Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [62,2,Mod(33,62)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(62, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("62.33");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 62 = 2 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 62.d (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.495072492532\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.1903140625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 6x^{6} + x^{5} + 29x^{4} + 43x^{3} + 194x^{2} + 209x + 361 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 33.1 | ||
Root | \(0.671745 + 2.06742i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 62.33 |
Dual form | 62.2.d.b.47.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/62\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | + | 0.587785i | 0.572061 | + | 0.415627i | ||||
\(3\) | −1.75865 | + | 1.27773i | −1.01536 | + | 0.737700i | −0.965326 | − | 0.261047i | \(-0.915932\pi\) |
−0.0500312 | + | 0.998748i | \(0.515932\pi\) | |||||||
\(4\) | 0.309017 | + | 0.951057i | 0.154508 | + | 0.475528i | ||||
\(5\) | 1.89927 | 0.849378 | 0.424689 | − | 0.905339i | \(-0.360383\pi\) | ||||
0.424689 | + | 0.905339i | \(0.360383\pi\) | |||||||
\(6\) | −2.17381 | −0.887455 | ||||||||
\(7\) | −0.500000 | − | 1.53884i | −0.188982 | − | 0.581628i | 0.811012 | − | 0.585030i | \(-0.198917\pi\) |
−0.999994 | + | 0.00340203i | \(0.998917\pi\) | |||||||
\(8\) | −0.309017 | + | 0.951057i | −0.109254 | + | 0.336249i | ||||
\(9\) | 0.533195 | − | 1.64101i | 0.177732 | − | 0.547002i | ||||
\(10\) | 1.53654 | + | 1.11636i | 0.485896 | + | 0.353024i | ||||
\(11\) | −1.87668 | − | 5.77584i | −0.565842 | − | 1.74148i | −0.665438 | − | 0.746453i | \(-0.731755\pi\) |
0.0995961 | − | 0.995028i | \(-0.468245\pi\) | |||||||
\(12\) | −1.75865 | − | 1.27773i | −0.507679 | − | 0.368850i | ||||
\(13\) | 1.34015 | − | 0.973673i | 0.371689 | − | 0.270048i | −0.386222 | − | 0.922406i | \(-0.626220\pi\) |
0.757911 | + | 0.652358i | \(0.226220\pi\) | |||||||
\(14\) | 0.500000 | − | 1.53884i | 0.133631 | − | 0.411273i | ||||
\(15\) | −3.34015 | + | 2.42676i | −0.862422 | + | 0.626586i | ||||
\(16\) | −0.809017 | + | 0.587785i | −0.202254 | + | 0.146946i | ||||
\(17\) | −0.586906 | + | 1.80631i | −0.142346 | + | 0.438094i | −0.996660 | − | 0.0816618i | \(-0.973977\pi\) |
0.854315 | + | 0.519756i | \(0.173977\pi\) | |||||||
\(18\) | 1.39592 | − | 1.01420i | 0.329022 | − | 0.239049i | ||||
\(19\) | 3.12344 | + | 2.26932i | 0.716567 | + | 0.520617i | 0.885286 | − | 0.465048i | \(-0.153963\pi\) |
−0.168718 | + | 0.985664i | \(0.553963\pi\) | |||||||
\(20\) | 0.586906 | + | 1.80631i | 0.131236 | + | 0.403903i | ||||
\(21\) | 2.84556 | + | 2.06742i | 0.620951 | + | 0.451147i | ||||
\(22\) | 1.87668 | − | 5.77584i | 0.400110 | − | 1.23141i | ||||
\(23\) | −2.88403 | + | 8.87614i | −0.601362 | + | 1.85080i | −0.0812718 | + | 0.996692i | \(0.525898\pi\) |
−0.520091 | + | 0.854111i | \(0.674102\pi\) | |||||||
\(24\) | −0.671745 | − | 2.06742i | −0.137119 | − | 0.422010i | ||||
\(25\) | −1.39279 | −0.278557 | ||||||||
\(26\) | 1.65651 | 0.324868 | ||||||||
\(27\) | −0.856169 | − | 2.63502i | −0.164770 | − | 0.507109i | ||||
\(28\) | 1.30902 | − | 0.951057i | 0.247381 | − | 0.179733i | ||||
\(29\) | −7.89064 | − | 5.73289i | −1.46526 | − | 1.06457i | −0.981955 | − | 0.189116i | \(-0.939438\pi\) |
−0.483300 | − | 0.875455i | \(-0.660562\pi\) | |||||||
\(30\) | −4.12865 | −0.753784 | ||||||||
\(31\) | 5.42912 | + | 1.23478i | 0.975098 | + | 0.221773i | ||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 10.6804 | + | 7.75978i | 1.85922 | + | 1.35080i | ||||
\(34\) | −1.53654 | + | 1.11636i | −0.263514 | + | 0.191454i | ||||
\(35\) | −0.949633 | − | 2.92267i | −0.160517 | − | 0.494021i | ||||
\(36\) | 1.72546 | 0.287576 | ||||||||
\(37\) | −0.864666 | −0.142150 | −0.0710751 | − | 0.997471i | \(-0.522643\pi\) | ||||
−0.0710751 | + | 0.997471i | \(0.522643\pi\) | |||||||
\(38\) | 1.19305 | + | 3.67183i | 0.193538 | + | 0.595649i | ||||
\(39\) | −1.11275 | + | 3.42470i | −0.178183 | + | 0.548391i | ||||
\(40\) | −0.586906 | + | 1.80631i | −0.0927979 | + | 0.285603i | ||||
\(41\) | −3.03654 | − | 2.20617i | −0.474228 | − | 0.344547i | 0.324859 | − | 0.945762i | \(-0.394683\pi\) |
−0.799087 | + | 0.601216i | \(0.794683\pi\) | |||||||
\(42\) | 1.08691 | + | 3.34515i | 0.167713 | + | 0.516168i | ||||
\(43\) | 5.63533 | + | 4.09431i | 0.859380 | + | 0.624376i | 0.927716 | − | 0.373286i | \(-0.121769\pi\) |
−0.0683359 | + | 0.997662i | \(0.521769\pi\) | |||||||
\(44\) | 4.91322 | − | 3.56967i | 0.740696 | − | 0.538147i | ||||
\(45\) | 1.01268 | − | 3.11671i | 0.150961 | − | 0.464611i | ||||
\(46\) | −7.55050 | + | 5.48576i | −1.11326 | + | 0.808831i | ||||
\(47\) | −1.50000 | + | 1.08981i | −0.218797 | + | 0.158966i | −0.691785 | − | 0.722103i | \(-0.743175\pi\) |
0.472988 | + | 0.881069i | \(0.343175\pi\) | |||||||
\(48\) | 0.671745 | − | 2.06742i | 0.0969580 | − | 0.298406i | ||||
\(49\) | 3.54508 | − | 2.57565i | 0.506441 | − | 0.367951i | ||||
\(50\) | −1.12679 | − | 0.818660i | −0.159352 | − | 0.115776i | ||||
\(51\) | −1.27582 | − | 3.92658i | −0.178651 | − | 0.549831i | ||||
\(52\) | 1.34015 | + | 0.973673i | 0.185845 | + | 0.135024i | ||||
\(53\) | −0.492652 | + | 1.51623i | −0.0676709 | + | 0.208270i | −0.979174 | − | 0.203024i | \(-0.934923\pi\) |
0.911503 | + | 0.411294i | \(0.134923\pi\) | |||||||
\(54\) | 0.856169 | − | 2.63502i | 0.116510 | − | 0.358580i | ||||
\(55\) | −3.56432 | − | 10.9699i | −0.480613 | − | 1.47918i | ||||
\(56\) | 1.61803 | 0.216219 | ||||||||
\(57\) | −8.39263 | −1.11163 | ||||||||
\(58\) | −3.01396 | − | 9.27600i | −0.395752 | − | 1.21800i | ||||
\(59\) | −1.07815 | + | 0.783323i | −0.140363 | + | 0.101980i | −0.655751 | − | 0.754977i | \(-0.727648\pi\) |
0.515388 | + | 0.856957i | \(0.327648\pi\) | |||||||
\(60\) | −3.34015 | − | 2.42676i | −0.431211 | − | 0.313293i | ||||
\(61\) | 4.11155 | 0.526431 | 0.263215 | − | 0.964737i | \(-0.415217\pi\) | ||||
0.263215 | + | 0.964737i | \(0.415217\pi\) | |||||||
\(62\) | 3.66646 | + | 4.19011i | 0.465641 | + | 0.532145i | ||||
\(63\) | −2.79185 | −0.351739 | ||||||||
\(64\) | −0.809017 | − | 0.587785i | −0.101127 | − | 0.0734732i | ||||
\(65\) | 2.54529 | − | 1.84926i | 0.315705 | − | 0.229373i | ||||
\(66\) | 4.07956 | + | 12.5556i | 0.502159 | + | 1.54549i | ||||
\(67\) | −6.86079 | −0.838179 | −0.419089 | − | 0.907945i | \(-0.637651\pi\) | ||||
−0.419089 | + | 0.907945i | \(0.637651\pi\) | |||||||
\(68\) | −1.89927 | −0.230320 | ||||||||
\(69\) | −6.26934 | − | 19.2951i | −0.754740 | − | 2.32285i | ||||
\(70\) | 0.949633 | − | 2.92267i | 0.113503 | − | 0.349326i | ||||
\(71\) | 0.694247 | − | 2.13667i | 0.0823920 | − | 0.253577i | −0.901371 | − | 0.433047i | \(-0.857438\pi\) |
0.983763 | + | 0.179470i | \(0.0574384\pi\) | |||||||
\(72\) | 1.39592 | + | 1.01420i | 0.164511 | + | 0.119524i | ||||
\(73\) | 2.02993 | + | 6.24748i | 0.237585 | + | 0.731213i | 0.996768 | + | 0.0803349i | \(0.0255990\pi\) |
−0.759183 | + | 0.650878i | \(0.774401\pi\) | |||||||
\(74\) | −0.699529 | − | 0.508238i | −0.0813186 | − | 0.0590814i | ||||
\(75\) | 2.44943 | − | 1.77961i | 0.282835 | − | 0.205492i | ||||
\(76\) | −1.19305 | + | 3.67183i | −0.136852 | + | 0.421188i | ||||
\(77\) | −7.94976 | + | 5.77584i | −0.905959 | + | 0.658218i | ||||
\(78\) | −2.91322 | + | 2.11658i | −0.329858 | + | 0.239656i | ||||
\(79\) | 1.14062 | − | 3.51046i | 0.128329 | − | 0.394957i | −0.866164 | − | 0.499761i | \(-0.833421\pi\) |
0.994493 | + | 0.104803i | \(0.0334213\pi\) | |||||||
\(80\) | −1.53654 | + | 1.11636i | −0.171790 | + | 0.124813i | ||||
\(81\) | 9.06032 | + | 6.58271i | 1.00670 | + | 0.731412i | ||||
\(82\) | −1.15985 | − | 3.56967i | −0.128085 | − | 0.394204i | ||||
\(83\) | 6.35410 | + | 4.61653i | 0.697453 | + | 0.506729i | 0.879102 | − | 0.476634i | \(-0.158143\pi\) |
−0.181649 | + | 0.983364i | \(0.558143\pi\) | |||||||
\(84\) | −1.08691 | + | 3.34515i | −0.118591 | + | 0.364986i | ||||
\(85\) | −1.11469 | + | 3.43066i | −0.120905 | + | 0.372108i | ||||
\(86\) | 2.15251 | + | 6.62473i | 0.232111 | + | 0.714363i | ||||
\(87\) | 21.2020 | 2.27309 | ||||||||
\(88\) | 6.07308 | 0.647392 | ||||||||
\(89\) | 3.50748 | + | 10.7949i | 0.371792 | + | 1.14426i | 0.945618 | + | 0.325280i | \(0.105459\pi\) |
−0.573826 | + | 0.818977i | \(0.694541\pi\) | |||||||
\(90\) | 2.65123 | − | 1.92623i | 0.279464 | − | 0.203043i | ||||
\(91\) | −2.16840 | − | 1.57544i | −0.227310 | − | 0.165151i | ||||
\(92\) | −9.33293 | −0.973025 | ||||||||
\(93\) | −11.1256 | + | 4.76542i | −1.15368 | + | 0.494151i | ||||
\(94\) | −1.85410 | −0.191236 | ||||||||
\(95\) | 5.93225 | + | 4.31003i | 0.608636 | + | 0.442200i | ||||
\(96\) | 1.75865 | − | 1.27773i | 0.179491 | − | 0.130408i | ||||
\(97\) | 3.43774 | + | 10.5803i | 0.349050 | + | 1.07427i | 0.959380 | + | 0.282118i | \(0.0910369\pi\) |
−0.610330 | + | 0.792147i | \(0.708963\pi\) | |||||||
\(98\) | 4.38197 | 0.442645 | ||||||||
\(99\) | −10.4788 | −1.05316 | ||||||||
\(100\) | −0.430395 | − | 1.32462i | −0.0430395 | − | 0.132462i | ||||
\(101\) | 4.50863 | − | 13.8761i | 0.448625 | − | 1.38073i | −0.429834 | − | 0.902908i | \(-0.641428\pi\) |
0.878459 | − | 0.477818i | \(-0.158572\pi\) | |||||||
\(102\) | 1.27582 | − | 3.92658i | 0.126325 | − | 0.388789i | ||||
\(103\) | −5.75023 | − | 4.17779i | −0.566587 | − | 0.411650i | 0.267277 | − | 0.963620i | \(-0.413876\pi\) |
−0.833864 | + | 0.551970i | \(0.813876\pi\) | |||||||
\(104\) | 0.511890 | + | 1.57544i | 0.0501949 | + | 0.154484i | ||||
\(105\) | 5.40447 | + | 3.92658i | 0.527422 | + | 0.383195i | ||||
\(106\) | −1.28978 | + | 0.937079i | −0.125274 | + | 0.0910172i | ||||
\(107\) | 2.69552 | − | 8.29597i | 0.260586 | − | 0.802002i | −0.732091 | − | 0.681207i | \(-0.761456\pi\) |
0.992677 | − | 0.120795i | \(-0.0385445\pi\) | |||||||
\(108\) | 2.24148 | − | 1.62853i | 0.215686 | − | 0.156705i | ||||
\(109\) | 0.194327 | − | 0.141187i | 0.0186131 | − | 0.0135232i | −0.578440 | − | 0.815725i | \(-0.696338\pi\) |
