Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [471,2,Mod(169,471)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(471, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("471.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 471 = 3 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 471.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.76095393520\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 301.4 | ||
Character | \(\chi\) | \(=\) | 471.301 |
Dual form | 471.2.e.b.169.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/471\mathbb{Z}\right)^\times\).
\(n\) | \(158\) | \(319\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.685532 | −0.484744 | −0.242372 | − | 0.970183i | \(-0.577925\pi\) | ||||
−0.242372 | + | 0.970183i | \(0.577925\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −1.53005 | −0.765023 | ||||||||
\(5\) | −0.295622 | + | 0.512033i | −0.132206 | + | 0.228988i | −0.924527 | − | 0.381117i | \(-0.875539\pi\) |
0.792321 | + | 0.610105i | \(0.208873\pi\) | |||||||
\(6\) | −0.342766 | + | 0.593688i | −0.139934 | + | 0.242372i | ||||
\(7\) | −1.98864 | −0.751634 | −0.375817 | − | 0.926694i | \(-0.622638\pi\) | ||||
−0.375817 | + | 0.926694i | \(0.622638\pi\) | |||||||
\(8\) | 2.41996 | 0.855585 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0.202658 | − | 0.351015i | 0.0640862 | − | 0.111001i | ||||
\(11\) | 0.0905346 | − | 0.156811i | 0.0272972 | − | 0.0472802i | −0.852054 | − | 0.523454i | \(-0.824643\pi\) |
0.879351 | + | 0.476174i | \(0.157977\pi\) | |||||||
\(12\) | −0.765023 | + | 1.32506i | −0.220843 | + | 0.382512i | ||||
\(13\) | 0.547853 | + | 0.948910i | 0.151947 | + | 0.263180i | 0.931943 | − | 0.362604i | \(-0.118112\pi\) |
−0.779996 | + | 0.625784i | \(0.784779\pi\) | |||||||
\(14\) | 1.36327 | 0.364350 | ||||||||
\(15\) | 0.295622 | + | 0.512033i | 0.0763293 | + | 0.132206i | ||||
\(16\) | 1.40113 | 0.350284 | ||||||||
\(17\) | −2.67424 | + | 4.63191i | −0.648597 | + | 1.12340i | 0.334861 | + | 0.942268i | \(0.391311\pi\) |
−0.983458 | + | 0.181136i | \(0.942023\pi\) | |||||||
\(18\) | 0.342766 | + | 0.593688i | 0.0807907 | + | 0.139934i | ||||
\(19\) | −2.51331 | + | 4.35318i | −0.576592 | + | 0.998687i | 0.419274 | + | 0.907860i | \(0.362285\pi\) |
−0.995867 | + | 0.0908275i | \(0.971049\pi\) | |||||||
\(20\) | 0.452316 | − | 0.783433i | 0.101141 | − | 0.175181i | ||||
\(21\) | −0.994318 | + | 1.72221i | −0.216978 | + | 0.375817i | ||||
\(22\) | −0.0620644 | + | 0.107499i | −0.0132322 | + | 0.0229188i | ||||
\(23\) | −3.48929 | −0.727568 | −0.363784 | − | 0.931483i | \(-0.618515\pi\) | ||||
−0.363784 | + | 0.931483i | \(0.618515\pi\) | |||||||
\(24\) | 1.20998 | − | 2.09575i | 0.246986 | − | 0.427792i | ||||
\(25\) | 2.32522 | + | 4.02739i | 0.465043 | + | 0.805478i | ||||
\(26\) | −0.375571 | − | 0.650508i | −0.0736555 | − | 0.127575i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.04271 | 0.575017 | ||||||||
\(29\) | −4.94532 | −0.918322 | −0.459161 | − | 0.888353i | \(-0.651850\pi\) | ||||
−0.459161 | + | 0.888353i | \(0.651850\pi\) | |||||||
\(30\) | −0.202658 | − | 0.351015i | −0.0370002 | − | 0.0640862i | ||||
\(31\) | 3.74771 | + | 6.49123i | 0.673109 | + | 1.16586i | 0.977018 | + | 0.213158i | \(0.0683748\pi\) |
−0.303909 | + | 0.952701i | \(0.598292\pi\) | |||||||
\(32\) | −5.80044 | −1.02538 | ||||||||
\(33\) | −0.0905346 | − | 0.156811i | −0.0157601 | − | 0.0272972i | ||||
\(34\) | 1.83327 | − | 3.17532i | 0.314404 | − | 0.544563i | ||||
\(35\) | 0.587885 | − | 1.01825i | 0.0993707 | − | 0.172115i | ||||
\(36\) | 0.765023 | + | 1.32506i | 0.127504 | + | 0.220843i | ||||
\(37\) | 2.38458 | + | 4.13022i | 0.392023 | + | 0.679004i | 0.992716 | − | 0.120476i | \(-0.0384419\pi\) |
−0.600693 | + | 0.799480i | \(0.705109\pi\) | |||||||
\(38\) | 1.72295 | − | 2.98424i | 0.279500 | − | 0.484108i | ||||
\(39\) | 1.09571 | 0.175453 | ||||||||
\(40\) | −0.715393 | + | 1.23910i | −0.113114 | + | 0.195919i | ||||
\(41\) | 6.49564 | 1.01445 | 0.507224 | − | 0.861814i | \(-0.330672\pi\) | ||||
0.507224 | + | 0.861814i | \(0.330672\pi\) | |||||||
\(42\) | 0.681637 | − | 1.18063i | 0.105179 | − | 0.182175i | ||||
\(43\) | 0.870301 | + | 1.50740i | 0.132720 | + | 0.229877i | 0.924724 | − | 0.380638i | \(-0.124296\pi\) |
−0.792004 | + | 0.610515i | \(0.790962\pi\) | |||||||
\(44\) | −0.138522 | + | 0.239927i | −0.0208830 | + | 0.0361704i | ||||
\(45\) | 0.591244 | 0.0881375 | ||||||||
\(46\) | 2.39202 | 0.352684 | ||||||||
\(47\) | −2.59427 | − | 4.49340i | −0.378413 | − | 0.655430i | 0.612419 | − | 0.790533i | \(-0.290197\pi\) |
−0.990831 | + | 0.135104i | \(0.956863\pi\) | |||||||
\(48\) | 0.700567 | − | 1.21342i | 0.101118 | − | 0.175142i | ||||
\(49\) | −3.04532 | −0.435046 | ||||||||
\(50\) | −1.59401 | − | 2.76090i | −0.225427 | − | 0.390451i | ||||
\(51\) | 2.67424 | + | 4.63191i | 0.374468 | + | 0.648597i | ||||
\(52\) | −0.838241 | − | 1.45188i | −0.116243 | − | 0.201339i | ||||
\(53\) | 1.27139 | + | 2.20210i | 0.174638 | + | 0.302482i | 0.940036 | − | 0.341075i | \(-0.110791\pi\) |
−0.765398 | + | 0.643558i | \(0.777458\pi\) | |||||||
\(54\) | 0.685532 | 0.0932891 | ||||||||
\(55\) | 0.0535281 | + | 0.0927134i | 0.00721773 | + | 0.0125015i | ||||
\(56\) | −4.81242 | −0.643087 | ||||||||
\(57\) | 2.51331 | + | 4.35318i | 0.332896 | + | 0.576592i | ||||
\(58\) | 3.39017 | 0.445151 | ||||||||
\(59\) | −9.94287 | −1.29445 | −0.647226 | − | 0.762299i | \(-0.724071\pi\) | ||||
−0.647226 | + | 0.762299i | \(0.724071\pi\) | |||||||
\(60\) | −0.452316 | − | 0.783433i | −0.0583937 | − | 0.101141i | ||||
\(61\) | 2.48663 | − | 4.30697i | 0.318380 | − | 0.551451i | −0.661770 | − | 0.749707i | \(-0.730195\pi\) |
0.980150 | + | 0.198256i | \(0.0635278\pi\) | |||||||
\(62\) | −2.56917 | − | 4.44994i | −0.326286 | − | 0.565143i | ||||
\(63\) | 0.994318 | + | 1.72221i | 0.125272 | + | 0.216978i | ||||
\(64\) | 1.17412 | 0.146765 | ||||||||
\(65\) | −0.647830 | −0.0803535 | ||||||||
\(66\) | 0.0620644 | + | 0.107499i | 0.00763959 | + | 0.0132322i | ||||
\(67\) | 1.85065 | 0.226093 | 0.113047 | − | 0.993590i | \(-0.463939\pi\) | ||||
0.113047 | + | 0.993590i | \(0.463939\pi\) | |||||||
\(68\) | 4.09170 | − | 7.08704i | 0.496192 | − | 0.859430i | ||||
\(69\) | −1.74465 | + | 3.02182i | −0.210031 | + | 0.363784i | ||||
\(70\) | −0.403014 | + | 0.698041i | −0.0481694 | + | 0.0834318i | ||||
\(71\) | −6.09127 | − | 10.5504i | −0.722901 | − | 1.25210i | −0.959832 | − | 0.280575i | \(-0.909475\pi\) |
0.236931 | − | 0.971526i | \(-0.423858\pi\) | |||||||
\(72\) | −1.20998 | − | 2.09575i | −0.142597 | − | 0.246986i | ||||
\(73\) | −4.82332 | + | 8.35423i | −0.564527 | + | 0.977789i | 0.432567 | + | 0.901602i | \(0.357608\pi\) |
−0.997094 | + | 0.0761870i | \(0.975725\pi\) | |||||||
\(74\) | −1.63471 | − | 2.83140i | −0.190031 | − | 0.329143i | ||||
\(75\) | 4.65043 | 0.536985 | ||||||||
\(76\) | 3.84548 | − | 6.66056i | 0.441106 | − | 0.764019i | ||||
\(77\) | −0.180041 | + | 0.311839i | −0.0205175 | + | 0.0355374i | ||||
\(78\) | −0.751142 | −0.0850501 | ||||||||
\(79\) | 5.82978 | 0.655901 | 0.327951 | − | 0.944695i | \(-0.393642\pi\) | ||||
0.327951 | + | 0.944695i | \(0.393642\pi\) | |||||||
\(80\) | −0.414206 | + | 0.717426i | −0.0463097 | + | 0.0802107i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −4.45297 | −0.491748 | ||||||||
\(83\) | −1.34867 | − | 2.33597i | −0.148036 | − | 0.256406i | 0.782465 | − | 0.622694i | \(-0.213962\pi\) |
−0.930502 | + | 0.366288i | \(0.880629\pi\) | |||||||
\(84\) | 1.52135 | − | 2.63506i | 0.165993 | − | 0.287509i | ||||
\(85\) | −1.58113 | − | 2.73859i | −0.171497 | − | 0.297042i | ||||
\(86\) | −0.596619 | − | 1.03337i | −0.0643350 | − | 0.111432i | ||||
\(87\) | −2.47266 | + | 4.28277i | −0.265097 | + | 0.459161i | ||||
\(88\) | 0.219090 | − | 0.379475i | 0.0233551 | − | 0.0404522i | ||||
\(89\) | −6.46211 | + | 11.1927i | −0.684983 | + | 1.18643i | 0.288459 | + | 0.957492i | \(0.406857\pi\) |
−0.973442 | + | 0.228933i | \(0.926476\pi\) | |||||||
\(90\) | −0.405317 | −0.0427241 | ||||||||
\(91\) | −1.08948 | − | 1.88704i | −0.114209 | − | 0.197815i | ||||
\(92\) | 5.33878 | 0.556606 | ||||||||
\(93\) | 7.49542 | 0.777239 | ||||||||
\(94\) | 1.77845 | + | 3.08037i | 0.183433 | + | 0.317716i | ||||
\(95\) | −1.48598 | − | 2.57379i | −0.152458 | − | 0.264065i | ||||
\(96\) | −2.90022 | + | 5.02333i | −0.296002 | + | 0.512691i | ||||
\(97\) | −7.64453 | − | 13.2407i | −0.776185 | − | 1.34439i | −0.934126 | − | 0.356943i | \(-0.883819\pi\) |
0.157941 | − | 0.987448i | \(-0.449514\pi\) | |||||||
\(98\) | 2.08767 | 0.210886 | ||||||||
\(99\) | −0.181069 | −0.0181981 | ||||||||
\(100\) | −3.55769 | − | 6.16209i | −0.355769 | − | 0.616209i | ||||
\(101\) | 0.605854 | 0.0602848 | 0.0301424 | − | 0.999546i | \(-0.490404\pi\) | ||||
0.0301424 | + | 0.999546i | \(0.490404\pi\) | |||||||
\(102\) | −1.83327 | − | 3.17532i | −0.181521 | − | 0.314404i | ||||
\(103\) | −2.54452 | −0.250719 | −0.125359 | − | 0.992111i | \(-0.540008\pi\) | ||||
−0.125359 | + | 0.992111i | \(0.540008\pi\) | |||||||
\(104\) | 1.32578 | + | 2.29632i | 0.130004 | + | 0.225173i | ||||
\(105\) | −0.587885 | − | 1.01825i | −0.0573717 | − | 0.0993707i | ||||
\(106\) | −0.871575 | − | 1.50961i | −0.0846549 | − | 0.146627i | ||||
\(107\) | −0.224047 | − | 0.388061i | −0.0216594 | − | 0.0375153i | 0.854993 | − | 0.518640i | \(-0.173562\pi\) |
−0.876652 | + | 0.481125i | \(0.840228\pi\) | |||||||
\(108\) | 1.53005 | 0.147229 | ||||||||
\(109\) | 2.44463 | − | 4.23422i | 0.234153 | − | 0.405564i | −0.724873 | − | 0.688882i | \(-0.758102\pi\) |
