Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(19,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.x (of order \(12\), degree \(4\), not 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 80.5 | ||
Character | \(\chi\) | \(=\) | 637.80 |
Dual form | 637.2.x.a.215.5 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0745816 | + | 0.278342i | 0.0527371 | + | 0.196818i | 0.987268 | − | 0.159063i | \(-0.0508475\pi\) |
−0.934531 | + | 0.355881i | \(0.884181\pi\) | |||||||
\(3\) | − | 1.06594i | − | 0.615419i | −0.951480 | − | 0.307710i | \(-0.900437\pi\) | ||
0.951480 | − | 0.307710i | \(-0.0995625\pi\) | |||||||
\(4\) | 1.66014 | − | 0.958482i | 0.830069 | − | 0.479241i | ||||
\(5\) | −0.133809 | + | 0.499383i | −0.0598414 | + | 0.223331i | −0.989370 | − | 0.145418i | \(-0.953547\pi\) |
0.929529 | + | 0.368749i | \(0.120214\pi\) | |||||||
\(6\) | 0.296695 | − | 0.0794993i | 0.121125 | − | 0.0324554i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.798123 | + | 0.798123i | 0.282179 | + | 0.282179i | ||||
\(9\) | 1.86378 | 0.621259 | ||||||||
\(10\) | −0.148979 | −0.0471114 | ||||||||
\(11\) | −2.70707 | − | 2.70707i | −0.816212 | − | 0.816212i | 0.169345 | − | 0.985557i | \(-0.445835\pi\) |
−0.985557 | + | 0.169345i | \(0.945835\pi\) | |||||||
\(12\) | −1.02168 | − | 1.76960i | −0.294934 | − | 0.510841i | ||||
\(13\) | 1.12494 | − | 3.42557i | 0.312003 | − | 0.950081i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.532311 | + | 0.142632i | 0.137442 | + | 0.0368275i | ||||
\(16\) | 1.75434 | − | 3.03860i | 0.438584 | − | 0.759650i | ||||
\(17\) | 2.26016 | + | 3.91471i | 0.548169 | + | 0.949457i | 0.998400 | + | 0.0565446i | \(0.0180083\pi\) |
−0.450231 | + | 0.892912i | \(0.648658\pi\) | |||||||
\(18\) | 0.139003 | + | 0.518768i | 0.0327634 | + | 0.122275i | ||||
\(19\) | 2.17974 | + | 2.17974i | 0.500066 | + | 0.500066i | 0.911458 | − | 0.411393i | \(-0.134957\pi\) |
−0.411393 | + | 0.911458i | \(0.634957\pi\) | |||||||
\(20\) | 0.256508 | + | 0.957300i | 0.0573569 | + | 0.214059i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.551594 | − | 0.955389i | 0.117600 | − | 0.203690i | ||||
\(23\) | −7.51600 | − | 4.33936i | −1.56719 | − | 0.904820i | −0.996494 | − | 0.0836605i | \(-0.973339\pi\) |
−0.570699 | − | 0.821159i | \(-0.693328\pi\) | |||||||
\(24\) | 0.850749 | − | 0.850749i | 0.173658 | − | 0.173658i | ||||
\(25\) | 4.09865 | + | 2.36636i | 0.819730 | + | 0.473271i | ||||
\(26\) | 1.03738 | + | 0.0576354i | 0.203447 | + | 0.0113032i | ||||
\(27\) | − | 5.18448i | − | 0.997754i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.26720 | + | 2.19486i | 0.235314 | + | 0.407575i | 0.959364 | − | 0.282172i | \(-0.0910549\pi\) |
−0.724050 | + | 0.689747i | \(0.757722\pi\) | |||||||
\(30\) | 0.158802i | 0.0289932i | ||||||||
\(31\) | −1.00987 | + | 0.270595i | −0.181378 | + | 0.0486002i | −0.348365 | − | 0.937359i | \(-0.613263\pi\) |
0.166987 | + | 0.985959i | \(0.446596\pi\) | |||||||
\(32\) | 3.15712 | + | 0.845949i | 0.558106 | + | 0.149544i | ||||
\(33\) | −2.88557 | + | 2.88557i | −0.502313 | + | 0.502313i | ||||
\(34\) | −0.921063 | + | 0.921063i | −0.157961 | + | 0.157961i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.09413 | − | 1.78640i | 0.515688 | − | 0.297733i | ||||
\(37\) | 0.176900 | − | 0.0474003i | 0.0290822 | − | 0.00779255i | −0.244249 | − | 0.969713i | \(-0.578541\pi\) |
0.273331 | + | 0.961920i | \(0.411875\pi\) | |||||||
\(38\) | −0.444144 | + | 0.769281i | −0.0720497 | + | 0.124794i | ||||
\(39\) | −3.65144 | − | 1.19912i | −0.584698 | − | 0.192013i | ||||
\(40\) | −0.505366 | + | 0.291773i | −0.0799053 | + | 0.0461334i | ||||
\(41\) | 1.79081 | − | 6.68338i | 0.279677 | − | 1.04377i | −0.672965 | − | 0.739674i | \(-0.734980\pi\) |
0.952642 | − | 0.304094i | \(-0.0983538\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.59244 | + | 2.65145i | 0.700341 | + | 0.404342i | 0.807474 | − | 0.589903i | \(-0.200834\pi\) |
−0.107134 | + | 0.994245i | \(0.534167\pi\) | |||||||
\(44\) | −7.08879 | − | 1.89943i | −1.06867 | − | 0.286351i | ||||
\(45\) | −0.249391 | + | 0.930740i | −0.0371770 | + | 0.138746i | ||||
\(46\) | 0.647273 | − | 2.41566i | 0.0954352 | − | 0.356169i | ||||
\(47\) | −9.03333 | − | 2.42047i | −1.31765 | − | 0.353063i | −0.469551 | − | 0.882905i | \(-0.655584\pi\) |
−0.848096 | + | 0.529843i | \(0.822251\pi\) | |||||||
\(48\) | −3.23896 | − | 1.87001i | −0.467503 | − | 0.269913i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.352973 | + | 1.31731i | −0.0499179 | + | 0.186296i | ||||
\(51\) | 4.17284 | − | 2.40919i | 0.584314 | − | 0.337354i | ||||
\(52\) | −1.41578 | − | 6.76515i | −0.196333 | − | 0.938158i | ||||
\(53\) | 0.512534 | − | 0.887735i | 0.0704019 | − | 0.121940i | −0.828676 | − | 0.559729i | \(-0.810905\pi\) |
0.899078 | + | 0.437789i | \(0.144238\pi\) | |||||||
\(54\) | 1.44306 | − | 0.386667i | 0.196376 | − | 0.0526187i | ||||
\(55\) | 1.71410 | − | 0.989634i | 0.231129 | − | 0.133442i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.32346 | − | 2.32346i | 0.307750 | − | 0.307750i | ||||
\(58\) | −0.516412 | + | 0.516412i | −0.0678083 | + | 0.0678083i | ||||
\(59\) | −0.503336 | − | 0.134868i | −0.0655287 | − | 0.0175584i | 0.225906 | − | 0.974149i | \(-0.427466\pi\) |
−0.291434 | + | 0.956591i | \(0.594133\pi\) | |||||||
\(60\) | 1.02042 | − | 0.273421i | 0.131736 | − | 0.0352985i | ||||
\(61\) | − | 8.53647i | − | 1.09298i | −0.837465 | − | 0.546491i | \(-0.815963\pi\) | ||
0.837465 | − | 0.546491i | \(-0.184037\pi\) | |||||||
\(62\) | −0.150636 | − | 0.260909i | −0.0191308 | − | 0.0331355i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 6.07549i | − | 0.759437i | ||||||
\(65\) | 1.56014 | + | 1.02015i | 0.193512 | + | 0.126534i | ||||
\(66\) | −1.01838 | − | 0.587965i | −0.125355 | − | 0.0723735i | ||||
\(67\) | −5.00628 | + | 5.00628i | −0.611615 | + | 0.611615i | −0.943367 | − | 0.331752i | \(-0.892360\pi\) |
0.331752 | + | 0.943367i | \(0.392360\pi\) | |||||||
\(68\) | 7.50436 | + | 4.33264i | 0.910037 | + | 0.525410i | ||||
\(69\) | −4.62549 | + | 8.01158i | −0.556843 | + | 0.964481i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.96522 | + | 7.33429i | 0.233228 | + | 0.870420i | 0.978940 | + | 0.204150i | \(0.0654432\pi\) |
−0.745711 | + | 0.666269i | \(0.767890\pi\) | |||||||
\(72\) | 1.48752 | + | 1.48752i | 0.175306 | + | 0.175306i | ||||
\(73\) | 3.20113 | + | 11.9468i | 0.374664 | + | 1.39826i | 0.853835 | + | 0.520543i | \(0.174271\pi\) |
−0.479171 | + | 0.877721i | \(0.659063\pi\) | |||||||
\(74\) | 0.0263870 | + | 0.0457036i | 0.00306742 | + | 0.00531294i | ||||
\(75\) | 2.52239 | − | 4.36890i | 0.291260 | − | 0.504477i | ||||
\(76\) | 5.70790 | + | 1.52943i | 0.654741 | + | 0.175437i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.0614358 | − | 1.10578i | 0.00695623 | − | 0.125205i | ||||
\(79\) | 3.77800 | + | 6.54369i | 0.425058 | + | 0.736222i | 0.996426 | − | 0.0844720i | \(-0.0269204\pi\) |
−0.571368 | + | 0.820694i | \(0.693587\pi\) | |||||||
\(80\) | 1.28268 | + | 1.28268i | 0.143408 | + | 0.143408i | ||||
\(81\) | 0.0650005 | 0.00722228 | ||||||||
\(82\) | 1.99383 | 0.220181 | ||||||||
\(83\) | 6.42827 | + | 6.42827i | 0.705594 | + | 0.705594i | 0.965606 | − | 0.260011i | \(-0.0837262\pi\) |
−0.260011 | + | 0.965606i | \(0.583726\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.25737 | + | 0.604861i | −0.244846 | + | 0.0656064i | ||||
\(86\) | −0.395498 | + | 1.47602i | −0.0426477 | + | 0.159163i | ||||
\(87\) | 2.33958 | − | 1.35076i | 0.250830 | − | 0.144817i | ||||
\(88\) | − | 4.32115i | − | 0.460636i | ||||||
\(89\) | 3.13675 | + | 11.7065i | 0.332495 | + | 1.24089i | 0.906560 | + | 0.422078i | \(0.138699\pi\) |
−0.574065 | + | 0.818810i | \(0.694634\pi\) | |||||||
\(90\) | −0.277664 | −0.0292684 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −16.6368 | −1.73451 | ||||||||
\(93\) | 0.288437 | + | 1.07646i | 0.0299095 | + | 0.111624i | ||||
\(94\) | − | 2.69488i | − | 0.277956i | ||||||
\(95\) | −1.38019 | + | 0.796855i | −0.141605 | + | 0.0817556i | ||||
\(96\) | 0.901729 | − | 3.36530i | 0.0920323 | − | 0.343469i | ||||
\(97\) | −13.1956 | + | 3.53575i | −1.33981 | + | 0.359001i | −0.856364 | − | 0.516373i | \(-0.827282\pi\) |
−0.483446 | + | 0.875374i | \(0.660615\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.04538 | − | 5.04538i | −0.507079 | − | 0.507079i | ||||
\(100\) | 9.07243 | 0.907243 | ||||||||
\(101\) | −1.11161 | −0.110610 | −0.0553049 | − | 0.998470i | \(-0.517613\pi\) | ||||
−0.0553049 | + | 0.998470i | \(0.517613\pi\) | |||||||
\(102\) | 0.981795 | + | 0.981795i | 0.0972122 | + | 0.0972122i | ||||
\(103\) | 0.214188 | + | 0.370984i | 0.0211046 | + | 0.0365542i | 0.876385 | − | 0.481612i | \(-0.159948\pi\) |
−0.855280 | + | 0.518166i | \(0.826615\pi\) | |||||||
\(104\) | 3.63187 | − | 1.83618i | 0.356134 | − | 0.180052i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.285320 | + | 0.0764512i | 0.0277127 | + | 0.00742559i | ||||
\(107\) | −2.50817 | + | 4.34428i | −0.242474 | + | 0.419977i | −0.961418 | − | 0.275090i | \(-0.911292\pi\) |
0.718944 | + | 0.695068i | \(0.244626\pi\) | |||||||
\(108\) | −4.96923 | − | 8.60696i | −0.478164 | − | 0.828205i | ||||
\(109\) | 0.219786 | + | 0.820253i | 0.0210517 | + | 0.0785660i | 0.975653 | − | 0.219322i | \(-0.0703845\pi\) |
−0.954601 | + | 0.297888i | \(0.903718\pi\) | |||||||
\(110\) | 0.403297 | + | 0.403297i | 0.0384529 | + | 0.0384529i | ||||
\(111\) | −0.0505257 | − | 0.188564i | −0.00479569 | − | 0.0178977i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.44889 | − | 4.24160i | 0.230372 | − | 0.399016i | −0.727546 | − | 0.686059i | \(-0.759339\pi\) |
0.957918 | + | 0.287043i | \(0.0926724\pi\) | |||||||
\(114\) | 0.820005 | + | 0.473430i | 0.0768005 | + | 0.0443408i | ||||