0.597053 | + | 0.802202i | \(0.296338\pi\) | |||||||
\(110\) | 3.56432 | − | 10.9699i | 0.339845 | − | 1.04594i | ||||
\(111\) | 1.52064 | − | 1.10481i | 0.144333 | − | 0.104864i | ||||
\(112\) | 1.30902 | + | 0.951057i | 0.123690 | + | 0.0898664i | ||||
\(113\) | −2.06519 | − | 6.35601i | −0.194277 | − | 0.597923i | −0.999984 | − | 0.00560910i | \(-0.998215\pi\) |
0.805707 | − | 0.592314i | \(-0.201785\pi\) | |||||||
\(114\) | −6.78978 | − | 4.93306i | −0.635921 | − | 0.462024i | ||||
\(115\) | −5.47755 | + | 16.8582i | −0.510784 | + | 1.57203i | ||||
\(116\) | 3.01396 | − | 9.27600i | 0.279839 | − | 0.861255i | ||||
\(117\) | −0.883243 | − | 2.71834i | −0.0816559 | − | 0.251311i | ||||
\(118\) | −1.33267 | −0.122682 | ||||||||
\(119\) | 3.07308 | 0.281709 | ||||||||
\(120\) | −1.27582 | − | 3.92658i | −0.116466 | − | 0.358446i | ||||
\(121\) | −20.9392 | + | 15.2132i | −1.90356 | + | 1.38302i | ||||
\(122\) | 3.32632 | + | 2.41671i | 0.301151 | + | 0.218799i | ||||
\(123\) | 8.15911 | 0.735683 | ||||||||
\(124\) | 0.503344 | + | 5.54497i | 0.0452016 | + | 0.497953i | ||||
\(125\) | −12.1416 | −1.08598 | ||||||||
\(126\) | −2.25865 | − | 1.64101i | −0.201217 | − | 0.146192i | ||||
\(127\) | 0.367930 | − | 0.267317i | 0.0326485 | − | 0.0237205i | −0.571341 | − | 0.820713i | \(-0.693577\pi\) |
0.603990 | + | 0.796992i | \(0.293577\pi\) | |||||||
\(128\) | −0.309017 | − | 0.951057i | −0.0273135 | − | 0.0840623i | ||||
\(129\) | −15.1420 | −1.33318 | ||||||||
\(130\) | 3.14616 | 0.275936 | ||||||||
\(131\) | 5.19565 | + | 15.9906i | 0.453946 | + | 1.39710i | 0.872368 | + | 0.488850i | \(0.162584\pi\) |
−0.418421 | + | 0.908253i | \(0.637416\pi\) | |||||||
\(132\) | −4.07956 | + | 12.5556i | −0.355080 | + | 1.09282i | ||||
\(133\) | 1.93039 | − | 5.94114i | 0.167386 | − | 0.515163i | ||||
\(134\) | −5.55050 | − | 4.03267i | −0.479490 | − | 0.348370i | ||||
\(135\) | −1.62609 | − | 5.00460i | −0.139952 | − | 0.430727i | ||||
\(136\) | −1.53654 | − | 1.11636i | −0.131757 | − | 0.0957271i | ||||
\(137\) | 15.6879 | − | 11.3979i | 1.34031 | − | 0.973790i | 0.340875 | − | 0.940109i | \(-0.389277\pi\) |
0.999433 | − | 0.0336817i | \(-0.0107232\pi\) | |||||||
\(138\) | 6.26934 | − | 19.2951i | 0.533682 | − | 1.64250i | ||||
\(139\) | 8.76753 | − | 6.36999i | 0.743652 | − | 0.540295i | −0.150200 | − | 0.988656i | \(-0.547992\pi\) |
0.893853 | + | 0.448360i | \(0.147992\pi\) | |||||||
\(140\) | 2.48617 | − | 1.80631i | 0.210120 | − | 0.152661i | ||||
\(141\) | 1.24548 | − | 3.83320i | 0.104889 | − | 0.322814i | ||||
\(142\) | 1.81756 | − | 1.32054i | 0.152527 | − | 0.110817i | ||||
\(143\) | −8.13881 | − | 5.91319i | −0.680601 | − | 0.494486i | ||||
\(144\) | 0.533195 | + | 1.64101i | 0.0444329 | + | 0.136750i | ||||
\(145\) | −14.9864 | − | 10.8883i | −1.24456 | − | 0.904222i | ||||
\(146\) | −2.02993 | + | 6.24748i | −0.167998 | + | 0.517045i | ||||
\(147\) | −2.94356 | + | 9.05935i | −0.242781 | + | 0.747203i | ||||
\(148\) | −0.267196 | − | 0.822346i | −0.0219634 | − | 0.0675964i | ||||
\(149\) | 3.18677 | 0.261070 | 0.130535 | − | 0.991444i | \(-0.458330\pi\) | ||||
0.130535 | + | 0.991444i | \(0.458330\pi\) | |||||||
\(150\) | 3.02766 | 0.247207 | ||||||||
\(151\) | −1.66039 | − | 5.11016i | −0.135121 | − | 0.415859i | 0.860488 | − | 0.509471i | \(-0.170159\pi\) |
−0.995609 | + | 0.0936117i | \(0.970159\pi\) | |||||||
\(152\) | −3.12344 | + | 2.26932i | −0.253345 | + | 0.184066i | ||||
\(153\) | 2.65123 | + | 1.92623i | 0.214339 | + | 0.155727i | ||||
\(154\) | −9.82645 | −0.791838 | ||||||||
\(155\) | 10.3113 | + | 2.34518i | 0.828227 | + | 0.188369i | ||||
\(156\) | −3.60094 | −0.288306 | ||||||||
\(157\) | −5.16646 | − | 3.75365i | −0.412329 | − | 0.299574i | 0.362215 | − | 0.932094i | \(-0.382021\pi\) |
−0.774544 | + | 0.632520i | \(0.782021\pi\) | |||||||
\(158\) | 2.98617 | − | 2.16958i | 0.237567 | − | 0.172603i | ||||
\(159\) | −1.07093 | − | 3.29599i | −0.0849304 | − | 0.261389i | ||||
\(160\) | −1.89927 | −0.150150 | ||||||||
\(161\) | 15.1010 | 1.19012 | ||||||||
\(162\) | 3.46073 | + | 10.6510i | 0.271901 | + | 0.836825i | ||||
\(163\) | 5.11610 | − | 15.7457i | 0.400724 | − | 1.23330i | −0.523690 | − | 0.851909i | \(-0.675445\pi\) |
0.924414 | − | 0.381391i | \(-0.124555\pi\) | |||||||
\(164\) | 1.15985 | − | 3.56967i | 0.0905694 | − | 0.278744i | ||||
\(165\) | 20.2850 | + | 14.7379i | 1.57918 | + | 1.14734i | ||||
\(166\) | 2.42705 | + | 7.46969i | 0.188376 | + | 0.579761i | ||||
\(167\) | −2.14603 | − | 1.55918i | −0.166065 | − | 0.120653i | 0.501649 | − | 0.865071i | \(-0.332727\pi\) |
−0.667714 | + | 0.744418i | \(0.732727\pi\) | |||||||
\(168\) | −2.84556 | + | 2.06742i | −0.219539 | + | 0.159505i | ||||
\(169\) | −3.16927 | + | 9.75401i | −0.243790 | + | 0.750308i | ||||
\(170\) | −2.91830 | + | 2.12027i | −0.223823 | + | 0.162617i | ||||
\(171\) | 5.38936 | − | 3.91560i | 0.412135 | − | 0.299434i | ||||
\(172\) | −2.15251 | + | 6.62473i | −0.164127 | + | 0.505131i | ||||
\(173\) | −2.63868 | + | 1.91711i | −0.200615 | + | 0.145755i | −0.683557 | − | 0.729897i | \(-0.739568\pi\) |
0.482942 | + | 0.875652i | \(0.339568\pi\) | |||||||
\(174\) | 17.1528 | + | 12.4622i | 1.30035 | + | 0.944758i | ||||
\(175\) | 0.696393 | + | 2.14328i | 0.0526424 | + | 0.162017i | ||||
\(176\) | 4.91322 | + | 3.56967i | 0.370348 | + | 0.269074i | ||||
\(177\) | 0.895213 | − | 2.75518i | 0.0672883 | − | 0.207092i | ||||
\(178\) | −3.50748 | + | 10.7949i | −0.262897 | + | 0.809112i | ||||
\(179\) | 0.464738 | + | 1.43032i | 0.0347362 | + | 0.106907i | 0.966921 | − | 0.255075i | \(-0.0821002\pi\) |
−0.932185 | + | 0.361982i | \(0.882100\pi\) | |||||||
\(180\) | 3.27710 | 0.244261 | ||||||||
\(181\) | −15.9657 | −1.18672 | −0.593359 | − | 0.804938i | \(-0.702199\pi\) | ||||
−0.593359 | + | 0.804938i | \(0.702199\pi\) | |||||||
\(182\) | −0.828255 | − | 2.54911i | −0.0613944 | − | 0.188952i | ||||
\(183\) | −7.23079 | + | 5.25347i | −0.534515 | + | 0.388348i | ||||
\(184\) | −7.55050 | − | 5.48576i | −0.556630 | − | 0.404415i | ||||
\(185\) | −1.64223 | −0.120739 | ||||||||
\(186\) | −11.8019 | − | 2.68418i | −0.865356 | − | 0.196814i | ||||
\(187\) | 11.5344 | 0.843478 | ||||||||
\(188\) | −1.50000 | − | 1.08981i | −0.109399 | − | 0.0794828i | ||||
\(189\) | −3.62679 | + | 2.63502i | −0.263810 | + | 0.191669i | ||||
\(190\) | 2.26592 | + | 6.97378i | 0.164387 | + | 0.505931i | ||||
\(191\) | −19.9830 | −1.44592 | −0.722960 | − | 0.690890i | \(-0.757219\pi\) | ||||
−0.722960 | + | 0.690890i | \(0.757219\pi\) | |||||||
\(192\) | 2.17381 | 0.156881 | ||||||||
\(193\) | 3.85097 | + | 11.8521i | 0.277199 | + | 0.853130i | 0.988629 | + | 0.150373i | \(0.0480476\pi\) |
−0.711431 | + | 0.702756i | \(0.751952\pi\) | |||||||
\(194\) | −3.43774 | + | 10.5803i | −0.246816 | + | 0.759620i | ||||
\(195\) | −2.11341 | + | 6.50442i | −0.151345 | + | 0.465791i | ||||
\(196\) | 3.54508 | + | 2.57565i | 0.253220 | + | 0.183975i | ||||
\(197\) | −3.44356 | − | 10.5982i | −0.245344 | − | 0.755090i | −0.995580 | − | 0.0939201i | \(-0.970060\pi\) |
0.750236 | − | 0.661170i | \(-0.229940\pi\) | |||||||
\(198\) | −8.47755 | − | 6.15930i | −0.602473 | − | 0.437722i | ||||
\(199\) | 11.7224 | − | 8.51680i | 0.830977 | − | 0.603740i | −0.0888588 | − | 0.996044i | \(-0.528322\pi\) |
0.919835 | + | 0.392304i | \(0.128322\pi\) | |||||||
\(200\) | 0.430395 | − | 1.32462i | 0.0304335 | − | 0.0936647i | ||||
\(201\) | 12.0657 | − | 8.76627i | 0.851051 | − | 0.618325i | ||||
\(202\) | 11.8037 | − | 8.57592i | 0.830508 | − | 0.603399i | ||||
\(203\) | −4.87668 | + | 15.0089i | −0.342276 | + | 1.05342i | ||||
\(204\) | 3.34015 | − | 2.42676i | 0.233857 | − | 0.169907i | ||||
\(205\) | −5.76720 | − | 4.19011i | −0.402798 | − | 0.292650i | ||||
\(206\) | −2.19639 | − | 6.75980i | −0.153030 | − | 0.470978i | ||||
\(207\) | 13.0280 | + | 9.46543i | 0.905512 | + | 0.657893i | ||||
\(208\) | −0.511890 | + | 1.57544i | −0.0354932 | + | 0.109237i | ||||
\(209\) | 7.24548 | − | 22.2993i | 0.501181 | − | 1.54248i | ||||
\(210\) | 2.06432 | + | 6.35333i | 0.142452 | + | 0.438422i | ||||
\(211\) | −12.3395 | −0.849483 | −0.424742 | − | 0.905315i | \(-0.639635\pi\) | ||||
−0.424742 | + | 0.905315i | \(0.639635\pi\) | |||||||
\(212\) | −1.59425 | −0.109494 | ||||||||
\(213\) | 1.50916 | + | 4.64473i | 0.103406 | + | 0.318251i | ||||
\(214\) | 7.05697 | − | 5.12719i | 0.482405 | − | 0.350488i | ||||
\(215\) | 10.7030 | + | 7.77619i | 0.729939 | + | 0.530331i | ||||
\(216\) | 2.77062 | 0.188517 | ||||||||
\(217\) | −0.814427 | − | 8.97194i | −0.0552869 | − | 0.609055i | ||||
\(218\) | 0.240201 | 0.0162685 | ||||||||
\(219\) | −11.5526 | − | 8.39343i | −0.780650 | − | 0.567175i | ||||
\(220\) | 9.33152 | − | 6.77975i | 0.629131 | − | 0.457090i | ||||
\(221\) | 0.972215 | + | 2.99217i | 0.0653983 | + | 0.201275i | ||||
\(222\) | 1.87962 | 0.126152 | ||||||||
\(223\) | −21.8887 | −1.46578 | −0.732888 | − | 0.680349i | \(-0.761828\pi\) | ||||
−0.732888 | + | 0.680349i | \(0.761828\pi\) | |||||||
\(224\) | 0.500000 | + | 1.53884i | 0.0334077 | + | 0.102818i | ||||
\(225\) | −0.742627 | + | 2.28557i | −0.0495085 | + | 0.152371i | ||||
\(226\) | 2.06519 | − | 6.35601i | 0.137375 | − | 0.422795i | ||||
\(227\) | −4.09351 | − | 2.97411i | −0.271696 | − | 0.197399i | 0.443591 | − | 0.896229i | \(-0.353704\pi\) |
−0.715287 | + | 0.698830i | \(0.753704\pi\) | |||||||
\(228\) | −2.59346 | − | 7.98186i | −0.171756 | − | 0.528612i | ||||
\(229\) | 18.1062 | + | 13.1549i | 1.19649 | + | 0.869302i | 0.993935 | − | 0.109969i | \(-0.0350752\pi\) |
0.202556 | + | 0.979271i | \(0.435075\pi\) | |||||||
\(230\) | −14.3404 | + | 10.4189i | −0.945578 | + | 0.687003i | ||||
\(231\) | 6.60086 | − | 20.3154i | 0.434305 | − | 1.33665i | ||||
\(232\) | 7.89064 | − | 5.73289i | 0.518046 | − | 0.376382i | ||||
\(233\) | 0.225584 | − | 0.163896i | 0.0147785 | − | 0.0107372i | −0.580371 | − | 0.814352i | \(-0.697093\pi\) |
0.595150 | + | 0.803615i | \(0.297093\pi\) | |||||||
\(234\) | 0.883243 | − | 2.71834i | 0.0577394 | − | 0.177704i | ||||
