | + | 0.168392i | ||||
\(865\) | 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 | ||||||||
\(873\) | −20.5118 | + | 40.5863i | −0.694220 | + | 1.37364i | ||||
\(874\) | 1.78286 | 0.0603062 | ||||||||
\(875\) | 9.57688 | 0.323758 | ||||||||
\(876\) | 15.9938 | + | 11.5800i | 0.540379 | + | 0.391252i | ||||
\(877\) | −11.7092 | + | 11.7092i | −0.395392 | + | 0.395392i | −0.876604 | − | 0.481212i | \(-0.840197\pi\) |
0.481212 | + | 0.876604i | \(0.340197\pi\) | |||||||
\(878\) | 16.1502 | − | 16.1502i | 0.545043 | − | 0.545043i | ||||
\(879\) | −44.7577 | − | 32.4060i | −1.50964 | − | 1.09303i | ||||
\(880\) | −7.43524 | −0.250642 | ||||||||
\(881\) | 34.9545 | 1.17765 | 0.588824 | − | 0.808261i | \(-0.299591\pi\) | ||||
0.588824 | + | 0.808261i | \(0.299591\pi\) | |||||||
\(882\) | 1.35317 | − | 2.67749i | 0.0455636 | − | 0.0901557i | ||||
\(883\) | − | 38.3261i | − | 1.28978i | −0.764277 | − | 0.644888i | \(-0.776904\pi\) | ||
0.764277 | − | 0.644888i | \(-0.223096\pi\) | |||||||
\(884\) | −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 | ||||
\(891\) | 4.05134 | − | 26.7159i | 0.135725 | − | 0.895018i | ||||
\(892\) | −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 | ||||||||
\(897\) | −1.23261 | − | 2.72044i | −0.0411557 | − | 0.0908327i | ||||
\(898\) | 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 | ||||
\(903\) | −6.44678 | − | 4.66767i | −0.214535 | − | 0.155330i | ||||
\(904\) | −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 | \(-0.944162\pi\) | ||
0.984653 | − | 0.174522i | \(-0.0558379\pi\) | |||||||
\(908\) | 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 | \(-0.286154\pi\) | |||||||
\(912\) | −5.23000 | − | 3.78669i | −0.173183 | − | 0.125390i | ||||
\(913\) | 42.3286 | 1.40087 | ||||||||
\(914\) | 9.72824 | 0.321781 | ||||||||
\(915\) | −33.3603 | + | 46.0758i | −1.10286 | + | 1.52322i | ||||
\(916\) | −12.2479 | + | 12.2479i | −0.404683 | + | 0.404683i | ||||
\(917\) | −7.16651 | + | 7.16651i | −0.236659 | + | 0.236659i | ||||
\(918\) | 4.80039 | − | 15.0260i | 0.158436 | − | 0.495933i | ||||
\(919\) | −55.3266 | −1.82506 | −0.912529 | − | 0.409013i | \(-0.865873\pi\) | ||||
−0.912529 | + | 0.409013i | \(0.865873\pi\) | |||||||
\(920\) | −1.18436 | −0.0390471 | ||||||||
\(921\) | −21.5685 | + | 29.7894i | −0.710705 | + | 0.981594i | ||||
\(922\) | − | 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 | \(-0.365487\pi\) |
−0.912032 | + | 0.410119i | \(0.865487\pi\) | |||||||
\(930\) | 7.36949 | − | 10.1784i | 0.241655 | − | 0.333763i | ||||
\(931\) | 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 | ||||||||
\(936\) | −2.16218 | + | 10.5983i | −0.0706732 | + | 0.346418i | ||||
\(937\) | 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 | −0.996989 | − | 0.0775433i | \(-0.975292\pi\) |
−0.0775433 | − | 0.996989i | \(-0.524708\pi\) | |||||||
\(942\) | 4.21304 | − | 5.81887i | 0.137268 | − | 0.189589i | ||||
\(943\) | 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 | \(-0.731442\pi\) |
0.747107 | + | 0.664703i | \(0.231442\pi\) | |||||||
\(948\) | 19.8429 | − | 3.17629i | 0.644469 | − | 0.103161i | ||||
\(949\) | 35.6975 | + | 20.3774i | 1.15879 | + | 0.661480i | ||||