\(115\) | 3.17272 | − | 3.17272i | 0.295857 | − | 0.295857i | ||||
\(116\) | 4.20747 | + | 2.42918i | 0.390653 | + | 0.225544i | ||||
\(117\) | 2.09665 | − | 6.38449i | 0.193835 | − | 0.590247i | ||||
\(118\) | − | 0.150158i | − | 0.0138232i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.311012 | + | 0.538688i | 0.0283914 | + | 0.0491753i | ||||
\(121\) | 3.65645i | 0.332404i | ||||||||
\(122\) | 2.37606 | − | 0.636663i | 0.215118 | − | 0.0576408i | ||||
\(123\) | −7.12406 | − | 1.90889i | −0.642355 | − | 0.172119i | ||||
\(124\) | −1.41717 | + | 1.41717i | −0.127266 | + | 0.127266i | ||||
\(125\) | −3.55803 | + | 3.55803i | −0.318240 | + | 0.318240i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.00665 | + | 1.73589i | −0.266797 | + | 0.154035i | −0.627431 | − | 0.778672i | \(-0.715894\pi\) |
0.360634 | + | 0.932707i | \(0.382560\pi\) | |||||||
\(128\) | 8.00532 | − | 2.14502i | 0.707577 | − | 0.189595i | ||||
\(129\) | 2.82628 | − | 4.89525i | 0.248840 | − | 0.431003i | ||||
\(130\) | −0.167593 | + | 0.510338i | −0.0146989 | + | 0.0447596i | ||||
\(131\) | −15.0157 | + | 8.66932i | −1.31193 | + | 0.757442i | −0.982415 | − | 0.186710i | \(-0.940218\pi\) |
−0.329512 | + | 0.944151i | \(0.606884\pi\) | |||||||
\(132\) | −2.02468 | + | 7.55620i | −0.176226 | + | 0.657683i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.76684 | − | 1.02008i | −0.152631 | − | 0.0881218i | ||||
\(135\) | 2.58904 | + | 0.693732i | 0.222829 | + | 0.0597070i | ||||
\(136\) | −1.32054 | + | 4.92831i | −0.113235 | + | 0.422599i | ||||
\(137\) | −2.44489 | + | 9.12446i | −0.208881 | + | 0.779555i | 0.779350 | + | 0.626589i | \(0.215549\pi\) |
−0.988231 | + | 0.152966i | \(0.951117\pi\) | |||||||
\(138\) | −2.57494 | − | 0.689952i | −0.219193 | − | 0.0587327i | ||||
\(139\) | 13.1525 | + | 7.59358i | 1.11558 | + | 0.644079i | 0.940268 | − | 0.340434i | \(-0.110574\pi\) |
0.175310 | + | 0.984513i | \(0.443907\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.58007 | + | 9.62897i | −0.217281 | + | 0.810905i | ||||
\(142\) | −1.89487 | + | 1.09401i | −0.159014 | + | 0.0918069i | ||||
\(143\) | −12.3185 | + | 6.22794i | −1.03013 | + | 0.520807i | ||||
\(144\) | 3.26969 | − | 5.66328i | 0.272475 | − | 0.471940i | ||||
\(145\) | −1.26564 | + | 0.339127i | −0.105106 | + | 0.0281630i | ||||
\(146\) | −3.08655 | + | 1.78202i | −0.255444 | + | 0.147481i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.248247 | − | 0.248247i | 0.0204057 | − | 0.0204057i | ||||
\(149\) | −10.1579 | + | 10.1579i | −0.832170 | + | 0.832170i | −0.987813 | − | 0.155643i | \(-0.950255\pi\) |
0.155643 | + | 0.987813i | \(0.450255\pi\) | |||||||
\(150\) | 1.40417 | + | 0.376247i | 0.114650 | + | 0.0307205i | ||||
\(151\) | −4.79468 | + | 1.28473i | −0.390185 | + | 0.104550i | −0.448578 | − | 0.893744i | \(-0.648069\pi\) |
0.0583923 | + | 0.998294i | \(0.481403\pi\) | |||||||
\(152\) | 3.47940i | 0.282216i | ||||||||
\(153\) | 4.21243 | + | 7.29615i | 0.340555 | + | 0.589859i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 0.540522i | − | 0.0434157i | ||||||
\(156\) | −7.21123 | + | 1.50913i | −0.577360 | + | 0.120827i | ||||
\(157\) | −3.02404 | − | 1.74593i | −0.241345 | − | 0.139340i | 0.374450 | − | 0.927247i | \(-0.377832\pi\) |
−0.615795 | + | 0.787907i | \(0.711165\pi\) | |||||||
\(158\) | −1.53961 | + | 1.53961i | −0.122485 | + | 0.122485i | ||||
\(159\) | −0.946269 | − | 0.546329i | −0.0750440 | − | 0.0433267i | ||||
\(160\) | −0.844906 | + | 1.46342i | −0.0667957 | + | 0.115693i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.00484784 | + | 0.0180924i | 0.000380882 | + | 0.00142147i | ||||
\(163\) | 1.62342 | + | 1.62342i | 0.127156 | + | 0.127156i | 0.767821 | − | 0.640665i | \(-0.221341\pi\) |
−0.640665 | + | 0.767821i | \(0.721341\pi\) | |||||||
\(164\) | −3.43291 | − | 12.8118i | −0.268065 | − | 1.00043i | ||||
\(165\) | −1.05489 | − | 1.82712i | −0.0821229 | − | 0.142241i | ||||
\(166\) | −1.30983 | + | 2.26869i | −0.101662 | + | 0.176085i | ||||
\(167\) | −20.2547 | − | 5.42723i | −1.56736 | − | 0.419972i | −0.632372 | − | 0.774665i | \(-0.717919\pi\) |
−0.934983 | + | 0.354693i | \(0.884585\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.4690 | − | 7.70714i | −0.805308 | − | 0.592857i | ||||
\(170\) | −0.336717 | − | 0.583210i | −0.0258250 | − | 0.0447302i | ||||
\(171\) | 4.06254 | + | 4.06254i | 0.310670 | + | 0.310670i | ||||
\(172\) | 10.1655 | 0.775108 | ||||||||
\(173\) | 20.0875 | 1.52723 | 0.763613 | − | 0.645674i | \(-0.223423\pi\) | ||||
0.763613 | + | 0.645674i | \(0.223423\pi\) | |||||||
\(174\) | 0.550463 | + | 0.550463i | 0.0417305 | + | 0.0417305i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.9748 | + | 3.47659i | −0.978013 | + | 0.262058i | ||||
\(177\) | −0.143761 | + | 0.536524i | −0.0108058 | + | 0.0403276i | ||||
\(178\) | −3.02447 | + | 1.74618i | −0.226694 | + | 0.130882i | ||||
\(179\) | 21.4282i | 1.60162i | 0.598919 | + | 0.800810i | \(0.295597\pi\) | ||||
−0.598919 | + | 0.800810i | \(0.704403\pi\) | |||||||
\(180\) | 0.478073 | + | 1.78419i | 0.0356335 | + | 0.132986i | ||||
\(181\) | 19.7532 | 1.46824 | 0.734121 | − | 0.679019i | \(-0.237595\pi\) | ||||
0.734121 | + | 0.679019i | \(0.237595\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.09934 | −0.672643 | ||||||||
\(184\) | −2.53534 | − | 9.46203i | −0.186908 | − | 0.697550i | ||||
\(185\) | 0.0946836i | 0.00696128i | ||||||||
\(186\) | −0.278112 | + | 0.160568i | −0.0203922 | + | 0.0117734i | ||||
\(187\) | 4.47898 | − | 16.7158i | 0.327536 | − | 1.22238i | ||||
\(188\) | −17.3166 | + | 4.63996i | −1.26294 | + | 0.338404i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.324735 | − | 0.324735i | −0.0235588 | − | 0.0235588i | ||||
\(191\) | −4.29877 | −0.311048 | −0.155524 | − | 0.987832i | \(-0.549707\pi\) | ||||
−0.155524 | + | 0.987832i | \(0.549707\pi\) | |||||||
\(192\) | −6.47610 | −0.467372 | ||||||||
\(193\) | −9.58390 | − | 9.58390i | −0.689864 | − | 0.689864i | 0.272337 | − | 0.962202i | \(-0.412203\pi\) |
−0.962202 | + | 0.272337i | \(0.912203\pi\) | |||||||
\(194\) | −1.96830 | − | 3.40919i | −0.141315 | − | 0.244766i | ||||
\(195\) | 1.08742 | − | 1.66301i | 0.0778716 | − | 0.119091i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.69905 | + | 0.991158i | 0.263546 | + | 0.0706171i | 0.388173 | − | 0.921587i | \(-0.373106\pi\) |
−0.124626 | + | 0.992204i | \(0.539773\pi\) | |||||||
\(198\) | 1.02805 | − | 1.78063i | 0.0730603 | − | 0.126544i | ||||
\(199\) | 5.25409 | + | 9.10036i | 0.372453 | + | 0.645107i | 0.989942 | − | 0.141472i | \(-0.0451835\pi\) |
−0.617489 | + | 0.786579i | \(0.711850\pi\) | |||||||
\(200\) | 1.38258 | + | 5.15987i | 0.0977634 | + | 0.364858i | ||||
\(201\) | 5.33638 | + | 5.33638i | 0.376400 | + | 0.376400i | ||||
\(202\) | −0.0829059 | − | 0.309409i | −0.00583324 | − | 0.0217700i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.61832 | − | 7.99917i | 0.323347 | − | 0.560054i | ||||
\(205\) | 3.09794 | + | 1.78860i | 0.216370 | + | 0.124921i | ||||
\(206\) | −0.0872861 | + | 0.0872861i | −0.00608151 | + | 0.00608151i | ||||
\(207\) | −14.0081 | − | 8.08761i | −0.973633 | − | 0.562128i | ||||
\(208\) | −8.43540 | − | 9.42785i | −0.584889 | − | 0.653704i | ||||
\(209\) | − | 11.8014i | − | 0.816319i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.87722 | − | 6.71554i | −0.266919 | − | 0.462317i | 0.701146 | − | 0.713018i | \(-0.252672\pi\) |
−0.968065 | + | 0.250701i | \(0.919339\pi\) | |||||||
\(212\) | − | 1.96502i | − | 0.134958i | ||||||
\(213\) | 7.81789 | − | 2.09480i | 0.535673 | − | 0.143533i | ||||
\(214\) | −1.39626 | − | 0.374126i | −0.0954463 | − | 0.0255748i | ||||
\(215\) | −1.93860 | + | 1.93860i | −0.132211 | + | 0.132211i | ||||
\(216\) | 4.13785 | − | 4.13785i | 0.281545 | − | 0.281545i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.211919 | + | 0.122352i | −0.0143530 | + | 0.00828669i | ||||
\(219\) | 12.7345 | − | 3.41220i | 0.860519 | − | 0.230575i | ||||
\(220\) | 1.89709 | − | 3.28586i | 0.127902 | − | 0.221533i | ||||
\(221\) | 15.9527 | − | 3.33849i | 1.07309 | − | 0.224571i | ||||
\(222\) | 0.0487172 | − | 0.0281269i | 0.00326968 | − | 0.00188775i | ||||
\(223\) | −6.07469 | + | 22.6710i | −0.406791 | + | 1.51817i | 0.393937 | + | 0.919138i | \(0.371113\pi\) |
−0.800728 | + | 0.599028i | \(0.795554\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.63897 | + | 4.41036i | 0.509265 | + | 0.294024i | ||||
\(226\) | 1.36326 | + | 0.365284i | 0.0906825 | + | 0.0242983i | ||||
\(227\) | −1.59493 | + | 5.95236i | −0.105859 | + | 0.395072i | −0.998441 | − | 0.0558131i | \(-0.982225\pi\) |
0.892582 | + | 0.450885i | \(0.148892\pi\) | |||||||
\(228\) | 1.63027 | − | 6.08426i | 0.107968 | − | 0.402940i | ||||
\(229\) | 11.0005 | + | 2.94756i | 0.726931 | + | 0.194780i | 0.603262 | − | 0.797543i | \(-0.293867\pi\) |
0.123669 | + | 0.992324i | \(0.460534\pi\) | |||||||
\(230\) | 1.11973 | + | 0.646475i | 0.0738326 | + | 0.0426273i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.740385 | + | 2.76315i | −0.0486086 | + | 0.181410i | ||||
\(233\) | −12.9075 | + | 7.45218i | −0.845602 | + | 0.488208i | −0.859164 | − | 0.511700i | \(-0.829016\pi\) |
0.0135628 | + | 0.999908i | \(0.495683\pi\) | |||||||
\(234\) | 1.93345 | + | 0.107420i | 0.126393 | + | 0.00702224i | ||||
\(235\) | 2.41749 | − | 4.18721i | 0.157700 | − | 0.273144i | ||||
\(236\) | −0.964876 | + | 0.258538i | −0.0628081 | + | 0.0168294i | ||||
\(237\) | 6.97516 | − | 4.02711i | 0.453085 | − | 0.261589i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.4619 | − | 20.4619i | 1.32357 | − | 1.32357i | 0.412706 | − | 0.910864i | \(-0.364584\pi\) |
0.910864 | − | 0.412706i | \(-0.135416\pi\) | |||||||
\(240\) | 1.36726 | − | 1.36726i | 0.0882560 | − | 0.0882560i | ||||