\(235\) | −2.84890 | + | 2.06985i | −0.185842 | + | 0.135022i | ||||
\(236\) | −1.07815 | − | 0.783323i | −0.0701817 | − | 0.0509900i | ||||
\(237\) | 2.47948 | + | 7.63107i | 0.161060 | + | 0.495691i | ||||
\(238\) | 2.48617 | + | 1.80631i | 0.161155 | + | 0.117086i | ||||
\(239\) | −2.41309 | + | 7.42674i | −0.156090 | + | 0.480396i | −0.998270 | − | 0.0588012i | \(-0.981272\pi\) |
0.842180 | + | 0.539197i | \(0.181272\pi\) | |||||||
\(240\) | 1.27582 | − | 3.92658i | 0.0823540 | − | 0.253459i | ||||
\(241\) | −4.79263 | − | 14.7502i | −0.308721 | − | 0.950145i | −0.978263 | − | 0.207370i | \(-0.933509\pi\) |
0.669542 | − | 0.742774i | \(-0.266491\pi\) | |||||||
\(242\) | −25.8823 | −1.66378 | ||||||||
\(243\) | −16.0330 | −1.02852 | ||||||||
\(244\) | 1.27054 | + | 3.91032i | 0.0813380 | + | 0.250333i | ||||
\(245\) | 6.73306 | − | 4.89186i | 0.430159 | − | 0.312529i | ||||
\(246\) | 6.60086 | + | 4.79581i | 0.420856 | + | 0.305769i | ||||
\(247\) | 6.39544 | 0.406932 | ||||||||
\(248\) | −2.85204 | + | 4.78183i | −0.181104 | + | 0.303646i | ||||
\(249\) | −17.0733 | −1.08198 | ||||||||
\(250\) | −9.82277 | − | 7.13666i | −0.621246 | − | 0.451362i | ||||
\(251\) | −12.0230 | + | 8.73520i | −0.758883 | + | 0.551361i | −0.898568 | − | 0.438835i | \(-0.855391\pi\) |
0.139685 | + | 0.990196i | \(0.455391\pi\) | |||||||
\(252\) | −0.862728 | − | 2.65520i | −0.0543467 | − | 0.167262i | ||||
\(253\) | 56.6796 | 3.56341 | ||||||||
\(254\) | 0.454786 | 0.0285358 | ||||||||
\(255\) | −2.42313 | − | 7.45761i | −0.151742 | − | 0.467014i | ||||
\(256\) | 0.309017 | − | 0.951057i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | 0.411817 | − | 1.26744i | 0.0256884 | − | 0.0790609i | −0.937390 | − | 0.348280i | \(-0.886766\pi\) |
0.963079 | + | 0.269219i | \(0.0867657\pi\) | |||||||
\(258\) | −12.2502 | − | 8.90026i | −0.762661 | − | 0.554106i | ||||
\(259\) | 0.432333 | + | 1.33058i | 0.0268639 | + | 0.0826784i | ||||
\(260\) | 2.54529 | + | 1.84926i | 0.157852 | + | 0.114686i | ||||
\(261\) | −13.6149 | + | 9.89184i | −0.842744 | + | 0.612289i | ||||
\(262\) | −5.19565 | + | 15.9906i | −0.320989 | + | 0.987901i | ||||
\(263\) | −11.1614 | + | 8.10922i | −0.688241 | + | 0.500036i | −0.876081 | − | 0.482163i | \(-0.839851\pi\) |
0.187841 | + | 0.982200i | \(0.439851\pi\) | |||||||
\(264\) | −10.6804 | + | 7.75978i | −0.657334 | + | 0.477581i | ||||
\(265\) | −0.935677 | + | 2.87972i | −0.0574782 | + | 0.176900i | ||||
\(266\) | 5.05384 | − | 3.67183i | 0.309871 | − | 0.225134i | ||||
\(267\) | −19.9614 | − | 14.5028i | −1.22162 | − | 0.887559i | ||||
\(268\) | −2.12010 | − | 6.52500i | −0.129506 | − | 0.398578i | ||||
\(269\) | 1.12472 | + | 0.817158i | 0.0685755 | + | 0.0498230i | 0.621545 | − | 0.783379i | \(-0.286505\pi\) |
−0.552969 | + | 0.833202i | \(0.686505\pi\) | |||||||
\(270\) | 1.62609 | − | 5.00460i | 0.0989608 | − | 0.304570i | ||||
\(271\) | 1.20630 | − | 3.71260i | 0.0732773 | − | 0.225524i | −0.907709 | − | 0.419599i | \(-0.862171\pi\) |
0.980987 | + | 0.194075i | \(0.0621706\pi\) | |||||||
\(272\) | −0.586906 | − | 1.80631i | −0.0355864 | − | 0.109524i | ||||
\(273\) | 5.82645 | 0.352633 | ||||||||
\(274\) | 19.3913 | 1.17147 | ||||||||
\(275\) | 2.61382 | + | 8.04451i | 0.157619 | + | 0.485102i | ||||
\(276\) | 16.4134 | − | 11.9250i | 0.987968 | − | 0.717801i | ||||
\(277\) | 5.88730 | + | 4.27737i | 0.353733 | + | 0.257002i | 0.750434 | − | 0.660946i | \(-0.229845\pi\) |
−0.396700 | + | 0.917948i | \(0.629845\pi\) | |||||||
\(278\) | 10.8373 | 0.649976 | ||||||||
\(279\) | 4.92106 | − | 8.25083i | 0.294616 | − | 0.493964i | ||||
\(280\) | 3.07308 | 0.183652 | ||||||||
\(281\) | 12.3703 | + | 8.98757i | 0.737952 | + | 0.536154i | 0.892069 | − | 0.451899i | \(-0.149253\pi\) |
−0.154117 | + | 0.988053i | \(0.549253\pi\) | |||||||
\(282\) | 3.26072 | − | 2.36905i | 0.194173 | − | 0.141075i | ||||
\(283\) | −5.62824 | − | 17.3219i | −0.334564 | − | 1.02968i | −0.966936 | − | 0.255018i | \(-0.917919\pi\) |
0.632372 | − | 0.774665i | \(-0.282081\pi\) | |||||||
\(284\) | 2.24663 | 0.133313 | ||||||||
\(285\) | −15.9398 | −0.944194 | ||||||||
\(286\) | −3.10875 | − | 9.56774i | −0.183824 | − | 0.565752i | ||||
\(287\) | −1.87668 | + | 5.77584i | −0.110777 | + | 0.340937i | ||||
\(288\) | −0.533195 | + | 1.64101i | −0.0314188 | + | 0.0966972i | ||||
\(289\) | 10.8350 | + | 7.87208i | 0.637352 | + | 0.463064i | ||||
\(290\) | −5.72431 | − | 17.6176i | −0.336143 | − | 1.03454i | ||||
\(291\) | −19.5646 | − | 14.2145i | −1.14690 | − | 0.833269i | ||||
\(292\) | −5.31443 | + | 3.86116i | −0.311003 | + | 0.225957i | ||||
\(293\) | −7.94027 | + | 24.4376i | −0.463875 | + | 1.42766i | 0.396516 | + | 0.918028i | \(0.370219\pi\) |
−0.860391 | + | 0.509634i | \(0.829781\pi\) | |||||||
\(294\) | −7.70635 | + | 5.59899i | −0.449443 | + | 0.326540i | ||||
\(295\) | −2.04770 | + | 1.48774i | −0.119222 | + | 0.0866195i | ||||
\(296\) | 0.267196 | − | 0.822346i | 0.0155305 | − | 0.0477979i | ||||
\(297\) | −13.6127 | + | 9.89019i | −0.789887 | + | 0.573887i | ||||
\(298\) | 2.57815 | + | 1.87314i | 0.149348 | + | 0.108508i | ||||
\(299\) | 4.77743 | + | 14.7034i | 0.276286 | + | 0.850321i | ||||
\(300\) | 2.44943 | + | 1.77961i | 0.141418 | + | 0.102746i | ||||
\(301\) | 3.48283 | − | 10.7190i | 0.200747 | − | 0.617835i | ||||
\(302\) | 1.66039 | − | 5.11016i | 0.0955448 | − | 0.294057i | ||||
\(303\) | 9.80090 | + | 30.1641i | 0.563047 | + | 1.73288i | ||||
\(304\) | −3.86079 | −0.221431 | ||||||||
\(305\) | 7.80894 | 0.447138 | ||||||||
\(306\) | 1.01268 | + | 3.11671i | 0.0578910 | + | 0.178170i | ||||
\(307\) | 19.4980 | − | 14.1661i | 1.11281 | − | 0.808503i | 0.129705 | − | 0.991553i | \(-0.458597\pi\) |
0.983104 | + | 0.183050i | \(0.0585970\pi\) | |||||||
\(308\) | −7.94976 | − | 5.77584i | −0.452980 | − | 0.329109i | ||||
\(309\) | 15.4508 | 0.878963 | ||||||||
\(310\) | 6.96359 | + | 7.95814i | 0.395505 | + | 0.451992i | ||||
\(311\) | 20.6382 | 1.17028 | 0.585142 | − | 0.810931i | \(-0.301039\pi\) | ||||
0.585142 | + | 0.810931i | \(0.301039\pi\) | |||||||
\(312\) | −2.91322 | − | 2.11658i | −0.164929 | − | 0.119828i | ||||
\(313\) | 8.02090 | − | 5.82753i | 0.453368 | − | 0.329391i | −0.337556 | − | 0.941305i | \(-0.609600\pi\) |
0.790924 | + | 0.611914i | \(0.209600\pi\) | |||||||
\(314\) | −1.97341 | − | 6.07354i | −0.111366 | − | 0.342750i | ||||
\(315\) | −5.30246 | −0.298760 | ||||||||
\(316\) | 3.69111 | 0.207641 | ||||||||
\(317\) | −4.11130 | − | 12.6533i | −0.230914 | − | 0.710679i | −0.997637 | − | 0.0687019i | \(-0.978114\pi\) |
0.766724 | − | 0.641977i | \(-0.221886\pi\) | |||||||
\(318\) | 1.07093 | − | 3.29599i | 0.0600549 | − | 0.184830i | ||||
\(319\) | −18.3040 | + | 56.3339i | −1.02483 | + | 3.15409i | ||||
\(320\) | −1.53654 | − | 1.11636i | −0.0858951 | − | 0.0624065i | ||||
\(321\) | 5.85956 | + | 18.0339i | 0.327049 | + | 1.00655i | ||||
\(322\) | 12.2170 | + | 8.87614i | 0.680824 | + | 0.494648i | ||||
\(323\) | −5.93225 | + | 4.31003i | −0.330079 | + | 0.239817i | ||||
\(324\) | −3.46073 | + | 10.6510i | −0.192263 | + | 0.591725i | ||||
\(325\) | −1.86654 | + | 1.35612i | −0.103537 | + | 0.0752239i | ||||
\(326\) | 13.3941 | − | 9.73139i | 0.741831 | − | 0.538972i | ||||
\(327\) | −0.161354 | + | 0.496596i | −0.00892289 | + | 0.0274618i | ||||
\(328\) | 3.03654 | − | 2.20617i | 0.167665 | − | 0.121816i | ||||
\(329\) | 2.42705 | + | 1.76336i | 0.133808 | + | 0.0972169i | ||||
\(330\) | 7.74817 | + | 23.8464i | 0.426523 | + | 1.31270i | ||||
\(331\) | 15.4639 | + | 11.2352i | 0.849974 | + | 0.617542i | 0.925139 | − | 0.379629i | \(-0.123948\pi\) |
−0.0751647 | + | 0.997171i | \(0.523948\pi\) | |||||||
\(332\) | −2.42705 | + | 7.46969i | −0.133202 | + | 0.409953i | ||||
\(333\) | −0.461035 | + | 1.41892i | −0.0252646 | + | 0.0777564i | ||||
\(334\) | −0.819709 | − | 2.52281i | −0.0448525 | − | 0.138042i | ||||
\(335\) | −13.0305 | −0.711931 | ||||||||
\(336\) | −3.51730 | −0.191884 | ||||||||
\(337\) | −6.41850 | − | 19.7541i | −0.349638 | − | 1.07608i | −0.959054 | − | 0.283225i | \(-0.908596\pi\) |
0.609415 | − | 0.792851i | \(-0.291404\pi\) | |||||||
\(338\) | −8.29726 | + | 6.02831i | −0.451311 | + | 0.327897i | ||||
\(339\) | 11.7532 | + | 8.53923i | 0.638348 | + | 0.463787i | ||||
\(340\) | −3.60721 | −0.195629 | ||||||||
\(341\) | −3.05685 | − | 33.6750i | −0.165538 | − | 1.82360i | ||||
\(342\) | 6.66162 | 0.360219 | ||||||||
\(343\) | −14.8992 | − | 10.8249i | −0.804480 | − | 0.584489i | ||||
\(344\) | −5.63533 | + | 4.09431i | −0.303837 | + | 0.220750i | ||||
\(345\) | −11.9072 | − | 36.6464i | −0.641060 | − | 1.97298i | ||||
\(346\) | −3.26159 | −0.175344 | ||||||||
\(347\) | 25.5798 | 1.37320 | 0.686598 | − | 0.727037i | \(-0.259103\pi\) | ||||
0.686598 | + | 0.727037i | \(0.259103\pi\) | |||||||
\(348\) | 6.55177 | + | 20.1643i | 0.351212 | + | 1.08092i | ||||
\(349\) | 0.149083 | − | 0.458830i | 0.00798022 | − | 0.0245606i | −0.946987 | − | 0.321272i | \(-0.895890\pi\) |
0.954967 | + | 0.296711i | \(0.0958898\pi\) | |||||||
\(350\) | −0.696393 | + | 2.14328i | −0.0372238 | + | 0.114563i | ||||
\(351\) | −3.71303 | − | 2.69768i | −0.198187 | − | 0.143991i | ||||
\(352\) | 1.87668 | + | 5.77584i | 0.100028 | + | 0.307853i | ||||
\(353\) | −14.8380 | − | 10.7804i | −0.789747 | − | 0.573785i | 0.118141 | − | 0.992997i | \(-0.462306\pi\) |
−0.907888 | + | 0.419212i | \(0.862306\pi\) | |||||||
\(354\) | 2.34370 | − | 1.70280i | 0.124566 | − | 0.0905026i | ||||
\(355\) | 1.31856 | − | 4.05811i | 0.0699819 | − | 0.215382i | ||||
\(356\) | −9.18269 | + | 6.67162i | −0.486682 | + | 0.353595i | ||||
\(357\) | −5.40447 | + | 3.92658i | −0.286035 | + | 0.207816i | ||||
\(358\) | −0.464738 | + | 1.43032i | −0.0245622 | + | 0.0755946i | ||||
\(359\) | 7.57308 | − | 5.50216i | 0.399692 | − | 0.290393i | −0.369724 | − | 0.929142i | \(-0.620548\pi\) |
0.769415 | + | 0.638749i | \(0.220548\pi\) | |||||||
\(360\) | 2.65123 | + | 1.92623i | 0.139732 | + | 0.101521i | ||||
\(361\) | −1.26521 | − | 3.89391i | −0.0665900 | − | 0.204943i | ||||
