Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,2,Mod(107,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([10, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.l (of order \(20\), degree \(8\), 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: | \(5.98878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{20})\) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 107.7 | ||
Character | \(\chi\) | \(=\) | 750.107 |
Dual form | 750.2.l.b.743.7 |
$q$-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 \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{13}{20}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.891007 | + | 0.453990i | 0.630037 | + | 0.321020i | ||||
\(3\) | −0.983013 | − | 1.42607i | −0.567543 | − | 0.823344i | ||||
\(4\) | 0.587785 | + | 0.809017i | 0.293893 | + | 0.404508i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.228447 | − | 1.71692i | −0.0932630 | − | 0.700929i | ||||
\(7\) | −0.462249 | − | 0.462249i | −0.174714 | − | 0.174714i | 0.614333 | − | 0.789047i | \(-0.289425\pi\) |
−0.789047 | + | 0.614333i | \(0.789425\pi\) | |||||||
\(8\) | 0.156434 | + | 0.987688i | 0.0553079 | + | 0.349201i | ||||
\(9\) | −1.06737 | + | 2.80370i | −0.355791 | + | 0.934566i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.73512 | − | 0.888693i | 0.824669 | − | 0.267951i | 0.133871 | − | 0.990999i | \(-0.457259\pi\) |
0.690798 | + | 0.723048i | \(0.257259\pi\) | |||||||
\(12\) | 0.575917 | − | 1.63350i | 0.166253 | − | 0.471551i | ||||
\(13\) | −1.97121 | − | 3.86872i | −0.546716 | − | 1.07299i | −0.984741 | − | 0.174028i | \(-0.944322\pi\) |
0.438025 | − | 0.898963i | \(-0.355678\pi\) | |||||||
\(14\) | −0.202010 | − | 0.621723i | −0.0539895 | − | 0.166163i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.309017 | + | 0.951057i | −0.0772542 | + | 0.237764i | ||||
\(17\) | 5.75574 | − | 0.911620i | 1.39597 | − | 0.221100i | 0.587305 | − | 0.809366i | \(-0.300189\pi\) |
0.808668 | + | 0.588266i | \(0.200189\pi\) | |||||||
\(18\) | −2.22389 | + | 2.01354i | −0.524175 | + | 0.474595i | ||||
\(19\) | 4.28299 | − | 5.89503i | 0.982585 | − | 1.35241i | 0.0471595 | − | 0.998887i | \(-0.484983\pi\) |
0.935425 | − | 0.353525i | \(-0.115017\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.204804 | + | 1.11360i | −0.0446920 | + | 0.243007i | ||||
\(22\) | 2.84047 | + | 0.449885i | 0.605589 | + | 0.0959159i | ||||
\(23\) | 0.316926 | − | 0.622003i | 0.0660837 | − | 0.129697i | −0.855602 | − | 0.517635i | \(-0.826813\pi\) |
0.921685 | + | 0.387938i | \(0.126813\pi\) | |||||||
\(24\) | 1.25474 | − | 1.19400i | 0.256123 | − | 0.243724i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 4.34197i | − | 0.851530i | ||||||
\(27\) | 5.04752 | − | 1.23392i | 0.971395 | − | 0.237468i | ||||
\(28\) | 0.102264 | − | 0.645670i | 0.0193261 | − | 0.122020i | ||||
\(29\) | −2.60237 | + | 1.89073i | −0.483247 | + | 0.351100i | −0.802582 | − | 0.596542i | \(-0.796541\pi\) |
0.319334 | + | 0.947642i | \(0.396541\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.82678 | − | 3.50686i | −0.866915 | − | 0.629850i | 0.0628427 | − | 0.998023i | \(-0.479983\pi\) |
−0.929757 | + | 0.368173i | \(0.879983\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −3.95600 | − | 3.02688i | −0.688651 | − | 0.526912i | ||||
\(34\) | 5.54227 | + | 1.80079i | 0.950491 | + | 0.308833i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.89562 | + | 0.784450i | −0.482604 | + | 0.130742i | ||||
\(37\) | 1.93977 | − | 0.988365i | 0.318897 | − | 0.162486i | −0.287213 | − | 0.957867i | \(-0.592729\pi\) |
0.606110 | + | 0.795380i | \(0.292729\pi\) | |||||||
\(38\) | 6.49246 | − | 3.30807i | 1.05322 | − | 0.536640i | ||||
\(39\) | −3.57936 | + | 6.61410i | −0.573156 | + | 1.05910i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.34331 | − | 2.06107i | −0.990659 | − | 0.321884i | −0.231532 | − | 0.972827i | \(-0.574374\pi\) |
−0.759127 | + | 0.650943i | \(0.774374\pi\) | |||||||
\(42\) | −0.688045 | + | 0.899243i | −0.106168 | + | 0.138756i | ||||
\(43\) | 5.08751 | − | 5.08751i | 0.775838 | − | 0.775838i | −0.203282 | − | 0.979120i | \(-0.565161\pi\) |
0.979120 | + | 0.203282i | \(0.0651609\pi\) | |||||||
\(44\) | 2.32663 | + | 1.69040i | 0.350753 | + | 0.254837i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.564767 | − | 0.410327i | 0.0832703 | − | 0.0604994i | ||||
\(47\) | −0.474965 | + | 2.99881i | −0.0692808 | + | 0.437422i | 0.928528 | + | 0.371262i | \(0.121075\pi\) |
−0.997809 | + | 0.0661599i | \(0.978925\pi\) | |||||||
\(48\) | 1.66004 | − | 0.494220i | 0.239607 | − | 0.0713345i | ||||
\(49\) | − | 6.57265i | − | 0.938950i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.95800 | − | 7.31198i | −0.974315 | − | 1.02388i | ||||
\(52\) | 1.97121 | − | 3.86872i | 0.273358 | − | 0.536495i | ||||
\(53\) | 2.23241 | + | 0.353579i | 0.306645 | + | 0.0485679i | 0.307861 | − | 0.951431i | \(-0.400387\pi\) |
−0.00121543 | + | 0.999999i | \(0.500387\pi\) | |||||||
\(54\) | 5.05756 | + | 1.19210i | 0.688247 | + | 0.162224i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.384246 | − | 0.528869i | 0.0513470 | − | 0.0706731i | ||||
\(57\) | −12.6170 | − | 0.312969i | −1.67116 | − | 0.0414538i | ||||