\(241\) | −17.7659 | − | 4.76037i | −1.14440 | − | 0.306642i | −0.363684 | − | 0.931522i | \(-0.618481\pi\) |
−0.780721 | + | 0.624880i | \(0.785148\pi\) | |||||||
\(242\) | −1.01774 | + | 0.272704i | −0.0654230 | + | 0.0175301i | ||||
\(243\) | − | 15.6227i | − | 1.00220i | ||||||
\(244\) | −8.18205 | − | 14.1717i | −0.523802 | − | 0.907252i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 2.12530i | − | 0.135504i | ||||||
\(247\) | 9.91891 | − | 5.01475i | 0.631125 | − | 0.319081i | ||||
\(248\) | −1.02197 | − | 0.590035i | −0.0648952 | − | 0.0374672i | ||||
\(249\) | 6.85213 | − | 6.85213i | 0.434236 | − | 0.434236i | ||||
\(250\) | −1.25571 | − | 0.724986i | −0.0794182 | − | 0.0458521i | ||||
\(251\) | 3.43367 | − | 5.94730i | 0.216731 | − | 0.375390i | −0.737075 | − | 0.675811i | \(-0.763794\pi\) |
0.953807 | + | 0.300421i | \(0.0971271\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.59937 | + | 32.0933i | 0.540638 | + | 2.01769i | ||||
\(254\) | −0.707412 | − | 0.707412i | −0.0443870 | − | 0.0443870i | ||||
\(255\) | 0.644744 | + | 2.40622i | 0.0403754 | + | 0.150683i | ||||
\(256\) | −4.88140 | − | 8.45483i | −0.305087 | − | 0.528427i | ||||
\(257\) | −4.16483 | + | 7.21370i | −0.259795 | + | 0.449978i | −0.966187 | − | 0.257843i | \(-0.916988\pi\) |
0.706392 | + | 0.707821i | \(0.250322\pi\) | |||||||
\(258\) | 1.57334 | + | 0.421576i | 0.0979521 | + | 0.0262462i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.56785 | + | 0.198225i | 0.221269 | + | 0.0122934i | ||||
\(261\) | 2.36179 | + | 4.09073i | 0.146191 | + | 0.253210i | ||||
\(262\) | −3.53293 | − | 3.53293i | −0.218265 | − | 0.218265i | ||||
\(263\) | −2.70372 | −0.166719 | −0.0833593 | − | 0.996520i | \(-0.526565\pi\) | ||||
−0.0833593 | + | 0.996520i | \(0.526565\pi\) | |||||||
\(264\) | −4.60607 | −0.283484 | ||||||||
\(265\) | 0.374738 | + | 0.374738i | 0.0230200 | + | 0.0230200i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.4784 | − | 3.34358i | 0.763666 | − | 0.204624i | ||||
\(268\) | −3.51270 | + | 13.1096i | −0.214572 | + | 0.800794i | ||||
\(269\) | 20.2332 | − | 11.6816i | 1.23364 | − | 0.712242i | 0.265853 | − | 0.964014i | \(-0.414346\pi\) |
0.967787 | + | 0.251771i | \(0.0810130\pi\) | |||||||
\(270\) | 0.772380i | 0.0470055i | ||||||||
\(271\) | −3.44030 | − | 12.8394i | −0.208983 | − | 0.779936i | −0.988198 | − | 0.153179i | \(-0.951049\pi\) |
0.779215 | − | 0.626756i | \(-0.215618\pi\) | |||||||
\(272\) | 15.8603 | 0.961673 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.72207 | −0.164446 | ||||||||
\(275\) | −4.68944 | − | 17.5012i | −0.282784 | − | 1.05536i | ||||
\(276\) | 17.7338i | 1.06745i | ||||||||
\(277\) | 4.19252 | − | 2.42055i | 0.251904 | − | 0.145437i | −0.368732 | − | 0.929536i | \(-0.620208\pi\) |
0.620636 | + | 0.784099i | \(0.286875\pi\) | |||||||
\(278\) | −1.13268 | + | 4.22723i | −0.0679338 | + | 0.253532i | ||||
\(279\) | −1.88218 | + | 0.504328i | −0.112683 | + | 0.0301933i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.60836 | + | 8.60836i | 0.513532 | + | 0.513532i | 0.915607 | − | 0.402075i | \(-0.131711\pi\) |
−0.402075 | + | 0.915607i | \(0.631711\pi\) | |||||||
\(282\) | −2.87257 | −0.171059 | ||||||||
\(283\) | 1.05573 | 0.0627569 | 0.0313784 | − | 0.999508i | \(-0.490010\pi\) | ||||
0.0313784 | + | 0.999508i | \(0.490010\pi\) | |||||||
\(284\) | 10.2923 | + | 10.2923i | 0.610736 | + | 0.610736i | ||||
\(285\) | 0.849397 | + | 1.47120i | 0.0503140 | + | 0.0871463i | ||||
\(286\) | −2.65224 | − | 2.96428i | −0.156830 | − | 0.175282i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.88418 | + | 1.57666i | 0.346729 | + | 0.0929056i | ||||
\(289\) | −1.71664 | + | 2.97331i | −0.100979 | + | 0.174900i | ||||
\(290\) | −0.188787 | − | 0.326989i | −0.0110860 | − | 0.0192014i | ||||
\(291\) | 3.76889 | + | 14.0657i | 0.220936 | + | 0.824544i | ||||
\(292\) | 16.7651 | + | 16.7651i | 0.981102 | + | 0.981102i | ||||
\(293\) | −5.31237 | − | 19.8260i | −0.310352 | − | 1.15825i | −0.928240 | − | 0.371983i | \(-0.878678\pi\) |
0.617888 | − | 0.786266i | \(-0.287989\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.134702 | − | 0.233311i | 0.00784266 | − | 0.0135839i | ||||
\(296\) | 0.179019 | + | 0.103357i | 0.0104053 | + | 0.00600749i | ||||
\(297\) | −14.0348 | + | 14.0348i | −0.814379 | + | 0.814379i | ||||
\(298\) | −3.58498 | − | 2.06979i | −0.207672 | − | 0.119900i | ||||
\(299\) | −23.3198 | + | 20.8650i | −1.34862 | + | 1.20665i | ||||
\(300\) | − | 9.67064i | − | 0.558335i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.715189 | − | 1.23874i | −0.0411545 | − | 0.0712817i | ||||
\(303\) | 1.18491i | 0.0680714i | ||||||||
\(304\) | 10.4473 | − | 2.79936i | 0.599196 | − | 0.160554i | ||||
\(305\) | 4.26297 | + | 1.14226i | 0.244097 | + | 0.0654056i | ||||
\(306\) | −1.71666 | + | 1.71666i | −0.0981347 | + | 0.0981347i | ||||
\(307\) | 7.23927 | − | 7.23927i | 0.413167 | − | 0.413167i | −0.469673 | − | 0.882840i | \(-0.655628\pi\) |
0.882840 | + | 0.469673i | \(0.155628\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.395446 | − | 0.228311i | 0.0224961 | − | 0.0129881i | ||||
\(310\) | 0.150450 | − | 0.0403130i | 0.00854499 | − | 0.00228962i | ||||
\(311\) | 4.86207 | − | 8.42134i | 0.275702 | − | 0.477531i | −0.694610 | − | 0.719387i | \(-0.744423\pi\) |
0.970312 | + | 0.241856i | \(0.0777562\pi\) | |||||||
\(312\) | −1.95725 | − | 3.87134i | −0.110808 | − | 0.219172i | ||||
\(313\) | −14.4470 | + | 8.34100i | −0.816595 | + | 0.471461i | −0.849241 | − | 0.528006i | \(-0.822940\pi\) |
0.0326459 | + | 0.999467i | \(0.489607\pi\) | |||||||
\(314\) | 0.260429 | − | 0.971933i | 0.0146968 | − | 0.0548494i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.5440 | + | 7.24228i | 0.705655 | + | 0.407410i | ||||
\(317\) | −10.2940 | − | 2.75827i | −0.578170 | − | 0.154920i | −0.0421288 | − | 0.999112i | \(-0.513414\pi\) |
−0.536041 | + | 0.844192i | \(0.680081\pi\) | |||||||
\(318\) | 0.0814921 | − | 0.304133i | 0.00456985 | − | 0.0170549i | ||||
\(319\) | 2.51123 | − | 9.37205i | 0.140602 | − | 0.524734i | ||||
\(320\) | 3.03400 | + | 0.812958i | 0.169606 | + | 0.0454457i | ||||
\(321\) | 4.63073 | + | 2.67355i | 0.258462 | + | 0.149223i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.60649 | + | 13.4596i | −0.200670 | + | 0.748911i | ||||
\(324\) | 0.107910 | − | 0.0623018i | 0.00599499 | − | 0.00346121i | ||||
\(325\) | 12.7169 | − | 11.3782i | 0.705404 | − | 0.631147i | ||||
\(326\) | −0.330790 | + | 0.572944i | −0.0183207 | + | 0.0317325i | ||||
\(327\) | 0.874339 | − | 0.234278i | 0.0483510 | − | 0.0129556i | ||||
\(328\) | 6.76344 | − | 3.90488i | 0.373449 | − | 0.215611i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.429889 | − | 0.429889i | 0.0236646 | − | 0.0236646i | ||||
\(331\) | 24.2449 | − | 24.2449i | 1.33262 | − | 1.33262i | 0.429598 | − | 0.903020i | \(-0.358655\pi\) |
0.903020 | − | 0.429598i | \(-0.141345\pi\) | |||||||
\(332\) | 16.8332 | + | 4.51044i | 0.923842 | + | 0.247543i | ||||
\(333\) | 0.329703 | − | 0.0883435i | 0.0180676 | − | 0.00484120i | ||||
\(334\) | − | 6.04251i | − | 0.330631i | ||||||
\(335\) | −1.83017 | − | 3.16994i | −0.0999927 | − | 0.173192i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 32.8040i | − | 1.78695i | −0.449117 | − | 0.893473i | \(-0.648261\pi\) | ||
0.449117 | − | 0.893473i | \(-0.351739\pi\) | |||||||
\(338\) | 1.36443 | − | 3.48878i | 0.0742151 | − | 0.189764i | ||||
\(339\) | −4.52128 | − | 2.61036i | −0.245562 | − | 0.141775i | ||||
\(340\) | −3.16780 | + | 3.16780i | −0.171798 | + | 0.171798i | ||||
\(341\) | 3.46631 | + | 2.00128i | 0.187711 | + | 0.108375i | ||||
\(342\) | −0.827787 | + | 1.43377i | −0.0447616 | + | 0.0775293i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.54915 | + | 5.78151i | 0.0835247 | + | 0.311718i | ||||
\(345\) | −3.38192 | − | 3.38192i | −0.182076 | − | 0.182076i | ||||
\(346\) | 1.49816 | + | 5.59121i | 0.0805416 | + | 0.300585i | ||||
\(347\) | −4.53276 | − | 7.85096i | −0.243331 | − | 0.421462i | 0.718330 | − | 0.695703i | \(-0.244907\pi\) |
−0.961661 | + | 0.274241i | \(0.911573\pi\) | |||||||
\(348\) | 2.58936 | − | 4.48490i | 0.138804 | − | 0.240416i | ||||
\(349\) | −27.6016 | − | 7.39582i | −1.47748 | − | 0.395889i | −0.571990 | − | 0.820261i | \(-0.693828\pi\) |
−0.905488 | + | 0.424372i | \(0.860495\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.7598 | − | 5.83225i | −0.947947 | − | 0.311303i | ||||
\(352\) | −6.25651 | − | 10.8366i | −0.333473 | − | 0.577593i | ||||
\(353\) | 14.2152 | + | 14.2152i | 0.756599 | + | 0.756599i | 0.975702 | − | 0.219103i | \(-0.0703129\pi\) |
−0.219103 | + | 0.975702i | \(0.570313\pi\) | |||||||
\(354\) | −0.160059 | −0.00850706 | ||||||||
\(355\) | −3.92559 | −0.208348 | ||||||||
\(356\) | 16.4279 | + | 16.4279i | 0.870678 | + | 0.870678i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.96438 | + | 1.59815i | −0.315227 | + | 0.0844649i | ||||
\(359\) | 7.98274 | − | 29.7920i | 0.421313 | − | 1.57236i | −0.350532 | − | 0.936551i | \(-0.613999\pi\) |
0.771845 | − | 0.635811i | \(-0.219334\pi\) | |||||||
\(360\) | −0.941889 | + | 0.543800i | −0.0496419 | + | 0.0286608i | ||||
\(361\) | − | 9.49750i | − | 0.499868i | ||||||
\(362\) | 1.47322 | + | 5.49814i | 0.0774309 | + | 0.288976i | ||||
\(363\) | 3.89754 | 0.204568 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.39436 | −0.334696 | ||||||||
\(366\) | −0.678643 | − | 2.53273i | −0.0354733 | − | 0.132388i | ||||
\(367\) | − | 5.30610i | − | 0.276976i | −0.990364 | − | 0.138488i | \(-0.955776\pi\) | ||
0.990364 | − | 0.138488i | \(-0.0442243\pi\) | |||||||
\(368\) | −26.3712 | + | 15.2254i | −1.37469 | + | 0.793679i | ||||
\(369\) | 3.33766 | − | 12.4563i | 0.173752 | − | 0.648451i | ||||