\(362\) | −12.9165 | − | 9.38438i | −0.678876 | − | 0.493232i | ||||
\(363\) | 17.3863 | − | 53.5095i | 0.912543 | − | 2.80852i | ||||
\(364\) | 0.828255 | − | 2.54911i | 0.0434124 | − | 0.133610i | ||||
\(365\) | 3.85538 | + | 11.8656i | 0.201800 | + | 0.621076i | ||||
\(366\) | −8.93774 | −0.467183 | ||||||||
\(367\) | −1.27429 | −0.0665173 | −0.0332586 | − | 0.999447i | \(-0.510589\pi\) | ||||
−0.0332586 | + | 0.999447i | \(0.510589\pi\) | |||||||
\(368\) | −2.88403 | − | 8.87614i | −0.150341 | − | 0.462701i | ||||
\(369\) | −5.23941 | + | 3.80666i | −0.272753 | + | 0.198167i | ||||
\(370\) | −1.32859 | − | 0.965279i | −0.0690702 | − | 0.0501825i | ||||
\(371\) | 2.57956 | 0.133924 | ||||||||
\(372\) | −7.97020 | − | 9.10852i | −0.413236 | − | 0.472255i | ||||
\(373\) | −14.8187 | −0.767283 | −0.383641 | − | 0.923482i | \(-0.625330\pi\) | ||||
−0.383641 | + | 0.923482i | \(0.625330\pi\) | |||||||
\(374\) | 9.33152 | + | 6.77975i | 0.482521 | + | 0.350572i | ||||
\(375\) | 21.3528 | − | 15.5137i | 1.10266 | − | 0.801126i | ||||
\(376\) | −0.572949 | − | 1.76336i | −0.0295476 | − | 0.0909381i | ||||
\(377\) | −16.1566 | −0.832105 | ||||||||
\(378\) | −4.48296 | −0.230578 | ||||||||
\(379\) | −4.36397 | − | 13.4309i | −0.224162 | − | 0.689901i | −0.998376 | − | 0.0569758i | \(-0.981854\pi\) |
0.774213 | − | 0.632925i | \(-0.218146\pi\) | |||||||
\(380\) | −2.26592 | + | 6.97378i | −0.116239 | + | 0.357747i | ||||
\(381\) | −0.305500 | + | 0.940233i | −0.0156513 | + | 0.0481696i | ||||
\(382\) | −16.1666 | − | 11.7457i | −0.827155 | − | 0.600963i | ||||
\(383\) | −5.41309 | − | 16.6598i | −0.276596 | − | 0.851276i | −0.988793 | − | 0.149295i | \(-0.952299\pi\) |
0.712196 | − | 0.701980i | \(-0.247701\pi\) | |||||||
\(384\) | 1.75865 | + | 1.27773i | 0.0897457 | + | 0.0652041i | ||||
\(385\) | −15.0987 | + | 10.9699i | −0.769502 | + | 0.559076i | ||||
\(386\) | −3.85097 | + | 11.8521i | −0.196009 | + | 0.603254i | ||||
\(387\) | 9.72352 | − | 7.06455i | 0.494274 | − | 0.359111i | ||||
\(388\) | −9.00013 | + | 6.53898i | −0.456912 | + | 0.331966i | ||||
\(389\) | −0.398729 | + | 1.22716i | −0.0202164 | + | 0.0622196i | −0.960656 | − | 0.277742i | \(-0.910414\pi\) |
0.940439 | + | 0.339961i | \(0.110414\pi\) | |||||||
\(390\) | −5.53299 | + | 4.01995i | −0.280174 | + | 0.203558i | ||||
\(391\) | −14.3404 | − | 10.4189i | −0.725225 | − | 0.526907i | ||||
\(392\) | 1.35410 | + | 4.16750i | 0.0683925 | + | 0.210490i | ||||
\(393\) | −29.5690 | − | 21.4832i | −1.49156 | − | 1.08368i | ||||
\(394\) | 3.44356 | − | 10.5982i | 0.173484 | − | 0.533929i | ||||
\(395\) | 2.16633 | − | 6.66729i | 0.109000 | − | 0.335468i | ||||
\(396\) | −3.23813 | − | 9.96595i | −0.162722 | − | 0.500808i | ||||
\(397\) | −22.5535 | −1.13193 | −0.565963 | − | 0.824430i | \(-0.691496\pi\) | ||||
−0.565963 | + | 0.824430i | \(0.691496\pi\) | |||||||
\(398\) | 14.4896 | 0.726300 | ||||||||
\(399\) | 4.19631 | + | 12.9149i | 0.210078 | + | 0.646555i | ||||
\(400\) | 1.12679 | − | 0.818660i | 0.0563394 | − | 0.0409330i | ||||
\(401\) | 6.37668 | + | 4.63293i | 0.318436 | + | 0.231358i | 0.735508 | − | 0.677516i | \(-0.236944\pi\) |
−0.417072 | + | 0.908874i | \(0.636944\pi\) | |||||||
\(402\) | 14.9141 | 0.743846 | ||||||||
\(403\) | 8.47808 | − | 3.63140i | 0.422323 | − | 0.180893i | ||||
\(404\) | 14.5902 | 0.725891 | ||||||||
\(405\) | 17.2080 | + | 12.5023i | 0.855070 | + | 0.621245i | ||||
\(406\) | −12.7673 | + | 9.27600i | −0.633632 | + | 0.460360i | ||||
\(407\) | 1.62270 | + | 4.99417i | 0.0804345 | + | 0.247552i | ||||
\(408\) | 4.12865 | 0.204398 | ||||||||
\(409\) | 35.3309 | 1.74700 | 0.873500 | − | 0.486824i | \(-0.161845\pi\) | ||||
0.873500 | + | 0.486824i | \(0.161845\pi\) | |||||||
\(410\) | −2.20287 | − | 6.77975i | −0.108792 | − | 0.334828i | ||||
\(411\) | −13.0260 | + | 40.0899i | −0.642525 | + | 1.97749i | ||||
\(412\) | 2.19639 | − | 6.75980i | 0.108209 | − | 0.333032i | ||||
\(413\) | 1.74449 | + | 1.26744i | 0.0858405 | + | 0.0623668i | ||||
\(414\) | 4.97627 | + | 15.3154i | 0.244570 | + | 0.752710i | ||||
\(415\) | 12.0681 | + | 8.76801i | 0.592401 | + | 0.430405i | ||||
\(416\) | −1.34015 | + | 0.973673i | −0.0657060 | + | 0.0477382i | ||||
\(417\) | −7.27988 | + | 22.4052i | −0.356497 | + | 1.09719i | ||||
\(418\) | 18.9689 | − | 13.7817i | 0.927800 | − | 0.674086i | ||||
\(419\) | −21.8178 | + | 15.8516i | −1.06587 | + | 0.774400i | −0.975165 | − | 0.221478i | \(-0.928912\pi\) |
−0.0907048 | + | 0.995878i | \(0.528912\pi\) | |||||||
\(420\) | −2.06432 | + | 6.35333i | −0.100729 | + | 0.310011i | ||||
\(421\) | −3.06019 | + | 2.22336i | −0.149145 | + | 0.108360i | −0.659855 | − | 0.751393i | \(-0.729382\pi\) |
0.510711 | + | 0.859753i | \(0.329382\pi\) | |||||||
\(422\) | −9.98283 | − | 7.25295i | −0.485956 | − | 0.353068i | ||||
\(423\) | 0.988598 | + | 3.04259i | 0.0480673 | + | 0.147936i | ||||
\(424\) | −1.28978 | − | 0.937079i | −0.0626372 | − | 0.0455086i | ||||
\(425\) | 0.817434 | − | 2.51580i | 0.0396514 | − | 0.122034i | ||||
\(426\) | −1.50916 | + | 4.64473i | −0.0731192 | + | 0.225038i | ||||
\(427\) | −2.05578 | − | 6.32703i | −0.0994860 | − | 0.306187i | ||||
\(428\) | 8.72290 | 0.421637 | ||||||||
\(429\) | 21.8688 | 1.05584 | ||||||||
\(430\) | 4.08818 | + | 12.5821i | 0.197150 | + | 0.606764i | ||||
\(431\) | 5.30881 | − | 3.85708i | 0.255716 | − | 0.185789i | −0.452540 | − | 0.891744i | \(-0.649482\pi\) |
0.708256 | + | 0.705955i | \(0.249482\pi\) | |||||||
\(432\) | 2.24148 | + | 1.62853i | 0.107843 | + | 0.0783527i | ||||
\(433\) | −18.9340 | −0.909908 | −0.454954 | − | 0.890515i | \(-0.650344\pi\) | ||||
−0.454954 | + | 0.890515i | \(0.650344\pi\) | |||||||
\(434\) | 4.61469 | − | 7.73716i | 0.221512 | − | 0.371396i | ||||
\(435\) | 40.2682 | 1.93071 | ||||||||
\(436\) | 0.194327 | + | 0.141187i | 0.00930657 | + | 0.00676162i | ||||
\(437\) | −29.1509 | + | 21.1794i | −1.39448 | + | 1.01315i | ||||
\(438\) | −4.41269 | − | 13.5809i | −0.210846 | − | 0.648918i | ||||
\(439\) | 17.9417 | 0.856311 | 0.428156 | − | 0.903705i | \(-0.359163\pi\) | ||||
0.428156 | + | 0.903705i | \(0.359163\pi\) | |||||||
\(440\) | 11.5344 | 0.549881 | ||||||||
\(441\) | −2.33644 | − | 7.19083i | −0.111259 | − | 0.342420i | ||||
\(442\) | −0.972215 | + | 2.99217i | −0.0462436 | + | 0.142323i | ||||
\(443\) | 8.88457 | − | 27.3439i | 0.422119 | − | 1.29915i | −0.483608 | − | 0.875285i | \(-0.660674\pi\) |
0.905726 | − | 0.423863i | \(-0.139326\pi\) | |||||||
\(444\) | 1.52064 | + | 1.10481i | 0.0721666 | + | 0.0524321i | ||||
\(445\) | 6.66163 | + | 20.5024i | 0.315792 | + | 0.971907i | ||||
\(446\) | −17.7083 | − | 12.8659i | −0.838514 | − | 0.609216i | ||||
\(447\) | −5.60441 | + | 4.07185i | −0.265080 | + | 0.192592i | ||||
\(448\) | −0.500000 | + | 1.53884i | −0.0236228 | + | 0.0727034i | ||||
\(449\) | 16.2031 | − | 11.7723i | 0.764673 | − | 0.555567i | −0.135667 | − | 0.990754i | \(-0.543318\pi\) |
0.900340 | + | 0.435187i | \(0.143318\pi\) | |||||||
\(450\) | −1.94422 | + | 1.41256i | −0.0916515 | + | 0.0665887i | ||||
\(451\) | −7.04389 | + | 21.6789i | −0.331684 | + | 1.02082i | ||||
\(452\) | 5.40674 | − | 3.92823i | 0.254312 | − | 0.184768i | ||||
\(453\) | 9.44947 | + | 6.86544i | 0.443975 | + | 0.322567i | ||||
\(454\) | −1.56358 | − | 4.81221i | −0.0733826 | − | 0.225848i | ||||
\(455\) | −4.11837 | − | 2.99217i | −0.193072 | − | 0.140275i | ||||
\(456\) | 2.59346 | − | 7.98186i | 0.121450 | − | 0.373785i | ||||
\(457\) | −5.19879 | + | 16.0002i | −0.243189 | + | 0.748459i | 0.752740 | + | 0.658318i | \(0.228732\pi\) |
−0.995929 | + | 0.0901410i | \(0.971268\pi\) | |||||||
\(458\) | 6.91595 | + | 21.2851i | 0.323161 | + | 0.994588i | ||||
\(459\) | 5.26215 | 0.245616 | ||||||||
\(460\) | −17.7257 | −0.826466 | ||||||||
\(461\) | −1.05251 | − | 3.23930i | −0.0490204 | − | 0.150869i | 0.923550 | − | 0.383478i | \(-0.125274\pi\) |
−0.972570 | + | 0.232609i | \(0.925274\pi\) | |||||||
\(462\) | 17.2813 | − | 12.5556i | 0.803998 | − | 0.584139i | ||||
\(463\) | −20.5873 | − | 14.9575i | −0.956773 | − | 0.695136i | −0.00437363 | − | 0.999990i | \(-0.501392\pi\) |
−0.952399 | + | 0.304854i | \(0.901392\pi\) | |||||||
\(464\) | 9.75337 | 0.452789 | ||||||||
\(465\) | −21.1306 | + | 9.05081i | −0.979906 | + | 0.419721i | ||||
\(466\) | 0.278837 | 0.0129169 | ||||||||
\(467\) | −4.15263 | − | 3.01707i | −0.192161 | − | 0.139613i | 0.487545 | − | 0.873098i | \(-0.337893\pi\) |
−0.679706 | + | 0.733485i | \(0.737893\pi\) | |||||||
\(468\) | 2.31236 | − | 1.68003i | 0.106889 | − | 0.0776593i | ||||
\(469\) | 3.43039 | + | 10.5577i | 0.158401 | + | 0.487508i | ||||
\(470\) | −3.52143 | −0.162432 | ||||||||
\(471\) | 13.8822 | 0.639657 | ||||||||
\(472\) | −0.411817 | − | 1.26744i | −0.0189554 | − | 0.0583388i | ||||
\(473\) | 13.0723 | − | 40.2325i | 0.601067 | − | 1.84989i | ||||
\(474\) | −2.47948 | + | 7.63107i | −0.113886 | + | 0.350507i | ||||
\(475\) | −4.35029 | − | 3.16067i | −0.199605 | − | 0.145022i | ||||
\(476\) | 0.949633 | + | 2.92267i | 0.0435264 | + | 0.133960i | ||||
\(477\) | 2.22546 | + | 1.61689i | 0.101897 | + | 0.0740322i | ||||
\(478\) | −6.31756 | + | 4.58998i | −0.288959 | + | 0.209941i | ||||
\(479\) | −1.48604 | + | 4.57357i | −0.0678991 | + | 0.208972i | −0.979249 | − | 0.202661i | \(-0.935041\pi\) |
0.911350 | + | 0.411632i | \(0.135041\pi\) | |||||||
\(480\) | 3.34015 | − | 2.42676i | 0.152456 | − | 0.110766i | ||||
\(481\) | −1.15878 | + | 0.841901i | −0.0528357 | + | 0.0383874i | ||||
\(482\) | 4.79263 | − | 14.7502i | 0.218299 | − | 0.671854i | ||||
\(483\) | −26.5574 | + | 19.2951i | −1.20840 | + | 0.877955i | ||||
\(484\) | −20.9392 | − | 15.2132i | −0.951782 | − | 0.691510i | ||||
\(485\) | 6.52919 | + | 20.0948i | 0.296475 | + | 0.912457i | ||||
\(486\) | −12.9710 | − | 9.42397i | −0.588376 | − | 0.427480i | ||||
\(487\) | −7.87235 | + | 24.2286i | −0.356730 | + | 1.09790i | 0.598269 | + | 0.801295i | \(0.295855\pi\) |
−0.954999 | + | 0.296608i | \(0.904145\pi\) | |||||||
\(488\) | −1.27054 | + | 3.91032i | −0.0575147 | + | 0.177012i | ||||