\(58\) | −3.17710 | + | 0.503203i | −0.417174 | + | 0.0660738i | ||||
\(59\) | 2.66341 | − | 8.19714i | 0.346747 | − | 1.06718i | −0.613895 | − | 0.789388i | \(-0.710398\pi\) |
0.960642 | − | 0.277790i | \(-0.0896018\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.77903 | + | 8.55298i | 0.355818 | + | 1.09510i | 0.955533 | + | 0.294883i | \(0.0952806\pi\) |
−0.599715 | + | 0.800214i | \(0.704719\pi\) | |||||||
\(62\) | −2.70861 | − | 5.31594i | −0.343994 | − | 0.675126i | ||||
\(63\) | 1.78940 | − | 0.802614i | 0.225443 | − | 0.101120i | ||||
\(64\) | −0.951057 | + | 0.309017i | −0.118882 | + | 0.0386271i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.15064 | − | 4.49296i | −0.264726 | − | 0.553045i | ||||
\(67\) | 2.22497 | + | 14.0479i | 0.271823 | + | 1.71622i | 0.624964 | + | 0.780654i | \(0.285114\pi\) |
−0.353141 | + | 0.935570i | \(0.614886\pi\) | |||||||
\(68\) | 4.12066 | + | 4.12066i | 0.499703 | + | 0.499703i | ||||
\(69\) | −1.19856 | + | 0.159477i | −0.144290 | + | 0.0191987i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.15246 | + | 9.84451i | 0.848840 | + | 1.16833i | 0.984117 | + | 0.177521i | \(0.0568077\pi\) |
−0.135277 | + | 0.990808i | \(0.543192\pi\) | |||||||
\(72\) | −2.93615 | − | 0.615636i | −0.346029 | − | 0.0725534i | ||||
\(73\) | −0.498794 | − | 0.254148i | −0.0583794 | − | 0.0297458i | 0.424557 | − | 0.905401i | \(-0.360430\pi\) |
−0.482937 | + | 0.875655i | \(0.660430\pi\) | |||||||
\(74\) | 2.17706 | 0.253078 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.28665 | 0.835837 | ||||||||
\(77\) | −1.67510 | − | 0.853507i | −0.190896 | − | 0.0972661i | ||||
\(78\) | −6.19197 | + | 4.26821i | −0.701102 | + | 0.483280i | ||||
\(79\) | 6.00067 | + | 8.25922i | 0.675128 | + | 0.929234i | 0.999863 | − | 0.0165708i | \(-0.00527490\pi\) |
−0.324734 | + | 0.945805i | \(0.605275\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.72143 | − | 5.98518i | −0.746826 | − | 0.665019i | ||||
\(82\) | −4.71623 | − | 4.71623i | −0.520820 | − | 0.520820i | ||||
\(83\) | −0.742236 | − | 4.68629i | −0.0814709 | − | 0.514387i | −0.994349 | − | 0.106156i | \(-0.966146\pi\) |
0.912879 | − | 0.408231i | \(-0.133854\pi\) | |||||||
\(84\) | −1.02130 | + | 0.488866i | −0.111433 | + | 0.0533396i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.84269 | − | 2.22332i | 0.737866 | − | 0.239747i | ||||
\(87\) | 5.25448 | + | 1.85256i | 0.563340 | + | 0.198615i | ||||
\(88\) | 1.30562 | + | 2.56242i | 0.139179 | + | 0.273155i | ||||
\(89\) | 1.78693 | + | 5.49959i | 0.189414 | + | 0.582956i | 0.999996 | − | 0.00266864i | \(-0.000849456\pi\) |
−0.810583 | + | 0.585624i | \(0.800849\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.877122 | + | 2.69950i | −0.0919473 | + | 0.282985i | ||||
\(92\) | 0.689496 | − | 0.109205i | 0.0718849 | − | 0.0113854i | ||||
\(93\) | −0.256256 | + | 10.3306i | −0.0265725 | + | 1.07124i | ||||
\(94\) | −1.78463 | + | 2.45633i | −0.184070 | + | 0.253351i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.70348 | + | 0.313291i | 0.173861 | + | 0.0319752i | ||||
\(97\) | −5.26300 | − | 0.833578i | −0.534377 | − | 0.0846370i | −0.116587 | − | 0.993181i | \(-0.537195\pi\) |
−0.417790 | + | 0.908544i | \(0.637195\pi\) | |||||||
\(98\) | 2.98392 | − | 5.85628i | 0.301422 | − | 0.591573i | ||||
\(99\) | −0.427760 | + | 8.61700i | −0.0429915 | + | 0.866042i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.5590i | 1.24967i | 0.780758 | + | 0.624833i | \(0.214833\pi\) | ||||
−0.780758 | + | 0.624833i | \(0.785167\pi\) | |||||||
\(102\) | −2.88006 | − | 9.67389i | −0.285168 | − | 0.957858i | ||||
\(103\) | 0.958193 | − | 6.04979i | 0.0944135 | − | 0.596104i | −0.894437 | − | 0.447194i | \(-0.852424\pi\) |
0.988851 | − | 0.148910i | \(-0.0475765\pi\) | |||||||
\(104\) | 3.51273 | − | 2.55215i | 0.344451 | − | 0.250258i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.82857 | + | 1.32854i | 0.177607 | + | 0.129039i | ||||
\(107\) | 0.411529 | − | 0.411529i | 0.0397840 | − | 0.0397840i | −0.686935 | − | 0.726719i | \(-0.741044\pi\) |
0.726719 | + | 0.686935i | \(0.241044\pi\) | |||||||
\(108\) | 3.96512 | + | 3.35825i | 0.381544 | + | 0.323148i | ||||
\(109\) | −11.0499 | − | 3.59033i | −1.05839 | − | 0.343891i | −0.272433 | − | 0.962175i | \(-0.587828\pi\) |
−0.785955 | + | 0.618284i | \(0.787828\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.31630 | − | 1.79469i | −0.314770 | − | 0.170344i | ||||
\(112\) | 0.582467 | − | 0.296782i | 0.0550380 | − | 0.0280433i | ||||
\(113\) | −12.6233 | + | 6.43189i | −1.18750 | + | 0.605061i | −0.932250 | − | 0.361814i | \(-0.882158\pi\) |
−0.255249 | + | 0.966875i | \(0.582158\pi\) | |||||||
\(114\) | −11.0997 | − | 6.00684i | −1.03958 | − | 0.562592i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.05927 | − | 0.994016i | −0.284046 | − | 0.0922921i | ||||
\(117\) | 12.9507 | − | 1.39732i | 1.19730 | − | 0.129182i | ||||
\(118\) | 6.09455 | − | 6.09455i | 0.561048 | − | 0.561048i | ||||
\(119\) | −3.08198 | − | 2.23919i | −0.282525 | − | 0.205266i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.20810 | + | 1.60428i | −0.200736 | + | 0.145844i | ||||