\(370\) | −0.0263544 | + | 0.00706165i | −0.00137010 | + | 0.000367118i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.51061 | + | 1.51061i | 0.0783216 | + | 0.0783216i | ||||
\(373\) | −24.5661 | −1.27199 | −0.635993 | − | 0.771695i | \(-0.719409\pi\) | ||||
−0.635993 | + | 0.771695i | \(0.719409\pi\) | |||||||
\(374\) | 4.98676 | 0.257859 | ||||||||
\(375\) | 3.79263 | + | 3.79263i | 0.195851 | + | 0.195851i | ||||
\(376\) | −5.27788 | − | 9.14155i | −0.272186 | − | 0.471439i | ||||
\(377\) | 8.94417 | − | 1.87179i | 0.460648 | − | 0.0964022i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.0045 | + | 5.62815i | 1.07893 | + | 0.289099i | 0.754158 | − | 0.656693i | \(-0.228045\pi\) |
0.324773 | + | 0.945792i | \(0.394712\pi\) | |||||||
\(380\) | −1.52754 | + | 2.64578i | −0.0783612 | + | 0.135726i | ||||
\(381\) | 1.85035 | + | 3.20490i | 0.0947963 | + | 0.164192i | ||||
\(382\) | −0.320609 | − | 1.19653i | −0.0164038 | − | 0.0612198i | ||||
\(383\) | 8.30305 | + | 8.30305i | 0.424266 | + | 0.424266i | 0.886670 | − | 0.462403i | \(-0.153013\pi\) |
−0.462403 | + | 0.886670i | \(0.653013\pi\) | |||||||
\(384\) | −2.28645 | − | 8.53317i | −0.116680 | − | 0.435456i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.95282 | − | 3.38239i | 0.0993961 | − | 0.172159i | ||||
\(387\) | 8.55929 | + | 4.94171i | 0.435093 | + | 0.251201i | ||||
\(388\) | −18.5176 | + | 18.5176i | −0.940087 | + | 0.940087i | ||||
\(389\) | 30.3210 | + | 17.5058i | 1.53733 | + | 0.887580i | 0.998994 | + | 0.0448528i | \(0.0142819\pi\) |
0.538341 | + | 0.842727i | \(0.319051\pi\) | |||||||
\(390\) | 0.543988 | + | 0.178644i | 0.0275459 | + | 0.00904599i | ||||
\(391\) | − | 39.2306i | − | 1.98398i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.24095 | + | 16.0058i | 0.466144 | + | 0.807385i | ||||
\(394\) | 1.10352i | 0.0555947i | ||||||||
\(395\) | −3.77334 | + | 1.01106i | −0.189857 | + | 0.0508721i | ||||
\(396\) | −13.2119 | − | 3.54012i | −0.663924 | − | 0.177898i | ||||
\(397\) | −5.66198 | + | 5.66198i | −0.284167 | + | 0.284167i | −0.834768 | − | 0.550601i | \(-0.814398\pi\) |
0.550601 | + | 0.834768i | \(0.314398\pi\) | |||||||
\(398\) | −2.14116 | + | 2.14116i | −0.107326 | + | 0.107326i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 14.3808 | − | 8.30277i | 0.719041 | − | 0.415139i | ||||
\(401\) | −26.3860 | + | 7.07012i | −1.31766 | + | 0.353065i | −0.848099 | − | 0.529837i | \(-0.822253\pi\) |
−0.469557 | + | 0.882902i | \(0.655586\pi\) | |||||||
\(402\) | −1.08735 | + | 1.88334i | −0.0542319 | + | 0.0939323i | ||||
\(403\) | −0.209111 | + | 3.76379i | −0.0104166 | + | 0.187488i | ||||
\(404\) | −1.84543 | + | 1.06546i | −0.0918138 | + | 0.0530087i | ||||
\(405\) | −0.00869768 | + | 0.0324602i | −0.000432191 | + | 0.00161296i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.607197 | − | 0.350565i | −0.0300976 | − | 0.0173769i | ||||
\(408\) | 5.25326 | + | 1.40761i | 0.260075 | + | 0.0696870i | ||||
\(409\) | 1.48087 | − | 5.52667i | 0.0732242 | − | 0.273276i | −0.919601 | − | 0.392855i | \(-0.871488\pi\) |
0.992825 | + | 0.119578i | \(0.0381542\pi\) | |||||||
\(410\) | −0.266793 | + | 0.995685i | −0.0131760 | + | 0.0491734i | ||||
\(411\) | 9.72610 | + | 2.60610i | 0.479753 | + | 0.128549i | ||||
\(412\) | 0.711163 | + | 0.410590i | 0.0350365 | + | 0.0202283i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.20637 | − | 4.50225i | 0.0592900 | − | 0.221273i | ||||
\(415\) | −4.07033 | + | 2.35001i | −0.199805 | + | 0.115357i | ||||
\(416\) | 6.44944 | − | 9.86329i | 0.316210 | − | 0.483588i | ||||
\(417\) | 8.09428 | − | 14.0197i | 0.396379 | − | 0.686548i | ||||
\(418\) | 3.28483 | − | 0.880167i | 0.160666 | − | 0.0430504i | ||||
\(419\) | −13.3221 | + | 7.69152i | −0.650828 | + | 0.375755i | −0.788773 | − | 0.614684i | \(-0.789283\pi\) |
0.137946 | + | 0.990440i | \(0.455950\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.76255 | − | 4.76255i | 0.232112 | − | 0.232112i | −0.581462 | − | 0.813574i | \(-0.697519\pi\) |
0.813574 | + | 0.581462i | \(0.197519\pi\) | |||||||
\(422\) | 1.58005 | − | 1.58005i | 0.0769156 | − | 0.0769156i | ||||
\(423\) | −16.8361 | − | 4.51123i | −0.818601 | − | 0.219343i | ||||
\(424\) | 1.11759 | − | 0.299456i | 0.0542748 | − | 0.0145429i | ||||
\(425\) | 21.3934i | 1.03773i | ||||||||
\(426\) | 1.16614 | + | 2.01982i | 0.0564997 | + | 0.0978604i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 9.61614i | 0.464814i | ||||||||
\(429\) | 6.63859 | + | 13.1308i | 0.320514 | + | 0.633961i | ||||
\(430\) | −0.684178 | − | 0.395010i | −0.0329940 | − | 0.0190491i | ||||
\(431\) | 11.9340 | − | 11.9340i | 0.574839 | − | 0.574839i | −0.358638 | − | 0.933477i | \(-0.616759\pi\) |
0.933477 | + | 0.358638i | \(0.116759\pi\) | |||||||
\(432\) | −15.7536 | − | 9.09533i | −0.757944 | − | 0.437599i | ||||
\(433\) | −4.63490 | + | 8.02787i | −0.222739 | + | 0.385795i | −0.955639 | − | 0.294542i | \(-0.904833\pi\) |
0.732900 | + | 0.680337i | \(0.238166\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.361488 | + | 1.34909i | 0.0173320 | + | 0.0646841i | ||||
\(436\) | 1.15107 | + | 1.15107i | 0.0551264 | + | 0.0551264i | ||||
\(437\) | −6.92422 | − | 25.8416i | −0.331231 | − | 1.23617i | ||||
\(438\) | 1.89952 | + | 3.29007i | 0.0907626 | + | 0.157205i | ||||
\(439\) | 8.70664 | − | 15.0803i | 0.415545 | − | 0.719745i | −0.579940 | − | 0.814659i | \(-0.696924\pi\) |
0.995486 | + | 0.0949136i | \(0.0302575\pi\) | |||||||
\(440\) | 2.15791 | + | 0.578210i | 0.102874 | + | 0.0275651i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.11902 | + | 4.19131i | 0.100791 | + | 0.199360i | ||||
\(443\) | −5.09769 | − | 8.82945i | −0.242198 | − | 0.419500i | 0.719142 | − | 0.694863i | \(-0.244535\pi\) |
−0.961340 | + | 0.275363i | \(0.911202\pi\) | |||||||
\(444\) | −0.264615 | − | 0.264615i | −0.0125581 | − | 0.0125581i | ||||
\(445\) | −6.26577 | −0.297026 | ||||||||
\(446\) | −6.76337 | −0.320255 | ||||||||
\(447\) | 10.8277 | + | 10.8277i | 0.512133 | + | 0.512133i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.5974 | + | 4.71520i | −0.830471 | + | 0.222524i | −0.648919 | − | 0.760857i | \(-0.724779\pi\) |
−0.181552 | + | 0.983381i | \(0.558112\pi\) | |||||||
\(450\) | −0.657863 | + | 2.45518i | −0.0310120 | + | 0.115738i | ||||
\(451\) | −22.9402 | + | 13.2445i | −1.08021 | + | 0.623661i | ||||
\(452\) | − | 9.38885i | − | 0.441615i | ||||||
\(453\) | 1.36944 | + | 5.11083i | 0.0643420 | + | 0.240128i | ||||
\(454\) | −1.77575 | −0.0833399 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.70882 | 0.173681 | ||||||||
\(457\) | 8.73128 | + | 32.5856i | 0.408432 | + | 1.52429i | 0.797637 | + | 0.603138i | \(0.206083\pi\) |
−0.389204 | + | 0.921151i | \(0.627250\pi\) | |||||||
\(458\) | 3.28173i | 0.153345i | ||||||||
\(459\) | 20.2957 | − | 11.7178i | 0.947324 | − | 0.546938i | ||||
\(460\) | 2.22616 | − | 8.30814i | 0.103795 | − | 0.387369i | ||||
\(461\) | −10.9633 | + | 2.93760i | −0.510611 | + | 0.136818i | −0.504920 | − | 0.863166i | \(-0.668478\pi\) |
−0.00569051 | + | 0.999984i | \(0.501811\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.05208 | − | 4.05208i | −0.188316 | − | 0.188316i | 0.606652 | − | 0.794968i | \(-0.292512\pi\) |
−0.794968 | + | 0.606652i | \(0.792512\pi\) | |||||||
\(464\) | 8.89241 | 0.412820 | ||||||||
\(465\) | −0.576162 | −0.0267189 | ||||||||
\(466\) | −3.03692 | − | 3.03692i | −0.140683 | − | 0.140683i | ||||
\(467\) | −18.1856 | − | 31.4984i | −0.841529 | − | 1.45757i | −0.888602 | − | 0.458680i | \(-0.848322\pi\) |
0.0470722 | − | 0.998891i | \(-0.485011\pi\) | |||||||
\(468\) | −2.63870 | − | 12.6087i | −0.121974 | − | 0.582839i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.34578 | + | 0.360600i | 0.0620762 | + | 0.0166333i | ||||
\(471\) | −1.86105 | + | 3.22344i | −0.0857528 | + | 0.148528i | ||||
\(472\) | −0.294082 | − | 0.509365i | −0.0135362 | − | 0.0234454i | ||||
\(473\) | −5.25440 | − | 19.6097i | −0.241598 | − | 0.901655i | ||||
\(474\) | 1.64113 | + | 1.64113i | 0.0753797 | + | 0.0753797i | ||||
\(475\) | 3.77594 | + | 14.0920i | 0.173252 | + | 0.646585i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.955249 | − | 1.65454i | 0.0437379 | − | 0.0757562i | ||||
\(478\) | 7.22149 | + | 4.16933i | 0.330303 | + | 0.190701i | ||||
\(479\) | 17.1877 | − | 17.1877i | 0.785327 | − | 0.785327i | −0.195397 | − | 0.980724i | \(-0.562600\pi\) |
0.980724 | + | 0.195397i | \(0.0625997\pi\) | |||||||
\(480\) | 1.55991 | + | 0.900617i | 0.0712000 | + | 0.0411073i | ||||
\(481\) | 0.0366301 | − | 0.659306i | 0.00167019 | − | 0.0300618i | ||||
\(482\) | − | 5.30005i | − | 0.241411i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.50464 | + | 6.07021i | 0.159302 | + | 0.275919i | ||||
\(485\) | − | 7.06278i | − | 0.320704i | ||||||
\(486\) | 4.34847 | − | 1.16517i | 0.197250 | − | 0.0528531i | ||||
\(487\) | −25.7327 | − | 6.89506i | −1.16606 | − | 0.312445i | −0.376677 | − | 0.926345i | \(-0.622933\pi\) |
−0.789384 | + | 0.613899i | \(0.789600\pi\) | |||||||
\(488\) | 6.81315 | − | 6.81315i | 0.308417 | − | 0.308417i | ||||
\(489\) | 1.73047 | − | 1.73047i | 0.0782544 | − | 0.0782544i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.2520 | + | 8.80574i | −0.688313 | + | 0.397398i | −0.802980 | − | 0.596006i | \(-0.796753\pi\) |
0.114667 | + | 0.993404i | \(0.463420\pi\) | |||||||
\(492\) | −13.6566 | + | 3.65927i | −0.615686 | + | 0.164972i | ||||
\(493\) | −5.72816 | + | 9.92147i | −0.257983 | + | 0.446840i | ||||
\(494\) | 2.13558 | + | 2.38684i | 0.0960845 | + | 0.107389i | ||||
\(495\) | 3.19469 | − | 1.84446i | 0.143591 | − | 0.0829022i | ||||
\(496\) | −0.949428 | + | 3.54331i | −0.0426306 | + | 0.159099i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.41828 | + | 1.39620i | 0.108366 | + | 0.0625650i | ||||