\(489\) | 11.1214 | + | 34.2282i | 0.502928 | + | 1.54785i | ||||
\(490\) | 8.32252 | 0.375973 | ||||||||
\(491\) | 27.6920 | 1.24972 | 0.624862 | − | 0.780735i | \(-0.285155\pi\) | ||||
0.624862 | + | 0.780735i | \(0.285155\pi\) | |||||||
\(492\) | 2.52131 | + | 7.75978i | 0.113669 | + | 0.349838i | ||||
\(493\) | 14.9864 | − | 10.8883i | 0.674955 | − | 0.490383i | ||||
\(494\) | 5.17402 | + | 3.75915i | 0.232790 | + | 0.169132i | ||||
\(495\) | −19.9021 | −0.894532 | ||||||||
\(496\) | −5.11803 | + | 2.19220i | −0.229807 | + | 0.0984326i | ||||
\(497\) | −3.63513 | −0.163058 | ||||||||
\(498\) | −13.8126 | − | 10.0355i | −0.618958 | − | 0.449699i | ||||
\(499\) | 0.423370 | − | 0.307597i | 0.0189527 | − | 0.0137699i | −0.578269 | − | 0.815846i | \(-0.696271\pi\) |
0.597221 | + | 0.802077i | \(0.296271\pi\) | |||||||
\(500\) | −3.75196 | − | 11.5474i | −0.167793 | − | 0.516413i | ||||
\(501\) | 5.76633 | 0.257621 | ||||||||
\(502\) | −14.8612 | −0.663288 | ||||||||
\(503\) | 7.67422 | + | 23.6188i | 0.342177 | + | 1.05311i | 0.963078 | + | 0.269222i | \(0.0867667\pi\) |
−0.620901 | + | 0.783889i | \(0.713233\pi\) | |||||||
\(504\) | 0.862728 | − | 2.65520i | 0.0384289 | − | 0.118272i | ||||
\(505\) | 8.56308 | − | 26.3545i | 0.381052 | − | 1.17276i | ||||
\(506\) | 45.8547 | + | 33.3154i | 2.03849 | + | 1.48105i | ||||
\(507\) | −6.88939 | − | 21.2034i | −0.305969 | − | 0.941675i | ||||
\(508\) | 0.367930 | + | 0.267317i | 0.0163242 | + | 0.0118603i | ||||
\(509\) | −17.1770 | + | 12.4798i | −0.761357 | + | 0.553158i | −0.899326 | − | 0.437278i | \(-0.855942\pi\) |
0.137969 | + | 0.990437i | \(0.455942\pi\) | |||||||
\(510\) | 2.42313 | − | 7.45761i | 0.107298 | − | 0.330229i | ||||
\(511\) | 8.59892 | − | 6.24748i | 0.380394 | − | 0.276372i | ||||
\(512\) | 0.809017 | − | 0.587785i | 0.0357538 | − | 0.0259767i | ||||
\(513\) | 3.30549 | − | 10.1732i | 0.145941 | − | 0.449160i | ||||
\(514\) | 1.07815 | − | 0.783323i | 0.0475552 | − | 0.0345509i | ||||
\(515\) | −10.9212 | − | 7.93473i | −0.481247 | − | 0.349646i | ||||
\(516\) | −4.67914 | − | 14.4009i | −0.205988 | − | 0.633965i | ||||
\(517\) | 9.10962 | + | 6.61852i | 0.400640 | + | 0.291082i | ||||
\(518\) | −0.432333 | + | 1.33058i | −0.0189956 | + | 0.0584625i | ||||
\(519\) | 2.19095 | − | 6.74306i | 0.0961721 | − | 0.295987i | ||||
\(520\) | 0.972215 | + | 2.99217i | 0.0426345 | + | 0.131215i | ||||
\(521\) | 19.0563 | 0.834873 | 0.417437 | − | 0.908706i | \(-0.362929\pi\) | ||||
0.417437 | + | 0.908706i | \(0.362929\pi\) | |||||||
\(522\) | −16.8290 | −0.736585 | ||||||||
\(523\) | 13.4949 | + | 41.5331i | 0.590092 | + | 1.81612i | 0.577781 | + | 0.816192i | \(0.303919\pi\) |
0.0123112 | + | 0.999924i | \(0.496081\pi\) | |||||||
\(524\) | −13.6024 | + | 9.88272i | −0.594223 | + | 0.431729i | ||||
\(525\) | −3.96325 | − | 2.87947i | −0.172971 | − | 0.125670i | ||||
\(526\) | −13.7962 | −0.601544 | ||||||||
\(527\) | −5.41678 | + | 9.08197i | −0.235958 | + | 0.395617i | ||||
\(528\) | −13.2017 | −0.574531 | ||||||||
\(529\) | −51.8608 | − | 37.6791i | −2.25482 | − | 1.63822i | ||||
\(530\) | −2.44963 | + | 1.77976i | −0.106405 | + | 0.0773080i | ||||
\(531\) | 0.710572 | + | 2.18692i | 0.0308362 | + | 0.0949041i | ||||
\(532\) | 6.24689 | 0.270837 | ||||||||
\(533\) | −6.21750 | −0.269310 | ||||||||
\(534\) | −7.62459 | − | 23.4661i | −0.329948 | − | 1.01548i | ||||
\(535\) | 5.11952 | − | 15.7563i | 0.221336 | − | 0.681203i | ||||
\(536\) | 2.12010 | − | 6.52500i | 0.0915744 | − | 0.281837i | ||||
\(537\) | −2.64488 | − | 1.92162i | −0.114135 | − | 0.0829239i | ||||
\(538\) | 0.429605 | + | 1.32219i | 0.0185216 | + | 0.0570036i | ||||
\(539\) | −21.5296 | − | 15.6422i | −0.927345 | − | 0.673755i | ||||
\(540\) | 4.25716 | − | 3.09301i | 0.183199 | − | 0.133102i | ||||
\(541\) | −7.71361 | + | 23.7401i | −0.331634 | + | 1.02067i | 0.636722 | + | 0.771093i | \(0.280290\pi\) |
−0.968356 | + | 0.249572i | \(0.919710\pi\) | |||||||
\(542\) | 3.15812 | − | 2.29451i | 0.135653 | − | 0.0985577i | ||||
\(543\) | 28.0780 | − | 20.3999i | 1.20494 | − | 0.875442i | ||||
\(544\) | 0.586906 | − | 1.80631i | 0.0251634 | − | 0.0774449i | ||||
\(545\) | 0.369078 | − | 0.268151i | 0.0158096 | − | 0.0114863i | ||||
\(546\) | 4.71369 | + | 3.42470i | 0.201727 | + | 0.146564i | ||||
\(547\) | −7.30267 | − | 22.4753i | −0.312239 | − | 0.960974i | −0.976876 | − | 0.213807i | \(-0.931414\pi\) |
0.664636 | − | 0.747167i | \(-0.268586\pi\) | |||||||
\(548\) | 15.6879 | + | 11.3979i | 0.670154 | + | 0.486895i | ||||
\(549\) | 2.19226 | − | 6.74708i | 0.0935634 | − | 0.287958i | ||||
\(550\) | −2.61382 | + | 8.04451i | −0.111454 | + | 0.343019i | ||||
\(551\) | −11.6363 | − | 35.8127i | −0.495721 | − | 1.52567i | ||||
\(552\) | 20.2880 | 0.863515 | ||||||||
\(553\) | −5.97234 | −0.253970 | ||||||||
\(554\) | 2.24875 | + | 6.92093i | 0.0955401 | + | 0.294042i | ||||
\(555\) | 2.88811 | − | 2.09833i | 0.122593 | − | 0.0890693i | ||||
\(556\) | 8.76753 | + | 6.36999i | 0.371826 | + | 0.270148i | ||||
\(557\) | −3.16671 | −0.134178 | −0.0670888 | − | 0.997747i | \(-0.521371\pi\) | ||||
−0.0670888 | + | 0.997747i | \(0.521371\pi\) | |||||||
\(558\) | 8.83094 | − | 3.78254i | 0.373843 | − | 0.160128i | ||||
\(559\) | 11.5387 | 0.488034 | ||||||||
\(560\) | 2.48617 | + | 1.80631i | 0.105060 | + | 0.0763305i | ||||
\(561\) | −20.2850 | + | 14.7379i | −0.856432 | + | 0.622234i | ||||
\(562\) | 4.72505 | + | 14.5422i | 0.199314 | + | 0.613426i | ||||
\(563\) | 8.30875 | 0.350172 | 0.175086 | − | 0.984553i | \(-0.443980\pi\) | ||||
0.175086 | + | 0.984553i | \(0.443980\pi\) | |||||||
\(564\) | 4.03047 | 0.169713 | ||||||||
\(565\) | −3.92235 | − | 12.0718i | −0.165015 | − | 0.507862i | ||||
\(566\) | 5.62824 | − | 17.3219i | 0.236573 | − | 0.728095i | ||||
\(567\) | 5.59958 | − | 17.2338i | 0.235160 | − | 0.723749i | ||||
\(568\) | 1.81756 | + | 1.32054i | 0.0762633 | + | 0.0554085i | ||||
\(569\) | 8.86252 | + | 27.2760i | 0.371536 | + | 1.14347i | 0.945786 | + | 0.324791i | \(0.105294\pi\) |
−0.574249 | + | 0.818680i | \(0.694706\pi\) | |||||||
\(570\) | −12.8956 | − | 9.36920i | −0.540137 | − | 0.392433i | ||||
\(571\) | −34.7095 | + | 25.2179i | −1.45255 | + | 1.05534i | −0.467321 | + | 0.884088i | \(0.654781\pi\) |
−0.985227 | + | 0.171251i | \(0.945219\pi\) | |||||||
\(572\) | 3.10875 | − | 9.56774i | 0.129983 | − | 0.400047i | ||||
\(573\) | 35.1431 | − | 25.5330i | 1.46812 | − | 1.06666i | ||||
\(574\) | −4.91322 | + | 3.56967i | −0.205074 | + | 0.148995i | ||||
\(575\) | 4.01684 | − | 12.3626i | 0.167514 | − | 0.515555i | ||||
\(576\) | −1.39592 | + | 1.01420i | −0.0581634 | + | 0.0422582i | ||||
\(577\) | 11.6647 | + | 8.47487i | 0.485606 | + | 0.352813i | 0.803492 | − | 0.595316i | \(-0.202973\pi\) |
−0.317886 | + | 0.948129i | \(0.602973\pi\) | |||||||
\(578\) | 4.13860 | + | 12.7373i | 0.172143 | + | 0.529802i | ||||
\(579\) | −21.9163 | − | 15.9231i | −0.910809 | − | 0.661742i | ||||
\(580\) | 5.72431 | − | 17.6176i | 0.237689 | − | 0.731531i | ||||
\(581\) | 3.92705 | − | 12.0862i | 0.162922 | − | 0.501421i | ||||
\(582\) | −7.47300 | − | 22.9995i | −0.309766 | − | 0.953362i | ||||
\(583\) | 9.68203 | 0.400989 | ||||||||
\(584\) | −6.56899 | −0.271827 | ||||||||
\(585\) | −1.67751 | − | 5.16286i | −0.0693567 | − | 0.213458i | ||||
\(586\) | −20.7879 | + | 15.1033i | −0.858740 | + | 0.623911i | ||||
\(587\) | 27.1406 | + | 19.7188i | 1.12021 | + | 0.813882i | 0.984241 | − | 0.176831i | \(-0.0565847\pi\) |
0.135971 | + | 0.990713i | \(0.456585\pi\) | |||||||
\(588\) | −9.52557 | −0.392828 | ||||||||
\(589\) | 14.1554 | + | 16.1771i | 0.583265 | + | 0.666568i | ||||
\(590\) | −2.53109 | −0.104203 | ||||||||
\(591\) | 19.5977 | + | 14.2386i | 0.806142 | + | 0.585696i | ||||
\(592\) | 0.699529 | − | 0.508238i | 0.0287505 | − | 0.0208884i | ||||
\(593\) | −4.13814 | − | 12.7359i | −0.169933 | − | 0.523000i | 0.829433 | − | 0.558607i | \(-0.188664\pi\) |
−0.999366 | + | 0.0356062i | \(0.988664\pi\) | |||||||
\(594\) | −16.8262 | −0.690387 | ||||||||
\(595\) | 5.83659 | 0.239277 | ||||||||
\(596\) | 0.984766 | + | 3.03080i | 0.0403376 | + | 0.124146i | ||||
\(597\) | −9.73334 | + | 29.9561i | −0.398359 | + | 1.22602i | ||||
\(598\) | −4.77743 | + | 14.7034i | −0.195364 | + | 0.601268i | ||||
\(599\) | −33.3873 | − | 24.2573i | −1.36417 | − | 0.991128i | −0.998167 | − | 0.0605137i | \(-0.980726\pi\) |
−0.366003 | − | 0.930614i | \(-0.619274\pi\) | |||||||
\(600\) | 0.935597 | + | 2.87947i | 0.0381956 | + | 0.117554i | ||||
\(601\) | −12.6935 | − | 9.22238i | −0.517779 | − | 0.376189i | 0.297987 | − | 0.954570i | \(-0.403685\pi\) |
−0.815767 | + | 0.578381i | \(0.803685\pi\) | |||||||
\(602\) | 9.11816 | − | 6.62473i | 0.371629 | − | 0.270004i | ||||
\(603\) | −3.65814 | + | 11.2586i | −0.148971 | + | 0.458485i | ||||
\(604\) | 4.34696 | − | 3.15825i | 0.176875 | − | 0.128507i | ||||
\(605\) | −39.7691 | + | 28.8940i | −1.61684 | + | 1.17471i | ||||
\(606\) | −9.80090 | + | 30.1641i | −0.398134 | + | 1.22533i | ||||
\(607\) | 7.41235 | − | 5.38539i | 0.300858 | − | 0.218586i | −0.427106 | − | 0.904202i | \(-0.640467\pi\) |
0.727964 | + | 0.685615i | \(0.240467\pi\) | |||||||
\(608\) | −3.12344 | − | 2.26932i | −0.126672 | − | 0.0920329i | ||||
\(609\) | −10.6010 | − | 32.6265i | −0.429574 | − | 1.32209i | ||||
\(610\) | 6.31756 | + | 4.58998i | 0.255791 | + | 0.185843i | ||||
\(611\) | −0.949096 | + | 2.92102i | −0.0383963 | + | 0.118172i | ||||
\(612\) | −1.01268 | + | 3.11671i | −0.0409351 | + | 0.125985i | ||||
\(613\) | −6.95075 | − | 21.3922i | −0.280738 | − | 0.864023i | −0.987644 | − | 0.156715i | \(-0.949909\pi\) |
0.706906 | − | 0.707308i | \(-0.250091\pi\) | |||||||
\(614\) | 24.1008 | 0.972630 | ||||||||
\(615\) | 15.4963 | 0.624872 | ||||||||
\(616\) | −3.03654 | − | 9.34551i | −0.122346 | − | 0.376541i | ||||
\(617\) | 0.598587 | − | 0.434899i | 0.0240982 | − | 0.0175084i | −0.575671 | − | 0.817681i | \(-0.695259\pi\) |
0.599769 | + | 0.800173i | \(0.295259\pi\) | |||||||