0.959026 | + | 0.283318i | \(0.0914351\pi\) | |||||||
\(110\) | −0.0366952 | − | 0.0635579i | −0.00349875 | − | 0.00606001i | ||||
\(111\) | 4.76917 | 0.452669 | ||||||||
\(112\) | −2.78635 | −0.263285 | ||||||||
\(113\) | 6.16196 | − | 10.6728i | 0.579669 | − | 1.00402i | −0.415848 | − | 0.909434i | \(-0.636515\pi\) |
0.995517 | − | 0.0945817i | \(-0.0301514\pi\) | |||||||
\(114\) | −1.72295 | − | 2.98424i | −0.161369 | − | 0.279500i | ||||
\(115\) | 1.03151 | − | 1.78663i | 0.0961890 | − | 0.166604i | ||||
\(116\) | 7.56656 | 0.702538 | ||||||||
\(117\) | 0.547853 | − | 0.948910i | 0.0506491 | − | 0.0877267i | ||||
\(118\) | 6.81615 | 0.627478 | ||||||||
\(119\) | 5.31808 | − | 9.21119i | 0.487508 | − | 0.844389i | ||||
\(120\) | 0.715393 | + | 1.23910i | 0.0653062 | + | 0.113114i | ||||
\(121\) | 5.48361 | + | 9.49789i | 0.498510 | + | 0.863444i | ||||
\(122\) | −1.70466 | + | 2.95256i | −0.154333 | + | 0.267312i | ||||
\(123\) | 3.24782 | − | 5.62539i | 0.292846 | − | 0.507224i | ||||
\(124\) | −5.73417 | − | 9.93188i | −0.514944 | − | 0.891909i | ||||
\(125\) | −5.70576 | −0.510339 | ||||||||
\(126\) | −0.681637 | − | 1.18063i | −0.0607250 | − | 0.105179i | ||||
\(127\) | 5.01838 | + | 8.69209i | 0.445310 | + | 0.771299i | 0.998074 | − | 0.0620390i | \(-0.0197603\pi\) |
−0.552764 | + | 0.833338i | \(0.686427\pi\) | |||||||
\(128\) | 10.7960 | 0.954239 | ||||||||
\(129\) | 1.74060 | 0.153251 | ||||||||
\(130\) | 0.444108 | 0.0389509 | ||||||||
\(131\) | −5.23597 | − | 9.06896i | −0.457469 | − | 0.792359i | 0.541358 | − | 0.840792i | \(-0.317910\pi\) |
−0.998826 | + | 0.0484333i | \(0.984577\pi\) | |||||||
\(132\) | 0.138522 | + | 0.239927i | 0.0120568 | + | 0.0208830i | ||||
\(133\) | 4.99806 | − | 8.65689i | 0.433386 | − | 0.750647i | ||||
\(134\) | −1.26868 | −0.109597 | ||||||||
\(135\) | 0.295622 | − | 0.512033i | 0.0254431 | − | 0.0440687i | ||||
\(136\) | −6.47154 | + | 11.2090i | −0.554930 | + | 0.961167i | ||||
\(137\) | 0.301018 | − | 0.521379i | 0.0257177 | − | 0.0445444i | −0.852880 | − | 0.522107i | \(-0.825146\pi\) |
0.878598 | + | 0.477562i | \(0.158480\pi\) | |||||||
\(138\) | 1.19601 | − | 2.07155i | 0.101811 | − | 0.176342i | ||||
\(139\) | −2.99356 | − | 5.18499i | −0.253910 | − | 0.439785i | 0.710689 | − | 0.703507i | \(-0.248383\pi\) |
−0.964599 | + | 0.263721i | \(0.915050\pi\) | |||||||
\(140\) | −0.899491 | + | 1.55796i | −0.0760209 | + | 0.131672i | ||||
\(141\) | −5.18853 | −0.436953 | ||||||||
\(142\) | 4.17576 | + | 7.23263i | 0.350422 | + | 0.606949i | ||||
\(143\) | 0.198399 | 0.0165909 | ||||||||
\(144\) | −0.700567 | − | 1.21342i | −0.0583806 | − | 0.101118i | ||||
\(145\) | 1.46195 | − | 2.53216i | 0.121408 | − | 0.210285i | ||||
\(146\) | 3.30654 | − | 5.72709i | 0.273651 | − | 0.473977i | ||||
\(147\) | −1.52266 | + | 2.63733i | −0.125587 | + | 0.217523i | ||||
\(148\) | −3.64852 | − | 6.31943i | −0.299907 | − | 0.519454i | ||||
\(149\) | 8.35338 | 0.684335 | 0.342168 | − | 0.939639i | \(-0.388839\pi\) | ||||
0.342168 | + | 0.939639i | \(0.388839\pi\) | |||||||
\(150\) | −3.18802 | −0.260301 | ||||||||
\(151\) | 9.61211 | − | 16.6487i | 0.782223 | − | 1.35485i | −0.148421 | − | 0.988924i | \(-0.547419\pi\) |
0.930644 | − | 0.365925i | \(-0.119247\pi\) | |||||||
\(152\) | −6.08210 | + | 10.5345i | −0.493323 | + | 0.854461i | ||||
\(153\) | 5.34847 | 0.432398 | ||||||||
\(154\) | 0.123423 | − | 0.213776i | 0.00994575 | − | 0.0172265i | ||||
\(155\) | −4.43163 | −0.355957 | ||||||||
\(156\) | −1.67648 | −0.134226 | ||||||||
\(157\) | −6.24016 | + | 10.8656i | −0.498019 | + | 0.867166i | ||||
\(158\) | −3.99650 | −0.317944 | ||||||||
\(159\) | 2.54277 | 0.201655 | ||||||||
\(160\) | 1.71474 | − | 2.97001i | 0.135562 | − | 0.234800i | ||||
\(161\) | 6.93894 | 0.546865 | ||||||||
\(162\) | 0.342766 | − | 0.593688i | 0.0269302 | − | 0.0466445i | ||||
\(163\) | −10.9088 | + | 18.8947i | −0.854446 | + | 1.47994i | 0.0227121 | + | 0.999742i | \(0.492770\pi\) |
−0.877158 | + | 0.480202i | \(0.840563\pi\) | |||||||
\(164\) | −9.93863 | −0.776076 | ||||||||
\(165\) | 0.107056 | 0.00833431 | ||||||||
\(166\) | 0.924559 | + | 1.60138i | 0.0717597 | + | 0.124291i | ||||
\(167\) | −3.10725 | + | 5.38192i | −0.240446 | + | 0.416465i | −0.960842 | − | 0.277099i | \(-0.910627\pi\) |
0.720395 | + | 0.693564i | \(0.243960\pi\) | |||||||
\(168\) | −2.40621 | + | 4.16768i | −0.185643 | + | 0.321543i | ||||
\(169\) | 5.89971 | − | 10.2186i | 0.453824 | − | 0.786046i | ||||
\(170\) | 1.08391 | + | 1.87739i | 0.0831323 | + | 0.143989i | ||||
\(171\) | 5.02661 | 0.384395 | ||||||||
\(172\) | −1.33160 | − | 2.30640i | −0.101534 | − | 0.175861i | ||||
\(173\) | 13.4951 | 1.02601 | 0.513007 | − | 0.858384i | \(-0.328531\pi\) | ||||
0.513007 | + | 0.858384i | \(0.328531\pi\) | |||||||
\(174\) | 1.69509 | − | 2.93597i | 0.128504 | − | 0.222576i | ||||
\(175\) | −4.62401 | − | 8.00902i | −0.349542 | − | 0.605425i | ||||
\(176\) | 0.126851 | − | 0.219713i | 0.00956177 | − | 0.0165615i | ||||
\(177\) | −4.97143 | + | 8.61078i | −0.373676 | + | 0.647226i | ||||
\(178\) | 4.42998 | − | 7.67296i | 0.332041 | − | 0.575113i | ||||
\(179\) | 2.00927 | − | 3.48016i | 0.150180 | − | 0.260120i | −0.781113 | − | 0.624389i | \(-0.785348\pi\) |
0.931294 | + | 0.364269i | \(0.118681\pi\) | |||||||
\(180\) | −0.904631 | −0.0674272 | ||||||||
\(181\) | −5.60593 | + | 9.70976i | −0.416685 | + | 0.721720i | −0.995604 | − | 0.0936652i | \(-0.970142\pi\) |
0.578918 | + | 0.815386i | \(0.303475\pi\) | |||||||
\(182\) | 0.746874 | + | 1.29362i | 0.0553620 | + | 0.0958898i | ||||
\(183\) | −2.48663 | − | 4.30697i | −0.183817 | − | 0.318380i | ||||
\(184\) | −8.44394 | −0.622496 | ||||||||
\(185\) | −2.81974 | −0.207312 | ||||||||
\(186\) | −5.13835 | −0.376762 | ||||||||
\(187\) | 0.484222 | + | 0.838697i | 0.0354098 | + | 0.0613316i | ||||
\(188\) | 3.96935 | + | 6.87511i | 0.289494 | + | 0.501419i | ||||
\(189\) | 1.98864 | 0.144652 | ||||||||
\(190\) | 1.01869 | + | 1.76441i | 0.0739032 | + | 0.128004i | ||||
\(191\) | 1.48550 | − | 2.57296i | 0.107487 | − | 0.186173i | −0.807265 | − | 0.590190i | \(-0.799053\pi\) |
0.914752 | + | 0.404017i | \(0.132386\pi\) | |||||||
\(192\) | 0.587059 | − | 1.01682i | 0.0423673 | − | 0.0733823i | ||||
\(193\) | 2.97960 | + | 5.16081i | 0.214476 | + | 0.371483i | 0.953110 | − | 0.302623i | \(-0.0978623\pi\) |
−0.738634 | + | 0.674106i | \(0.764529\pi\) | |||||||
\(194\) | 5.24057 | + | 9.07693i | 0.376251 | + | 0.651686i | ||||
\(195\) | −0.323915 | + | 0.561038i | −0.0231960 | + | 0.0401767i | ||||
\(196\) | 4.65949 | 0.332820 | ||||||||
\(197\) | −7.55021 | + | 13.0773i | −0.537930 | + | 0.931723i | 0.461085 | + | 0.887356i | \(0.347460\pi\) |
−0.999015 | + | 0.0443666i | \(0.985873\pi\) | |||||||
\(198\) | 0.124129 | 0.00882144 | ||||||||
\(199\) | 3.46155 | − | 5.99558i | 0.245383 | − | 0.425015i | −0.716856 | − | 0.697221i | \(-0.754420\pi\) |
0.962239 | + | 0.272206i | \(0.0877531\pi\) | |||||||
\(200\) | 5.62692 | + | 9.74612i | 0.397884 | + | 0.689155i | ||||
\(201\) | 0.925326 | − | 1.60271i | 0.0652675 | − | 0.113047i | ||||
\(202\) | −0.415332 | −0.0292227 | ||||||||
\(203\) | 9.83444 | 0.690242 | ||||||||
\(204\) | −4.09170 | − | 7.08704i | −0.286477 | − | 0.496192i | ||||
\(205\) | −1.92025 | + | 3.32598i | −0.134116 | + | 0.232296i | ||||
\(206\) | 1.74435 | 0.121534 | ||||||||
\(207\) | 1.74465 | + | 3.02182i | 0.121261 | + | 0.210031i | ||||
\(208\) | 0.767616 | + | 1.32955i | 0.0532246 | + | 0.0921877i | ||||
\(209\) | 0.455083 | + | 0.788226i | 0.0314787 | + | 0.0545228i | ||||
\(210\) | 0.403014 | + | 0.698041i | 0.0278106 | + | 0.0481694i | ||||
\(211\) | −5.79437 | −0.398901 | −0.199451 | − | 0.979908i | \(-0.563916\pi\) | ||||
−0.199451 | + | 0.979908i | \(0.563916\pi\) | |||||||
\(212\) | −1.94528 | − | 3.36932i | −0.133602 | − | 0.231406i | ||||
\(213\) | −12.1825 | −0.834734 | ||||||||
\(214\) | 0.153591 | + | 0.266028i | 0.0104993 | + | 0.0181853i | ||||
\(215\) | −1.02912 | −0.0701854 | ||||||||
\(216\) | −2.41996 | −0.164657 | ||||||||
\(217\) | −7.45284 | − | 12.9087i | −0.505932 | − | 0.876299i | ||||
\(218\) | −1.67587 | + | 2.90269i | −0.113504 | + | 0.196595i | ||||
\(219\) | 4.82332 | + | 8.35423i | 0.325930 | + | 0.564527i | ||||
\(220\) | −0.0819004 | − | 0.141856i | −0.00552173 | − | 0.00956391i | ||||
\(221\) | −5.86036 | −0.394210 | ||||||||
\(222\) | −3.26942 | −0.219429 | ||||||||
\(223\) | −6.56662 | − | 11.3737i | −0.439734 | − | 0.761641i | 0.557935 | − | 0.829885i | \(-0.311594\pi\) |
−0.997669 | + | 0.0682435i | \(0.978261\pi\) | |||||||
\(224\) | 11.5350 | 0.770712 | ||||||||
\(225\) | 2.32522 | − | 4.02739i | 0.155014 | − | 0.268493i | ||||
\(226\) | −4.22422 | + | 7.31657i | −0.280991 | + | 0.486691i | ||||
\(227\) | −7.60672 | + | 13.1752i | −0.504876 | + | 0.874471i | 0.495108 | + | 0.868831i | \(0.335128\pi\) |
−0.999984 | + | 0.00563952i | \(0.998205\pi\) | |||||||
\(228\) | −3.84548 | − | 6.66056i | −0.254673 | − | 0.441106i | ||||
\(229\) | 14.7263 | + | 25.5067i | 0.973141 | + | 1.68553i | 0.685940 | + | 0.727658i | \(0.259391\pi\) |
0.287201 | + | 0.957870i | \(0.407275\pi\) | |||||||
\(230\) | −0.707134 | + | 1.22479i | −0.0466271 | + | 0.0807604i | ||||
\(231\) | 0.180041 | + | 0.311839i | 0.0118458 | + | 0.0205175i | ||||
\(232\) | −11.9675 | −0.785702 | ||||||||
\(233\) | −13.5125 | + | 23.4044i | −0.885235 | + | 1.53327i | −0.0397910 | + | 0.999208i | \(0.512669\pi\) |
−0.845444 | + | 0.534064i | \(0.820664\pi\) | |||||||