\(499\) | 14.6796 | + | 3.93339i | 0.657149 | + | 0.176083i | 0.571959 | − | 0.820282i | \(-0.306184\pi\) |
0.0851901 | + | 0.996365i | \(0.472850\pi\) | |||||||
\(500\) | −2.49651 | + | 9.31712i | −0.111648 | + | 0.416674i | ||||
\(501\) | −5.78508 | + | 21.5902i | −0.258459 | + | 0.964580i | ||||
\(502\) | 1.91147 | + | 0.512177i | 0.0853132 | + | 0.0228596i | ||||
\(503\) | 3.91743 | + | 2.26173i | 0.174669 | + | 0.100845i | 0.584786 | − | 0.811188i | \(-0.301179\pi\) |
−0.410116 | + | 0.912033i | \(0.634512\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.148744 | − | 0.555122i | 0.00661904 | − | 0.0247026i | ||||
\(506\) | −8.29156 | + | 4.78713i | −0.368605 | + | 0.212814i | ||||
\(507\) | −8.21533 | + | 11.1593i | −0.364856 | + | 0.495602i | ||||
\(508\) | −3.32764 | + | 5.76364i | −0.147640 | + | 0.255720i | ||||
\(509\) | 37.1230 | − | 9.94708i | 1.64545 | − | 0.440897i | 0.687115 | − | 0.726548i | \(-0.258877\pi\) |
0.958334 | + | 0.285652i | \(0.0922100\pi\) | |||||||
\(510\) | −0.621666 | + | 0.358919i | −0.0275278 | + | 0.0158932i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 13.7099 | − | 13.7099i | 0.605896 | − | 0.605896i | ||||
\(513\) | 11.3008 | − | 11.3008i | 0.498943 | − | 0.498943i | ||||
\(514\) | −2.31850 | − | 0.621239i | −0.102265 | − | 0.0274017i | ||||
\(515\) | −0.213924 | + | 0.0573207i | −0.00942660 | + | 0.00252585i | ||||
\(516\) | − | 10.8357i | − | 0.477017i | ||||||
\(517\) | 17.9015 | + | 31.0063i | 0.787306 | + | 1.36365i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 21.4121i | − | 0.939885i | ||||||
\(520\) | 0.430979 | + | 2.05939i | 0.0188997 | + | 0.0903103i | ||||
\(521\) | −31.7542 | − | 18.3333i | −1.39117 | − | 0.803195i | −0.397729 | − | 0.917503i | \(-0.630202\pi\) |
−0.993445 | + | 0.114308i | \(0.963535\pi\) | |||||||
\(522\) | −0.962478 | + | 0.962478i | −0.0421265 | + | 0.0421265i | ||||
\(523\) | −9.11850 | − | 5.26457i | −0.398724 | − | 0.230203i | 0.287209 | − | 0.957868i | \(-0.407272\pi\) |
−0.685933 | + | 0.727664i | \(0.740606\pi\) | |||||||
\(524\) | −16.6188 | + | 28.7845i | −0.725994 | + | 1.25746i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.201648 | − | 0.752560i | −0.00879226 | − | 0.0328132i | ||||
\(527\) | −3.34177 | − | 3.34177i | −0.145570 | − | 0.145570i | ||||
\(528\) | 3.70583 | + | 13.8303i | 0.161275 | + | 0.601888i | ||||
\(529\) | 26.1601 | + | 45.3107i | 1.13740 | + | 1.97003i | ||||
\(530\) | −0.0763569 | + | 0.132254i | −0.00331673 | + | 0.00574475i | ||||
\(531\) | −0.938106 | − | 0.251365i | −0.0407103 | − | 0.0109083i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20.8798 | − | 13.6530i | −0.904404 | − | 0.591375i | ||||
\(534\) | 1.86132 | + | 3.22390i | 0.0805472 | + | 0.139512i | ||||
\(535\) | −1.83384 | − | 1.83384i | −0.0792839 | − | 0.0792839i | ||||
\(536\) | −7.99126 | −0.345170 | ||||||||
\(537\) | 22.8411 | 0.985668 | ||||||||
\(538\) | 4.76052 | + | 4.76052i | 0.205241 | + | 0.205241i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.96310 | − | 1.32986i | 0.213578 | − | 0.0572280i | ||||
\(541\) | 3.17473 | − | 11.8482i | 0.136492 | − | 0.509396i | −0.863495 | − | 0.504357i | \(-0.831729\pi\) |
0.999987 | − | 0.00503858i | \(-0.00160384\pi\) | |||||||
\(542\) | 3.31715 | − | 1.91516i | 0.142484 | − | 0.0822632i | ||||
\(543\) | − | 21.0556i | − | 0.903584i | ||||||
\(544\) | 3.82396 | + | 14.2712i | 0.163951 | + | 0.611873i | ||||
\(545\) | −0.439030 | −0.0188060 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −46.5673 | −1.99108 | −0.995538 | − | 0.0943609i | \(-0.969919\pi\) | ||||
−0.995538 | + | 0.0943609i | \(0.969919\pi\) | |||||||
\(548\) | 4.68677 | + | 17.4912i | 0.200209 | + | 0.747189i | ||||
\(549\) | − | 15.9101i | − | 0.679026i | ||||||
\(550\) | 4.52158 | − | 2.61054i | 0.192801 | − | 0.111314i | ||||
\(551\) | −2.02205 | + | 7.54639i | −0.0861421 | + | 0.321487i | ||||
\(552\) | −10.0859 | + | 2.70252i | −0.429286 | + | 0.115027i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.986426 | + | 0.986426i | 0.0419092 | + | 0.0419092i | ||||
\(555\) | 0.100927 | 0.00428410 | ||||||||
\(556\) | 29.1132 | 1.23468 | ||||||||
\(557\) | −13.2888 | − | 13.2888i | −0.563066 | − | 0.563066i | 0.367111 | − | 0.930177i | \(-0.380347\pi\) |
−0.930177 | + | 0.367111i | \(0.880347\pi\) | |||||||
\(558\) | −0.280752 | − | 0.486276i | −0.0118852 | − | 0.0205857i | ||||
\(559\) | 14.2489 | − | 12.7490i | 0.602666 | − | 0.539224i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.8180 | − | 4.77432i | −0.752276 | − | 0.201572i | ||||
\(562\) | −1.75404 | + | 3.03809i | −0.0739899 | + | 0.128154i | ||||
\(563\) | 9.35345 | + | 16.2007i | 0.394201 | + | 0.682776i | 0.992999 | − | 0.118124i | \(-0.0376881\pi\) |
−0.598798 | + | 0.800900i | \(0.704355\pi\) | |||||||
\(564\) | 4.94591 | + | 18.4584i | 0.208260 | + | 0.777238i | ||||
\(565\) | 1.79050 | + | 1.79050i | 0.0753269 | + | 0.0753269i | ||||
\(566\) | 0.0787383 | + | 0.293855i | 0.00330962 | + | 0.0123517i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.28518 | + | 7.42215i | −0.179802 | + | 0.311426i | ||||
\(569\) | 5.84529 | + | 3.37478i | 0.245047 | + | 0.141478i | 0.617494 | − | 0.786575i | \(-0.288148\pi\) |
−0.372447 | + | 0.928053i | \(0.621481\pi\) | |||||||
\(570\) | −0.346148 | + | 0.346148i | −0.0144985 | + | 0.0144985i | ||||
\(571\) | −5.33385 | − | 3.07950i | −0.223215 | − | 0.128873i | 0.384223 | − | 0.923240i | \(-0.374469\pi\) |
−0.607438 | + | 0.794367i | \(0.707803\pi\) | |||||||
\(572\) | −14.4811 | + | 22.1463i | −0.605486 | + | 0.925985i | ||||
\(573\) | 4.58222i | 0.191425i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20.5369 | − | 35.5710i | −0.856450 | − | 1.48341i | ||||
\(576\) | − | 11.3234i | − | 0.471807i | ||||||
\(577\) | 19.5588 | − | 5.24075i | 0.814242 | − | 0.218175i | 0.172414 | − | 0.985025i | \(-0.444843\pi\) |
0.641827 | + | 0.766849i | \(0.278177\pi\) | |||||||
\(578\) | −0.955626 | − | 0.256059i | −0.0397488 | − | 0.0106507i | ||||
\(579\) | −10.2158 | + | 10.2158i | −0.424556 | + | 0.424556i | ||||
\(580\) | −1.77609 | + | 1.77609i | −0.0737482 | + | 0.0737482i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3.63398 | + | 2.09808i | −0.150633 | + | 0.0869682i | ||||
\(583\) | −3.79062 | + | 1.01569i | −0.156992 | + | 0.0420658i | ||||
\(584\) | −6.98010 | + | 12.0899i | −0.288839 | + | 0.500283i | ||||
\(585\) | 2.90776 | + | 1.90134i | 0.120221 | + | 0.0786105i | ||||
\(586\) | 5.12222 | − | 2.95731i | 0.211597 | − | 0.122165i | ||||
\(587\) | 3.35452 | − | 12.5192i | 0.138456 | − | 0.516725i | −0.861504 | − | 0.507751i | \(-0.830477\pi\) |
0.999960 | − | 0.00897355i | \(-0.00285641\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.79108 | − | 1.61143i | −0.115004 | − | 0.0663979i | ||||
\(590\) | 0.0749865 | + | 0.0200926i | 0.00308715 | + | 0.000827199i | ||||
\(591\) | 1.05651 | − | 3.94296i | 0.0434591 | − | 0.162192i | ||||
\(592\) | 0.166312 | − | 0.620685i | 0.00683538 | − | 0.0255100i | ||||
\(593\) | 2.52797 | + | 0.677366i | 0.103811 | + | 0.0278161i | 0.310351 | − | 0.950622i | \(-0.399554\pi\) |
−0.206540 | + | 0.978438i | \(0.566220\pi\) | |||||||
\(594\) | −4.95320 | − | 2.85973i | −0.203232 | − | 0.117336i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.12739 | + | 26.5998i | −0.291949 | + | 1.08957i | ||||
\(597\) | 9.70041 | − | 5.60053i | 0.397011 | − | 0.229215i | ||||
\(598\) | −7.54684 | − | 4.93475i | −0.308613 | − | 0.201797i | ||||
\(599\) | −11.8359 | + | 20.5003i | −0.483600 | + | 0.837620i | −0.999823 | − | 0.0188345i | \(-0.994004\pi\) |
0.516222 | + | 0.856455i | \(0.327338\pi\) | |||||||
\(600\) | 5.50010 | − | 1.47375i | 0.224540 | − | 0.0601654i | ||||
\(601\) | −39.8779 | + | 23.0235i | −1.62665 | + | 0.939149i | −0.641573 | + | 0.767062i | \(0.721718\pi\) |
−0.985082 | + | 0.172087i | \(0.944949\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.33060 | + | 9.33060i | −0.379971 | + | 0.379971i | ||||
\(604\) | −6.72844 | + | 6.72844i | −0.273776 | + | 0.273776i | ||||
\(605\) | −1.82597 | − | 0.489267i | −0.0742362 | − | 0.0198915i | ||||
\(606\) | −0.329811 | + | 0.0883725i | −0.0133976 | + | 0.00358989i | ||||
\(607\) | 8.41264i | 0.341458i | 0.985318 | + | 0.170729i | \(0.0546123\pi\) | ||||
−0.985318 | + | 0.170729i | \(0.945388\pi\) | |||||||
\(608\) | 5.03775 | + | 8.72564i | 0.204308 | + | 0.353872i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.27176i | 0.0514919i | ||||||||
\(611\) | −18.4535 | + | 28.2214i | −0.746548 | + | 1.14171i | ||||
\(612\) | 13.9865 | + | 8.07508i | 0.565369 | + | 0.326416i | ||||
\(613\) | −14.9915 | + | 14.9915i | −0.605502 | + | 0.605502i | −0.941767 | − | 0.336265i | \(-0.890836\pi\) |
0.336265 | + | 0.941767i | \(0.390836\pi\) | |||||||
\(614\) | 2.55491 | + | 1.47508i | 0.103108 | + | 0.0595293i | ||||
\(615\) | 1.90653 | − | 3.30221i | 0.0768788 | − | 0.133158i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.51730 | + | 28.0549i | 0.302635 | + | 1.12945i | 0.934962 | + | 0.354748i | \(0.115433\pi\) |
−0.632327 | + | 0.774702i | \(0.717900\pi\) | |||||||
\(618\) | 0.0930415 | + | 0.0930415i | 0.00374268 | + | 0.00374268i | ||||
\(619\) | −6.66289 | − | 24.8662i | −0.267804 | − | 0.999458i | −0.960512 | − | 0.278240i | \(-0.910249\pi\) |
0.692708 | − | 0.721218i | \(-0.256418\pi\) | |||||||
\(620\) | −0.518080 | − | 0.897341i | −0.0208066 | − | 0.0360381i | ||||
\(621\) | −22.4973 | + | 38.9665i | −0.902787 | + | 1.56367i | ||||
\(622\) | 2.70664 | + | 0.725241i | 0.108526 | + | 0.0290795i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −10.0495 | + | 8.99160i | −0.402302 | + | 0.359952i | ||||
\(625\) | 10.5311 | + | 18.2403i | 0.421242 | + | 0.729613i | ||||
\(626\) | −3.39914 | − | 3.39914i | −0.135857 | − | 0.135857i | ||||