\(122\) | −1.40684 | + | 8.88241i | −0.127369 | + | 0.804176i | ||||
\(123\) | 3.29632 | + | 11.0721i | 0.297219 | + | 0.998336i | ||||
\(124\) | − | 5.96622i | − | 0.535783i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.95874 | + | 0.0972348i | 0.174499 | + | 0.00866236i | ||||
\(127\) | −6.58036 | + | 12.9147i | −0.583912 | + | 1.14599i | 0.390369 | + | 0.920658i | \(0.372347\pi\) |
−0.974282 | + | 0.225334i | \(0.927653\pi\) | |||||||
\(128\) | −0.987688 | − | 0.156434i | −0.0873001 | − | 0.0138270i | ||||
\(129\) | −12.2563 | − | 2.25408i | −1.07910 | − | 0.198460i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.23088 | + | 4.44693i | −0.282283 | + | 0.388530i | −0.926489 | − | 0.376323i | \(-0.877188\pi\) |
0.644205 | + | 0.764853i | \(0.277188\pi\) | |||||||
\(132\) | 0.123522 | − | 4.97962i | 0.0107512 | − | 0.433421i | ||||
\(133\) | −4.70477 | + | 0.745163i | −0.407956 | + | 0.0646138i | ||||
\(134\) | −4.39515 | + | 13.5269i | −0.379683 | + | 1.16854i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.80079 | + | 5.54227i | 0.154417 | + | 0.475246i | ||||
\(137\) | −9.55034 | − | 18.7436i | −0.815941 | − | 1.60137i | −0.798858 | − | 0.601520i | \(-0.794562\pi\) |
−0.0170834 | − | 0.999854i | \(-0.505438\pi\) | |||||||
\(138\) | −1.14033 | − | 0.402042i | −0.0970713 | − | 0.0342241i | ||||
\(139\) | 11.0917 | − | 3.60392i | 0.940788 | − | 0.305681i | 0.201821 | − | 0.979422i | \(-0.435314\pi\) |
0.738967 | + | 0.673742i | \(0.235314\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.74342 | − | 2.27053i | 0.399468 | − | 0.191214i | ||||
\(142\) | 1.90357 | + | 12.0187i | 0.159744 | + | 1.00858i | ||||
\(143\) | −8.82961 | − | 8.82961i | −0.738369 | − | 0.738369i | ||||
\(144\) | −2.33664 | − | 1.88152i | −0.194720 | − | 0.156793i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.329048 | − | 0.452896i | −0.0272322 | − | 0.0374819i | ||||
\(147\) | −9.37309 | + | 6.46100i | −0.773079 | + | 0.532894i | ||||
\(148\) | 1.93977 | + | 0.988365i | 0.159449 | + | 0.0812431i | ||||
\(149\) | −10.0289 | −0.821602 | −0.410801 | − | 0.911725i | \(-0.634751\pi\) | ||||
−0.410801 | + | 0.911725i | \(0.634751\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.9175 | 1.45811 | 0.729054 | − | 0.684456i | \(-0.239960\pi\) | ||||
0.729054 | + | 0.684456i | \(0.239960\pi\) | |||||||
\(152\) | 6.49246 | + | 3.30807i | 0.526608 | + | 0.268320i | ||||
\(153\) | −3.58761 | + | 17.1104i | −0.290041 | + | 1.38329i | ||||
\(154\) | −1.10504 | − | 1.52096i | −0.0890469 | − | 0.122562i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.45481 | + | 0.991909i | −0.596863 | + | 0.0794163i | ||||
\(157\) | 6.42991 | + | 6.42991i | 0.513163 | + | 0.513163i | 0.915494 | − | 0.402331i | \(-0.131800\pi\) |
−0.402331 | + | 0.915494i | \(0.631800\pi\) | |||||||
\(158\) | 1.59703 | + | 10.0833i | 0.127053 | + | 0.802181i | ||||
\(159\) | −1.69026 | − | 3.53116i | −0.134046 | − | 0.280039i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.434019 | + | 0.141021i | −0.0342055 | + | 0.0111140i | ||||
\(162\) | −3.27163 | − | 8.38430i | −0.257043 | − | 0.658733i | ||||
\(163\) | 4.21139 | + | 8.26532i | 0.329862 | + | 0.647390i | 0.995060 | − | 0.0992767i | \(-0.0316529\pi\) |
−0.665198 | + | 0.746667i | \(0.731653\pi\) | |||||||
\(164\) | −2.06107 | − | 6.34331i | −0.160942 | − | 0.495329i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.46619 | − | 4.51248i | 0.113799 | − | 0.350237i | ||||
\(167\) | 5.01819 | − | 0.794803i | 0.388319 | − | 0.0615037i | 0.0407774 | − | 0.999168i | \(-0.487017\pi\) |
0.347542 | + | 0.937665i | \(0.387017\pi\) | |||||||
\(168\) | −1.13193 | − | 0.0280779i | −0.0873299 | − | 0.00216626i | ||||
\(169\) | −3.44013 | + | 4.73493i | −0.264625 | + | 0.364226i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.9563 | + | 18.3004i | 0.914323 | + | 1.39947i | ||||
\(172\) | 7.10625 | + | 1.12552i | 0.541846 | + | 0.0858200i | ||||
\(173\) | −8.65954 | + | 16.9953i | −0.658373 | + | 1.29213i | 0.284404 | + | 0.958705i | \(0.408204\pi\) |
−0.942777 | + | 0.333425i | \(0.891796\pi\) | |||||||
\(174\) | 3.84073 | + | 4.03612i | 0.291165 | + | 0.305978i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.87587i | 0.216777i | ||||||||
\(177\) | −14.3079 | + | 4.25967i | −1.07545 | + | 0.320177i | ||||
\(178\) | −0.904600 | + | 5.71142i | −0.0678026 | + | 0.428089i | ||||
\(179\) | 3.24712 | − | 2.35917i | 0.242701 | − | 0.176332i | −0.459785 | − | 0.888030i | \(-0.652073\pi\) |
0.702486 | + | 0.711698i | \(0.252073\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.30770 | + | 2.40319i | 0.245860 | + | 0.178628i | 0.703890 | − | 0.710309i | \(-0.251445\pi\) |
−0.458030 | + | 0.888937i | \(0.651445\pi\) | |||||||
\(182\) | −2.00707 | + | 2.00707i | −0.148774 | + | 0.148774i | ||||
\(183\) | 9.46535 | − | 12.3708i | 0.699699 | − | 0.914475i | ||||
\(184\) | 0.663923 | + | 0.215722i | 0.0489451 | + | 0.0159032i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.91833 | + | 9.08832i | −0.360629 | + | 0.666388i | ||||
\(187\) | 14.9325 | − | 7.60848i | 1.09197 | − | 0.556387i | ||||
\(188\) | −2.70527 | + | 1.37840i | −0.197302 | + | 0.100530i | ||||