\(950\) | 4.22307i | 0.137014i | ||||||||
\(951\) | 28.2585 | − | 39.0294i | 0.916346 | − | 1.26562i | ||||
\(952\) | −3.03575 | −0.0983891 | ||||||||
\(953\) | −5.10013 | −0.165209 | −0.0826047 | − | 0.996582i | \(-0.526324\pi\) | ||||
−0.0826047 | + | 0.996582i | \(0.526324\pi\) | |||||||
\(954\) | −7.98382 | + | 15.7974i | −0.258486 | + | 0.511460i | ||||
\(955\) | 1.49685 | − | 1.49685i | 0.0484368 | − | 0.0484368i | ||||
\(956\) | 11.2898 | − | 11.2898i | 0.365139 | − | 0.365139i | ||||
\(957\) | 18.4109 | − | 25.4282i | 0.595139 | − | 0.821979i | ||||
\(958\) | 0.757750 | 0.0244818 | ||||||||
\(959\) | −5.75578 | −0.185864 | ||||||||
\(960\) | 3.47430 | + | 2.51550i | 0.112132 | + | 0.0811874i | ||||
\(961\) | 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 | −0.210376 | + | 0.977621i | \(0.567469\pi\) |
−0.977621 | + | 0.210376i | \(0.932531\pi\) | |||||||
\(968\) | −1.40413 | − | 1.40413i | −0.0451306 | − | 0.0451306i | ||||
\(969\) | 15.8770 | + | 11.4954i | 0.510041 | + | 0.369286i | ||||
\(970\) | 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 | ||||||||
\(975\) | 6.44390 | − | 2.91969i | 0.206370 | − | 0.0935048i | ||||
\(976\) | −13.2619 | −0.424503 | ||||||||
\(977\) | −24.4879 | − | 24.4879i | −0.783437 | − | 0.783437i | 0.196972 | − | 0.980409i | \(-0.436889\pi\) |
−0.980409 | + | 0.196972i | \(0.936889\pi\) | |||||||
\(978\) | 32.2688 | − | 5.16532i | 1.03184 | − | 0.165169i | ||||
\(979\) | − | 46.3962i | − | 1.48283i | ||||||
\(980\) | −1.75112 | − | 1.75112i | −0.0559374 | − | 0.0559374i | ||||
\(981\) | −5.64473 | + | 11.1691i | −0.180222 | + | 0.356602i | ||||
\(982\) | 22.8390 | + | 22.8390i | 0.728821 | + | 0.728821i | ||||
\(983\) | −10.8336 | + | 10.8336i | −0.345537 | + | 0.345537i | −0.858444 | − | 0.512907i | \(-0.828568\pi\) |
0.512907 | + | 0.858444i | \(0.328568\pi\) | |||||||
\(984\) | −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 | ||||||||
\(990\) | −19.9078 | − | 10.0611i | −0.632710 | − | 0.319764i | ||||
\(991\) | 49.1490 | 1.56127 | 0.780635 | − | 0.624988i | \(-0.214896\pi\) | ||||
0.780635 | + | 0.624988i | \(0.214896\pi\) | |||||||
\(992\) | 2.92963 | 0.0930159 | ||||||||
\(993\) | 8.29125 | + | 6.00313i | 0.263115 | + | 0.190503i | ||||
\(994\) | −7.36537 | + | 7.36537i | −0.233615 | + | 0.233615i | ||||
\(995\) | 1.36256 | − | 1.36256i | 0.0431961 | − | 0.0431961i | ||||
\(996\) | −19.7790 | − | 14.3206i | −0.626723 | − | 0.453767i | ||||
\(997\) | −3.17797 | −0.100647 | −0.0503237 | − | 0.998733i | \(-0.516025\pi\) | ||||
−0.0503237 | + | 0.998733i | \(0.516025\pi\) | |||||||
\(998\) | 34.6609 | 1.09717 | ||||||||
\(999\) | −9.42368 | + | 29.4977i | −0.298152 | + | 0.933267i |
(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.d.239.8 | yes | 20 | |
3.2 | odd | 2 | 546.2.p.c.239.3 | ✓ | 20 | ||
13.8 | odd | 4 | 546.2.p.c.281.3 | yes | 20 | ||
39.8 | even | 4 | inner | 546.2.p.d.281.8 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.p.c.239.3 | ✓ | 20 | 3.2 | odd | 2 | ||
546.2.p.c.281.3 | yes | 20 | 13.8 | odd | 4 | ||
546.2.p.d.239.8 | yes | 20 | 1.1 | even | 1 | trivial | |
546.2.p.d.281.8 | yes | 20 | 39.8 | even | 4 | inner |