\(618\) | 12.4999 | + | 9.08172i | 0.502821 | + | 0.365321i | ||||
\(619\) | −14.3089 | −0.575123 | −0.287561 | − | 0.957762i | \(-0.592845\pi\) | ||||
−0.287561 | + | 0.957762i | \(0.592845\pi\) | |||||||
\(620\) | 0.955984 | + | 10.5314i | 0.0383932 | + | 0.422950i | ||||
\(621\) | 25.8580 | 1.03765 | ||||||||
\(622\) | 16.6967 | + | 12.1308i | 0.669475 | + | 0.486402i | ||||
\(623\) | 14.8579 | − | 10.7949i | 0.595270 | − | 0.432489i | ||||
\(624\) | −1.11275 | − | 3.42470i | −0.0445457 | − | 0.137098i | ||||
\(625\) | −16.0962 | −0.643848 | ||||||||
\(626\) | 9.91438 | 0.396258 | ||||||||
\(627\) | 15.7503 | + | 48.4745i | 0.629007 | + | 1.93588i | ||||
\(628\) | 1.97341 | − | 6.07354i | 0.0787478 | − | 0.242361i | ||||
\(629\) | 0.507477 | − | 1.56185i | 0.0202344 | − | 0.0622752i | ||||
\(630\) | −4.28978 | − | 3.11671i | −0.170909 | − | 0.124173i | ||||
\(631\) | 1.44839 | + | 4.45767i | 0.0576594 | + | 0.177457i | 0.975738 | − | 0.218941i | \(-0.0702601\pi\) |
−0.918079 | + | 0.396398i | \(0.870260\pi\) | |||||||
\(632\) | 2.98617 | + | 2.16958i | 0.118784 | + | 0.0863013i | ||||
\(633\) | 21.7008 | − | 15.7665i | 0.862529 | − | 0.626664i | ||||
\(634\) | 4.11130 | − | 12.6533i | 0.163281 | − | 0.502526i | ||||
\(635\) | 0.698797 | − | 0.507706i | 0.0277309 | − | 0.0201477i | ||||
\(636\) | 2.80374 | − | 2.03703i | 0.111175 | − | 0.0807736i | ||||
\(637\) | 2.24308 | − | 6.90350i | 0.0888742 | − | 0.273527i | ||||
\(638\) | −47.9205 | + | 34.8163i | −1.89719 | + | 1.37839i | ||||
\(639\) | −3.13612 | − | 2.27853i | −0.124063 | − | 0.0901371i | ||||
\(640\) | −0.586906 | − | 1.80631i | −0.0231995 | − | 0.0714007i | ||||
\(641\) | −1.67736 | − | 1.21868i | −0.0662519 | − | 0.0481348i | 0.554166 | − | 0.832406i | \(-0.313037\pi\) |
−0.620418 | + | 0.784271i | \(0.713037\pi\) | |||||||
\(642\) | −5.85956 | + | 18.0339i | −0.231258 | + | 0.711740i | ||||
\(643\) | −9.91736 | + | 30.5225i | −0.391102 | + | 1.20369i | 0.540853 | + | 0.841117i | \(0.318101\pi\) |
−0.931956 | + | 0.362572i | \(0.881899\pi\) | |||||||
\(644\) | 4.66646 | + | 14.3619i | 0.183884 | + | 0.565938i | ||||
\(645\) | −28.7587 | −1.13237 | ||||||||
\(646\) | −7.33267 | −0.288500 | ||||||||
\(647\) | 4.47916 | + | 13.7854i | 0.176094 | + | 0.541961i | 0.999682 | − | 0.0252277i | \(-0.00803107\pi\) |
−0.823588 | + | 0.567189i | \(0.808031\pi\) | |||||||
\(648\) | −9.06032 | + | 6.58271i | −0.355923 | + | 0.258593i | ||||
\(649\) | 6.54770 | + | 4.75718i | 0.257020 | + | 0.186736i | ||||
\(650\) | −2.30717 | −0.0904945 | ||||||||
\(651\) | 12.8961 | + | 14.7379i | 0.505436 | + | 0.577623i | ||||
\(652\) | 16.5560 | 0.648384 | ||||||||
\(653\) | 6.22331 | + | 4.52150i | 0.243537 | + | 0.176940i | 0.702858 | − | 0.711331i | \(-0.251907\pi\) |
−0.459321 | + | 0.888271i | \(0.651907\pi\) | |||||||
\(654\) | −0.422430 | + | 0.306913i | −0.0165183 | + | 0.0120013i | ||||
\(655\) | 9.86793 | + | 30.3704i | 0.385572 | + | 1.18667i | ||||
\(656\) | 3.75337 | 0.146544 | ||||||||
\(657\) | 11.3345 | 0.442201 | ||||||||
\(658\) | 0.927051 | + | 2.85317i | 0.0361402 | + | 0.111228i | ||||
\(659\) | −1.29700 | + | 3.99175i | −0.0505239 | + | 0.155497i | −0.973135 | − | 0.230234i | \(-0.926051\pi\) |
0.922611 | + | 0.385731i | \(0.126051\pi\) | |||||||
\(660\) | −7.74817 | + | 23.8464i | −0.301597 | + | 0.928220i | ||||
\(661\) | −24.3110 | − | 17.6630i | −0.945589 | − | 0.687011i | 0.00417051 | − | 0.999991i | \(-0.498672\pi\) |
−0.949759 | + | 0.312981i | \(0.898672\pi\) | |||||||
\(662\) | 5.90669 | + | 18.1789i | 0.229570 | + | 0.706544i | ||||
\(663\) | −5.53299 | − | 4.01995i | −0.214883 | − | 0.156122i | ||||
\(664\) | −6.35410 | + | 4.61653i | −0.246587 | + | 0.179156i | ||||
\(665\) | 3.66633 | − | 11.2838i | 0.142174 | − | 0.437568i | ||||
\(666\) | −1.20701 | + | 0.876941i | −0.0467705 | + | 0.0339808i | ||||
\(667\) | 73.6428 | − | 53.5046i | 2.85146 | − | 2.07171i | ||||
\(668\) | 0.819709 | − | 2.52281i | 0.0317155 | − | 0.0976103i | ||||
\(669\) | 38.4946 | − | 27.9679i | 1.48829 | − | 1.08130i | ||||
\(670\) | −10.5419 | − | 7.65912i | −0.407268 | − | 0.295897i | ||||
\(671\) | −7.71609 | − | 23.7477i | −0.297876 | − | 0.916769i | ||||
\(672\) | −2.84556 | − | 2.06742i | −0.109770 | − | 0.0797524i | ||||
\(673\) | −9.21418 | + | 28.3583i | −0.355181 | + | 1.09313i | 0.600724 | + | 0.799456i | \(0.294879\pi\) |
−0.955905 | + | 0.293677i | \(0.905121\pi\) | |||||||
\(674\) | 6.41850 | − | 19.7541i | 0.247232 | − | 0.760901i | ||||
\(675\) | 1.19246 | + | 3.67002i | 0.0458978 | + | 0.141259i | ||||
\(676\) | −10.2560 | −0.394460 | ||||||||
\(677\) | −5.12916 | −0.197130 | −0.0985648 | − | 0.995131i | \(-0.531425\pi\) | ||||
−0.0985648 | + | 0.995131i | \(0.531425\pi\) | |||||||
\(678\) | 4.48934 | + | 13.8168i | 0.172412 | + | 0.530630i | ||||
\(679\) | 14.5625 | − | 10.5803i | 0.558858 | − | 0.406034i | ||||
\(680\) | −2.91830 | − | 2.12027i | −0.111912 | − | 0.0813085i | ||||
\(681\) | 10.9992 | 0.421490 | ||||||||
\(682\) | 17.3206 | − | 29.0404i | 0.663241 | − | 1.11202i | ||||
\(683\) | −43.6430 | −1.66995 | −0.834977 | − | 0.550286i | \(-0.814519\pi\) | ||||
−0.834977 | + | 0.550286i | \(0.814519\pi\) | |||||||
\(684\) | 5.38936 | + | 3.91560i | 0.206067 | + | 0.149717i | ||||
\(685\) | 29.7955 | − | 21.6477i | 1.13843 | − | 0.827116i | ||||
\(686\) | −5.69098 | − | 17.5150i | −0.217283 | − | 0.668728i | ||||
\(687\) | −48.6510 | −1.85615 | ||||||||
\(688\) | −6.96566 | −0.265563 | ||||||||
\(689\) | 0.816083 | + | 2.51164i | 0.0310903 | + | 0.0956860i | ||||
\(690\) | 11.9072 | − | 36.6464i | 0.453298 | − | 1.39511i | ||||
\(691\) | −7.35864 | + | 22.6476i | −0.279936 | + | 0.861554i | 0.707935 | + | 0.706278i | \(0.249627\pi\) |
−0.987871 | + | 0.155277i | \(0.950373\pi\) | |||||||
\(692\) | −2.63868 | − | 1.91711i | −0.100307 | − | 0.0728777i | ||||
\(693\) | 5.23941 | + | 16.1253i | 0.199029 | + | 0.612548i | ||||
\(694\) | 20.6945 | + | 15.0354i | 0.785553 | + | 0.570737i | ||||
\(695\) | 16.6519 | − | 12.0983i | 0.631642 | − | 0.458915i | ||||
\(696\) | −6.55177 | + | 20.1643i | −0.248344 | + | 0.764325i | ||||
\(697\) | 5.76720 | − | 4.19011i | 0.218448 | − | 0.158712i | ||||
\(698\) | 0.390304 | − | 0.283572i | 0.0147732 | − | 0.0107334i | ||||
\(699\) | −0.187307 | + | 0.576472i | −0.00708461 | + | 0.0218042i | ||||
\(700\) | −1.82318 | + | 1.32462i | −0.0689098 | + | 0.0500659i | ||||
\(701\) | 42.0765 | + | 30.5704i | 1.58921 | + | 1.15463i | 0.905060 | + | 0.425285i | \(0.139826\pi\) |
0.684149 | + | 0.729343i | \(0.260174\pi\) | |||||||
\(702\) | −1.41825 | − | 4.36493i | −0.0535285 | − | 0.164744i | ||||
\(703\) | −2.70073 | − | 1.96220i | −0.101860 | − | 0.0740057i | ||||
\(704\) | −1.87668 | + | 5.77584i | −0.0707302 | + | 0.217685i | ||||
\(705\) | 2.36550 | − | 7.28027i | 0.0890900 | − | 0.274191i | ||||
\(706\) | −5.66761 | − | 17.4431i | −0.213303 | − | 0.656480i | ||||
\(707\) | −23.6075 | −0.887850 | ||||||||
\(708\) | 2.89697 | 0.108875 | ||||||||
\(709\) | −14.6436 | − | 45.0682i | −0.549950 | − | 1.69257i | −0.708920 | − | 0.705289i | \(-0.750817\pi\) |
0.158970 | − | 0.987283i | \(-0.449183\pi\) | |||||||
\(710\) | 3.45204 | − | 2.50805i | 0.129553 | − | 0.0941255i | ||||
\(711\) | −5.15251 | − | 3.74351i | −0.193234 | − | 0.140393i | ||||
\(712\) | −11.3504 | −0.425376 | ||||||||
\(713\) | −26.6178 | + | 44.6285i | −0.996846 | + | 1.67135i | ||||
\(714\) | −6.68029 | −0.250004 | ||||||||
\(715\) | −15.4578 | − | 11.2307i | −0.578088 | − | 0.420005i | ||||
\(716\) | −1.21670 | + | 0.883985i | −0.0454702 | + | 0.0330361i | ||||
\(717\) | −5.24561 | − | 16.1443i | −0.195901 | − | 0.602921i | ||||
\(718\) | 9.36084 | 0.349343 | ||||||||
\(719\) | −24.9373 | −0.930005 | −0.465003 | − | 0.885309i | \(-0.653947\pi\) | ||||
−0.465003 | + | 0.885309i | \(0.653947\pi\) | |||||||
\(720\) | 1.01268 | + | 3.11671i | 0.0377403 | + | 0.116153i | ||||
\(721\) | −3.55384 | + | 10.9376i | −0.132352 | + | 0.407337i | ||||
\(722\) | 1.26521 | − | 3.89391i | 0.0470862 | − | 0.144916i | ||||
\(723\) | 27.2754 | + | 19.8168i | 1.01438 | + | 0.736993i | ||||
\(724\) | −4.93366 | − | 15.1842i | −0.183358 | − | 0.564318i | ||||
\(725\) | 10.9900 | + | 7.98469i | 0.408158 | + | 0.296544i | ||||
\(726\) | 45.5179 | − | 33.0707i | 1.68933 | − | 1.22737i | ||||
\(727\) | 5.42643 | − | 16.7008i | 0.201255 | − | 0.619400i | −0.798591 | − | 0.601874i | \(-0.794421\pi\) |
0.999846 | − | 0.0175262i | \(-0.00557905\pi\) | |||||||
\(728\) | 2.16840 | − | 1.57544i | 0.0803663 | − | 0.0583895i | ||||
\(729\) | 1.01552 | − | 0.737820i | 0.0376119 | − | 0.0273267i | ||||
\(730\) | −3.85538 | + | 11.8656i | −0.142694 | + | 0.439167i | ||||
\(731\) | −10.7030 | + | 7.77619i | −0.395865 | + | 0.287613i | ||||
\(732\) | −7.23079 | − | 5.25347i | −0.267258 | − | 0.194174i | ||||
\(733\) | 13.5095 | + | 41.5779i | 0.498984 | + | 1.53571i | 0.810655 | + | 0.585524i | \(0.199111\pi\) |
−0.311672 | + | 0.950190i | \(0.600889\pi\) | |||||||
\(734\) | −1.03092 | − | 0.749007i | −0.0380520 | − | 0.0276464i | ||||
\(735\) | −5.59061 | + | 17.2061i | −0.206213 | + | 0.634657i | ||||
\(736\) | 2.88403 | − | 8.87614i | 0.106307 | − | 0.327179i | ||||
\(737\) | 12.8755 | + | 39.6268i | 0.474276 | + | 1.45967i | ||||
\(738\) | −6.47627 | −0.238395 | ||||||||
\(739\) | −29.7646 | −1.09491 | −0.547454 | − | 0.836836i | \(-0.684403\pi\) | ||||
−0.547454 | + | 0.836836i | \(0.684403\pi\) | |||||||
\(740\) | −0.507477 | − | 1.56185i | −0.0186552 | − | 0.0574149i | ||||
\(741\) | −11.2473 | + | 8.17167i | −0.413181 | + | 0.300194i | ||||
\(742\) | 2.08691 | + | 1.51623i | 0.0766127 | + | 0.0556624i | ||||
\(743\) | −2.28066 | −0.0836692 | −0.0418346 | − | 0.999125i | \(-0.513320\pi\) | ||||
−0.0418346 | + | 0.999125i | \(0.513320\pi\) | |||||||
\(744\) | −1.09417 | − | 12.0537i | −0.0401144 | − | 0.441910i | ||||
\(745\) | 6.05253 | 0.221747 | ||||||||
\(746\) | −11.9886 | − | 8.71021i | −0.438933 | − | 0.318903i | ||||
\(747\) | 10.9637 | − | 7.96561i | 0.401141 | − | 0.291446i | ||||
\(748\) | 3.56432 | + | 10.9699i | 0.130325 | + | 0.401098i | ||||