\(234\) | −0.375571 | + | 0.650508i | −0.0245518 | + | 0.0425250i | ||||
\(235\) | 3.06769 | 0.200114 | ||||||||
\(236\) | 15.2130 | 0.990285 | ||||||||
\(237\) | 2.91489 | − | 5.04874i | 0.189342 | − | 0.327951i | ||||
\(238\) | −3.64572 | + | 6.31456i | −0.236317 | + | 0.409312i | ||||
\(239\) | −11.3807 | −0.736156 | −0.368078 | − | 0.929795i | \(-0.619984\pi\) | ||||
−0.368078 | + | 0.929795i | \(0.619984\pi\) | |||||||
\(240\) | 0.414206 | + | 0.717426i | 0.0267369 | + | 0.0463097i | ||||
\(241\) | −12.5201 | + | 21.6855i | −0.806492 | + | 1.39688i | 0.108788 | + | 0.994065i | \(0.465303\pi\) |
−0.915279 | + | 0.402819i | \(0.868030\pi\) | |||||||
\(242\) | −3.75919 | − | 6.51110i | −0.241650 | − | 0.418549i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −3.80466 | + | 6.58986i | −0.243568 | + | 0.421872i | ||||
\(245\) | 0.900265 | − | 1.55930i | 0.0575158 | − | 0.0996203i | ||||
\(246\) | −2.22648 | + | 3.85638i | −0.141955 | + | 0.245874i | ||||
\(247\) | −5.50770 | −0.350446 | ||||||||
\(248\) | 9.06931 | + | 15.7085i | 0.575901 | + | 0.997491i | ||||
\(249\) | −2.69735 | −0.170938 | ||||||||
\(250\) | 3.91148 | 0.247384 | ||||||||
\(251\) | −1.77636 | − | 3.07675i | −0.112123 | − | 0.194203i | 0.804503 | − | 0.593949i | \(-0.202432\pi\) |
−0.916626 | + | 0.399746i | \(0.869098\pi\) | |||||||
\(252\) | −1.52135 | − | 2.63506i | −0.0958362 | − | 0.165993i | ||||
\(253\) | −0.315902 | + | 0.547158i | −0.0198606 | + | 0.0343995i | ||||
\(254\) | −3.44026 | − | 5.95871i | −0.215861 | − | 0.373883i | ||||
\(255\) | −3.16225 | −0.198028 | ||||||||
\(256\) | −9.74922 | −0.609326 | ||||||||
\(257\) | 4.41344 | + | 7.64431i | 0.275303 | + | 0.476839i | 0.970212 | − | 0.242259i | \(-0.0778885\pi\) |
−0.694909 | + | 0.719098i | \(0.744555\pi\) | |||||||
\(258\) | −1.19324 | −0.0742877 | ||||||||
\(259\) | −4.74207 | − | 8.21351i | −0.294658 | − | 0.510363i | ||||
\(260\) | 0.991210 | 0.0614723 | ||||||||
\(261\) | 2.47266 | + | 4.28277i | 0.153054 | + | 0.265097i | ||||
\(262\) | 3.58942 | + | 6.21706i | 0.221755 | + | 0.384091i | ||||
\(263\) | 9.09873 | + | 15.7595i | 0.561052 | + | 0.971770i | 0.997405 | + | 0.0719948i | \(0.0229365\pi\) |
−0.436353 | + | 0.899775i | \(0.643730\pi\) | |||||||
\(264\) | −0.219090 | − | 0.379475i | −0.0134841 | − | 0.0233551i | ||||
\(265\) | −1.50340 | −0.0923531 | ||||||||
\(266\) | −3.42633 | + | 5.93457i | −0.210082 | + | 0.363872i | ||||
\(267\) | 6.46211 | + | 11.1927i | 0.395475 | + | 0.684983i | ||||
\(268\) | −2.83158 | −0.172966 | ||||||||
\(269\) | 14.1282 | 0.861409 | 0.430705 | − | 0.902493i | \(-0.358265\pi\) | ||||
0.430705 | + | 0.902493i | \(0.358265\pi\) | |||||||
\(270\) | −0.202658 | + | 0.351015i | −0.0123334 | + | 0.0213621i | ||||
\(271\) | 2.82402 | + | 4.89135i | 0.171547 | + | 0.297128i | 0.938961 | − | 0.344024i | \(-0.111790\pi\) |
−0.767414 | + | 0.641152i | \(0.778457\pi\) | |||||||
\(272\) | −3.74696 | + | 6.48993i | −0.227193 | + | 0.393510i | ||||
\(273\) | −2.17896 | −0.131877 | ||||||||
\(274\) | −0.206358 | + | 0.357422i | −0.0124665 | + | 0.0215927i | ||||
\(275\) | 0.842050 | 0.0507775 | ||||||||
\(276\) | 2.66939 | − | 4.62352i | 0.160678 | − | 0.278303i | ||||
\(277\) | −6.43152 | − | 11.1397i | −0.386433 | − | 0.669321i | 0.605534 | − | 0.795819i | \(-0.292959\pi\) |
−0.991967 | + | 0.126498i | \(0.959626\pi\) | |||||||
\(278\) | 2.05218 | + | 3.55448i | 0.123081 | + | 0.213183i | ||||
\(279\) | 3.74771 | − | 6.49123i | 0.224370 | − | 0.388620i | ||||
\(280\) | 1.42266 | − | 2.46412i | 0.0850201 | − | 0.147259i | ||||
\(281\) | 4.83912 | + | 8.38159i | 0.288677 | + | 0.500004i | 0.973494 | − | 0.228711i | \(-0.0734512\pi\) |
−0.684817 | + | 0.728715i | \(0.740118\pi\) | |||||||
\(282\) | 3.55690 | 0.211810 | ||||||||
\(283\) | 8.41371 | + | 14.5730i | 0.500143 | + | 0.866273i | 1.00000 | 0.000165084i | \(5.25478e-5\pi\) | |
−0.499857 | + | 0.866108i | \(0.666614\pi\) | |||||||
\(284\) | 9.31993 | + | 16.1426i | 0.553036 | + | 0.957887i | ||||
\(285\) | −2.97196 | −0.176044 | ||||||||
\(286\) | −0.136009 | −0.00804236 | ||||||||
\(287\) | −12.9175 | −0.762494 | ||||||||
\(288\) | 2.90022 | + | 5.02333i | 0.170897 | + | 0.296002i | ||||
\(289\) | −5.80307 | − | 10.0512i | −0.341357 | − | 0.591248i | ||||
\(290\) | −1.00221 | + | 1.73588i | −0.0588518 | + | 0.101934i | ||||
\(291\) | −15.2891 | −0.896261 | ||||||||
\(292\) | 7.37990 | − | 12.7824i | 0.431876 | − | 0.748031i | ||||
\(293\) | 14.8252 | − | 25.6780i | 0.866097 | − | 1.50012i | 0.000142243 | − | 1.00000i | \(-0.499955\pi\) |
0.865954 | − | 0.500123i | \(-0.166712\pi\) | |||||||
\(294\) | 1.04383 | − | 1.80797i | 0.0608776 | − | 0.105443i | ||||
\(295\) | 2.93933 | − | 5.09107i | 0.171135 | − | 0.296414i | ||||
\(296\) | 5.77060 | + | 9.99497i | 0.335409 | + | 0.580946i | ||||
\(297\) | −0.0905346 | + | 0.156811i | −0.00525335 | + | 0.00909907i | ||||
\(298\) | −5.72650 | −0.331728 | ||||||||
\(299\) | −1.91162 | − | 3.31102i | −0.110552 | − | 0.191481i | ||||
\(300\) | −7.11537 | −0.410806 | ||||||||
\(301\) | −1.73071 | − | 2.99768i | −0.0997566 | − | 0.172783i | ||||
\(302\) | −6.58941 | + | 11.4132i | −0.379178 | + | 0.656755i | ||||
\(303\) | 0.302927 | − | 0.524685i | 0.0174027 | − | 0.0301424i | ||||
\(304\) | −3.52148 | + | 6.09938i | −0.201971 | + | 0.349824i | ||||
\(305\) | 1.47020 | + | 2.54647i | 0.0841837 | + | 0.145810i | ||||
\(306\) | −3.66655 | −0.209603 | ||||||||
\(307\) | 2.98155 | 0.170166 | 0.0850830 | − | 0.996374i | \(-0.472884\pi\) | ||||
0.0850830 | + | 0.996374i | \(0.472884\pi\) | |||||||
\(308\) | 0.275470 | − | 0.477129i | 0.0156964 | − | 0.0271869i | ||||
\(309\) | −1.27226 | + | 2.20362i | −0.0723762 | + | 0.125359i | ||||
\(310\) | 3.03802 | 0.172548 | ||||||||
\(311\) | 6.76973 | − | 11.7255i | 0.383876 | − | 0.664893i | −0.607736 | − | 0.794139i | \(-0.707922\pi\) |
0.991613 | + | 0.129246i | \(0.0412555\pi\) | |||||||
\(312\) | 2.65157 | 0.150115 | ||||||||
\(313\) | 8.47960 | 0.479295 | 0.239648 | − | 0.970860i | \(-0.422968\pi\) | ||||
0.239648 | + | 0.970860i | \(0.422968\pi\) | |||||||
\(314\) | 4.27783 | − | 7.44869i | 0.241412 | − | 0.420354i | ||||
\(315\) | −1.17577 | −0.0662471 | ||||||||
\(316\) | −8.91983 | −0.501780 | ||||||||
\(317\) | −3.17994 | + | 5.50781i | −0.178603 | + | 0.309349i | −0.941402 | − | 0.337286i | \(-0.890491\pi\) |
0.762799 | + | 0.646635i | \(0.223824\pi\) | |||||||
\(318\) | −1.74315 | −0.0977510 | ||||||||
\(319\) | −0.447722 | + | 0.775478i | −0.0250676 | + | 0.0434184i | ||||
\(320\) | −0.347095 | + | 0.601186i | −0.0194032 | + | 0.0336073i | ||||
\(321\) | −0.448094 | −0.0250102 | ||||||||
\(322\) | −4.75686 | −0.265090 | ||||||||
\(323\) | −13.4424 | − | 23.2828i | −0.747952 | − | 1.29549i | ||||
\(324\) | 0.765023 | − | 1.32506i | 0.0425013 | − | 0.0736144i | ||||
\(325\) | −2.54775 | + | 4.41284i | −0.141324 | + | 0.244780i | ||||
\(326\) | 7.47835 | − | 12.9529i | 0.414188 | − | 0.717394i | ||||
\(327\) | −2.44463 | − | 4.23422i | −0.135188 | − | 0.234153i | ||||
\(328\) | 15.7192 | 0.867946 | ||||||||
\(329\) | 5.15905 | + | 8.93574i | 0.284428 | + | 0.492643i | ||||
\(330\) | −0.0733904 | −0.00404001 | ||||||||
\(331\) | 10.4800 | − | 18.1520i | 0.576035 | − | 0.997723i | −0.419893 | − | 0.907574i | \(-0.637932\pi\) |
0.995928 | − | 0.0901490i | \(-0.0287343\pi\) | |||||||
\(332\) | 2.06353 | + | 3.57415i | 0.113251 | + | 0.196157i | ||||
\(333\) | 2.38458 | − | 4.13022i | 0.130674 | − | 0.226335i | ||||
\(334\) | 2.13012 | − | 3.68948i | 0.116555 | − | 0.201879i | ||||
\(335\) | −0.547094 | + | 0.947594i | −0.0298909 | + | 0.0517726i | ||||
\(336\) | −1.39317 | + | 2.41305i | −0.0760038 | + | 0.131643i | ||||
\(337\) | −2.63357 | −0.143460 | −0.0717298 | − | 0.997424i | \(-0.522852\pi\) | ||||
−0.0717298 | + | 0.997424i | \(0.522852\pi\) | |||||||
\(338\) | −4.04444 | + | 7.00518i | −0.219989 | + | 0.381031i | ||||
\(339\) | −6.16196 | − | 10.6728i | −0.334672 | − | 0.579669i | ||||
\(340\) | 2.41920 | + | 4.19017i | 0.131199 | + | 0.227244i | ||||
\(341\) | 1.35719 | 0.0734960 | ||||||||
\(342\) | −3.44590 | −0.186333 | ||||||||
\(343\) | 19.9765 | 1.07863 | ||||||||
\(344\) | 2.10609 | + | 3.64786i | 0.113553 | + | 0.196679i | ||||
\(345\) | −1.03151 | − | 1.78663i | −0.0555348 | − | 0.0961890i | ||||
\(346\) | −9.25133 | −0.497354 | ||||||||
\(347\) | −3.09400 | − | 5.35897i | −0.166095 | − | 0.287685i | 0.770949 | − | 0.636897i | \(-0.219782\pi\) |
−0.937044 | + | 0.349213i | \(0.886449\pi\) | |||||||
\(348\) | 3.78328 | − | 6.55284i | 0.202805 | − | 0.351269i | ||||
\(349\) | 14.9150 | − | 25.8335i | 0.798379 | − | 1.38283i | −0.122292 | − | 0.992494i | \(-0.539024\pi\) |
0.920671 | − | 0.390339i | \(-0.127642\pi\) | |||||||
\(350\) | 3.16990 | + | 5.49044i | 0.169439 | + | 0.293476i | ||||
\(351\) | −0.547853 | − | 0.948910i | −0.0292422 | − | 0.0506491i | ||||
\(352\) | −0.525141 | + | 0.909570i | −0.0279901 | + | 0.0484803i | ||||
\(353\) | −30.6761 | −1.63272 | −0.816362 | − | 0.577540i | \(-0.804013\pi\) | ||||
−0.816362 | + | 0.577540i | \(0.804013\pi\) | |||||||
\(354\) | 3.40808 | − | 5.90296i | 0.181137 | − | 0.313739i | ||||
\(355\) | 7.20286 | 0.382288 | ||||||||
\(356\) | 9.88733 | − | 17.1254i | 0.524028 | − | 0.907643i | ||||
\(357\) | −5.31808 | − | 9.21119i | −0.281463 | − | 0.487508i | ||||
\(358\) | −1.37742 | + | 2.38576i | −0.0727990 | + | 0.126091i | ||||
\(359\) | 35.8732 | 1.89332 | 0.946658 | − | 0.322239i | \(-0.104435\pi\) | ||||
0.946658 | + | 0.322239i | \(0.104435\pi\) | |||||||
\(360\) | 1.43079 | 0.0754091 | ||||||||