\(189\) | −2.90359 | − | 1.76283i | −0.211205 | − | 0.128227i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.5725 | − | 3.76012i | −0.837354 | − | 0.272073i | −0.141214 | − | 0.989979i | \(-0.545101\pi\) |
−0.696140 | + | 0.717906i | \(0.745101\pi\) | |||||||
\(192\) | 1.37558 | + | 1.05251i | 0.0992741 | + | 0.0759583i | ||||
\(193\) | 9.01719 | − | 9.01719i | 0.649071 | − | 0.649071i | −0.303697 | − | 0.952769i | \(-0.598221\pi\) |
0.952769 | + | 0.303697i | \(0.0982211\pi\) | |||||||
\(194\) | −4.31093 | − | 3.13208i | −0.309507 | − | 0.224870i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.31739 | − | 3.86331i | 0.379813 | − | 0.275951i | ||||
\(197\) | −0.0641446 | + | 0.404993i | −0.00457012 | + | 0.0288546i | −0.989868 | − | 0.141990i | \(-0.954650\pi\) |
0.985298 | + | 0.170845i | \(0.0546498\pi\) | |||||||
\(198\) | −4.29318 | + | 7.48361i | −0.305103 | + | 0.531837i | ||||
\(199\) | 10.9949i | 0.779406i | 0.920941 | + | 0.389703i | \(0.127422\pi\) | ||||
−0.920941 | + | 0.389703i | \(0.872578\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.8462 | − | 16.9822i | 1.25877 | − | 1.19783i | ||||
\(202\) | −5.70166 | + | 11.1901i | −0.401168 | + | 0.787336i | ||||
\(203\) | 2.07693 | + | 0.328953i | 0.145772 | + | 0.0230880i | ||||
\(204\) | 1.82570 | − | 9.92702i | 0.127825 | − | 0.695030i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.60030 | − | 4.95539i | 0.250845 | − | 0.345259i | ||||
\(207\) | 1.40563 | + | 1.55247i | 0.0976980 | + | 0.107904i | ||||
\(208\) | 4.28851 | − | 0.679234i | 0.297355 | − | 0.0470964i | ||||
\(209\) | 6.47560 | − | 19.9298i | 0.447927 | − | 1.37858i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.64735 | + | 20.4585i | 0.457623 | + | 1.40842i | 0.868028 | + | 0.496515i | \(0.165387\pi\) |
−0.410406 | + | 0.911903i | \(0.634613\pi\) | |||||||
\(212\) | 1.02613 | + | 2.01389i | 0.0704747 | + | 0.138314i | ||||
\(213\) | 7.00804 | − | 19.8772i | 0.480183 | − | 1.36196i | ||||
\(214\) | 0.553505 | − | 0.179845i | 0.0378368 | − | 0.0122939i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.00833 | + | 4.79235i | 0.136650 | + | 0.326078i | ||||
\(217\) | 0.610130 | + | 3.85221i | 0.0414184 | + | 0.261505i | ||||
\(218\) | −8.21555 | − | 8.21555i | −0.556427 | − | 0.556427i | ||||
\(219\) | 0.127887 | + | 0.961148i | 0.00864179 | + | 0.0649484i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.8726 | − | 20.4704i | −1.00044 | − | 1.37699i | ||||
\(222\) | −2.14008 | − | 3.10465i | −0.143633 | − | 0.208370i | ||||
\(223\) | −5.65554 | − | 2.88164i | −0.378723 | − | 0.192969i | 0.254258 | − | 0.967137i | \(-0.418169\pi\) |
−0.632981 | + | 0.774167i | \(0.718169\pi\) | |||||||
\(224\) | 0.653718 | 0.0436784 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.1675 | −0.942405 | ||||||||
\(227\) | −12.5844 | − | 6.41208i | −0.835257 | − | 0.425584i | −0.0165960 | − | 0.999862i | \(-0.505283\pi\) |
−0.818660 | + | 0.574278i | \(0.805283\pi\) | |||||||
\(228\) | −7.16287 | − | 10.3913i | −0.474373 | − | 0.688181i | ||||
\(229\) | −8.94288 | − | 12.3088i | −0.590962 | − | 0.813389i | 0.403882 | − | 0.914811i | \(-0.367661\pi\) |
−0.994844 | + | 0.101422i | \(0.967661\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.429482 | + | 3.22783i | 0.0282579 | + | 0.212375i | ||||
\(232\) | −2.27455 | − | 2.27455i | −0.149332 | − | 0.149332i | ||||
\(233\) | 1.18798 | + | 7.50060i | 0.0778271 | + | 0.491381i | 0.995556 | + | 0.0941731i | \(0.0300207\pi\) |
−0.917729 | + | 0.397208i | \(0.869979\pi\) | |||||||
\(234\) | 12.1736 | + | 4.63450i | 0.795811 | + | 0.302967i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.19714 | − | 2.66341i | 0.533589 | − | 0.173373i | ||||
\(237\) | 5.87951 | − | 16.6763i | 0.381915 | − | 1.08324i | ||||
\(238\) | −1.72949 | − | 3.39432i | −0.112106 | − | 0.220021i | ||||
\(239\) | −3.85885 | − | 11.8763i | −0.249608 | − | 0.768215i | −0.994844 | − | 0.101414i | \(-0.967663\pi\) |
0.745236 | − | 0.666801i | \(-0.232337\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.01360 | − | 21.5856i | 0.451786 | − | 1.39045i | −0.423082 | − | 0.906092i | \(-0.639052\pi\) |
0.874868 | − | 0.484362i | \(-0.160948\pi\) | |||||||
\(242\) | −2.69576 | + | 0.426966i | −0.173290 | + | 0.0274464i | ||||
\(243\) | −1.92805 | + | 15.4688i | −0.123684 | + | 0.992322i | ||||
\(244\) | −5.28603 | + | 7.27560i | −0.338403 | + | 0.465772i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.08958 | + | 11.3618i | −0.133226 | + | 0.724402i | ||||
\(247\) | −31.2489 | − | 4.94934i | −1.98832 | − | 0.314919i | ||||
\(248\) | 2.70861 | − | 5.31594i | 0.171997 | − | 0.337563i | ||||
\(249\) | −5.95337 | + | 5.66517i | −0.377279 | + | 0.359015i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 8.40399i | − | 0.530455i | −0.964186 | − | 0.265228i | \(-0.914553\pi\) | ||
0.964186 | − | 0.265228i | \(-0.0854471\pi\) | |||||||
\(252\) | 1.70111 | + | 0.975888i | 0.107160 | + | 0.0614751i | ||||
\(253\) | 0.314061 | − | 1.98290i | 0.0197448 | − | 0.124664i | ||||
\(254\) | −11.7263 | + | 8.51964i | −0.735773 | + | 0.534570i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | −21.2293 | + | 21.2293i | −1.32425 | + | 1.32425i | −0.413942 | + | 0.910303i | \(0.635848\pi\) |