\(749\) | −14.1139 | −0.515713 | ||||||||
\(750\) | 26.3936 | 0.963757 | ||||||||
\(751\) | −5.99819 | − | 18.4605i | −0.218877 | − | 0.673634i | −0.998856 | − | 0.0478281i | \(-0.984770\pi\) |
0.779978 | − | 0.625806i | \(-0.215230\pi\) | |||||||
\(752\) | 0.572949 | − | 1.76336i | 0.0208933 | − | 0.0643030i | ||||
\(753\) | 9.98294 | − | 30.7243i | 0.363798 | − | 1.11966i | ||||
\(754\) | −13.0709 | − | 9.49659i | −0.476015 | − | 0.345845i | ||||
\(755\) | −3.15353 | − | 9.70556i | −0.114769 | − | 0.353221i | ||||
\(756\) | −3.62679 | − | 2.63502i | −0.131905 | − | 0.0958346i | ||||
\(757\) | −6.54909 | + | 4.75819i | −0.238031 | + | 0.172939i | −0.700405 | − | 0.713745i | \(-0.746997\pi\) |
0.462375 | + | 0.886685i | \(0.346997\pi\) | |||||||
\(758\) | 4.36397 | − | 13.4309i | 0.158507 | − | 0.487833i | ||||
\(759\) | −99.6796 | + | 72.4214i | −3.61814 | + | 2.62873i | ||||
\(760\) | −5.93225 | + | 4.31003i | −0.215185 | + | 0.156341i | ||||
\(761\) | 9.90195 | − | 30.4751i | 0.358945 | − | 1.10472i | −0.594741 | − | 0.803917i | \(-0.702745\pi\) |
0.953686 | − | 0.300803i | \(-0.0972546\pi\) | |||||||
\(762\) | −0.799810 | + | 0.581096i | −0.0289741 | + | 0.0210509i | ||||
\(763\) | −0.314427 | − | 0.228445i | −0.0113830 | − | 0.00827026i | ||||
\(764\) | −6.17509 | − | 19.0050i | −0.223407 | − | 0.687576i | ||||
\(765\) | 5.03539 | + | 3.65843i | 0.182055 | + | 0.132271i | ||||
\(766\) | 5.41309 | − | 16.6598i | 0.195583 | − | 0.601943i | ||||
\(767\) | −0.682180 | + | 2.09953i | −0.0246321 | + | 0.0758097i | ||||
\(768\) | 0.671745 | + | 2.06742i | 0.0242395 | + | 0.0746015i | ||||
\(769\) | 45.6918 | 1.64769 | 0.823844 | − | 0.566817i | \(-0.191825\pi\) | ||||
0.823844 | + | 0.566817i | \(0.191825\pi\) | |||||||
\(770\) | −18.6630 | −0.672569 | ||||||||
\(771\) | 0.895213 | + | 2.75518i | 0.0322403 | + | 0.0992254i | ||||
\(772\) | −10.0820 | + | 7.32497i | −0.362858 | + | 0.263632i | ||||
\(773\) | −30.6866 | − | 22.2951i | −1.10372 | − | 0.801901i | −0.122058 | − | 0.992523i | \(-0.538949\pi\) |
−0.981663 | + | 0.190622i | \(0.938949\pi\) | |||||||
\(774\) | 12.0189 | 0.432011 | ||||||||
\(775\) | −7.56160 | − | 1.71979i | −0.271621 | − | 0.0617765i | ||||
\(776\) | −11.1248 | −0.399356 | ||||||||
\(777\) | −2.46045 | − | 1.78762i | −0.0882683 | − | 0.0641307i | ||||
\(778\) | −1.04389 | + | 0.758428i | −0.0374252 | + | 0.0271910i | ||||
\(779\) | −4.47795 | − | 13.7817i | −0.160439 | − | 0.493782i | ||||
\(780\) | −6.83915 | −0.244881 | ||||||||
\(781\) | −13.6440 | −0.488220 | ||||||||
\(782\) | −5.47755 | − | 16.8582i | −0.195877 | − | 0.602846i | ||||
\(783\) | −8.35053 | + | 25.7003i | −0.298424 | + | 0.918453i | ||||
\(784\) | −1.35410 | + | 4.16750i | −0.0483608 | + | 0.148839i | ||||
\(785\) | −9.81249 | − | 7.12919i | −0.350223 | − | 0.254452i | ||||
\(786\) | −11.2944 | − | 34.7605i | −0.402857 | − | 1.23987i | ||||
\(787\) | −11.7239 | − | 8.51788i | −0.417910 | − | 0.303630i | 0.358886 | − | 0.933381i | \(-0.383157\pi\) |
−0.776796 | + | 0.629752i | \(0.783157\pi\) | |||||||
\(788\) | 9.01536 | − | 6.55004i | 0.321159 | − | 0.233336i | ||||
\(789\) | 9.26755 | − | 28.5226i | 0.329933 | − | 1.01543i | ||||
\(790\) | 5.67154 | − | 4.12061i | 0.201784 | − | 0.146605i | ||||
\(791\) | −8.74829 | + | 6.35601i | −0.311054 | + | 0.225994i | ||||
\(792\) | 3.23813 | − | 9.96595i | 0.115062 | − | 0.354125i | ||||
\(793\) | 5.51008 | − | 4.00331i | 0.195669 | − | 0.142162i | ||||
\(794\) | −18.2461 | − | 13.2566i | −0.647532 | − | 0.470459i | ||||
\(795\) | −2.03398 | − | 6.25996i | −0.0721380 | − | 0.222018i | ||||
\(796\) | 11.7224 | + | 8.51680i | 0.415488 | + | 0.301870i | ||||
\(797\) | 10.4387 | − | 32.1270i | 0.369757 | − | 1.13800i | −0.577191 | − | 0.816609i | \(-0.695851\pi\) |
0.946948 | − | 0.321387i | \(-0.104149\pi\) | |||||||
\(798\) | −4.19631 | + | 12.9149i | −0.148548 | + | 0.457183i | ||||
\(799\) | −1.08818 | − | 3.34908i | −0.0384971 | − | 0.118482i | ||||
\(800\) | 1.39279 | 0.0492425 | ||||||||
\(801\) | 19.5847 | 0.691990 | ||||||||
\(802\) | 2.43568 | + | 7.49624i | 0.0860067 | + | 0.264702i | ||||
\(803\) | 32.2749 | − | 23.4491i | 1.13896 | − | 0.827501i | ||||
\(804\) | 12.0657 | + | 8.76627i | 0.425525 | + | 0.309162i | ||||
\(805\) | 28.6808 | 1.01087 | ||||||||
\(806\) | 8.99339 | + | 2.04543i | 0.316779 | + | 0.0720471i | ||||
\(807\) | −3.02210 | −0.106383 | ||||||||
\(808\) | 11.8037 | + | 8.57592i | 0.415254 | + | 0.301700i | ||||
\(809\) | 22.6804 | − | 16.4783i | 0.797401 | − | 0.579346i | −0.112749 | − | 0.993623i | \(-0.535966\pi\) |
0.910151 | + | 0.414278i | \(0.135966\pi\) | |||||||
\(810\) | 6.57286 | + | 20.2292i | 0.230947 | + | 0.710781i | ||||
\(811\) | 26.0368 | 0.914277 | 0.457139 | − | 0.889396i | \(-0.348874\pi\) | ||||
0.457139 | + | 0.889396i | \(0.348874\pi\) | |||||||
\(812\) | −15.7813 | −0.553814 | ||||||||
\(813\) | 2.62226 | + | 8.07049i | 0.0919667 | + | 0.283044i | ||||
\(814\) | −1.62270 | + | 4.99417i | −0.0568758 | + | 0.175046i | ||||
\(815\) | 9.71683 | − | 29.9053i | 0.340366 | − | 1.04754i | ||||
\(816\) | 3.34015 | + | 2.42676i | 0.116928 | + | 0.0849535i | ||||
\(817\) | 8.31037 | + | 25.5767i | 0.290743 | + | 0.894815i | ||||
\(818\) | 28.5833 | + | 20.7670i | 0.999391 | + | 0.726100i | ||||
\(819\) | −3.74148 | + | 2.71834i | −0.130738 | + | 0.0949866i | ||||
\(820\) | 2.20287 | − | 6.77975i | 0.0769277 | − | 0.236759i | ||||
\(821\) | −10.3302 | + | 7.50536i | −0.360528 | + | 0.261939i | −0.753272 | − | 0.657709i | \(-0.771526\pi\) |
0.392744 | + | 0.919648i | \(0.371526\pi\) | |||||||
\(822\) | −34.1025 | + | 24.7769i | −1.18946 | + | 0.864195i | ||||
\(823\) | 0.451669 | − | 1.39010i | 0.0157442 | − | 0.0484557i | −0.942876 | − | 0.333145i | \(-0.891890\pi\) |
0.958620 | + | 0.284689i | \(0.0918903\pi\) | |||||||
\(824\) | 5.75023 | − | 4.17779i | 0.200319 | − | 0.145540i | ||||
\(825\) | −14.8755 | − | 10.8077i | −0.517900 | − | 0.376276i | ||||
\(826\) | 0.666334 | + | 2.05077i | 0.0231847 | + | 0.0713553i | ||||
\(827\) | 15.0184 | + | 10.9115i | 0.522242 | + | 0.379431i | 0.817448 | − | 0.576003i | \(-0.195388\pi\) |
−0.295206 | + | 0.955434i | \(0.595388\pi\) | |||||||
\(828\) | −4.97627 | + | 15.3154i | −0.172937 | + | 0.532246i | ||||
\(829\) | 3.23920 | − | 9.96924i | 0.112502 | − | 0.346246i | −0.878916 | − | 0.476977i | \(-0.841732\pi\) |
0.991418 | + | 0.130731i | \(0.0417324\pi\) | |||||||
\(830\) | 4.60962 | + | 14.1869i | 0.160002 | + | 0.492436i | ||||
\(831\) | −15.8190 | −0.548756 | ||||||||
\(832\) | −1.65651 | −0.0574292 | ||||||||
\(833\) | 2.57180 | + | 7.91519i | 0.0891076 | + | 0.274245i | ||||
\(834\) | −19.0590 | + | 13.8471i | −0.659958 | + | 0.479487i | ||||
\(835\) | −4.07588 | − | 2.96130i | −0.141052 | − | 0.102480i | ||||
\(836\) | 23.4469 | 0.810927 | ||||||||
\(837\) | −1.39457 | − | 15.3630i | −0.0482035 | − | 0.531023i | ||||
\(838\) | −26.9683 | −0.931605 | ||||||||
\(839\) | 24.1746 | + | 17.5639i | 0.834600 | + | 0.606372i | 0.920857 | − | 0.389900i | \(-0.127491\pi\) |
−0.0862569 | + | 0.996273i | \(0.527491\pi\) | |||||||
\(840\) | −5.40447 | + | 3.92658i | −0.186472 | + | 0.135480i | ||||
\(841\) | 20.4347 | + | 62.8917i | 0.704646 | + | 2.16868i | ||||
\(842\) | −3.78260 | −0.130357 | ||||||||
\(843\) | −33.2388 | −1.14481 | ||||||||
\(844\) | −3.81310 | − | 11.7355i | −0.131252 | − | 0.403953i | ||||
\(845\) | −6.01929 | + | 18.5255i | −0.207070 | + | 0.637295i | ||||
\(846\) | −0.988598 | + | 3.04259i | −0.0339887 | + | 0.104606i | ||||
\(847\) | 33.8803 | + | 24.6155i | 1.16414 | + | 0.845799i | ||||
\(848\) | −0.492652 | − | 1.51623i | −0.0169177 | − | 0.0520674i | ||||
\(849\) | 32.0309 | + | 23.2718i | 1.09930 | + | 0.798687i | ||||
\(850\) | 2.14007 | − | 1.55485i | 0.0734038 | − | 0.0533310i | ||||
\(851\) | 2.49372 | − | 7.67489i | 0.0854837 | − | 0.263092i | ||||
\(852\) | −3.95104 | + | 2.87060i | −0.135360 | + | 0.0983451i | ||||
\(853\) | 1.70447 | − | 1.23837i | 0.0583601 | − | 0.0424011i | −0.558223 | − | 0.829691i | \(-0.688517\pi\) |
0.616583 | + | 0.787290i | \(0.288517\pi\) | |||||||
\(854\) | 2.05578 | − | 6.32703i | 0.0703472 | − | 0.216507i | ||||
\(855\) | 10.2358 | − | 7.43677i | 0.350058 | − | 0.254332i | ||||
\(856\) | 7.05697 | + | 5.12719i | 0.241202 | + | 0.175244i | ||||
\(857\) | 14.9490 | + | 46.0084i | 0.510649 | + | 1.57162i | 0.791062 | + | 0.611736i | \(0.209529\pi\) |
−0.280413 | + | 0.959879i | \(0.590471\pi\) | |||||||
\(858\) | 17.6922 | + | 12.8542i | 0.604003 | + | 0.438834i | ||||
\(859\) | −6.52447 | + | 20.0803i | −0.222612 | + | 0.685130i | 0.775913 | + | 0.630840i | \(0.217289\pi\) |
−0.998525 | + | 0.0542898i | \(0.982711\pi\) | |||||||
\(860\) | −4.08818 | + | 12.5821i | −0.139406 | + | 0.429047i | ||||
\(861\) | −4.07956 | − | 12.5556i | −0.139031 | − | 0.427893i | ||||
\(862\) | 6.56205 | 0.223504 | ||||||||
\(863\) | 31.6402 | 1.07704 | 0.538522 | − | 0.842611i | \(-0.318983\pi\) | ||||
0.538522 | + | 0.842611i | \(0.318983\pi\) | |||||||
\(864\) | 0.856169 | + | 2.63502i | 0.0291274 | + | 0.0896451i | ||||
\(865\) | −5.01155 | + | 3.64111i | −0.170398 | + | 0.123801i | ||||
\(866\) | −15.3179 | − | 11.1291i | −0.520523 | − | 0.378182i | ||||
\(867\) | −29.1134 | −0.988743 | ||||||||
\(868\) | 8.28115 | − | 3.54705i | 0.281081 | − | 0.120395i | ||||
\(869\) | −22.4164 | −0.760425 | ||||||||
\(870\) | 32.5777 | + | 23.6691i | 1.10449 | + | 0.802456i | ||||
\(871\) | −9.19446 | + | 6.68016i | −0.311542 | + | 0.226349i | ||||
\(872\) | 0.0742263 | + | 0.228445i | 0.00251362 | + | 0.00773612i | ||||
\(873\) | 19.1953 | 0.649662 | ||||||||
\(874\) | −36.0325 | −1.21882 | ||||||||
\(875\) | 6.07080 | + | 18.6840i | 0.205231 | + | 0.631635i | ||||
\(876\) | 4.41269 | − | 13.5809i | 0.149091 | − | 0.458854i | ||||
\(877\) | −10.5882 | + | 32.5871i | −0.357538 | + | 1.10039i | 0.596986 | + | 0.802252i | \(0.296365\pi\) |
−0.954523 | + | 0.298136i | \(0.903635\pi\) | |||||||
\(878\) | 14.5152 | + | 10.5459i | 0.489863 | + | 0.355906i | ||||