\(361\) | −3.13343 | − | 5.42725i | −0.164917 | − | 0.285645i | ||||
\(362\) | 3.84304 | − | 6.65635i | 0.201986 | − | 0.349850i | ||||
\(363\) | 10.9672 | 0.575629 | ||||||||
\(364\) | 1.66696 | + | 2.88725i | 0.0873723 | + | 0.151333i | ||||
\(365\) | −2.85176 | − | 4.93939i | −0.149268 | − | 0.258540i | ||||
\(366\) | 1.70466 | + | 2.95256i | 0.0891041 | + | 0.154333i | ||||
\(367\) | −8.24032 | − | 14.2727i | −0.430141 | − | 0.745027i | 0.566744 | − | 0.823894i | \(-0.308203\pi\) |
−0.996885 | + | 0.0788674i | \(0.974870\pi\) | |||||||
\(368\) | −4.88897 | −0.254855 | ||||||||
\(369\) | −3.24782 | − | 5.62539i | −0.169075 | − | 0.292846i | ||||
\(370\) | 1.93302 | 0.100493 | ||||||||
\(371\) | −2.52832 | − | 4.37919i | −0.131264 | − | 0.227356i | ||||
\(372\) | −11.4683 | −0.594606 | ||||||||
\(373\) | −21.8203 | −1.12981 | −0.564906 | − | 0.825155i | \(-0.691088\pi\) | ||||
−0.564906 | + | 0.825155i | \(0.691088\pi\) | |||||||
\(374\) | −0.331949 | − | 0.574953i | −0.0171647 | − | 0.0297301i | ||||
\(375\) | −2.85288 | + | 4.94133i | −0.147322 | + | 0.255169i | ||||
\(376\) | −6.27802 | − | 10.8738i | −0.323764 | − | 0.560776i | ||||
\(377\) | −2.70931 | − | 4.69266i | −0.139536 | − | 0.241684i | ||||
\(378\) | −1.36327 | −0.0701192 | ||||||||
\(379\) | 13.4235 | 0.689517 | 0.344758 | − | 0.938691i | \(-0.387961\pi\) | ||||
0.344758 | + | 0.938691i | \(0.387961\pi\) | |||||||
\(380\) | 2.27362 | + | 3.93802i | 0.116634 | + | 0.202016i | ||||
\(381\) | 10.0368 | 0.514199 | ||||||||
\(382\) | −1.01836 | + | 1.76385i | −0.0521037 | + | 0.0902462i | ||||
\(383\) | 9.54562 | − | 16.5335i | 0.487759 | − | 0.844823i | −0.512142 | − | 0.858901i | \(-0.671148\pi\) |
0.999901 | + | 0.0140780i | \(0.00448133\pi\) | |||||||
\(384\) | 5.39799 | − | 9.34960i | 0.275465 | − | 0.477120i | ||||
\(385\) | −0.106448 | − | 0.184373i | −0.00542509 | − | 0.00939653i | ||||
\(386\) | −2.04261 | − | 3.53790i | −0.103966 | − | 0.180074i | ||||
\(387\) | 0.870301 | − | 1.50740i | 0.0442399 | − | 0.0766257i | ||||
\(388\) | 11.6965 | + | 20.2589i | 0.593799 | + | 1.02849i | ||||
\(389\) | 3.14148 | 0.159279 | 0.0796397 | − | 0.996824i | \(-0.474623\pi\) | ||||
0.0796397 | + | 0.996824i | \(0.474623\pi\) | |||||||
\(390\) | 0.222054 | − | 0.384609i | 0.0112441 | − | 0.0194754i | ||||
\(391\) | 9.33119 | − | 16.1621i | 0.471899 | − | 0.817352i | ||||
\(392\) | −7.36956 | −0.372219 | ||||||||
\(393\) | −10.4719 | −0.528239 | ||||||||
\(394\) | 5.17591 | − | 8.96494i | 0.260759 | − | 0.451647i | ||||
\(395\) | −1.72341 | + | 2.98504i | −0.0867142 | + | 0.150193i | ||||
\(396\) | 0.277044 | 0.0139220 | ||||||||
\(397\) | −13.7048 | − | 23.7375i | −0.687825 | − | 1.19135i | −0.972540 | − | 0.232736i | \(-0.925232\pi\) |
0.284715 | − | 0.958612i | \(-0.408101\pi\) | |||||||
\(398\) | −2.37300 | + | 4.11016i | −0.118948 | + | 0.206024i | ||||
\(399\) | −4.99806 | − | 8.65689i | −0.250216 | − | 0.433386i | ||||
\(400\) | 3.25794 | + | 5.64291i | 0.162897 | + | 0.282146i | ||||
\(401\) | 1.24249 | − | 2.15206i | 0.0620472 | − | 0.107469i | −0.833333 | − | 0.552771i | \(-0.813570\pi\) |
0.895380 | + | 0.445302i | \(0.146904\pi\) | |||||||
\(402\) | −0.634340 | + | 1.09871i | −0.0316380 | + | 0.0547987i | ||||
\(403\) | −4.10639 | + | 7.11248i | −0.204554 | + | 0.354298i | ||||
\(404\) | −0.926985 | −0.0461192 | ||||||||
\(405\) | −0.295622 | − | 0.512033i | −0.0146896 | − | 0.0254431i | ||||
\(406\) | −6.74182 | −0.334591 | ||||||||
\(407\) | 0.863550 | 0.0428046 | ||||||||
\(408\) | 6.47154 | + | 11.2090i | 0.320389 | + | 0.554930i | ||||
\(409\) | 16.2849 | + | 28.2063i | 0.805238 | + | 1.39471i | 0.916130 | + | 0.400881i | \(0.131296\pi\) |
−0.110892 | + | 0.993832i | \(0.535371\pi\) | |||||||
\(410\) | 1.31640 | − | 2.28006i | 0.0650121 | − | 0.112604i | ||||
\(411\) | −0.301018 | − | 0.521379i | −0.0148481 | − | 0.0257177i | ||||
\(412\) | 3.89323 | 0.191806 | ||||||||
\(413\) | 19.7728 | 0.972954 | ||||||||
\(414\) | −1.19601 | − | 2.07155i | −0.0587807 | − | 0.101811i | ||||
\(415\) | 1.59479 | 0.0782853 | ||||||||
\(416\) | −3.17779 | − | 5.50409i | −0.155804 | − | 0.269860i | ||||
\(417\) | −5.98711 | −0.293190 | ||||||||
\(418\) | −0.311974 | − | 0.540354i | −0.0152591 | − | 0.0264296i | ||||
\(419\) | −10.8030 | − | 18.7114i | −0.527762 | − | 0.914111i | −0.999476 | − | 0.0323595i | \(-0.989698\pi\) |
0.471714 | − | 0.881752i | \(-0.343635\pi\) | |||||||
\(420\) | 0.899491 | + | 1.55796i | 0.0438907 | + | 0.0760209i | ||||
\(421\) | 19.8594 | + | 34.3975i | 0.967888 | + | 1.67643i | 0.701646 | + | 0.712526i | \(0.252449\pi\) |
0.266243 | + | 0.963906i | \(0.414218\pi\) | |||||||
\(422\) | 3.97223 | 0.193365 | ||||||||
\(423\) | −2.59427 | + | 4.49340i | −0.126138 | + | 0.218477i | ||||
\(424\) | 3.07670 | + | 5.32900i | 0.149418 | + | 0.258799i | ||||
\(425\) | −24.8727 | −1.20650 | ||||||||
\(426\) | 8.35152 | 0.404633 | ||||||||
\(427\) | −4.94500 | + | 8.56499i | −0.239305 | + | 0.414489i | ||||
\(428\) | 0.342802 | + | 0.593751i | 0.0165700 | + | 0.0287000i | ||||
\(429\) | 0.0991994 | − | 0.171818i | 0.00478939 | − | 0.00829547i | ||||
\(430\) | 0.705495 | 0.0340220 | ||||||||
\(431\) | 7.38181 | − | 12.7857i | 0.355569 | − | 0.615864i | −0.631646 | − | 0.775257i | \(-0.717620\pi\) |
0.987215 | + | 0.159393i | \(0.0509537\pi\) | |||||||
\(432\) | −1.40113 | −0.0674121 | ||||||||
\(433\) | −8.25178 | + | 14.2925i | −0.396555 | + | 0.686854i | −0.993298 | − | 0.115578i | \(-0.963128\pi\) |
0.596743 | + | 0.802432i | \(0.296461\pi\) | |||||||
\(434\) | 5.10916 | + | 8.84932i | 0.245247 | + | 0.424781i | ||||
\(435\) | −1.46195 | − | 2.53216i | −0.0700949 | − | 0.121408i | ||||
\(436\) | −3.74039 | + | 6.47854i | −0.179132 | + | 0.310266i | ||||
\(437\) | 8.76966 | − | 15.1895i | 0.419510 | − | 0.726613i | ||||
\(438\) | −3.30654 | − | 5.72709i | −0.157992 | − | 0.273651i | ||||
\(439\) | −2.01532 | −0.0961859 | −0.0480930 | − | 0.998843i | \(-0.515314\pi\) | ||||
−0.0480930 | + | 0.998843i | \(0.515314\pi\) | |||||||
\(440\) | 0.129536 | + | 0.224362i | 0.00617537 | + | 0.0106961i | ||||
\(441\) | 1.52266 | + | 2.63733i | 0.0725077 | + | 0.125587i | ||||
\(442\) | 4.01746 | 0.191091 | ||||||||
\(443\) | −30.9706 | −1.47146 | −0.735730 | − | 0.677275i | \(-0.763161\pi\) | ||||
−0.735730 | + | 0.677275i | \(0.763161\pi\) | |||||||
\(444\) | −7.29705 | −0.346303 | ||||||||
\(445\) | −3.82069 | − | 6.61763i | −0.181118 | − | 0.313706i | ||||
\(446\) | 4.50163 | + | 7.79705i | 0.213158 | + | 0.369201i | ||||
\(447\) | 4.17669 | − | 7.23424i | 0.197551 | − | 0.342168i | ||||
\(448\) | −2.33489 | −0.110313 | ||||||||
\(449\) | 3.65567 | − | 6.33181i | 0.172522 | − | 0.298817i | −0.766779 | − | 0.641911i | \(-0.778142\pi\) |
0.939301 | + | 0.343094i | \(0.111475\pi\) | |||||||
\(450\) | −1.59401 | + | 2.76090i | −0.0751423 | + | 0.130150i | ||||
\(451\) | 0.588080 | − | 1.01858i | 0.0276916 | − | 0.0479633i | ||||
\(452\) | −9.42809 | + | 16.3299i | −0.443460 | + | 0.768095i | ||||
\(453\) | −9.61211 | − | 16.6487i | −0.451617 | − | 0.782223i | ||||
\(454\) | 5.21465 | − | 9.03204i | 0.244736 | − | 0.423895i | ||||
\(455\) | 1.28830 | 0.0603964 | ||||||||
\(456\) | 6.08210 | + | 10.5345i | 0.284820 | + | 0.493323i | ||||
\(457\) | −28.5275 | −1.33446 | −0.667229 | − | 0.744853i | \(-0.732520\pi\) | ||||
−0.667229 | + | 0.744853i | \(0.732520\pi\) | |||||||
\(458\) | −10.0953 | − | 17.4856i | −0.471724 | − | 0.817050i | ||||
\(459\) | 2.67424 | − | 4.63191i | 0.124823 | − | 0.216199i | ||||
\(460\) | −1.57826 | + | 2.73363i | −0.0735868 | + | 0.127456i | ||||
\(461\) | −10.9099 | + | 18.8965i | −0.508124 | + | 0.880097i | 0.491831 | + | 0.870690i | \(0.336328\pi\) |
−0.999956 | + | 0.00940663i | \(0.997006\pi\) | |||||||
\(462\) | −0.123423 | − | 0.213776i | −0.00574218 | − | 0.00994575i | ||||
\(463\) | 19.8383 | 0.921965 | 0.460982 | − | 0.887409i | \(-0.347497\pi\) | ||||
0.460982 | + | 0.887409i | \(0.347497\pi\) | |||||||
\(464\) | −6.92905 | −0.321673 | ||||||||
\(465\) | −2.21581 | + | 3.83790i | −0.102756 | + | 0.177978i | ||||
\(466\) | 9.26327 | − | 16.0444i | 0.429112 | − | 0.743245i | ||||
\(467\) | 14.3212 | 0.662707 | 0.331353 | − | 0.943507i | \(-0.392495\pi\) | ||||
0.331353 | + | 0.943507i | \(0.392495\pi\) | |||||||
\(468\) | −0.838241 | + | 1.45188i | −0.0387477 | + | 0.0671130i | ||||
\(469\) | −3.68028 | −0.169939 | ||||||||
\(470\) | −2.10300 | −0.0970041 | ||||||||
\(471\) | 6.28977 | + | 10.8369i | 0.289817 | + | 0.499339i | ||||
\(472\) | −24.0613 | −1.10751 | ||||||||
\(473\) | 0.315169 | 0.0144915 | ||||||||
\(474\) | −1.99825 | + | 3.46107i | −0.0917826 | + | 0.158972i | ||||
\(475\) | −23.3759 | −1.07256 | ||||||||
\(476\) | −8.13691 | + | 14.0935i | −0.372955 | + | 0.645977i | ||||
\(477\) | 1.27139 | − | 2.20210i | 0.0582128 | − | 0.100827i | ||||
\(478\) | 7.80183 | 0.356848 | ||||||||
\(479\) | 23.4968 | 1.07360 | 0.536799 | − | 0.843710i | \(-0.319633\pi\) | ||||
0.536799 | + | 0.843710i | \(0.319633\pi\) | |||||||
\(480\) | −1.71474 | − | 2.97001i | −0.0782667 | − | 0.135562i | ||||
\(481\) | −2.61281 | + | 4.52551i | −0.119134 | + | 0.206346i | ||||
\(482\) | 8.58294 | − | 14.8661i | 0.390942 | − | 0.677132i | ||||
\(483\) | 3.46947 | − | 6.00930i | 0.157866 | − | 0.273432i | ||||
\(484\) | −8.39017 | − | 14.5322i | −0.381371 | − | 0.660555i | ||||
\(485\) | 9.03957 | 0.410466 | ||||||||
\(486\) | −0.342766 | − | 0.593688i | −0.0155482 | − | 0.0269302i | ||||
\(487\) | 1.11030 | 0.0503125 | 0.0251563 | − | 0.999684i | \(-0.491992\pi\) | ||||
0.0251563 | + | 0.999684i | \(0.491992\pi\) | |||||||