−0.910303 | + | 0.413942i | \(0.864152\pi\) | |||||||
\(258\) | −9.89707 | − | 7.57262i | −0.616165 | − | 0.471451i | ||||
\(259\) | −1.35353 | − | 0.439788i | −0.0841042 | − | 0.0273271i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.52334 | − | 9.31436i | −0.156191 | − | 0.576545i | ||||
\(262\) | −4.89760 | + | 2.49545i | −0.302575 | + | 0.154169i | ||||
\(263\) | −3.75527 | + | 1.91341i | −0.231560 | + | 0.117986i | −0.565921 | − | 0.824459i | \(-0.691479\pi\) |
0.334361 | + | 0.942445i | \(0.391479\pi\) | |||||||
\(264\) | 2.37076 | − | 4.38080i | 0.145910 | − | 0.269620i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.53028 | − | 1.47198i | −0.277769 | − | 0.0902527i | ||||
\(267\) | 6.08625 | − | 7.95446i | 0.372473 | − | 0.486805i | ||||
\(268\) | −10.0572 | + | 10.0572i | −0.614340 | + | 0.614340i | ||||
\(269\) | 16.4085 | + | 11.9215i | 1.00044 | + | 0.726865i | 0.962183 | − | 0.272402i | \(-0.0878182\pi\) |
0.0382610 | + | 0.999268i | \(0.487818\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.48031 | + | 3.98168i | −0.332905 | + | 0.241870i | −0.741662 | − | 0.670773i | \(-0.765962\pi\) |
0.408757 | + | 0.912643i | \(0.365962\pi\) | |||||||
\(272\) | −0.911620 | + | 5.75574i | −0.0552751 | + | 0.348993i | ||||
\(273\) | 4.71191 | − | 1.40281i | 0.285178 | − | 0.0849017i | ||||
\(274\) | − | 21.0364i | − | 1.27086i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.833518 | − | 0.875921i | −0.0501719 | − | 0.0527243i | ||||
\(277\) | 11.1150 | − | 21.8145i | 0.667837 | − | 1.31070i | −0.269742 | − | 0.962933i | \(-0.586938\pi\) |
0.937579 | − | 0.347772i | \(-0.113062\pi\) | |||||||
\(278\) | 11.5189 | + | 1.82442i | 0.690861 | + | 0.109422i | ||||
\(279\) | 14.9841 | − | 9.78970i | 0.897077 | − | 0.586094i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.8968 | + | 16.3745i | −0.709702 | + | 0.976820i | 0.290102 | + | 0.956996i | \(0.406311\pi\) |
−0.999803 | + | 0.0198246i | \(0.993689\pi\) | |||||||
\(282\) | 5.25722 | + | 0.130408i | 0.313063 | + | 0.00776566i | ||||
\(283\) | 8.20158 | − | 1.29900i | 0.487533 | − | 0.0772177i | 0.0921715 | − | 0.995743i | \(-0.470619\pi\) |
0.395362 | + | 0.918525i | \(0.370619\pi\) | |||||||
\(284\) | −3.76027 | + | 11.5729i | −0.223131 | + | 0.686726i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.85868 | − | 11.8758i | −0.228168 | − | 0.702230i | ||||
\(287\) | 1.97946 | + | 3.88491i | 0.116844 | + | 0.229319i | ||||
\(288\) | −1.22777 | − | 2.73726i | −0.0723469 | − | 0.161295i | ||||
\(289\) | 16.1295 | − | 5.24081i | 0.948797 | − | 0.308283i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.98486 | + | 8.32485i | 0.233596 | + | 0.488011i | ||||
\(292\) | −0.0875735 | − | 0.552918i | −0.00512485 | − | 0.0323571i | ||||
\(293\) | 1.20804 | + | 1.20804i | 0.0705747 | + | 0.0705747i | 0.741513 | − | 0.670938i | \(-0.234109\pi\) |
−0.670938 | + | 0.741513i | \(0.734109\pi\) | |||||||
\(294\) | −11.2847 | + | 1.50150i | −0.658138 | + | 0.0875694i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.27964 | + | 1.76128i | 0.0743778 | + | 0.102372i | ||||
\(297\) | 12.7090 | − | 7.86061i | 0.737450 | − | 0.456119i | ||||
\(298\) | −8.93584 | − | 4.55304i | −0.517639 | − | 0.263750i | ||||
\(299\) | −3.03109 | −0.175292 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.70339 | −0.271099 | ||||||||
\(302\) | 15.9646 | + | 8.13439i | 0.918661 | + | 0.468081i | ||||
\(303\) | 17.9100 | − | 12.3456i | 1.02891 | − | 0.709239i | ||||
\(304\) | 4.28299 | + | 5.89503i | 0.245646 | + | 0.338103i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −10.9645 | + | 13.6167i | −0.626801 | + | 0.778417i | ||||
\(307\) | −4.52656 | − | 4.52656i | −0.258344 | − | 0.258344i | 0.566036 | − | 0.824380i | \(-0.308476\pi\) |
−0.824380 | + | 0.566036i | \(0.808476\pi\) | |||||||
\(308\) | −0.294098 | − | 1.85686i | −0.0167578 | − | 0.105805i | ||||
\(309\) | −9.56936 | + | 4.58057i | −0.544382 | + | 0.260579i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 32.9364 | − | 10.7017i | 1.86765 | − | 0.606838i | 0.875274 | − | 0.483628i | \(-0.160681\pi\) |
0.992381 | − | 0.123210i | \(-0.0393188\pi\) | |||||||
\(312\) | −7.09260 | − | 2.50062i | −0.401540 | − | 0.141569i | ||||
\(313\) | 11.8701 | + | 23.2965i | 0.670940 | + | 1.31679i | 0.935808 | + | 0.352509i | \(0.114671\pi\) |
−0.264869 | + | 0.964285i | \(0.585329\pi\) | |||||||
\(314\) | 2.80998 | + | 8.64821i | 0.158576 | + | 0.488047i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.15474 | + | 9.70929i | −0.177468 | + | 0.546190i | ||||
\(317\) | 13.4990 | − | 2.13804i | 0.758181 | − | 0.120084i | 0.234638 | − | 0.972083i | \(-0.424610\pi\) |
0.523544 | + | 0.851999i | \(0.324610\pi\) | |||||||
\(318\) | 0.0970796 | − | 3.91365i | 0.00544396 | − | 0.219466i | ||||
\(319\) | −5.43750 | + | 7.48407i | −0.304441 | + | 0.419028i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.991408 | − | 0.182332i | −0.0553350 | − | 0.0101768i | ||||
\(322\) | −0.450736 | − | 0.0713896i | −0.0251185 | − | 0.00397838i | ||||
\(323\) | 19.2777 | − | 37.8347i | 1.07264 | − | 2.10518i | ||||
\(324\) | 0.891349 | − | 8.95575i | 0.0495194 | − | 0.497542i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.27639i | 0.513772i | ||||||||