\(627\) | −12.5795 | −0.502379 | ||||||||
\(628\) | −6.69377 | −0.267111 | ||||||||
\(629\) | 0.585381 | + | 0.585381i | 0.0233407 | + | 0.0233407i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.24248 | − | 1.13677i | 0.168891 | − | 0.0452541i | −0.173383 | − | 0.984855i | \(-0.555470\pi\) |
0.342273 | + | 0.939600i | \(0.388803\pi\) | |||||||
\(632\) | −2.20736 | + | 8.23797i | −0.0878040 | + | 0.327689i | ||||
\(633\) | −7.15834 | + | 4.13287i | −0.284519 | + | 0.164267i | ||||
\(634\) | − | 3.07098i | − | 0.121964i | ||||||
\(635\) | −0.464557 | − | 1.73375i | −0.0184354 | − | 0.0688018i | ||||
\(636\) | −2.09458 | −0.0830557 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.79593 | 0.110692 | ||||||||
\(639\) | 3.66273 | + | 13.6695i | 0.144895 | + | 0.540756i | ||||
\(640\) | 4.28475i | 0.169369i | ||||||||
\(641\) | −17.4189 | + | 10.0568i | −0.688005 | + | 0.397220i | −0.802864 | − | 0.596162i | \(-0.796692\pi\) |
0.114859 | + | 0.993382i | \(0.463358\pi\) | |||||||
\(642\) | −0.398795 | + | 1.48832i | −0.0157392 | + | 0.0587395i | ||||
\(643\) | 3.80955 | − | 1.02077i | 0.150234 | − | 0.0402551i | −0.182918 | − | 0.983128i | \(-0.558554\pi\) |
0.333152 | + | 0.942873i | \(0.391888\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.06643 | + | 2.06643i | 0.0813654 | + | 0.0813654i | ||||
\(646\) | −4.01535 | −0.157982 | ||||||||
\(647\) | 7.52305 | 0.295762 | 0.147881 | − | 0.989005i | \(-0.452755\pi\) | ||||
0.147881 | + | 0.989005i | \(0.452755\pi\) | |||||||
\(648\) | 0.0518784 | + | 0.0518784i | 0.00203798 | + | 0.00203798i | ||||
\(649\) | 0.997466 | + | 1.72766i | 0.0391540 | + | 0.0678167i | ||||
\(650\) | 4.11547 | + | 2.69104i | 0.161422 | + | 0.105551i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.25113 | + | 1.13909i | 0.166487 | + | 0.0446100i | ||||
\(653\) | 5.29139 | − | 9.16495i | 0.207068 | − | 0.358652i | −0.743722 | − | 0.668489i | \(-0.766941\pi\) |
0.950790 | + | 0.309837i | \(0.100275\pi\) | |||||||
\(654\) | 0.130419 | + | 0.225893i | 0.00509979 | + | 0.00883310i | ||||
\(655\) | −2.32007 | − | 8.65863i | −0.0906527 | − | 0.338320i | ||||
\(656\) | −17.1664 | − | 17.1664i | −0.670237 | − | 0.670237i | ||||
\(657\) | 5.96619 | + | 22.2661i | 0.232763 | + | 0.868685i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.76883 | − | 4.79576i | 0.107858 | − | 0.186816i | −0.807044 | − | 0.590491i | \(-0.798934\pi\) |
0.914902 | + | 0.403675i | \(0.132267\pi\) | |||||||
\(660\) | −3.50252 | − | 2.02218i | −0.136335 | − | 0.0787133i | ||||
\(661\) | 9.40996 | − | 9.40996i | 0.366005 | − | 0.366005i | −0.500013 | − | 0.866018i | \(-0.666671\pi\) |
0.866018 | + | 0.500013i | \(0.166671\pi\) | |||||||
\(662\) | 8.55659 | + | 4.94015i | 0.332561 | + | 0.192004i | ||||
\(663\) | −3.55862 | − | 17.0045i | −0.138205 | − | 0.660401i | ||||
\(664\) | 10.2611i | 0.398208i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.0491795 | + | 0.0851813i | 0.00190567 | + | 0.00330071i | ||||
\(667\) | − | 21.9954i | − | 0.851666i | ||||||
\(668\) | −38.8275 | + | 10.4038i | −1.50228 | + | 0.402535i | ||||
\(669\) | 24.1659 | + | 6.47524i | 0.934308 | + | 0.250347i | ||||
\(670\) | 0.745832 | − | 0.745832i | 0.0288140 | − | 0.0288140i | ||||
\(671\) | −23.1088 | + | 23.1088i | −0.892106 | + | 0.892106i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.8942 | − | 7.44448i | 0.497035 | − | 0.286963i | −0.230453 | − | 0.973083i | \(-0.574021\pi\) |
0.727488 | + | 0.686120i | \(0.240687\pi\) | |||||||
\(674\) | 9.13073 | − | 2.44657i | 0.351703 | − | 0.0942384i | ||||
\(675\) | 12.2683 | − | 21.2494i | 0.472208 | − | 0.817889i | ||||
\(676\) | −24.7671 | − | 2.76058i | −0.952583 | − | 0.106176i | ||||
\(677\) | −10.7184 | + | 6.18827i | −0.411942 | + | 0.237835i | −0.691624 | − | 0.722258i | \(-0.743104\pi\) |
0.279682 | + | 0.960093i | \(0.409771\pi\) | |||||||
\(678\) | 0.389370 | − | 1.45315i | 0.0149536 | − | 0.0558078i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.28441 | − | 1.31891i | −0.0876033 | − | 0.0505778i | ||||
\(681\) | 6.34484 | + | 1.70010i | 0.243135 | + | 0.0651478i | ||||
\(682\) | −0.298517 | + | 1.11408i | −0.0114308 | + | 0.0426603i | ||||
\(683\) | 7.35708 | − | 27.4570i | 0.281511 | − | 1.05061i | −0.669841 | − | 0.742505i | \(-0.733638\pi\) |
0.951351 | − | 0.308108i | \(-0.0996957\pi\) | |||||||
\(684\) | 10.6383 | + | 2.85051i | 0.406764 | + | 0.108992i | ||||
\(685\) | −4.22945 | − | 2.44188i | −0.161599 | − | 0.0932993i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.14192 | − | 11.7258i | 0.119872 | − | 0.447367i | ||||
\(688\) | 16.1134 | − | 9.30306i | 0.614317 | − | 0.354676i | ||||
\(689\) | −2.46442 | − | 2.75437i | −0.0938870 | − | 0.104933i | ||||
\(690\) | 0.689102 | − | 1.19356i | 0.0262336 | − | 0.0454380i | ||||
\(691\) | 11.3072 | − | 3.02975i | 0.430145 | − | 0.115257i | −0.0372491 | − | 0.999306i | \(-0.511859\pi\) |
0.467394 | + | 0.884049i | \(0.345193\pi\) | |||||||
\(692\) | 33.3481 | − | 19.2535i | 1.26770 | − | 0.731909i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.84719 | − | 1.84719i | 0.0701186 | − | 0.0701186i | ||||
\(695\) | −5.55203 | + | 5.55203i | −0.210601 | + | 0.210601i | ||||
\(696\) | 2.94535 | + | 0.789203i | 0.111643 | + | 0.0299147i | ||||
\(697\) | 30.2110 | − | 8.09501i | 1.14432 | − | 0.306621i | ||||
\(698\) | − | 8.23427i | − | 0.311672i | ||||||
\(699\) | 7.94355 | + | 13.7586i | 0.300453 | + | 0.520399i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 0.431477i | − | 0.0162966i | −0.999967 | − | 0.00814832i | \(-0.997406\pi\) | ||
0.999967 | − | 0.00814832i | \(-0.00259372\pi\) | |||||||
\(702\) | 0.298810 | − | 5.37828i | 0.0112779 | − | 0.202990i | ||||
\(703\) | 0.488916 | + | 0.282276i | 0.0184398 | + | 0.0106462i | ||||
\(704\) | −16.4468 | + | 16.4468i | −0.619862 | + | 0.619862i | ||||
\(705\) | −4.46331 | − | 2.57689i | −0.168098 | − | 0.0970514i | ||||
\(706\) | −2.89650 | + | 5.01689i | −0.109011 | + | 0.188813i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.275585 | + | 1.02850i | 0.0103571 | + | 0.0386533i | ||||
\(709\) | −3.00200 | − | 3.00200i | −0.112743 | − | 0.112743i | 0.648485 | − | 0.761227i | \(-0.275403\pi\) |
−0.761227 | + | 0.648485i | \(0.775403\pi\) | |||||||
\(710\) | −0.292776 | − | 1.09266i | −0.0109877 | − | 0.0410067i | ||||
\(711\) | 7.04135 | + | 12.1960i | 0.264071 | + | 0.457385i | ||||
\(712\) | −6.83973 | + | 11.8468i | −0.256330 | + | 0.443976i | ||||
\(713\) | 8.76441 | + | 2.34842i | 0.328230 | + | 0.0879488i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.46179 | − | 6.98503i | −0.0546680 | − | 0.261225i | ||||
\(716\) | 20.5385 | + | 35.5738i | 0.767562 | + | 1.32946i | ||||
\(717\) | −21.8111 | − | 21.8111i | −0.814550 | − | 0.814550i | ||||
\(718\) | 8.88774 | 0.331688 | ||||||||
\(719\) | −11.7915 | −0.439748 | −0.219874 | − | 0.975528i | \(-0.570565\pi\) | ||||
−0.219874 | + | 0.975528i | \(0.570565\pi\) | |||||||
\(720\) | 2.39063 | + | 2.39063i | 0.0890935 | + | 0.0890935i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.64356 | − | 0.708339i | 0.0983830 | − | 0.0263616i | ||||
\(723\) | −5.07425 | + | 18.9374i | −0.188714 | + | 0.704289i | ||||
\(724\) | 32.7930 | − | 18.9330i | 1.21874 | − | 0.703641i | ||||
\(725\) | 11.9946i | 0.445469i | ||||||||
\(726\) | 0.290685 | + | 1.08485i | 0.0107883 | + | 0.0402626i | ||||
\(727\) | −9.73102 | −0.360904 | −0.180452 | − | 0.983584i | \(-0.557756\pi\) | ||||
−0.180452 | + | 0.983584i | \(0.557756\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.4579 | −0.609550 | ||||||||
\(730\) | −0.476902 | − | 1.77982i | −0.0176509 | − | 0.0658741i | ||||
\(731\) | 23.9708i | 0.886591i | ||||||||
\(732\) | −15.1062 | + | 8.72155i | −0.558340 | + | 0.322358i | ||||
\(733\) | 3.92510 | − | 14.6487i | 0.144977 | − | 0.541061i | −0.854779 | − | 0.518991i | \(-0.826308\pi\) |
0.999756 | − | 0.0220699i | \(-0.00702565\pi\) | |||||||
\(734\) | 1.47691 | − | 0.395738i | 0.0545139 | − | 0.0146069i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −20.0581 | − | 20.0581i | −0.739350 | − | 0.739350i | ||||
\(737\) | 27.1047 | 0.998415 | ||||||||
\(738\) | 3.71605 | 0.136790 | ||||||||
\(739\) | 1.66045 | + | 1.66045i | 0.0610807 | + | 0.0610807i | 0.736987 | − | 0.675907i | \(-0.236248\pi\) |
−0.675907 | + | 0.736987i | \(0.736248\pi\) | |||||||
\(740\) | 0.0907525 | + | 0.157188i | 0.00333613 | + | 0.00577834i | ||||
\(741\) | −5.34541 | − | 10.5729i | −0.196368 | − | 0.388407i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.0211 | + | 7.24029i | 0.991309 | + | 0.265620i | 0.717800 | − | 0.696249i | \(-0.245149\pi\) |
0.273509 | + | 0.961870i | \(0.411816\pi\) | |||||||
\(744\) | −0.628940 | + | 1.08936i | −0.0230581 | + | 0.0399377i | ||||
\(745\) | −3.71348 | − | 6.43193i | −0.136051 | − | 0.235648i | ||||
\(746\) | −1.83218 | − | 6.83779i | −0.0670809 | − | 0.250349i | ||||
\(747\) | 11.9809 | + | 11.9809i | 0.438357 | + | 0.438357i | ||||
\(748\) | −8.58605 | − | 32.0436i | −0.313937 | − | 1.17163i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.772789 | + | 1.33851i | −0.0282183 | + | 0.0488755i | ||||
\(751\) | −4.51677 | − | 2.60776i | −0.164819 | − | 0.0951584i | 0.415321 | − | 0.909675i | \(-0.363669\pi\) |
−0.580141 | + | 0.814516i | \(0.697002\pi\) | |||||||
\(752\) | −23.2024 | + | 23.2024i | −0.846103 | + | 0.846103i | ||||
\(753\) | −6.33944 | − | 3.66008i | −0.231022 | − | 0.133381i | ||||
\(754\) | 1.18807 | + | 2.34994i | 0.0432669 | + | 0.0855798i | ||||
\(755\) | − | 2.56629i | − | 0.0933969i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.3674 | + | 17.9569i | 0.376811 | + | 0.652656i | 0.990596 | − | 0.136817i | \(-0.0436872\pi\) |
−0.613785 | + | 0.789473i | \(0.710354\pi\) | |||||||