\(488\) | 6.01754 | − | 10.4227i | 0.272401 | − | 0.471813i | ||||
\(489\) | 10.9088 | + | 18.8947i | 0.493315 | + | 0.854446i | ||||
\(490\) | −0.617160 | + | 1.06895i | −0.0278805 | + | 0.0482904i | ||||
\(491\) | 9.43185 | − | 16.3364i | 0.425654 | − | 0.737254i | −0.570828 | − | 0.821070i | \(-0.693378\pi\) |
0.996481 | + | 0.0838164i | \(0.0267109\pi\) | |||||||
\(492\) | −4.96931 | + | 8.60710i | −0.224034 | + | 0.388038i | ||||
\(493\) | 13.2249 | − | 22.9063i | 0.595622 | − | 1.03165i | ||||
\(494\) | 3.77570 | 0.169877 | ||||||||
\(495\) | 0.0535281 | − | 0.0927134i | 0.00240591 | − | 0.00416716i | ||||
\(496\) | 5.25105 | + | 9.09508i | 0.235779 | + | 0.408381i | ||||
\(497\) | 12.1133 | + | 20.9809i | 0.543357 | + | 0.941122i | ||||
\(498\) | 1.84912 | 0.0828610 | ||||||||
\(499\) | 6.79203 | 0.304053 | 0.152026 | − | 0.988376i | \(-0.451420\pi\) | ||||
0.152026 | + | 0.988376i | \(0.451420\pi\) | |||||||
\(500\) | 8.73008 | 0.390421 | ||||||||
\(501\) | 3.10725 | + | 5.38192i | 0.138822 | + | 0.240446i | ||||
\(502\) | 1.21775 | + | 2.10921i | 0.0543510 | + | 0.0941386i | ||||
\(503\) | −15.2512 | −0.680017 | −0.340008 | − | 0.940422i | \(-0.610430\pi\) | ||||
−0.340008 | + | 0.940422i | \(0.610430\pi\) | |||||||
\(504\) | 2.40621 | + | 4.16768i | 0.107181 | + | 0.185643i | ||||
\(505\) | −0.179104 | + | 0.310217i | −0.00797002 | + | 0.0138045i | ||||
\(506\) | 0.216561 | − | 0.375094i | 0.00962730 | − | 0.0166750i | ||||
\(507\) | −5.89971 | − | 10.2186i | −0.262015 | − | 0.453824i | ||||
\(508\) | −7.67836 | − | 13.2993i | −0.340672 | − | 0.590061i | ||||
\(509\) | −5.99929 | + | 10.3911i | −0.265914 | + | 0.460576i | −0.967803 | − | 0.251710i | \(-0.919007\pi\) |
0.701889 | + | 0.712287i | \(0.252340\pi\) | |||||||
\(510\) | 2.16782 | 0.0959929 | ||||||||
\(511\) | 9.59183 | − | 16.6135i | 0.424318 | − | 0.734939i | ||||
\(512\) | −14.9086 | −0.658872 | ||||||||
\(513\) | 2.51331 | − | 4.35318i | 0.110965 | − | 0.192197i | ||||
\(514\) | −3.02556 | − | 5.24042i | −0.133452 | − | 0.231145i | ||||
\(515\) | 0.752215 | − | 1.30288i | 0.0331466 | − | 0.0574115i | ||||
\(516\) | −2.66320 | −0.117241 | ||||||||
\(517\) | −0.939483 | −0.0413184 | ||||||||
\(518\) | 3.25084 | + | 5.63062i | 0.142834 | + | 0.247395i | ||||
\(519\) | 6.74756 | − | 11.6871i | 0.296185 | − | 0.513007i | ||||
\(520\) | −1.56772 | −0.0687492 | ||||||||
\(521\) | 4.56978 | + | 7.91510i | 0.200206 | + | 0.346767i | 0.948595 | − | 0.316494i | \(-0.102506\pi\) |
−0.748389 | + | 0.663260i | \(0.769172\pi\) | |||||||
\(522\) | −1.69509 | − | 2.93597i | −0.0741919 | − | 0.128504i | ||||
\(523\) | 0.927346 | + | 1.60621i | 0.0405500 | + | 0.0702346i | 0.885588 | − | 0.464471i | \(-0.153756\pi\) |
−0.845038 | + | 0.534706i | \(0.820422\pi\) | |||||||
\(524\) | 8.01127 | + | 13.8759i | 0.349974 | + | 0.606173i | ||||
\(525\) | −9.24802 | −0.403617 | ||||||||
\(526\) | −6.23747 | − | 10.8036i | −0.271967 | − | 0.471060i | ||||
\(527\) | −40.0891 | −1.74631 | ||||||||
\(528\) | −0.126851 | − | 0.219713i | −0.00552049 | − | 0.00956177i | ||||
\(529\) | −10.8248 | −0.470645 | ||||||||
\(530\) | 1.03063 | 0.0447676 | ||||||||
\(531\) | 4.97143 | + | 8.61078i | 0.215742 | + | 0.373676i | ||||
\(532\) | −7.64726 | + | 13.2454i | −0.331551 | + | 0.574262i | ||||
\(533\) | 3.55866 | + | 6.16377i | 0.154143 | + | 0.266983i | ||||
\(534\) | −4.42998 | − | 7.67296i | −0.191704 | − | 0.332041i | ||||
\(535\) | 0.264933 | 0.0114541 | ||||||||
\(536\) | 4.47850 | 0.193442 | ||||||||
\(537\) | −2.00927 | − | 3.48016i | −0.0867066 | − | 0.150180i | ||||
\(538\) | −9.68531 | −0.417563 | ||||||||
\(539\) | −0.275707 | + | 0.477539i | −0.0118755 | + | 0.0205691i | ||||
\(540\) | −0.452316 | + | 0.783433i | −0.0194646 | + | 0.0337136i | ||||
\(541\) | 9.49089 | − | 16.4387i | 0.408045 | − | 0.706755i | −0.586625 | − | 0.809858i | \(-0.699544\pi\) |
0.994671 | + | 0.103103i | \(0.0328772\pi\) | |||||||
\(542\) | −1.93596 | − | 3.35318i | −0.0831565 | − | 0.144031i | ||||
\(543\) | 5.60593 | + | 9.70976i | 0.240573 | + | 0.416685i | ||||
\(544\) | 15.5117 | − | 26.8671i | 0.665060 | − | 1.15192i | ||||
\(545\) | 1.44537 | + | 2.50346i | 0.0619129 | + | 0.107236i | ||||
\(546\) | 1.49375 | 0.0639265 | ||||||||
\(547\) | 9.32423 | − | 16.1500i | 0.398675 | − | 0.690526i | −0.594888 | − | 0.803809i | \(-0.702803\pi\) |
0.993563 | + | 0.113283i | \(0.0361368\pi\) | |||||||
\(548\) | −0.460572 | + | 0.797734i | −0.0196747 | + | 0.0340775i | ||||
\(549\) | −4.97326 | −0.212253 | ||||||||
\(550\) | −0.577252 | −0.0246141 | ||||||||
\(551\) | 12.4291 | − | 21.5278i | 0.529497 | − | 0.917117i | ||||
\(552\) | −4.22197 | + | 7.31267i | −0.179699 | + | 0.311248i | ||||
\(553\) | −11.5933 | −0.492998 | ||||||||
\(554\) | 4.40901 | + | 7.63663i | 0.187321 | + | 0.324449i | ||||
\(555\) | −1.40987 | + | 2.44197i | −0.0598457 | + | 0.103656i | ||||
\(556\) | 4.58028 | + | 7.93328i | 0.194247 | + | 0.336446i | ||||
\(557\) | 3.18619 | + | 5.51864i | 0.135003 | + | 0.233832i | 0.925599 | − | 0.378506i | \(-0.123562\pi\) |
−0.790596 | + | 0.612339i | \(0.790229\pi\) | |||||||
\(558\) | −2.56917 | + | 4.44994i | −0.108762 | + | 0.188381i | ||||
\(559\) | −0.953594 | + | 1.65167i | −0.0403327 | + | 0.0698583i | ||||
\(560\) | 0.823706 | − | 1.42670i | 0.0348079 | − | 0.0602891i | ||||
\(561\) | 0.968444 | 0.0408877 | ||||||||
\(562\) | −3.31737 | − | 5.74585i | −0.139935 | − | 0.242374i | ||||
\(563\) | 9.27270 | 0.390798 | 0.195399 | − | 0.980724i | \(-0.437400\pi\) | ||||
0.195399 | + | 0.980724i | \(0.437400\pi\) | |||||||
\(564\) | 7.93869 | 0.334279 | ||||||||
\(565\) | 3.64323 | + | 6.31025i | 0.153272 | + | 0.265474i | ||||
\(566\) | −5.76786 | − | 9.99023i | −0.242441 | − | 0.419921i | ||||
\(567\) | 0.994318 | − | 1.72221i | 0.0417575 | − | 0.0723260i | ||||
\(568\) | −14.7406 | − | 25.5315i | −0.618503 | − | 1.07128i | ||||
\(569\) | 17.6701 | 0.740768 | 0.370384 | − | 0.928879i | \(-0.379226\pi\) | ||||
0.370384 | + | 0.928879i | \(0.379226\pi\) | |||||||
\(570\) | 2.03737 | 0.0853361 | ||||||||
\(571\) | −11.7389 | − | 20.3324i | −0.491258 | − | 0.850884i | 0.508691 | − | 0.860949i | \(-0.330130\pi\) |
−0.999949 | + | 0.0100649i | \(0.996796\pi\) | |||||||
\(572\) | −0.303559 | −0.0126925 | ||||||||
\(573\) | −1.48550 | − | 2.57296i | −0.0620576 | − | 0.107487i | ||||
\(574\) | 8.85533 | 0.369614 | ||||||||
\(575\) | −8.11336 | − | 14.0527i | −0.338350 | − | 0.586040i | ||||
\(576\) | −0.587059 | − | 1.01682i | −0.0244608 | − | 0.0423673i | ||||
\(577\) | 19.0131 | + | 32.9317i | 0.791526 | + | 1.37096i | 0.925022 | + | 0.379914i | \(0.124046\pi\) |
−0.133496 | + | 0.991049i | \(0.542620\pi\) | |||||||
\(578\) | 3.97819 | + | 6.89043i | 0.165471 | + | 0.286604i | ||||
\(579\) | 5.95919 | 0.247656 | ||||||||
\(580\) | −2.23684 | + | 3.87433i | −0.0928799 | + | 0.160873i | ||||
\(581\) | 2.68202 | + | 4.64540i | 0.111269 | + | 0.192724i | ||||
\(582\) | 10.4811 | 0.434457 | ||||||||
\(583\) | 0.460418 | 0.0190686 | ||||||||
\(584\) | −11.6722 | + | 20.2169i | −0.483000 | + | 0.836581i | ||||
\(585\) | 0.323915 | + | 0.561038i | 0.0133922 | + | 0.0231960i | ||||
\(586\) | −10.1631 | + | 17.6031i | −0.419835 | + | 0.727176i | ||||
\(587\) | −1.08572 | −0.0448124 | −0.0224062 | − | 0.999749i | \(-0.507133\pi\) | ||||
−0.0224062 | + | 0.999749i | \(0.507133\pi\) | |||||||
\(588\) | 2.32974 | − | 4.03523i | 0.0960770 | − | 0.166410i | ||||
\(589\) | −37.6766 | −1.55244 | ||||||||
\(590\) | −2.01501 | + | 3.49009i | −0.0829565 | + | 0.143685i | ||||
\(591\) | 7.55021 | + | 13.0773i | 0.310574 | + | 0.537930i | ||||
\(592\) | 3.34112 | + | 5.78699i | 0.137319 | + | 0.237844i | ||||
\(593\) | −15.8785 | + | 27.5024i | −0.652053 | + | 1.12939i | 0.330571 | + | 0.943781i | \(0.392759\pi\) |
−0.982624 | + | 0.185607i | \(0.940575\pi\) | |||||||
\(594\) | 0.0620644 | − | 0.107499i | 0.00254653 | − | 0.00441072i | ||||
\(595\) | 3.14429 | + | 5.44606i | 0.128903 | + | 0.223267i | ||||
\(596\) | −12.7811 | −0.523532 | ||||||||
\(597\) | −3.46155 | − | 5.99558i | −0.141672 | − | 0.245383i | ||||
\(598\) | 1.31048 | + | 2.26981i | 0.0535894 | + | 0.0928195i | ||||
\(599\) | 36.2616 | 1.48161 | 0.740803 | − | 0.671722i | \(-0.234445\pi\) | ||||
0.740803 | + | 0.671722i | \(0.234445\pi\) | |||||||
\(600\) | 11.2538 | 0.459436 | ||||||||
\(601\) | 32.1521 | 1.31151 | 0.655755 | − | 0.754973i | \(-0.272350\pi\) | ||||
0.655755 | + | 0.754973i | \(0.272350\pi\) | |||||||
\(602\) | 1.18646 | + | 2.05501i | 0.0483564 | + | 0.0837558i | ||||
\(603\) | −0.925326 | − | 1.60271i | −0.0376822 | − | 0.0652675i | ||||
\(604\) | −14.7070 | + | 25.4732i | −0.598419 | + | 1.03649i | ||||
\(605\) | −6.48430 | −0.263624 | ||||||||
\(606\) | −0.207666 | + | 0.359688i | −0.00843586 | + | 0.0146113i | ||||
\(607\) | 3.96939 | − | 6.87518i | 0.161112 | − | 0.279055i | −0.774155 | − | 0.632995i | \(-0.781825\pi\) |
0.935268 | + | 0.353941i | \(0.115158\pi\) | |||||||
\(608\) | 14.5783 | − | 25.2503i | 0.591228 | − | 1.02404i | ||||
\(609\) | 4.91722 | − | 8.51687i | 0.199256 | − | 0.345121i | ||||
\(610\) | −1.00787 | − | 1.74569i | −0.0408075 | − | 0.0706807i | ||||
\(611\) | 2.84255 | − | 4.92345i | 0.114997 | − | 0.199181i | ||||
\(612\) | −8.18341 | −0.330795 | ||||||||
\(613\) | 6.97443 | + | 12.0801i | 0.281695 | + | 0.487909i | 0.971802 | − | 0.235797i | \(-0.0757702\pi\) |
−0.690108 | + | 0.723707i | \(0.742437\pi\) | |||||||
\(614\) | −2.04395 | −0.0824870 | ||||||||
\(615\) | 1.92025 | + | 3.32598i | 0.0774321 | + | 0.134116i | ||||