\(327\) | 5.74211 | + | 19.2873i | 0.317540 | + | 1.06659i | ||||
\(328\) | 1.04338 | − | 6.58764i | 0.0576110 | − | 0.363741i | ||||
\(329\) | 1.60575 | − | 1.16664i | 0.0885278 | − | 0.0643192i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.55071 | − | 6.21245i | −0.469989 | − | 0.341467i | 0.327448 | − | 0.944869i | \(-0.393811\pi\) |
−0.797437 | + | 0.603402i | \(0.793811\pi\) | |||||||
\(332\) | 3.35501 | − | 3.35501i | 0.184130 | − | 0.184130i | ||||
\(333\) | 0.700614 | + | 6.49349i | 0.0383934 | + | 0.355841i | ||||
\(334\) | 4.83207 | + | 1.57004i | 0.264399 | + | 0.0859085i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.995806 | − | 0.538901i | −0.0543257 | − | 0.0293995i | ||||
\(337\) | 28.0951 | − | 14.3152i | 1.53044 | − | 0.779796i | 0.532652 | − | 0.846334i | \(-0.321195\pi\) |
0.997784 | + | 0.0665380i | \(0.0211954\pi\) | |||||||
\(338\) | −5.21479 | + | 2.65707i | −0.283647 | + | 0.144526i | ||||
\(339\) | 21.5812 | + | 11.6791i | 1.17213 | + | 0.634323i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.3183 | − | 5.30214i | −0.883686 | − | 0.287127i | ||||
\(342\) | 2.34496 | + | 21.7338i | 0.126801 | + | 1.17523i | ||||
\(343\) | −6.27394 | + | 6.27394i | −0.338761 | + | 0.338761i | ||||
\(344\) | 5.82074 | + | 4.22901i | 0.313833 | + | 0.228013i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.4314 | + | 11.2116i | −0.829598 | + | 0.602738i | ||||
\(347\) | 2.04407 | − | 12.9057i | 0.109731 | − | 0.692816i | −0.870083 | − | 0.492905i | \(-0.835935\pi\) |
0.979814 | − | 0.199911i | \(-0.0640652\pi\) | |||||||
\(348\) | 1.58976 | + | 5.33987i | 0.0852200 | + | 0.286247i | ||||
\(349\) | 30.4326i | 1.62902i | 0.580151 | + | 0.814509i | \(0.302993\pi\) | ||||
−0.580151 | + | 0.814509i | \(0.697007\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.7234 | − | 17.0951i | −0.785878 | − | 0.912471i | ||||
\(352\) | −1.30562 | + | 2.56242i | −0.0695897 | + | 0.136577i | ||||
\(353\) | 2.87776 | + | 0.455793i | 0.153168 | + | 0.0242594i | 0.232547 | − | 0.972585i | \(-0.425294\pi\) |
−0.0793796 | + | 0.996844i | \(0.525294\pi\) | |||||||
\(354\) | −14.6823 | − | 2.70025i | −0.780355 | − | 0.143517i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.39893 | + | 4.67823i | −0.180143 | + | 0.247946i | ||||
\(357\) | −0.163624 | + | 6.59628i | −0.00865988 | + | 0.349112i | ||||
\(358\) | 3.96424 | − | 0.627874i | 0.209517 | − | 0.0331842i | ||||
\(359\) | −2.44510 | + | 7.52523i | −0.129047 | + | 0.397167i | −0.994617 | − | 0.103622i | \(-0.966957\pi\) |
0.865569 | + | 0.500789i | \(0.166957\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.5360 | − | 32.4266i | −0.554528 | − | 1.70666i | ||||
\(362\) | 1.85616 | + | 3.64292i | 0.0975577 | + | 0.191468i | ||||
\(363\) | 4.45841 | + | 1.57189i | 0.234006 | + | 0.0825027i | ||||
\(364\) | −2.69950 | + | 0.877122i | −0.141492 | + | 0.0459737i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 14.0499 | − | 6.72527i | 0.734401 | − | 0.351536i | ||||
\(367\) | −3.44380 | − | 21.7433i | −0.179765 | − | 1.13499i | −0.898262 | − | 0.439460i | \(-0.855170\pi\) |
0.718497 | − | 0.695530i | \(-0.244830\pi\) | |||||||
\(368\) | 0.493624 | + | 0.493624i | 0.0257319 | + | 0.0257319i | ||||
\(369\) | 12.5493 | − | 15.5848i | 0.653289 | − | 0.811312i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.868488 | − | 1.19537i | −0.0450897 | − | 0.0620606i | ||||
\(372\) | −8.50827 | + | 5.86487i | −0.441133 | + | 0.304080i | ||||
\(373\) | −19.0344 | − | 9.69853i | −0.985566 | − | 0.502171i | −0.114545 | − | 0.993418i | \(-0.536541\pi\) |
−0.871020 | + | 0.491247i | \(0.836541\pi\) | |||||||
\(374\) | 16.7591 | 0.866593 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.03619 | −0.156580 | ||||||||
\(377\) | 12.4445 | + | 6.34081i | 0.640926 | + | 0.326568i | ||||
\(378\) | −1.78681 | − | 2.88890i | −0.0919034 | − | 0.148589i | ||||
\(379\) | −0.581554 | − | 0.800441i | −0.0298724 | − | 0.0411159i | 0.793820 | − | 0.608153i | \(-0.208089\pi\) |
−0.823692 | + | 0.567038i | \(0.808089\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 24.8859 | − | 3.31122i | 1.27494 | − | 0.169639i | ||||
\(382\) | −8.60408 | − | 8.60408i | −0.440223 | − | 0.440223i | ||||
\(383\) | 1.97847 | + | 12.4916i | 0.101095 | + | 0.638289i | 0.985253 | + | 0.171102i | \(0.0547326\pi\) |
−0.884158 | + | 0.467187i | \(0.845267\pi\) | |||||||
\(384\) | 0.747823 | + | 1.56229i | 0.0381622 | + | 0.0797254i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.1281 | − | 3.94066i | 0.617304 | − | 0.200574i | ||||
\(387\) | 8.83357 | + | 19.6941i | 0.449036 | + | 1.00111i | ||||
\(388\) | −2.41914 | − | 4.74782i | −0.122813 | − | 0.241034i | ||||
\(389\) | 8.45598 | + | 26.0248i | 0.428735 | + | 1.31951i | 0.899372 | + | 0.437185i | \(0.144024\pi\) |
−0.470636 | + | 0.882327i | \(0.655976\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.25712 | − | 3.86900i | 0.0635751 | − | 0.195664i | ||||
\(392\) | 6.49173 | − | 1.02819i | 0.327882 | − | 0.0519314i | ||||
\(393\) | 9.51764 | + | 0.236089i | 0.480102 | + | 0.0119091i | ||||