\(758\) | 6.26621i | 0.227599i | ||||||||
\(759\) | 34.2094 | − | 9.16639i | 1.24172 | − | 0.332719i | ||||
\(760\) | −1.73755 | − | 0.465576i | −0.0630276 | − | 0.0168882i | ||||
\(761\) | 27.8103 | − | 27.8103i | 1.00812 | − | 1.00812i | 0.00815767 | − | 0.999967i | \(-0.497403\pi\) |
0.999967 | − | 0.00815767i | \(-0.00259669\pi\) | |||||||
\(762\) | −0.754057 | + | 0.754057i | −0.0273166 | + | 0.0273166i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −7.13656 | + | 4.12029i | −0.258192 | + | 0.149067i | ||||
\(765\) | −4.20724 | + | 1.12733i | −0.152113 | + | 0.0407586i | ||||
\(766\) | −1.69184 | + | 2.93034i | −0.0611285 | + | 0.105878i | ||||
\(767\) | −1.02823 | + | 1.57249i | −0.0371271 | + | 0.0567793i | ||||
\(768\) | −9.01232 | + | 5.20326i | −0.325204 | + | 0.187757i | ||||
\(769\) | −2.96518 | + | 11.0662i | −0.106927 | + | 0.399057i | −0.998557 | − | 0.0537084i | \(-0.982896\pi\) |
0.891630 | + | 0.452765i | \(0.149563\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.68935 | + | 4.43945i | 0.276925 | + | 0.159883i | ||||
\(772\) | −25.0966 | − | 6.72462i | −0.903247 | − | 0.242024i | ||||
\(773\) | −12.1267 | + | 45.2574i | −0.436167 | + | 1.62780i | 0.302091 | + | 0.953279i | \(0.402315\pi\) |
−0.738258 | + | 0.674518i | \(0.764351\pi\) | |||||||
\(774\) | −0.737121 | + | 2.75097i | −0.0264953 | + | 0.0988816i | ||||
\(775\) | −4.77944 | − | 1.28065i | −0.171682 | − | 0.0460022i | ||||
\(776\) | −13.3537 | − | 7.70974i | −0.479369 | − | 0.276764i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.61122 | + | 9.74522i | −0.0936169 | + | 0.349383i | ||||
\(779\) | 18.4715 | − | 10.6645i | 0.661810 | − | 0.382096i | ||||
\(780\) | 0.211295 | − | 3.80310i | 0.00756559 | − | 0.136173i | ||||
\(781\) | 14.5344 | − | 25.1744i | 0.520083 | − | 0.900811i | ||||
\(782\) | 10.9195 | − | 2.92588i | 0.390482 | − | 0.104629i | ||||
\(783\) | 11.3792 | − | 6.56979i | 0.406660 | − | 0.234785i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.27653 | − | 1.27653i | 0.0455615 | − | 0.0455615i | ||||
\(786\) | −3.76588 | + | 3.76588i | −0.134325 | + | 0.134325i | ||||
\(787\) | 7.83322 | + | 2.09890i | 0.279224 | + | 0.0748179i | 0.395713 | − | 0.918374i | \(-0.370497\pi\) |
−0.116489 | + | 0.993192i | \(0.537164\pi\) | |||||||
\(788\) | 7.09094 | − | 1.90001i | 0.252604 | − | 0.0676852i | ||||
\(789\) | 2.88200i | 0.102602i | ||||||||
\(790\) | −0.562843 | − | 0.974873i | −0.0200251 | − | 0.0346844i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 8.05366i | − | 0.286174i | ||||||
\(793\) | −29.2422 | − | 9.60305i | −1.03842 | − | 0.341014i | ||||
\(794\) | −1.99825 | − | 1.15369i | −0.0709152 | − | 0.0409429i | ||||
\(795\) | 0.399447 | − | 0.399447i | 0.0141669 | − | 0.0141669i | ||||
\(796\) | 17.4451 | + | 10.0719i | 0.618323 | + | 0.356989i | ||||
\(797\) | 5.11594 | − | 8.86106i | 0.181216 | − | 0.313875i | −0.761079 | − | 0.648659i | \(-0.775330\pi\) |
0.942295 | + | 0.334784i | \(0.108663\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.9413 | − | 40.8335i | −0.387076 | − | 1.44459i | ||||
\(800\) | 10.9381 | + | 10.9381i | 0.386721 | + | 0.386721i | ||||
\(801\) | 5.84621 | + | 21.8183i | 0.206566 | + | 0.770913i | ||||
\(802\) | −3.93583 | − | 6.81705i | −0.138979 | − | 0.240718i | ||||
\(803\) | 23.6751 | − | 41.0064i | 0.835475 | − | 1.44709i | ||||
\(804\) | 13.9740 | + | 3.74431i | 0.492824 | + | 0.132052i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.06322 | + | 0.222505i | −0.0374502 | + | 0.00783740i | ||||
\(807\) | −12.4519 | − | 21.5673i | −0.438328 | − | 0.759206i | ||||
\(808\) | −0.887205 | − | 0.887205i | −0.0312118 | − | 0.0312118i | ||||
\(809\) | 11.6750 | 0.410473 | 0.205236 | − | 0.978712i | \(-0.434204\pi\) | ||||
0.205236 | + | 0.978712i | \(0.434204\pi\) | |||||||
\(810\) | −0.00968373 | −0.000340252 | ||||||||
\(811\) | 19.1328 | + | 19.1328i | 0.671843 | + | 0.671843i | 0.958141 | − | 0.286298i | \(-0.0924246\pi\) |
−0.286298 | + | 0.958141i | \(0.592425\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.6860 | + | 3.66714i | −0.479988 | + | 0.128612i | ||||
\(814\) | 0.0522914 | − | 0.195154i | 0.00183281 | − | 0.00684015i | ||||
\(815\) | −1.02794 | + | 0.593481i | −0.0360071 | + | 0.0207887i | ||||
\(816\) | − | 16.9061i | − | 0.591832i | ||||||
\(817\) | 4.23085 | + | 15.7898i | 0.148019 | + | 0.552414i | ||||
\(818\) | 1.64875 | 0.0576472 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.85735 | 0.239469 | ||||||||
\(821\) | −7.02461 | − | 26.2162i | −0.245161 | − | 0.914952i | −0.973303 | − | 0.229526i | \(-0.926283\pi\) |
0.728142 | − | 0.685426i | \(-0.240384\pi\) | |||||||
\(822\) | 2.90155i | 0.101203i | ||||||||
\(823\) | 24.0565 | − | 13.8890i | 0.838557 | − | 0.484141i | −0.0182167 | − | 0.999834i | \(-0.505799\pi\) |
0.856773 | + | 0.515693i | \(0.172466\pi\) | |||||||
\(824\) | −0.125143 | + | 0.467039i | −0.00435956 | + | 0.0162701i | ||||
\(825\) | −18.6552 | + | 4.99864i | −0.649491 | + | 0.174030i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.1851 | + | 30.1851i | 1.04964 | + | 1.04964i | 0.998702 | + | 0.0509356i | \(0.0162203\pi\) |
0.0509356 | + | 0.998702i | \(0.483780\pi\) | |||||||
\(828\) | −31.0073 | −1.07758 | ||||||||
\(829\) | −27.9611 | −0.971130 | −0.485565 | − | 0.874201i | \(-0.661386\pi\) | ||||
−0.485565 | + | 0.874201i | \(0.661386\pi\) | |||||||
\(830\) | −0.957679 | − | 0.957679i | −0.0332415 | − | 0.0332415i | ||||
\(831\) | −2.58015 | − | 4.46896i | −0.0895046 | − | 0.155026i | ||||
\(832\) | −20.8120 | − | 6.83459i | −0.721527 | − | 0.236947i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.50596 | + | 1.20737i | 0.156029 | + | 0.0418078i | ||||
\(835\) | 5.42053 | − | 9.38864i | 0.187585 | − | 0.324907i | ||||
\(836\) | −11.3114 | − | 19.5920i | −0.391214 | − | 0.677602i | ||||
\(837\) | 1.40289 | + | 5.23567i | 0.0484911 | + | 0.180971i | ||||
\(838\) | −3.13446 | − | 3.13446i | −0.108278 | − | 0.108278i | ||||
\(839\) | −8.74827 | − | 32.6490i | −0.302024 | − | 1.12717i | −0.935477 | − | 0.353387i | \(-0.885030\pi\) |
0.633453 | − | 0.773781i | \(-0.281637\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.2884 | − | 19.5521i | 0.389255 | − | 0.674209i | ||||
\(842\) | 1.68082 | + | 0.970419i | 0.0579247 | + | 0.0334429i | ||||
\(843\) | 9.17597 | − | 9.17597i | 0.316037 | − | 0.316037i | ||||
\(844\) | −12.8734 | − | 7.43249i | −0.443122 | − | 0.255837i | ||||
\(845\) | 5.24967 | − | 4.19676i | 0.180594 | − | 0.144373i | ||||
\(846\) | − | 5.02266i | − | 0.172683i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.79831 | − | 3.11477i | −0.0617544 | − | 0.106962i | ||||
\(849\) | − | 1.12535i | − | 0.0386218i | ||||||
\(850\) | −5.95468 | + | 1.59555i | −0.204244 | + | 0.0547269i | ||||
\(851\) | −1.53527 | − | 0.411374i | −0.0526283 | − | 0.0141017i | ||||
\(852\) | 10.9710 | − | 10.9710i | 0.375859 | − | 0.375859i | ||||
\(853\) | 18.1560 | − | 18.1560i | 0.621649 | − | 0.621649i | −0.324304 | − | 0.945953i | \(-0.605130\pi\) |
0.945953 | + | 0.324304i | \(0.105130\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.57237 | + | 1.48516i | −0.0879733 | + | 0.0507914i | ||||
\(856\) | −5.46910 | + | 1.46544i | −0.186930 | + | 0.0500877i | ||||
\(857\) | −0.942085 | + | 1.63174i | −0.0321810 | + | 0.0557392i | −0.881667 | − | 0.471871i | \(-0.843579\pi\) |
0.849486 | + | 0.527611i | \(0.176912\pi\) | |||||||
\(858\) | −3.15974 | + | 2.82712i | −0.107872 | + | 0.0965162i | ||||
\(859\) | 1.31631 | − | 0.759972i | 0.0449119 | − | 0.0259299i | −0.477376 | − | 0.878699i | \(-0.658412\pi\) |
0.522288 | + | 0.852769i | \(0.325079\pi\) | |||||||
\(860\) | −1.36023 | + | 5.07646i | −0.0463835 | + | 0.173106i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.21178 | + | 2.43167i | 0.143454 | + | 0.0828231i | ||||
\(863\) | −8.87371 | − | 2.37770i | −0.302065 | − | 0.0809380i | 0.104603 | − | 0.994514i | \(-0.466643\pi\) |
−0.406668 | + | 0.913576i | \(0.633309\pi\) | |||||||
\(864\) | 4.38581 | − | 16.3681i | 0.149208 | − | 0.556853i | ||||
\(865\) | −2.68790 | + | 10.0314i | −0.0913914 | + | 0.341077i | ||||
\(866\) | −2.58017 | − | 0.691356i | −0.0876779 | − | 0.0234932i | ||||
\(867\) | 3.16936 | + | 1.82983i | 0.107637 | + | 0.0621443i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.48691 | − | 27.9415i | 0.253976 | − | 0.947851i | ||||
\(870\) | −0.348549 | + | 0.201235i | −0.0118169 | + | 0.00682251i | ||||
\(871\) | 11.5176 | + | 22.7811i | 0.390258 | + | 0.771910i | ||||
\(872\) | −0.479247 | + | 0.830080i | −0.0162293 | + | 0.0281100i | ||||
\(873\) | −24.5937 | + | 6.58985i | −0.832369 | + | 0.223033i | ||||
\(874\) | 6.67638 | − | 3.85461i | 0.225832 | − | 0.130384i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 17.8705 | − | 17.8705i | 0.603789 | − | 0.603789i | ||||
\(877\) | −2.00585 | + | 2.00585i | −0.0677326 | + | 0.0677326i | −0.740162 | − | 0.672429i | \(-0.765251\pi\) |
0.672429 | + | 0.740162i | \(0.265251\pi\) | |||||||
\(878\) | 4.84685 | + | 1.29871i | 0.163573 | + | 0.0438293i | ||||
\(879\) | −21.1333 | + | 5.66265i | −0.712809 | + | 0.190997i | ||||
\(880\) | − | 6.94461i | − | 0.234103i | ||||||
\(881\) | −16.7491 | − | 29.0103i | −0.564292 | − | 0.977383i | −0.997115 | − | 0.0759037i | \(-0.975816\pi\) |
0.432823 | − | 0.901479i | \(-0.357517\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.3459i | 1.22314i | 0.791192 | + | 0.611568i | \(0.209461\pi\) | ||||
−0.791192 | + | 0.611568i | \(0.790539\pi\) | |||||||
\(884\) | 23.2837 | − | 20.8327i | 0.783117 | − | 0.700679i | ||||
\(885\) | −0.248695 | − | 0.143584i | −0.00835978 | − | 0.00482652i | ||||
\(886\) | 2.07742 | − | 2.07742i | 0.0697921 | − | 0.0697921i | ||||
\(887\) | −21.2724 | − | 12.2816i | −0.714258 | − | 0.412377i | 0.0983776 | − | 0.995149i | \(-0.468635\pi\) |