\(616\) | −0.435691 | + | 0.754638i | −0.0175545 | + | 0.0304052i | ||||
\(617\) | −11.2040 | + | 19.4059i | −0.451056 | + | 0.781252i | −0.998452 | − | 0.0556220i | \(-0.982286\pi\) |
0.547396 | + | 0.836874i | \(0.315619\pi\) | |||||||
\(618\) | 0.872173 | − | 1.51065i | 0.0350840 | − | 0.0607672i | ||||
\(619\) | 10.8292 | + | 18.7568i | 0.435263 | + | 0.753898i | 0.997317 | − | 0.0732024i | \(-0.0233219\pi\) |
−0.562054 | + | 0.827101i | \(0.689989\pi\) | |||||||
\(620\) | 6.78059 | 0.272315 | ||||||||
\(621\) | 3.48929 | 0.140021 | ||||||||
\(622\) | −4.64087 | + | 8.03822i | −0.186082 | + | 0.322303i | ||||
\(623\) | 12.8508 | − | 22.2582i | 0.514856 | − | 0.891758i | ||||
\(624\) | 1.53523 | 0.0614585 | ||||||||
\(625\) | −9.93933 | + | 17.2154i | −0.397573 | + | 0.688617i | ||||
\(626\) | −5.81303 | −0.232336 | ||||||||
\(627\) | 0.910165 | 0.0363485 | ||||||||
\(628\) | 9.54774 | − | 16.6248i | 0.380996 | − | 0.663402i | ||||
\(629\) | −25.5078 | −1.01706 | ||||||||
\(630\) | 0.806028 | 0.0321129 | ||||||||
\(631\) | −8.43252 | + | 14.6055i | −0.335693 | + | 0.581438i | −0.983618 | − | 0.180267i | \(-0.942304\pi\) |
0.647925 | + | 0.761704i | \(0.275637\pi\) | |||||||
\(632\) | 14.1078 | 0.561179 | ||||||||
\(633\) | −2.89719 | + | 5.01808i | −0.115153 | + | 0.199451i | ||||
\(634\) | 2.17995 | − | 3.77578i | 0.0865768 | − | 0.149955i | ||||
\(635\) | −5.93418 | −0.235491 | ||||||||
\(636\) | −3.89056 | −0.154271 | ||||||||
\(637\) | −1.66839 | − | 2.88974i | −0.0661040 | − | 0.114496i | ||||
\(638\) | 0.306928 | − | 0.531615i | 0.0121514 | − | 0.0210468i | ||||
\(639\) | −6.09127 | + | 10.5504i | −0.240967 | + | 0.417367i | ||||
\(640\) | −3.19153 | + | 5.52790i | −0.126156 | + | 0.218509i | ||||
\(641\) | −8.44391 | − | 14.6253i | −0.333514 | − | 0.577664i | 0.649684 | − | 0.760204i | \(-0.274901\pi\) |
−0.983198 | + | 0.182541i | \(0.941568\pi\) | |||||||
\(642\) | 0.307183 | 0.0121235 | ||||||||
\(643\) | 14.9181 | + | 25.8389i | 0.588312 | + | 1.01899i | 0.994454 | + | 0.105177i | \(0.0335408\pi\) |
−0.406141 | + | 0.913810i | \(0.633126\pi\) | |||||||
\(644\) | −10.6169 | −0.418364 | ||||||||
\(645\) | −0.514560 | + | 0.891244i | −0.0202608 | + | 0.0350927i | ||||
\(646\) | 9.21516 | + | 15.9611i | 0.362566 | + | 0.627982i | ||||
\(647\) | −22.6508 | + | 39.2324i | −0.890495 | + | 1.54238i | −0.0512124 | + | 0.998688i | \(0.516309\pi\) |
−0.839283 | + | 0.543695i | \(0.817025\pi\) | |||||||
\(648\) | −1.20998 | + | 2.09575i | −0.0475325 | + | 0.0823287i | ||||
\(649\) | −0.900174 | + | 1.55915i | −0.0353349 | + | 0.0612019i | ||||
\(650\) | 1.74657 | − | 3.02514i | 0.0685060 | − | 0.118656i | ||||
\(651\) | −14.9057 | −0.584199 | ||||||||
\(652\) | 16.6910 | − | 28.9097i | 0.653671 | − | 1.13219i | ||||
\(653\) | −3.21195 | − | 5.56325i | −0.125693 | − | 0.217707i | 0.796311 | − | 0.604888i | \(-0.206782\pi\) |
−0.922004 | + | 0.387181i | \(0.873449\pi\) | |||||||
\(654\) | 1.67587 | + | 2.90269i | 0.0655316 | + | 0.113504i | ||||
\(655\) | 6.19147 | 0.241921 | ||||||||
\(656\) | 9.10126 | 0.355344 | ||||||||
\(657\) | 9.64664 | 0.376351 | ||||||||
\(658\) | −3.53669 | − | 6.12573i | −0.137875 | − | 0.238806i | ||||
\(659\) | −21.7671 | − | 37.7017i | −0.847926 | − | 1.46865i | −0.883056 | − | 0.469268i | \(-0.844518\pi\) |
0.0351294 | − | 0.999383i | \(-0.488816\pi\) | |||||||
\(660\) | −0.163801 | −0.00637594 | ||||||||
\(661\) | −13.2846 | − | 23.0096i | −0.516711 | − | 0.894970i | −0.999812 | − | 0.0194053i | \(-0.993823\pi\) |
0.483100 | − | 0.875565i | \(-0.339511\pi\) | |||||||
\(662\) | −7.18440 | + | 12.4438i | −0.279230 | + | 0.483640i | ||||
\(663\) | −2.93018 | + | 5.07522i | −0.113799 | + | 0.197105i | ||||
\(664\) | −3.26374 | − | 5.65296i | −0.126658 | − | 0.219377i | ||||
\(665\) | 2.95507 | + | 5.11833i | 0.114593 | + | 0.198480i | ||||
\(666\) | −1.63471 | + | 2.83140i | −0.0633437 | + | 0.109714i | ||||
\(667\) | 17.2557 | 0.668142 | ||||||||
\(668\) | 4.75424 | − | 8.23458i | 0.183947 | − | 0.318606i | ||||
\(669\) | −13.1332 | −0.507761 | ||||||||
\(670\) | 0.375050 | − | 0.649606i | 0.0144895 | − | 0.0250965i | ||||
\(671\) | −0.450252 | − | 0.779859i | −0.0173818 | − | 0.0301061i | ||||
\(672\) | 5.76748 | − | 9.98958i | 0.222486 | − | 0.385356i | ||||
\(673\) | 36.1561 | 1.39371 | 0.696857 | − | 0.717210i | \(-0.254581\pi\) | ||||
0.696857 | + | 0.717210i | \(0.254581\pi\) | |||||||
\(674\) | 1.80539 | 0.0695412 | ||||||||
\(675\) | −2.32522 | − | 4.02739i | −0.0894976 | − | 0.155014i | ||||
\(676\) | −9.02683 | + | 15.6349i | −0.347186 | + | 0.601344i | ||||
\(677\) | 22.4956 | 0.864574 | 0.432287 | − | 0.901736i | \(-0.357707\pi\) | ||||
0.432287 | + | 0.901736i | \(0.357707\pi\) | |||||||
\(678\) | 4.22422 | + | 7.31657i | 0.162230 | + | 0.280991i | ||||
\(679\) | 15.2022 | + | 26.3310i | 0.583407 | + | 1.01049i | ||||
\(680\) | −3.82626 | − | 6.62728i | −0.146730 | − | 0.254145i | ||||
\(681\) | 7.60672 | + | 13.1752i | 0.291490 | + | 0.504876i | ||||
\(682\) | −0.930397 | −0.0356267 | ||||||||
\(683\) | −14.3221 | − | 24.8065i | −0.548018 | − | 0.949196i | −0.998410 | − | 0.0563647i | \(-0.982049\pi\) |
0.450392 | − | 0.892831i | \(-0.351284\pi\) | |||||||
\(684\) | −7.69095 | −0.294071 | ||||||||
\(685\) | 0.177975 | + | 0.308262i | 0.00680009 | + | 0.0117781i | ||||
\(686\) | −13.6945 | −0.522859 | ||||||||
\(687\) | 29.4526 | 1.12369 | ||||||||
\(688\) | 1.21941 | + | 2.11208i | 0.0464895 | + | 0.0805221i | ||||
\(689\) | −1.39307 | + | 2.41286i | −0.0530716 | + | 0.0919227i | ||||
\(690\) | 0.707134 | + | 1.22479i | 0.0269201 | + | 0.0466271i | ||||
\(691\) | −5.00995 | − | 8.67749i | −0.190587 | − | 0.330107i | 0.754858 | − | 0.655889i | \(-0.227706\pi\) |
−0.945445 | + | 0.325782i | \(0.894373\pi\) | |||||||
\(692\) | −20.6481 | −0.784925 | ||||||||
\(693\) | 0.360081 | 0.0136783 | ||||||||
\(694\) | 2.12104 | + | 3.67374i | 0.0805135 | + | 0.139453i | ||||
\(695\) | 3.53985 | 0.134274 | ||||||||
\(696\) | −5.98373 | + | 10.3641i | −0.226813 | + | 0.392851i | ||||
\(697\) | −17.3709 | + | 30.0872i | −0.657968 | + | 1.13963i | ||||
\(698\) | −10.2247 | + | 17.7097i | −0.387010 | + | 0.670320i | ||||
\(699\) | 13.5125 | + | 23.4044i | 0.511091 | + | 0.885235i | ||||
\(700\) | 7.07495 | + | 12.2542i | 0.267408 | + | 0.463164i | ||||
\(701\) | 21.4926 | − | 37.2263i | 0.811765 | − | 1.40602i | −0.0998619 | − | 0.995001i | \(-0.531840\pi\) |
0.911627 | − | 0.411018i | \(-0.134827\pi\) | |||||||
\(702\) | 0.375571 | + | 0.650508i | 0.0141750 | + | 0.0245518i | ||||
\(703\) | −23.9728 | −0.904150 | ||||||||
\(704\) | 0.106298 | − | 0.184114i | 0.00400627 | − | 0.00693906i | ||||
\(705\) | 1.53384 | − | 2.65670i | 0.0577679 | − | 0.100057i | ||||
\(706\) | 21.0294 | 0.791453 | ||||||||
\(707\) | −1.20482 | −0.0453121 | ||||||||
\(708\) | 7.60652 | − | 13.1749i | 0.285871 | − | 0.495143i | ||||
\(709\) | 14.7802 | − | 25.6000i | 0.555082 | − | 0.961429i | −0.442816 | − | 0.896613i | \(-0.646020\pi\) |
0.997897 | − | 0.0648167i | \(-0.0206463\pi\) | |||||||
\(710\) | −4.93779 | −0.185312 | ||||||||
\(711\) | −2.91489 | − | 5.04874i | −0.109317 | − | 0.189342i | ||||
\(712\) | −15.6381 | + | 27.0859i | −0.586061 | + | 1.01509i | ||||
\(713\) | −13.0769 | − | 22.6498i | −0.489732 | − | 0.848241i | ||||
\(714\) | 3.64572 | + | 6.31456i | 0.136437 | + | 0.236317i | ||||
\(715\) | −0.0586511 | + | 0.101587i | −0.00219343 | + | 0.00379913i | ||||
\(716\) | −3.07428 | + | 5.32481i | −0.114891 | + | 0.198998i | ||||
\(717\) | −5.69035 | + | 9.85598i | −0.212510 | + | 0.368078i | ||||
\(718\) | −24.5922 | −0.917774 | ||||||||
\(719\) | 0.351749 | + | 0.609247i | 0.0131180 | + | 0.0227211i | 0.872510 | − | 0.488596i | \(-0.162491\pi\) |
−0.859392 | + | 0.511318i | \(0.829158\pi\) | |||||||
\(720\) | 0.828412 | 0.0308731 | ||||||||
\(721\) | 5.06012 | 0.188449 | ||||||||
\(722\) | 2.14806 | + | 3.72055i | 0.0799426 | + | 0.138465i | ||||
\(723\) | 12.5201 | + | 21.6855i | 0.465628 | + | 0.806492i | ||||
\(724\) | 8.57733 | − | 14.8564i | 0.318774 | − | 0.552133i | ||||
\(725\) | −11.4989 | − | 19.9167i | −0.427059 | − | 0.739689i | ||||
\(726\) | −7.51837 | −0.279033 | ||||||||
\(727\) | −36.4655 | −1.35243 | −0.676215 | − | 0.736704i | \(-0.736381\pi\) | ||||
−0.676215 | + | 0.736704i | \(0.736381\pi\) | |||||||
\(728\) | −2.63650 | − | 4.56655i | −0.0977152 | − | 0.169248i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.95497 | + | 3.38611i | 0.0723567 | + | 0.125326i | ||||
\(731\) | −9.30956 | −0.344326 | ||||||||
\(732\) | 3.80466 | + | 6.58986i | 0.140624 | + | 0.243568i | ||||
\(733\) | −14.6608 | − | 25.3933i | −0.541509 | − | 0.937922i | −0.998818 | − | 0.0486136i | \(-0.984520\pi\) |
0.457308 | − | 0.889308i | \(-0.348814\pi\) | |||||||
\(734\) | 5.64900 | + | 9.78436i | 0.208509 | + | 0.361147i | ||||
\(735\) | −0.900265 | − | 1.55930i | −0.0332068 | − | 0.0575158i | ||||
\(736\) | 20.2394 | 0.746035 | ||||||||
\(737\) | 0.167548 | − | 0.290202i | 0.00617171 | − | 0.0106897i | ||||
\(738\) | 2.22648 | + | 3.85638i | 0.0819580 | + | 0.141955i | ||||
\(739\) | −2.73404 | −0.100573 | −0.0502867 | − | 0.998735i | \(-0.516013\pi\) | ||||
−0.0502867 | + | 0.998735i | \(0.516013\pi\) | |||||||
\(740\) | 4.31434 | 0.158598 | ||||||||
\(741\) | −2.75385 | + | 4.76980i | −0.101165 | + | 0.175223i | ||||
\(742\) | 1.73325 | + | 3.00207i | 0.0636295 | + | 0.110210i | ||||
\(743\) | −14.0214 | + | 24.2858i | −0.514397 | + | 0.890961i | 0.485464 | + | 0.874257i | \(0.338651\pi\) |
−0.999860 | + | 0.0167044i | \(0.994683\pi\) | |||||||