\(394\) | −0.241016 | + | 0.331731i | −0.0121422 | + | 0.0167123i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −7.22273 | + | 4.71888i | −0.362956 | + | 0.237133i | ||||
\(397\) | −3.51235 | − | 0.556301i | −0.176280 | − | 0.0279199i | 0.0676706 | − | 0.997708i | \(-0.478443\pi\) |
−0.243950 | + | 0.969788i | \(0.578443\pi\) | |||||||
\(398\) | −4.99157 | + | 9.79650i | −0.250205 | + | 0.491054i | ||||
\(399\) | 5.68751 | + | 5.97685i | 0.284732 | + | 0.299217i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.6499i | 0.831458i | 0.909489 | + | 0.415729i | \(0.136473\pi\) | ||||
−0.909489 | + | 0.415729i | \(0.863527\pi\) | |||||||
\(402\) | 23.6108 | − | 7.02929i | 1.17760 | − | 0.350589i | ||||
\(403\) | −4.05246 | + | 25.5862i | −0.201867 | + | 1.27454i | ||||
\(404\) | −10.1604 | + | 7.38199i | −0.505501 | + | 0.367268i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.70122 | + | 1.23601i | 0.0844299 | + | 0.0613419i | ||||
\(407\) | 4.42716 | − | 4.42716i | 0.219446 | − | 0.219446i | ||||
\(408\) | 6.13348 | − | 8.01618i | 0.303653 | − | 0.396860i | ||||
\(409\) | −4.09420 | − | 1.33029i | −0.202445 | − | 0.0657784i | 0.206039 | − | 0.978544i | \(-0.433943\pi\) |
−0.408484 | + | 0.912765i | \(0.633943\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.3417 | + | 32.0447i | −0.855401 | + | 1.58065i | ||||
\(412\) | 5.45760 | − | 2.78078i | 0.268876 | − | 0.136999i | ||||
\(413\) | −5.02028 | + | 2.55796i | −0.247032 | + | 0.125869i | ||||
\(414\) | 0.547617 | + | 2.02141i | 0.0269139 | + | 0.0993467i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.12946 | + | 1.34174i | 0.202463 | + | 0.0657843i | ||||
\(417\) | −16.0428 | − | 12.2749i | −0.785618 | − | 0.601105i | ||||
\(418\) | 14.8178 | − | 14.8178i | 0.724761 | − | 0.724761i | ||||
\(419\) | 5.84455 | + | 4.24631i | 0.285525 | + | 0.207446i | 0.721324 | − | 0.692598i | \(-0.243534\pi\) |
−0.435799 | + | 0.900044i | \(0.643534\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.7630 | + | 8.54631i | −0.573293 | + | 0.416521i | −0.836300 | − | 0.548272i | \(-0.815286\pi\) |
0.263007 | + | 0.964794i | \(0.415286\pi\) | |||||||
\(422\) | −3.36511 | + | 21.2464i | −0.163811 | + | 1.03426i | ||||
\(423\) | −7.90079 | − | 4.53251i | −0.384150 | − | 0.220378i | ||||
\(424\) | 2.26024i | 0.109767i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 15.2683 | − | 14.5291i | 0.739750 | − | 0.703939i | ||||
\(427\) | 2.66900 | − | 5.23821i | 0.129162 | − | 0.253495i | ||||
\(428\) | 0.574824 | + | 0.0910432i | 0.0277852 | + | 0.00440074i | ||||
\(429\) | −3.91205 | + | 21.2713i | −0.188876 | + | 1.02699i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.43967 | − | 3.35792i | 0.117515 | − | 0.161745i | −0.746207 | − | 0.665714i | \(-0.768127\pi\) |
0.863722 | + | 0.503968i | \(0.168127\pi\) | |||||||
\(432\) | −0.386242 | + | 5.18178i | −0.0185831 | + | 0.249308i | ||||
\(433\) | −28.8682 | + | 4.57227i | −1.38732 | + | 0.219729i | −0.805020 | − | 0.593248i | \(-0.797846\pi\) |
−0.582296 | + | 0.812977i | \(0.697846\pi\) | |||||||
\(434\) | −1.20524 | + | 3.70934i | −0.0578532 | + | 0.178054i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.59033 | − | 11.0499i | −0.171945 | − | 0.529194i | ||||
\(437\) | −2.30933 | − | 4.53232i | −0.110470 | − | 0.216810i | ||||
\(438\) | −0.322404 | + | 0.914449i | −0.0154051 | + | 0.0436941i | ||||
\(439\) | 10.7432 | − | 3.49067i | 0.512744 | − | 0.166601i | −0.0412056 | − | 0.999151i | \(-0.513120\pi\) |
0.553950 | + | 0.832550i | \(0.313120\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.4277 | + | 7.01546i | 0.877511 | + | 0.334070i | ||||
\(442\) | −3.95823 | − | 24.9913i | −0.188274 | − | 1.18871i | ||||
\(443\) | −12.3286 | − | 12.3286i | −0.585749 | − | 0.585749i | 0.350728 | − | 0.936477i | \(-0.385934\pi\) |
−0.936477 | + | 0.350728i | \(0.885934\pi\) | |||||||
\(444\) | −0.497343 | − | 3.73784i | −0.0236028 | − | 0.177390i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.73089 | − | 5.13513i | −0.176663 | − | 0.243155i | ||||
\(447\) | 9.85857 | + | 14.3020i | 0.466294 | + | 0.676461i | ||||
\(448\) | 0.582467 | + | 0.296782i | 0.0275190 | + | 0.0140216i | ||||
\(449\) | 11.4060 | 0.538284 | 0.269142 | − | 0.963101i | \(-0.413260\pi\) | ||||
0.269142 | + | 0.963101i | \(0.413260\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.1813 | −0.903214 | ||||||||
\(452\) | −12.6233 | − | 6.43189i | −0.593750 | − | 0.302531i | ||||
\(453\) | −17.6132 | − | 25.5517i | −0.827538 | − | 1.20052i | ||||
\(454\) | −8.30177 | − | 11.4264i | −0.389621 | − | 0.536268i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.66461 | − | 12.5106i | −0.0779527 | − | 0.585862i | ||||
\(457\) | 4.54539 | + | 4.54539i | 0.212624 | + | 0.212624i | 0.805381 | − | 0.592757i | \(-0.201961\pi\) |
−0.592757 | + | 0.805381i | \(0.701961\pi\) | |||||||
\(458\) | −2.38008 | − | 15.0272i | −0.111214 | − | 0.702176i | ||||
\(459\) | 27.9273 | − | 11.7035i | 1.30354 | − | 0.546274i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.3653 | − | 5.96726i | 0.855359 | − | 0.277923i | 0.151670 | − | 0.988431i | \(-0.451535\pi\) |
0.703689 | + | 0.710508i | \(0.251535\pi\) | |||||||
\(462\) | −1.08273 | + | 3.07100i | −0.0503732 | + | 0.142876i | ||||