\(879\) | −17.2606 | − | 53.1228i | −0.582187 | − | 1.79179i | ||||
\(880\) | 9.33152 | + | 6.77975i | 0.314565 | + | 0.228545i | ||||
\(881\) | −6.86526 | + | 4.98790i | −0.231296 | + | 0.168047i | −0.697397 | − | 0.716685i | \(-0.745659\pi\) |
0.466100 | + | 0.884732i | \(0.345659\pi\) | |||||||
\(882\) | 2.33644 | − | 7.19083i | 0.0786721 | − | 0.242128i | ||||
\(883\) | −7.31076 | + | 5.31158i | −0.246027 | + | 0.178749i | −0.703964 | − | 0.710236i | \(-0.748588\pi\) |
0.457937 | + | 0.888984i | \(0.348588\pi\) | |||||||
\(884\) | −2.54529 | + | 1.84926i | −0.0856075 | + | 0.0621975i | ||||
\(885\) | 1.70025 | − | 5.23282i | 0.0571532 | − | 0.175899i | ||||
\(886\) | 23.2601 | − | 16.8995i | 0.781439 | − | 0.567748i | ||||
\(887\) | 33.3608 | + | 24.2381i | 1.12015 | + | 0.813835i | 0.984231 | − | 0.176886i | \(-0.0566023\pi\) |
0.135916 | + | 0.990720i | \(0.456602\pi\) | |||||||
\(888\) | 0.580834 | + | 1.78762i | 0.0194915 | + | 0.0599888i | ||||
\(889\) | −0.595323 | − | 0.432528i | −0.0199665 | − | 0.0145065i | ||||
\(890\) | −6.66163 | + | 20.5024i | −0.223298 | + | 0.687242i | ||||
\(891\) | 21.0173 | − | 64.6846i | 0.704106 | − | 2.16702i | ||||
\(892\) | −6.76398 | − | 20.8174i | −0.226475 | − | 0.697018i | ||||
\(893\) | −7.15830 | −0.239543 | ||||||||
\(894\) | −6.92744 | −0.231688 | ||||||||
\(895\) | 0.882662 | + | 2.71655i | 0.0295041 | + | 0.0908044i | ||||
\(896\) | −1.30902 | + | 0.951057i | −0.0437312 | + | 0.0317726i | ||||
\(897\) | −27.1889 | − | 19.7539i | −0.907811 | − | 0.659563i | ||||
\(898\) | 20.0282 | 0.668349 | ||||||||
\(899\) | −35.7604 | − | 40.8677i | −1.19267 | − | 1.36301i | ||||
\(900\) | −2.40319 | −0.0801064 | ||||||||
\(901\) | −2.44963 | − | 1.77976i | −0.0816091 | − | 0.0592925i | ||||
\(902\) | −18.4411 | + | 13.3983i | −0.614023 | + | 0.446114i | ||||
\(903\) | 7.57101 | + | 23.3012i | 0.251947 | + | 0.775415i | ||||
\(904\) | 6.68310 | 0.222277 | ||||||||
\(905\) | −30.3230 | −1.00797 | ||||||||
\(906\) | 3.60938 | + | 11.1085i | 0.119914 | + | 0.369056i | ||||
\(907\) | −1.08451 | + | 3.33777i | −0.0360105 | + | 0.110829i | −0.967446 | − | 0.253078i | \(-0.918557\pi\) |
0.931436 | + | 0.363906i | \(0.118557\pi\) | |||||||
\(908\) | 1.56358 | − | 4.81221i | 0.0518893 | − | 0.159699i | ||||
\(909\) | −20.3668 | − | 14.7974i | −0.675525 | − | 0.490797i | ||||
\(910\) | −1.57308 | − | 4.84144i | −0.0521470 | − | 0.160492i | ||||
\(911\) | 18.4348 | + | 13.3937i | 0.610772 | + | 0.443752i | 0.849686 | − | 0.527289i | \(-0.176791\pi\) |
−0.238914 | + | 0.971041i | \(0.576791\pi\) | |||||||
\(912\) | 6.78978 | − | 4.93306i | 0.224832 | − | 0.163350i | ||||
\(913\) | 14.7397 | − | 45.3640i | 0.487812 | − | 1.50133i | ||||
\(914\) | −13.6106 | + | 9.88868i | −0.450199 | + | 0.327089i | ||||
\(915\) | −13.7332 | + | 9.97775i | −0.454005 | + | 0.329854i | ||||
\(916\) | −6.91595 | + | 21.2851i | −0.228509 | + | 0.703280i | ||||
\(917\) | 22.0091 | − | 15.9906i | 0.726806 | − | 0.528055i | ||||
\(918\) | 4.25716 | + | 3.09301i | 0.140507 | + | 0.102085i | ||||
\(919\) | −8.24023 | − | 25.3608i | −0.271820 | − | 0.836576i | −0.990043 | − | 0.140764i | \(-0.955044\pi\) |
0.718223 | − | 0.695813i | \(-0.244956\pi\) | |||||||
\(920\) | −14.3404 | − | 10.4189i | −0.472789 | − | 0.343501i | ||||
\(921\) | −16.1896 | + | 49.8265i | −0.533466 | + | 1.64184i | ||||
\(922\) | 1.05251 | − | 3.23930i | 0.0346627 | − | 0.106681i | ||||
\(923\) | −1.15003 | − | 3.53942i | −0.0378536 | − | 0.116502i | ||||
\(924\) | 21.3608 | 0.702720 | ||||||||
\(925\) | 1.20429 | 0.0395970 | ||||||||
\(926\) | −7.86365 | − | 24.2018i | −0.258415 | − | 0.795321i | ||||
\(927\) | −9.92177 | + | 7.20859i | −0.325874 | + | 0.236761i | ||||
\(928\) | 7.89064 | + | 5.73289i | 0.259023 | + | 0.188191i | ||||
\(929\) | 36.6687 | 1.20306 | 0.601530 | − | 0.798850i | \(-0.294558\pi\) | ||||
0.601530 | + | 0.798850i | \(0.294558\pi\) | |||||||
\(930\) | −22.4149 | − | 5.09797i | −0.735014 | − | 0.167169i | ||||
\(931\) | 16.9178 | 0.554460 | ||||||||
\(932\) | 0.225584 | + | 0.163896i | 0.00738925 | + | 0.00536860i | ||||
\(933\) | −36.2954 | + | 26.3701i | −1.18826 | + | 0.863319i | ||||
\(934\) | −1.58617 | − | 4.88172i | −0.0519009 | − | 0.159735i | ||||
\(935\) | 21.9069 | 0.716432 | ||||||||
\(936\) | 2.85824 | 0.0934243 | ||||||||
\(937\) | −6.83050 | − | 21.0221i | −0.223143 | − | 0.686763i | −0.998475 | − | 0.0552089i | \(-0.982418\pi\) |
0.775332 | − | 0.631554i | \(-0.217582\pi\) | |||||||
\(938\) | −3.43039 | + | 10.5577i | −0.112006 | + | 0.344720i | ||||
\(939\) | −6.65993 | + | 20.4972i | −0.217339 | + | 0.668900i | ||||
\(940\) | −2.84890 | − | 2.06985i | −0.0929209 | − | 0.0675110i | ||||
\(941\) | −16.7645 | − | 51.5960i | −0.546509 | − | 1.68198i | −0.717376 | − | 0.696687i | \(-0.754657\pi\) |
0.170867 | − | 0.985294i | \(-0.445343\pi\) | |||||||
\(942\) | 11.2309 | + | 8.15974i | 0.365923 | + | 0.265859i | ||||
\(943\) | 28.3398 | − | 20.5901i | 0.922871 | − | 0.670505i | ||||
\(944\) | 0.411817 | − | 1.26744i | 0.0134035 | − | 0.0412518i | ||||
\(945\) | −6.88824 | + | 5.00460i | −0.224074 | + | 0.162800i | ||||
\(946\) | 34.2238 | − | 24.8651i | 1.11271 | − | 0.808433i | ||||
\(947\) | 1.58752 | − | 4.88588i | 0.0515874 | − | 0.158770i | −0.921944 | − | 0.387323i | \(-0.873400\pi\) |
0.973531 | + | 0.228554i | \(0.0733997\pi\) | |||||||
\(948\) | −6.49137 | + | 4.71626i | −0.210830 | + | 0.153177i | ||||
\(949\) | 8.80341 | + | 6.39605i | 0.285771 | + | 0.207625i | ||||
\(950\) | −1.66166 | − | 5.11408i | −0.0539115 | − | 0.165923i | ||||
\(951\) | 23.3979 | + | 16.9996i | 0.758728 | + | 0.551248i | ||||
\(952\) | −0.949633 | + | 2.92267i | −0.0307778 | + | 0.0947243i | ||||
\(953\) | −5.84114 | + | 17.9772i | −0.189213 | + | 0.582338i | −0.999995 | − | 0.00300954i | \(-0.999042\pi\) |
0.810782 | + | 0.585348i | \(0.199042\pi\) | |||||||
\(954\) | 0.850048 | + | 2.61618i | 0.0275213 | + | 0.0847019i | ||||
\(955\) | −37.9531 | −1.22813 | ||||||||
\(956\) | −7.80894 | −0.252559 | ||||||||
\(957\) | −39.7894 | − | 122.459i | −1.28621 | − | 3.95855i | ||||
\(958\) | −3.89051 | + | 2.82662i | −0.125697 | + | 0.0913240i | ||||
\(959\) | −25.3835 | − | 18.4422i | −0.819678 | − | 0.595531i | ||||
\(960\) | 4.12865 | 0.133252 | ||||||||
\(961\) | 27.9506 | + | 13.4075i | 0.901633 | + | 0.432501i | ||||
\(962\) | −1.43233 | −0.0461801 | ||||||||
\(963\) | −12.1765 | − | 8.84674i | −0.392382 | − | 0.285082i | ||||
\(964\) | 12.5473 | − | 9.11613i | 0.404121 | − | 0.293611i | ||||
\(965\) | 7.31401 | + | 22.5102i | 0.235446 | + | 0.724629i | ||||
\(966\) | −32.8267 | −1.05618 | ||||||||
\(967\) | 4.22699 | 0.135931 | 0.0679655 | − | 0.997688i | \(-0.478349\pi\) | ||||
0.0679655 | + | 0.997688i | \(0.478349\pi\) | |||||||
\(968\) | −7.99806 | − | 24.6155i | −0.257067 | − | 0.791172i | ||||
\(969\) | 4.92568 | − | 15.1597i | 0.158236 | − | 0.486999i | ||||
\(970\) | −6.52919 | + | 20.0948i | −0.209640 | + | 0.645205i | ||||
\(971\) | 21.2923 | + | 15.4698i | 0.683303 | + | 0.496449i | 0.874452 | − | 0.485113i | \(-0.161221\pi\) |
−0.191149 | + | 0.981561i | \(0.561221\pi\) | |||||||
\(972\) | −4.95448 | − | 15.2483i | −0.158915 | − | 0.489090i | ||||
\(973\) | −14.1862 | − | 10.3069i | −0.454788 | − | 0.330423i | ||||
\(974\) | −20.6101 | + | 14.9741i | −0.660390 | + | 0.479801i | ||||
\(975\) | 1.54983 | − | 4.76988i | 0.0496342 | − | 0.152758i | ||||
\(976\) | −3.32632 | + | 2.41671i | −0.106473 | + | 0.0773570i | ||||
\(977\) | −24.5499 | + | 17.8365i | −0.785420 | + | 0.570641i | −0.906601 | − | 0.421989i | \(-0.861332\pi\) |
0.121180 | + | 0.992630i | \(0.461332\pi\) | |||||||
\(978\) | −11.1214 | + | 34.2282i | −0.355624 | + | 1.09450i | ||||
\(979\) | 55.7672 | − | 40.5173i | 1.78233 | − | 1.29494i | ||||
\(980\) | 6.73306 | + | 4.89186i | 0.215080 | + | 0.156265i | ||||
\(981\) | −0.128074 | − | 0.394171i | −0.00408909 | − | 0.0125849i | ||||
\(982\) | 22.4033 | + | 16.2770i | 0.714919 | + | 0.519419i | ||||
\(983\) | 6.59107 | − | 20.2852i | 0.210222 | − | 0.646998i | −0.789236 | − | 0.614090i | \(-0.789523\pi\) |
0.999458 | − | 0.0329081i | \(-0.0104769\pi\) | |||||||
\(984\) | −2.52131 | + | 7.75978i | −0.0803763 | + | 0.247373i | ||||
\(985\) | −6.54024 | − | 20.1288i | −0.208389 | − | 0.641357i | ||||
\(986\) | 18.5242 | 0.589932 | ||||||||
\(987\) | −6.52143 | −0.207580 | ||||||||
\(988\) | 1.97630 | + | 6.08242i | 0.0628745 | + | 0.193508i | ||||
\(989\) | −52.5942 | + | 38.2119i | −1.67240 | + | 1.21507i | ||||
\(990\) | −16.1011 | − | 11.6981i | −0.511727 | − | 0.371792i | ||||
\(991\) | −42.7649 | −1.35847 | −0.679237 | − | 0.733919i | \(-0.737689\pi\) | ||||
−0.679237 | + | 0.733919i | \(0.737689\pi\) | |||||||
\(992\) | −5.42912 | − | 1.23478i | −0.172375 | − | 0.0392043i | ||||
\(993\) | −41.5512 | −1.31859 | ||||||||
\(994\) | −2.94088 | − | 2.13667i | −0.0932790 | − | 0.0677712i | ||||
\(995\) | 22.2639 | − | 16.1757i | 0.705813 | − | 0.512803i | ||||
\(996\) | −5.27595 | − | 16.2377i | −0.167175 | − | 0.514511i | ||||
\(997\) | 20.0121 | 0.633788 | 0.316894 | − | 0.948461i | \(-0.397360\pi\) | ||||
0.316894 | + | 0.948461i | \(0.397360\pi\) | |||||||
\(998\) | 0.523314 | 0.0165652 | ||||||||
\(999\) | 0.740299 | + | 2.27841i | 0.0234220 | + | 0.0720856i |
(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 | 62.2.d.b.33.1 | ✓ | 8 | |
3.2 | odd | 2 | 558.2.i.g.343.1 | 8 | |||
4.3 | odd | 2 | 496.2.n.d.33.2 | 8 | |||
31.4 | even | 5 | 1922.2.a.i.1.4 | 4 | |||
31.16 | even | 5 | inner | 62.2.d.b.47.1 | yes | 8 | |
31.27 | odd | 10 | 1922.2.a.l.1.1 | 4 | |||
93.47 | odd | 10 | 558.2.i.g.109.1 | 8 | |||
124.47 | odd | 10 | 496.2.n.d.481.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
62.2.d.b.33.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
62.2.d.b.47.1 | yes | 8 | 31.16 | even | 5 | inner | |
496.2.n.d.33.2 | 8 | 4.3 | odd | 2 | |||
496.2.n.d.481.2 | 8 | 124.47 | odd | 10 | |||
558.2.i.g.109.1 | 8 | 93.47 | odd | 10 | |||
558.2.i.g.343.1 | 8 | 3.2 | odd | 2 | |||
1922.2.a.i.1.4 | 4 | 31.4 | even | 5 | |||
1922.2.a.l.1.1 | 4 | 31.27 | odd | 10 |