\(744\) | 18.1386 | 0.664994 | ||||||||
\(745\) | −2.46944 | + | 4.27720i | −0.0904734 | + | 0.156705i | ||||
\(746\) | 14.9585 | 0.547670 | ||||||||
\(747\) | −1.34867 | + | 2.33597i | −0.0493454 | + | 0.0854688i | ||||
\(748\) | −0.740882 | − | 1.28325i | −0.0270893 | − | 0.0469201i | ||||
\(749\) | 0.445548 | + | 0.771712i | 0.0162800 | + | 0.0281978i | ||||
\(750\) | 1.95574 | − | 3.38744i | 0.0714135 | − | 0.123692i | ||||
\(751\) | 4.70165 | − | 8.14349i | 0.171566 | − | 0.297160i | −0.767402 | − | 0.641166i | \(-0.778451\pi\) |
0.938967 | + | 0.344006i | \(0.111784\pi\) | |||||||
\(752\) | −3.63491 | − | 6.29586i | −0.132552 | − | 0.229586i | ||||
\(753\) | −3.55272 | −0.129468 | ||||||||
\(754\) | 1.85732 | + | 3.21697i | 0.0676395 | + | 0.117155i | ||||
\(755\) | 5.68311 | + | 9.84343i | 0.206829 | + | 0.358239i | ||||
\(756\) | −3.04271 | −0.110662 | ||||||||
\(757\) | −5.49527 | −0.199729 | −0.0998645 | − | 0.995001i | \(-0.531841\pi\) | ||||
−0.0998645 | + | 0.995001i | \(0.531841\pi\) | |||||||
\(758\) | −9.20221 | −0.334239 | ||||||||
\(759\) | 0.315902 | + | 0.547158i | 0.0114665 | + | 0.0198606i | ||||
\(760\) | −3.59601 | − | 6.22847i | −0.130441 | − | 0.225930i | ||||
\(761\) | −10.3720 | + | 17.9648i | −0.375983 | + | 0.651222i | −0.990474 | − | 0.137702i | \(-0.956028\pi\) |
0.614490 | + | 0.788924i | \(0.289362\pi\) | |||||||
\(762\) | −6.88052 | −0.249255 | ||||||||
\(763\) | −4.86147 | + | 8.42032i | −0.175997 | + | 0.304836i | ||||
\(764\) | −2.27288 | + | 3.93675i | −0.0822300 | + | 0.142427i | ||||
\(765\) | −1.58113 | + | 2.73859i | −0.0571658 | + | 0.0990140i | ||||
\(766\) | −6.54383 | + | 11.3342i | −0.236438 | + | 0.409523i | ||||
\(767\) | −5.44723 | − | 9.43489i | −0.196688 | − | 0.340674i | ||||
\(768\) | −4.87461 | + | 8.44308i | −0.175897 | + | 0.304663i | ||||
\(769\) | 39.6200 | 1.42873 | 0.714366 | − | 0.699772i | \(-0.246715\pi\) | ||||
0.714366 | + | 0.699772i | \(0.246715\pi\) | |||||||
\(770\) | 0.0729734 | + | 0.126394i | 0.00262978 | + | 0.00455491i | ||||
\(771\) | 8.82689 | 0.317893 | ||||||||
\(772\) | −4.55892 | − | 7.89628i | −0.164079 | − | 0.284193i | ||||
\(773\) | −17.1924 | + | 29.7781i | −0.618367 | + | 1.07104i | 0.371417 | + | 0.928466i | \(0.378872\pi\) |
−0.989784 | + | 0.142577i | \(0.954461\pi\) | |||||||
\(774\) | −0.596619 | + | 1.03337i | −0.0214450 | + | 0.0371439i | ||||
\(775\) | −17.4285 | + | 30.1870i | −0.626049 | + | 1.08435i | ||||
\(776\) | −18.4995 | − | 32.0420i | −0.664092 | − | 1.15024i | ||||
\(777\) | −9.48415 | −0.340242 | ||||||||
\(778\) | −2.15359 | −0.0772098 | ||||||||
\(779\) | −16.3255 | + | 28.2767i | −0.584923 | + | 1.01312i | ||||
\(780\) | 0.495605 | − | 0.858413i | 0.0177455 | − | 0.0307361i | ||||
\(781\) | −2.20588 | −0.0789328 | ||||||||
\(782\) | −6.39683 | + | 11.0796i | −0.228750 | + | 0.396207i | ||||
\(783\) | 4.94532 | 0.176731 | ||||||||
\(784\) | −4.26691 | −0.152389 | ||||||||
\(785\) | −3.71879 | − | 6.40727i | −0.132729 | − | 0.228685i | ||||
\(786\) | 7.17885 | 0.256061 | ||||||||
\(787\) | 21.6244 | 0.770828 | 0.385414 | − | 0.922744i | \(-0.374059\pi\) | ||||
0.385414 | + | 0.922744i | \(0.374059\pi\) | |||||||
\(788\) | 11.5522 | − | 20.0089i | 0.411529 | − | 0.712789i | ||||
\(789\) | 18.1975 | 0.647847 | ||||||||
\(790\) | 1.18145 | − | 2.04634i | 0.0420342 | − | 0.0728054i | ||||
\(791\) | −12.2539 | + | 21.2244i | −0.435699 | + | 0.754652i | ||||
\(792\) | −0.438180 | −0.0155701 | ||||||||
\(793\) | 5.44923 | 0.193508 | ||||||||
\(794\) | 9.39509 | + | 16.2728i | 0.333419 | + | 0.577499i | ||||
\(795\) | −0.751700 | + | 1.30198i | −0.0266600 | + | 0.0461765i | ||||
\(796\) | −5.29633 | + | 9.17351i | −0.187723 | + | 0.325146i | ||||
\(797\) | −0.711741 | + | 1.23277i | −0.0252111 | + | 0.0436670i | −0.878356 | − | 0.478008i | \(-0.841359\pi\) |
0.853145 | + | 0.521675i | \(0.174692\pi\) | |||||||
\(798\) | 3.42633 | + | 5.93457i | 0.121291 | + | 0.210082i | ||||
\(799\) | 27.7507 | 0.981750 | ||||||||
\(800\) | −13.4873 | − | 23.3606i | −0.476847 | − | 0.825923i | ||||
\(801\) | 12.9242 | 0.456655 | ||||||||
\(802\) | −0.851769 | + | 1.47531i | −0.0300770 | + | 0.0520949i | ||||
\(803\) | 0.873355 | + | 1.51269i | 0.0308200 | + | 0.0533818i | ||||
\(804\) | −1.41579 | + | 2.45222i | −0.0499311 | + | 0.0864832i | ||||
\(805\) | −2.05130 | + | 3.55296i | −0.0722989 | + | 0.125225i | ||||
\(806\) | 2.81506 | − | 4.87583i | 0.0991563 | − | 0.171744i | ||||
\(807\) | 7.06408 | − | 12.2353i | 0.248667 | − | 0.430705i | ||||
\(808\) | 1.46614 | 0.0515787 | ||||||||
\(809\) | −21.9603 | + | 38.0363i | −0.772081 | + | 1.33728i | 0.164339 | + | 0.986404i | \(0.447451\pi\) |
−0.936420 | + | 0.350880i | \(0.885882\pi\) | |||||||
\(810\) | 0.202658 | + | 0.351015i | 0.00712069 | + | 0.0123334i | ||||
\(811\) | 14.4836 | + | 25.0863i | 0.508587 | + | 0.880899i | 0.999951 | + | 0.00994421i | \(0.00316539\pi\) |
−0.491363 | + | 0.870955i | \(0.663501\pi\) | |||||||
\(812\) | −15.0471 | −0.528051 | ||||||||
\(813\) | 5.64805 | 0.198086 | ||||||||
\(814\) | −0.591991 | −0.0207493 | ||||||||
\(815\) | −6.44979 | − | 11.1714i | −0.225926 | − | 0.391316i | ||||
\(816\) | 3.74696 | + | 6.48993i | 0.131170 | + | 0.227193i | ||||
\(817\) | −8.74933 | −0.306100 | ||||||||
\(818\) | −11.1638 | − | 19.3363i | −0.390334 | − | 0.676079i | ||||
\(819\) | −1.08948 | + | 1.88704i | −0.0380696 | + | 0.0659384i | ||||
\(820\) | 2.93808 | − | 5.08890i | 0.102602 | − | 0.177712i | ||||
\(821\) | −5.50448 | − | 9.53403i | −0.192108 | − | 0.332740i | 0.753841 | − | 0.657057i | \(-0.228199\pi\) |
−0.945948 | + | 0.324317i | \(0.894866\pi\) | |||||||
\(822\) | 0.206358 | + | 0.357422i | 0.00719755 | + | 0.0124665i | ||||
\(823\) | −18.7499 | + | 32.4757i | −0.653579 | + | 1.13203i | 0.328669 | + | 0.944445i | \(0.393400\pi\) |
−0.982248 | + | 0.187587i | \(0.939933\pi\) | |||||||
\(824\) | −6.15762 | −0.214511 | ||||||||
\(825\) | 0.421025 | − | 0.729237i | 0.0146582 | − | 0.0253888i | ||||
\(826\) | −13.5549 | −0.471634 | ||||||||
\(827\) | −2.16791 | + | 3.75493i | −0.0753856 | + | 0.130572i | −0.901254 | − | 0.433291i | \(-0.857352\pi\) |
0.825868 | + | 0.563863i | \(0.190685\pi\) | |||||||
\(828\) | −2.66939 | − | 4.62352i | −0.0927677 | − | 0.160678i | ||||
\(829\) | 4.91476 | − | 8.51262i | 0.170697 | − | 0.295656i | −0.767967 | − | 0.640490i | \(-0.778731\pi\) |
0.938664 | + | 0.344834i | \(0.112065\pi\) | |||||||
\(830\) | −1.09328 | −0.0379483 | ||||||||
\(831\) | −12.8630 | −0.446214 | ||||||||
\(832\) | 0.643244 | + | 1.11413i | 0.0223005 | + | 0.0386256i | ||||
\(833\) | 8.14391 | − | 14.1057i | 0.282170 | − | 0.488732i | ||||
\(834\) | 4.10435 | 0.142122 | ||||||||
\(835\) | −1.83715 | − | 3.18203i | −0.0635770 | − | 0.110119i | ||||
\(836\) | −0.696298 | − | 1.20602i | −0.0240820 | − | 0.0417112i | ||||
\(837\) | −3.74771 | − | 6.49123i | −0.129540 | − | 0.224370i | ||||
\(838\) | 7.40582 | + | 12.8273i | 0.255830 | + | 0.443110i | ||||
\(839\) | −14.7713 | −0.509961 | −0.254980 | − | 0.966946i | \(-0.582069\pi\) | ||||
−0.254980 | + | 0.966946i | \(0.582069\pi\) | |||||||
\(840\) | −1.42266 | − | 2.46412i | −0.0490864 | − | 0.0850201i | ||||
\(841\) | −4.54384 | −0.156684 | ||||||||
\(842\) | −13.6143 | − | 23.5806i | −0.469178 | − | 0.812641i | ||||
\(843\) | 9.67823 | 0.333336 | ||||||||
\(844\) | 8.86566 | 0.305169 | ||||||||
\(845\) | 3.48817 | + | 6.04169i | 0.119997 | + | 0.207840i | ||||
\(846\) | 1.77845 | − | 3.08037i | 0.0611444 | − | 0.105905i | ||||
\(847\) | −10.9049 | − | 18.8878i | −0.374697 | − | 0.648994i | ||||
\(848\) | 1.78138 | + | 3.08544i | 0.0611729 | + | 0.105955i | ||||
\(849\) | 16.8274 | 0.577515 | ||||||||
\(850\) | 17.0510 | 0.584845 | ||||||||
\(851\) | −8.32051 | − | 14.4116i | −0.285224 | − | 0.494022i | ||||
\(852\) | 18.6399 | 0.638591 | ||||||||
\(853\) | −4.56911 | + | 7.91393i | −0.156443 | + | 0.270968i | −0.933584 | − | 0.358360i | \(-0.883336\pi\) |
0.777140 | + | 0.629327i | \(0.216669\pi\) | |||||||
\(854\) | 3.38995 | − | 5.87157i | 0.116002 | − | 0.200921i | ||||
\(855\) | −1.48598 | + | 2.57379i | −0.0508194 | + | 0.0880218i | ||||
\(856\) | −0.542185 | − | 0.939091i | −0.0185315 | − | 0.0320975i | ||||
\(857\) | 14.4362 | + | 25.0042i | 0.493131 | + | 0.854128i | 0.999969 | − | 0.00791372i | \(-0.00251904\pi\) |
−0.506838 | + | 0.862041i | \(0.669186\pi\) | |||||||
\(858\) | −0.0680043 | + | 0.117787i | −0.00232163 | + | 0.00402118i | ||||
\(859\) | 5.68442 | + | 9.84570i | 0.193950 | + | 0.335931i | 0.946556 | − | 0.322540i | \(-0.104537\pi\) |
−0.752606 | + | 0.658471i | \(0.771203\pi\) | |||||||
\(860\) | 1.57460 | 0.0536935 | ||||||||
\(861\) | −6.45873 | + | 11.1869i | −0.220113 | + | 0.381247i | ||||
\(862\) | −5.06046 | + | 8.76498i | −0.172360 | + | 0.298536i | ||||
\(863\) | 5.91901 | 0.201485 | 0.100743 | − | 0.994913i | \(-0.467878\pi\) | ||||
0.100743 | + | 0.994913i | \(0.467878\pi\) | |||||||
\(864\) | 5.80044 | 0.197335 | ||||||||
\(865\) | −3.98945 | + | 6.90994i | −0.135645 | + | 0.234945i | ||||
\(866\) | 5.65686 | − | 9.79797i | 0.192228 | − | 0.332949i | ||||
\(867\) | −11.6061 | −0.394165 | ||||||||
\(868\) | 11.4032 | + | 19.7509i | 0.387049 | + | 0.670389i | ||||
\(869\) | 0.527797 | − | 0.914171i | 0.0179043 | − | 0.0310111i | ||||
\(870\) | 1.00221 | + | 1.73588i | 0.0339781 | + | 0.0588518i | ||||
\(871\) | 1.01389 | + | 1.75610i | 0.0343542 | + | 0.0595033i | ||||
\(872\) | 5.91589 | − | 10.2466i | 0.200337 | − | 0.346995i | ||||
\(873\) | −7.64453 | + | 13.2407i | −0.258728 | + | 0.448130i | ||||