−0.812636 | + | 0.582772i | \(0.801968\pi\) | |||||||
\(888\) | 0.110172 | − | 0.190823i | 0.00369713 | − | 0.00640361i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.467311 | − | 1.74403i | −0.0156643 | − | 0.0584599i | ||||
\(891\) | −0.175961 | − | 0.175961i | −0.00589491 | − | 0.00589491i | ||||
\(892\) | 11.6450 | + | 43.4596i | 0.389902 | + | 1.45513i | ||||
\(893\) | −14.4143 | − | 24.9663i | −0.482356 | − | 0.835465i | ||||
\(894\) | −2.20626 | + | 3.82136i | −0.0737885 | + | 0.127805i | ||||
\(895\) | −10.7009 | − | 2.86730i | −0.357691 | − | 0.0958431i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 22.2408 | + | 24.8575i | 0.742598 | + | 0.829968i | ||||
\(898\) | −2.62488 | − | 4.54642i | −0.0875934 | − | 0.151716i | ||||
\(899\) | −1.87363 | − | 1.87363i | −0.0624891 | − | 0.0624891i | ||||
\(900\) | 16.9090 | 0.563633 | ||||||||
\(901\) | 4.63363 | 0.154369 | ||||||||
\(902\) | −5.39743 | − | 5.39743i | −0.179715 | − | 0.179715i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.33983 | − | 1.43080i | 0.177600 | − | 0.0475878i | ||||
\(905\) | −2.64316 | + | 9.86440i | −0.0878616 | + | 0.327904i | ||||
\(906\) | −1.32042 | + | 0.762347i | −0.0438681 | + | 0.0253273i | ||||
\(907\) | 34.2066i | 1.13581i | 0.823094 | + | 0.567905i | \(0.192246\pi\) | ||||
−0.823094 | + | 0.567905i | \(0.807754\pi\) | |||||||
\(908\) | 3.05742 | + | 11.4105i | 0.101464 | + | 0.378669i | ||||
\(909\) | −2.07180 | −0.0687173 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49.8898 | 1.65292 | 0.826462 | − | 0.562993i | \(-0.190350\pi\) | ||||
0.826462 | + | 0.562993i | \(0.190350\pi\) | |||||||
\(912\) | −2.98394 | − | 11.1362i | −0.0988081 | − | 0.368757i | ||||
\(913\) | − | 34.8036i | − | 1.15183i | ||||||
\(914\) | −8.41875 | + | 4.86057i | −0.278468 | + | 0.160773i | ||||
\(915\) | 1.21758 | − | 4.54406i | 0.0402519 | − | 0.150222i | ||||
\(916\) | 21.0875 | − | 5.65037i | 0.696750 | − | 0.186694i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4.77523 | + | 4.77523i | 0.157606 | + | 0.157606i | ||||
\(919\) | −2.71652 | −0.0896098 | −0.0448049 | − | 0.998996i | \(-0.514267\pi\) | ||||
−0.0448049 | + | 0.998996i | \(0.514267\pi\) | |||||||
\(920\) | 5.06444 | 0.166970 | ||||||||
\(921\) | −7.71661 | − | 7.71661i | −0.254271 | − | 0.254271i | ||||
\(922\) | −1.63532 | − | 2.83245i | −0.0538563 | − | 0.0932818i | ||||
\(923\) | 27.3348 | + | 1.51869i | 0.899737 | + | 0.0499882i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.837217 | + | 0.224332i | 0.0275275 | + | 0.00737598i | ||||
\(926\) | 0.825655 | − | 1.43008i | 0.0271327 | − | 0.0469952i | ||||
\(927\) | 0.399198 | + | 0.691432i | 0.0131114 | + | 0.0227096i | ||||
\(928\) | 2.14398 | + | 8.00144i | 0.0703796 | + | 0.262660i | ||||
\(929\) | −17.7678 | − | 17.7678i | −0.582942 | − | 0.582942i | 0.352768 | − | 0.935711i | \(-0.385240\pi\) |
−0.935711 | + | 0.352768i | \(0.885240\pi\) | |||||||
\(930\) | −0.0429711 | − | 0.160370i | −0.00140908 | − | 0.00525875i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −14.2855 | + | 24.7433i | −0.467939 | + | 0.810494i | ||||
\(933\) | −8.97662 | − | 5.18266i | −0.293881 | − | 0.169673i | ||||
\(934\) | 7.41102 | − | 7.41102i | 0.242496 | − | 0.242496i | ||||
\(935\) | 7.74826 | + | 4.47346i | 0.253395 | + | 0.146298i | ||||
\(936\) | 6.76899 | − | 3.42223i | 0.221251 | − | 0.111859i | ||||
\(937\) | − | 3.14878i | − | 0.102866i | −0.998676 | − | 0.0514330i | \(-0.983621\pi\) | ||
0.998676 | − | 0.0514330i | \(-0.0163789\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.89099 | + | 15.3996i | 0.290146 | + | 0.502548i | ||||
\(940\) | − | 9.26848i | − | 0.302304i | ||||||
\(941\) | −9.35203 | + | 2.50587i | −0.304867 | + | 0.0816890i | −0.408010 | − | 0.912978i | \(-0.633777\pi\) |
0.103142 | + | 0.994667i | \(0.467110\pi\) | |||||||
\(942\) | −1.03602 | − | 0.277601i | −0.0337553 | − | 0.00904472i | ||||
\(943\) | −42.4613 | + | 42.4613i | −1.38273 | + | 1.38273i | ||||
\(944\) | −1.29283 | + | 1.29283i | −0.0420781 | + | 0.0420781i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.06633 | − | 2.92504i | 0.164720 | − | 0.0951014i | ||||
\(947\) | 42.4440 | − | 11.3728i | 1.37925 | − | 0.369568i | 0.508399 | − | 0.861122i | \(-0.330238\pi\) |
0.870847 | + | 0.491554i | \(0.163571\pi\) | |||||||
\(948\) | 7.71982 | − | 13.3711i | 0.250728 | − | 0.434274i | ||||
\(949\) | 44.5256 | + | 2.47378i | 1.44536 | + | 0.0803023i | ||||
\(950\) | −3.64078 | + | 2.10201i | −0.118123 | + | 0.0681981i | ||||
\(951\) | −2.94015 | + | 10.9728i | −0.0953408 | + | 0.355817i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.0074 | − | 9.81922i | −0.550923 | − | 0.318076i | 0.198571 | − | 0.980086i | \(-0.436370\pi\) |
−0.749494 | + | 0.662011i | \(0.769703\pi\) | |||||||
\(954\) | 0.531772 | + | 0.142488i | 0.0172168 | + | 0.00461322i | ||||
\(955\) | 0.575216 | − | 2.14673i | 0.0186135 | − | 0.0694667i | ||||
\(956\) | 14.3572 | − | 53.5819i | 0.464346 | − | 1.73296i | ||||
\(957\) | −9.99001 | − | 2.67682i | −0.322931 | − | 0.0865292i | ||||
\(958\) | 6.06595 | + | 3.50218i | 0.195982 | + | 0.113150i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.866562 | − | 3.23405i | 0.0279682 | − | 0.104379i | ||||
\(961\) | −25.9002 | + | 14.9535i | −0.835489 | + | 0.482370i | ||||
\(962\) | 0.186245 | − | 0.0389763i | 0.00600477 | − | 0.00125665i | ||||
\(963\) | −4.67467 | + | 8.09677i | −0.150639 | + | 0.260915i | ||||
\(964\) | −34.0567 | + | 9.12545i | −1.09689 | + | 0.293911i | ||||
\(965\) | 6.06846 | − | 3.50363i | 0.195351 | − | 0.112786i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.4539 | + | 22.4539i | −0.722068 | + | 0.722068i | −0.969026 | − | 0.246958i | \(-0.920569\pi\) |
0.246958 | + | 0.969026i | \(0.420569\pi\) | |||||||
\(968\) | −2.91829 | + | 2.91829i | −0.0937975 | + | 0.0937975i | ||||
\(969\) | 14.3471 | + | 3.84429i | 0.460894 | + | 0.123496i | ||||
\(970\) | 1.96587 | − | 0.526753i | 0.0631202 | − | 0.0169130i | ||||
\(971\) | 39.0812i | 1.25417i | 0.778949 | + | 0.627087i | \(0.215753\pi\) | ||||
−0.778949 | + | 0.627087i | \(0.784247\pi\) | |||||||
\(972\) | −14.9741 | − | 25.9359i | −0.480295 | − | 0.831895i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 7.67675i | − | 0.245979i | ||||||
\(975\) | −12.1284 | − | 13.5554i | −0.388420 | − | 0.434119i | ||||
\(976\) | −25.9389 | − | 14.9758i | −0.830285 | − | 0.479365i | ||||
\(977\) | 19.0847 | − | 19.0847i | 0.610572 | − | 0.610572i | −0.332523 | − | 0.943095i | \(-0.607900\pi\) |
0.943095 | + | 0.332523i | \(0.107900\pi\) | |||||||
\(978\) | 0.610723 | + | 0.352601i | 0.0195288 | + | 0.0112749i | ||||
\(979\) | 23.1989 | − | 40.1817i | 0.741441 | − | 1.28421i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.409633 | + | 1.52877i | 0.0130786 | + | 0.0488099i | ||||
\(982\) | −3.58853 | − | 3.58853i | −0.114515 | − | 0.114515i | ||||
\(983\) | −3.22784 | − | 12.0465i | −0.102952 | − | 0.384223i | 0.895153 | − | 0.445760i | \(-0.147066\pi\) |
−0.998105 | + | 0.0615370i | \(0.980400\pi\) | |||||||
\(984\) | −4.16235 | − | 7.20941i | −0.132691 | − | 0.229827i | ||||
\(985\) | −0.989935 | + | 1.71462i | −0.0315420 | + | 0.0546323i | ||||
\(986\) | −3.18878 | − | 0.854431i | −0.101551 | − | 0.0272106i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.6602 | − | 17.8323i | 0.370961 | − | 0.567320i | ||||
\(989\) | −23.0112 | − | 39.8565i | −0.731713 | − | 1.26736i | ||||
\(990\) | 0.751656 | + | 0.751656i | 0.0238892 | + | 0.0238892i | ||||
\(991\) | −22.1128 | −0.702436 | −0.351218 | − | 0.936294i | \(-0.614232\pi\) | ||||
−0.351218 | + | 0.936294i | \(0.614232\pi\) | |||||||
\(992\) | −3.41720 | −0.108496 | ||||||||
\(993\) | −25.8435 | − | 25.8435i | −0.820119 | − | 0.820119i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.24761 | + | 1.40609i | −0.166361 | + | 0.0445762i | ||||
\(996\) | 4.80785 | − | 17.9431i | 0.152343 | − | 0.568550i | ||||
\(997\) | −29.9386 | + | 17.2851i | −0.948167 | + | 0.547424i | −0.892511 | − | 0.451026i | \(-0.851058\pi\) |
−0.0556556 | + | 0.998450i | \(0.517725\pi\) | |||||||
\(998\) | 4.37931i | 0.138625i | ||||||||
\(999\) | −0.245746 | − | 0.917136i | −0.00777505 | − | 0.0290169i |
(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 | 637.2.x.a.80.5 | 28 | ||
7.2 | even | 3 | 91.2.ba.a.54.5 | yes | 28 | ||
7.3 | odd | 6 | 637.2.bd.a.587.3 | 28 | |||
7.4 | even | 3 | 637.2.bd.b.587.3 | 28 | |||
7.5 | odd | 6 | 637.2.bb.a.509.5 | 28 | |||
7.6 | odd | 2 | 91.2.w.a.80.5 | yes | 28 | ||
13.7 | odd | 12 | 637.2.bb.a.423.5 | 28 | |||
21.2 | odd | 6 | 819.2.et.b.145.3 | 28 | |||
21.20 | even | 2 | 819.2.gh.b.262.3 | 28 | |||
91.20 | even | 12 | 91.2.ba.a.59.5 | yes | 28 | ||
91.33 | even | 12 | inner | 637.2.x.a.215.5 | 28 | ||
91.46 | odd | 12 | 637.2.bd.a.293.3 | 28 | |||
91.59 | even | 12 | 637.2.bd.b.293.3 | 28 | |||
91.72 | odd | 12 | 91.2.w.a.33.5 | ✓ | 28 | ||
273.20 | odd | 12 | 819.2.et.b.514.3 | 28 | |||
273.254 | even | 12 | 819.2.gh.b.397.3 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.w.a.33.5 | ✓ | 28 | 91.72 | odd | 12 | ||
91.2.w.a.80.5 | yes | 28 | 7.6 | odd | 2 | ||
91.2.ba.a.54.5 | yes | 28 | 7.2 | even | 3 | ||
91.2.ba.a.59.5 | yes | 28 | 91.20 | even | 12 | ||
637.2.x.a.80.5 | 28 | 1.1 | even | 1 | trivial | ||
637.2.x.a.215.5 | 28 | 91.33 | even | 12 | inner | ||
637.2.bb.a.423.5 | 28 | 13.7 | odd | 12 | |||
637.2.bb.a.509.5 | 28 | 7.5 | odd | 6 | |||
637.2.bd.a.293.3 | 28 | 91.46 | odd | 12 | |||
637.2.bd.a.587.3 | 28 | 7.3 | odd | 6 | |||
637.2.bd.b.293.3 | 28 | 91.59 | even | 12 | |||
637.2.bd.b.587.3 | 28 | 7.4 | even | 3 | |||
819.2.et.b.145.3 | 28 | 21.2 | odd | 6 | |||
819.2.et.b.514.3 | 28 | 273.20 | odd | 12 | |||
819.2.gh.b.262.3 | 28 | 21.20 | even | 2 | |||
819.2.gh.b.397.3 | 28 | 273.254 | even | 12 |