\(874\) | −6.01188 | + | 10.4129i | −0.203355 | + | 0.352221i | ||||
\(875\) | 11.3467 | 0.383588 | ||||||||
\(876\) | −7.37990 | − | 12.7824i | −0.249344 | − | 0.431876i | ||||
\(877\) | 17.5293 | 0.591921 | 0.295961 | − | 0.955200i | \(-0.404360\pi\) | ||||
0.295961 | + | 0.955200i | \(0.404360\pi\) | |||||||
\(878\) | 1.38157 | 0.0466256 | ||||||||
\(879\) | −14.8252 | − | 25.6780i | −0.500041 | − | 0.866097i | ||||
\(880\) | 0.0750000 | + | 0.129904i | 0.00252825 | + | 0.00437906i | ||||
\(881\) | 23.1894 | − | 40.1653i | 0.781271 | − | 1.35320i | −0.149930 | − | 0.988697i | \(-0.547905\pi\) |
0.931201 | − | 0.364505i | \(-0.118762\pi\) | |||||||
\(882\) | −1.04383 | − | 1.80797i | −0.0351477 | − | 0.0608776i | ||||
\(883\) | −28.6150 | −0.962973 | −0.481486 | − | 0.876454i | \(-0.659903\pi\) | ||||
−0.481486 | + | 0.876454i | \(0.659903\pi\) | |||||||
\(884\) | 8.96662 | 0.301580 | ||||||||
\(885\) | −2.93933 | − | 5.09107i | −0.0988046 | − | 0.171135i | ||||
\(886\) | 21.2314 | 0.713281 | ||||||||
\(887\) | −3.41901 | − | 5.92189i | −0.114799 | − | 0.198838i | 0.802900 | − | 0.596113i | \(-0.203289\pi\) |
−0.917699 | + | 0.397276i | \(0.869956\pi\) | |||||||
\(888\) | 11.5412 | 0.387297 | ||||||||
\(889\) | −9.97974 | − | 17.2854i | −0.334710 | − | 0.579734i | ||||
\(890\) | 2.61920 | + | 4.53659i | 0.0877959 | + | 0.152067i | ||||
\(891\) | 0.0905346 | + | 0.156811i | 0.00303302 | + | 0.00525335i | ||||
\(892\) | 10.0472 | + | 17.4023i | 0.336406 | + | 0.582673i | ||||
\(893\) | 26.0807 | 0.872759 | ||||||||
\(894\) | −2.86325 | + | 4.95930i | −0.0957615 | + | 0.165864i | ||||
\(895\) | 1.18797 | + | 2.05763i | 0.0397095 | + | 0.0687789i | ||||
\(896\) | −21.4693 | −0.717239 | ||||||||
\(897\) | −3.82324 | −0.127654 | ||||||||
\(898\) | −2.50608 | + | 4.34066i | −0.0836290 | + | 0.144850i | ||||
\(899\) | −18.5336 | − | 32.1012i | −0.618131 | − | 1.07063i | ||||
\(900\) | −3.55769 | + | 6.16209i | −0.118590 | + | 0.205403i | ||||
\(901\) | −13.5999 | −0.453080 | ||||||||
\(902\) | −0.403148 | + | 0.698272i | −0.0134233 | + | 0.0232499i | ||||
\(903\) | −3.46142 | −0.115189 | ||||||||
\(904\) | 14.9117 | − | 25.8278i | 0.495956 | − | 0.859020i | ||||
\(905\) | −3.31447 | − | 5.74084i | −0.110177 | − | 0.190832i | ||||
\(906\) | 6.58941 | + | 11.4132i | 0.218918 | + | 0.379178i | ||||
\(907\) | 22.0464 | − | 38.1855i | 0.732038 | − | 1.26793i | −0.223972 | − | 0.974595i | \(-0.571903\pi\) |
0.956011 | − | 0.293332i | \(-0.0947641\pi\) | |||||||
\(908\) | 11.6386 | − | 20.1587i | 0.386242 | − | 0.668990i | ||||
\(909\) | −0.302927 | − | 0.524685i | −0.0100475 | − | 0.0174027i | ||||
\(910\) | −0.883170 | −0.0292768 | ||||||||
\(911\) | −10.4393 | − | 18.0814i | −0.345869 | − | 0.599063i | 0.639642 | − | 0.768673i | \(-0.279083\pi\) |
−0.985511 | + | 0.169610i | \(0.945749\pi\) | |||||||
\(912\) | 3.52148 | + | 6.09938i | 0.116608 | + | 0.201971i | ||||
\(913\) | −0.488407 | −0.0161639 | ||||||||
\(914\) | 19.5565 | 0.646871 | ||||||||
\(915\) | 2.94041 | 0.0972069 | ||||||||
\(916\) | −22.5319 | − | 39.0264i | −0.744475 | − | 1.28947i | ||||
\(917\) | 10.4124 | + | 18.0349i | 0.343849 | + | 0.595564i | ||||
\(918\) | −1.83327 | + | 3.17532i | −0.0605070 | + | 0.104801i | ||||
\(919\) | −20.5096 | −0.676549 | −0.338275 | − | 0.941047i | \(-0.609843\pi\) | ||||
−0.338275 | + | 0.941047i | \(0.609843\pi\) | |||||||
\(920\) | 2.49622 | − | 4.32357i | 0.0822978 | − | 0.142544i | ||||
\(921\) | 1.49078 | − | 2.58210i | 0.0491227 | − | 0.0850830i | ||||
\(922\) | 7.47908 | − | 12.9541i | 0.246310 | − | 0.426622i | ||||
\(923\) | 6.67425 | − | 11.5601i | 0.219686 | − | 0.380507i | ||||
\(924\) | −0.275470 | − | 0.477129i | −0.00906231 | − | 0.0156964i | ||||
\(925\) | −11.0893 | + | 19.2073i | −0.364615 | + | 0.631532i | ||||
\(926\) | −13.5998 | −0.446917 | ||||||||
\(927\) | 1.27226 | + | 2.20362i | 0.0417864 | + | 0.0723762i | ||||
\(928\) | 28.6850 | 0.941632 | ||||||||
\(929\) | 4.59258 | + | 7.95458i | 0.150678 | + | 0.260981i | 0.931477 | − | 0.363801i | \(-0.118521\pi\) |
−0.780799 | + | 0.624782i | \(0.785188\pi\) | |||||||
\(930\) | 1.51901 | − | 2.63100i | 0.0498103 | − | 0.0862740i | ||||
\(931\) | 7.65383 | − | 13.2568i | 0.250844 | − | 0.434475i | ||||
\(932\) | 20.6748 | − | 35.8098i | 0.677225 | − | 1.17299i | ||||
\(933\) | −6.76973 | − | 11.7255i | −0.221631 | − | 0.383876i | ||||
\(934\) | −9.81765 | −0.321243 | ||||||||
\(935\) | −0.572587 | −0.0187256 | ||||||||
\(936\) | 1.32578 | − | 2.29632i | 0.0433346 | − | 0.0750577i | ||||
\(937\) | 7.40026 | − | 12.8176i | 0.241756 | − | 0.418733i | −0.719459 | − | 0.694535i | \(-0.755610\pi\) |
0.961215 | + | 0.275802i | \(0.0889433\pi\) | |||||||
\(938\) | 2.52295 | 0.0823771 | ||||||||
\(939\) | 4.23980 | − | 7.34355i | 0.138361 | − | 0.239648i | ||||
\(940\) | −4.69371 | −0.153092 | ||||||||
\(941\) | −0.195440 | −0.00637118 | −0.00318559 | − | 0.999995i | \(-0.501014\pi\) | ||||
−0.00318559 | + | 0.999995i | \(0.501014\pi\) | |||||||
\(942\) | −4.31184 | − | 7.42905i | −0.140487 | − | 0.242052i | ||||
\(943\) | −22.6652 | −0.738080 | ||||||||
\(944\) | −13.9313 | −0.453425 | ||||||||
\(945\) | −0.587885 | + | 1.01825i | −0.0191239 | + | 0.0331236i | ||||
\(946\) | −0.216059 | −0.00702467 | ||||||||
\(947\) | −18.6159 | + | 32.2437i | −0.604935 | + | 1.04778i | 0.387127 | + | 0.922026i | \(0.373468\pi\) |
−0.992062 | + | 0.125752i | \(0.959866\pi\) | |||||||
\(948\) | −4.45992 | + | 7.72480i | −0.144851 | + | 0.250890i | ||||
\(949\) | −10.5699 | −0.343113 | ||||||||
\(950\) | 16.0249 | 0.519918 | ||||||||
\(951\) | 3.17994 | + | 5.50781i | 0.103116 | + | 0.178603i | ||||
\(952\) | 12.8695 | − | 22.2907i | 0.417104 | − | 0.722446i | ||||
\(953\) | 25.2785 | − | 43.7836i | 0.818850 | − | 1.41829i | −0.0876810 | − | 0.996149i | \(-0.527946\pi\) |
0.906530 | − | 0.422140i | \(-0.138721\pi\) | |||||||
\(954\) | −0.871575 | + | 1.50961i | −0.0282183 | + | 0.0488755i | ||||
\(955\) | 0.878293 | + | 1.52125i | 0.0284209 | + | 0.0492264i | ||||
\(956\) | 17.4130 | 0.563177 | ||||||||
\(957\) | 0.447722 | + | 0.775478i | 0.0144728 | + | 0.0250676i | ||||
\(958\) | −16.1078 | −0.520421 | ||||||||
\(959\) | −0.598616 | + | 1.03683i | −0.0193303 | + | 0.0334811i | ||||
\(960\) | 0.347095 | + | 0.601186i | 0.0112024 | + | 0.0194032i | ||||
\(961\) | −12.5907 | + | 21.8077i | −0.406151 | + | 0.703474i | ||||
\(962\) | 1.79116 | − | 3.10238i | 0.0577493 | − | 0.100025i | ||||
\(963\) | −0.224047 | + | 0.388061i | −0.00721982 | + | 0.0125051i | ||||
\(964\) | 19.1564 | − | 33.1798i | 0.616985 | − | 1.06865i | ||||
\(965\) | −3.52334 | −0.113420 | ||||||||
\(966\) | −2.37843 | + | 4.11956i | −0.0765248 | + | 0.132545i | ||||
\(967\) | 5.22487 | + | 9.04974i | 0.168021 | + | 0.291020i | 0.937724 | − | 0.347382i | \(-0.112929\pi\) |
−0.769703 | + | 0.638402i | \(0.779596\pi\) | |||||||
\(968\) | 13.2701 | + | 22.9845i | 0.426517 | + | 0.738750i | ||||
\(969\) | −26.8847 | −0.863661 | ||||||||
\(970\) | −6.19691 | −0.198971 | ||||||||
\(971\) | 46.3976 | 1.48897 | 0.744485 | − | 0.667639i | \(-0.232695\pi\) | ||||
0.744485 | + | 0.667639i | \(0.232695\pi\) | |||||||
\(972\) | −0.765023 | − | 1.32506i | −0.0245381 | − | 0.0425013i | ||||
\(973\) | 5.95310 | + | 10.3111i | 0.190847 | + | 0.330558i | ||||
\(974\) | −0.761146 | −0.0243887 | ||||||||
\(975\) | 2.54775 | + | 4.41284i | 0.0815934 | + | 0.141324i | ||||
\(976\) | 3.48410 | − | 6.03464i | 0.111523 | − | 0.193164i | ||||
\(977\) | −17.1151 | + | 29.6442i | −0.547560 | + | 0.948402i | 0.450881 | + | 0.892584i | \(0.351110\pi\) |
−0.998441 | + | 0.0558177i | \(0.982223\pi\) | |||||||
\(978\) | −7.47835 | − | 12.9529i | −0.239131 | − | 0.414188i | ||||
\(979\) | 1.17009 | + | 2.02666i | 0.0373962 | + | 0.0647722i | ||||
\(980\) | −1.37745 | + | 2.38581i | −0.0440009 | + | 0.0762118i | ||||
\(981\) | −4.88925 | −0.156102 | ||||||||
\(982\) | −6.46583 | + | 11.1992i | −0.206333 | + | 0.357379i | ||||
\(983\) | 17.4499 | 0.556565 | 0.278282 | − | 0.960499i | \(-0.410235\pi\) | ||||
0.278282 | + | 0.960499i | \(0.410235\pi\) | |||||||
\(984\) | 7.85959 | − | 13.6132i | 0.250554 | − | 0.433973i | ||||
\(985\) | −4.46402 | − | 7.73191i | −0.142235 | − | 0.246359i | ||||
\(986\) | −9.06612 | + | 15.7030i | −0.288724 | + | 0.500085i | ||||
\(987\) | 10.3181 | 0.328429 | ||||||||
\(988\) | 8.42703 | 0.268099 | ||||||||
\(989\) | −3.03673 | − | 5.25978i | −0.0965625 | − | 0.167251i | ||||
\(990\) | −0.0366952 | + | 0.0635579i | −0.00116625 | + | 0.00202000i | ||||
\(991\) | 30.7424 | 0.976564 | 0.488282 | − | 0.872686i | \(-0.337624\pi\) | ||||
0.488282 | + | 0.872686i | \(0.337624\pi\) | |||||||
\(992\) | −21.7384 | − | 37.6520i | −0.690194 | − | 1.19545i | ||||
\(993\) | −10.4800 | − | 18.1520i | −0.332574 | − | 0.576035i | ||||
\(994\) | −8.30407 | − | 14.3831i | −0.263389 | − | 0.456203i | ||||
\(995\) | 2.04662 | + | 3.54485i | 0.0648822 | + | 0.112379i | ||||
\(996\) | 4.12707 | 0.130771 | ||||||||
\(997\) | −8.48607 | − | 14.6983i | −0.268757 | − | 0.465500i | 0.699784 | − | 0.714354i | \(-0.253279\pi\) |
−0.968541 | + | 0.248854i | \(0.919946\pi\) | |||||||
\(998\) | −4.65615 | −0.147388 | ||||||||
\(999\) | −2.38458 | − | 4.13022i | −0.0754449 | − | 0.130674i |
(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 | 471.2.e.b.301.4 | yes | 22 | |
157.12 | even | 3 | inner | 471.2.e.b.169.4 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
471.2.e.b.169.4 | ✓ | 22 | 157.12 | even | 3 | inner | |
471.2.e.b.301.4 | yes | 22 | 1.1 | even | 1 | trivial |