\(463\) | −2.03171 | − | 3.98746i | −0.0944216 | − | 0.185313i | 0.838965 | − | 0.544186i | \(-0.183161\pi\) |
−0.933387 | + | 0.358873i | \(0.883161\pi\) | |||||||
\(464\) | −0.994016 | − | 3.05927i | −0.0461460 | − | 0.142023i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.34671 | + | 7.22242i | −0.108709 | + | 0.334572i | ||||
\(467\) | −1.74215 | + | 0.275929i | −0.0806170 | + | 0.0127685i | −0.196613 | − | 0.980481i | \(-0.562994\pi\) |
0.115996 | + | 0.993250i | \(0.462994\pi\) | |||||||
\(468\) | 8.74271 | + | 9.65605i | 0.404132 | + | 0.446351i | ||||
\(469\) | 5.46513 | − | 7.52211i | 0.252356 | − | 0.347339i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.84884 | − | 15.4902i | 0.131268 | − | 0.713752i | ||||
\(472\) | 8.51287 | + | 1.34831i | 0.391837 | + | 0.0620609i | ||||
\(473\) | 9.39370 | − | 18.4362i | 0.431923 | − | 0.847696i | ||||
\(474\) | 12.8096 | − | 12.1895i | 0.588363 | − | 0.559881i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 3.80954i | − | 0.174610i | ||||||
\(477\) | −3.37414 | + | 5.88161i | −0.154491 | + | 0.269300i | ||||
\(478\) | 1.95347 | − | 12.3338i | 0.0893498 | − | 0.564133i | ||||
\(479\) | 13.7743 | − | 10.0076i | 0.629363 | − | 0.457259i | −0.226817 | − | 0.973937i | \(-0.572832\pi\) |
0.856179 | + | 0.516679i | \(0.172832\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.64742 | − | 5.55617i | −0.348692 | − | 0.253340i | ||||
\(482\) | 16.0488 | − | 16.0488i | 0.731005 | − | 0.731005i | ||||
\(483\) | 0.627753 | + | 0.480317i | 0.0285637 | + | 0.0218552i | ||||
\(484\) | −2.59578 | − | 0.843419i | −0.117990 | − | 0.0383372i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −8.74057 | + | 12.9075i | −0.396480 | + | 0.585494i | ||||
\(487\) | −25.0891 | + | 12.7835i | −1.13690 | + | 0.579277i | −0.918043 | − | 0.396481i | \(-0.870231\pi\) |
−0.218852 | + | 0.975758i | \(0.570231\pi\) | |||||||
\(488\) | −8.01294 | + | 4.08280i | −0.362729 | + | 0.184820i | ||||
\(489\) | 7.64711 | − | 14.1307i | 0.345814 | − | 0.639011i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.69557 | + | 2.82536i | 0.392426 | + | 0.127507i | 0.498582 | − | 0.866843i | \(-0.333854\pi\) |
−0.106156 | + | 0.994349i | \(0.533854\pi\) | |||||||
\(492\) | −7.01997 | + | 9.17479i | −0.316485 | + | 0.413631i | ||||
\(493\) | −13.2549 | + | 13.2549i | −0.596972 | + | 0.596972i | ||||
\(494\) | −25.5960 | − | 18.5966i | −1.15162 | − | 0.836701i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.82678 | − | 3.50686i | 0.216729 | − | 0.157463i | ||||
\(497\) | 1.24440 | − | 7.85683i | 0.0558189 | − | 0.352427i | ||||
\(498\) | −7.87642 | + | 2.34493i | −0.352951 | + | 0.105079i | ||||
\(499\) | − | 12.9235i | − | 0.578536i | −0.957248 | − | 0.289268i | \(-0.906588\pi\) | ||
0.957248 | − | 0.289268i | \(-0.0934119\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.06639 | − | 6.37500i | −0.271026 | − | 0.284814i | ||||
\(502\) | 3.81533 | − | 7.48801i | 0.170287 | − | 0.334206i | ||||
\(503\) | 22.2567 | + | 3.52512i | 0.992379 | + | 0.157177i | 0.631450 | − | 0.775416i | \(-0.282460\pi\) |
0.360928 | + | 0.932594i | \(0.382460\pi\) | |||||||
\(504\) | 1.07266 | + | 1.64181i | 0.0477799 | + | 0.0731320i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.18005 | − | 1.62420i | 0.0524595 | − | 0.0722044i | ||||
\(507\) | 10.1341 | + | 0.251380i | 0.450069 | + | 0.0111642i | ||||
\(508\) | −14.3160 | + | 2.26744i | −0.635171 | + | 0.100601i | ||||
\(509\) | −1.15005 | + | 3.53949i | −0.0509750 | + | 0.156885i | −0.973304 | − | 0.229522i | \(-0.926284\pi\) |
0.922329 | + | 0.386407i | \(0.126284\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.113087 | + | 0.348047i | 0.00500268 | + | 0.0153967i | ||||
\(512\) | −0.453990 | − | 0.891007i | −0.0200637 | − | 0.0393773i | ||||
\(513\) | 14.3445 | − | 35.0401i | 0.633324 | − | 1.54706i | ||||
\(514\) | −28.5533 | + | 9.27753i | −1.25943 | + | 0.409214i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.38046 | − | 11.2404i | −0.236861 | − | 0.494832i | ||||
\(517\) | 1.36594 | + | 8.62420i | 0.0600739 | + | 0.379292i | ||||
\(518\) | −1.00634 | − | 1.00634i | −0.0442162 | − | 0.0442162i | ||||
\(519\) | 32.7490 | − | 4.35746i | 1.43752 | − | 0.191271i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.0327 | − | 34.4546i | −1.09670 | − | 1.50948i | −0.839683 | − | 0.543077i | \(-0.817259\pi\) |
−0.257021 | − | 0.966406i | \(-0.582741\pi\) | |||||||
\(522\) | 1.98032 | − | 9.44473i | 0.0866762 | − | 0.413385i | ||||
\(523\) | 19.8847 | + | 10.1317i | 0.869495 | + | 0.443030i | 0.831028 | − | 0.556230i | \(-0.187753\pi\) |
0.0384667 | + | 0.999260i | \(0.487753\pi\) | |||||||
\(524\) | −5.49670 | −0.240125 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.21464 | −0.183767 | ||||||||
\(527\) | −30.9786 | − | 15.7844i | −1.34945 | − | 0.687579i | ||||
\(528\) | 4.10120 | − | 2.82702i | 0.178482 | − | 0.123030i | ||||
\(529\) | 13.2326 | + | 18.2131i | 0.575331 | + | 0.791875i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.1395 | + | 16.2168i | 0.873978 | + | 0.703750i | ||||
\(532\) | −3.36825 | − | 3.36825i | −0.146032 | − | 0.146032i | ||||
\(533\) | 4.53032 | + | 28.6033i | 0.196230 | + | 1.23895i | ||||
\(534\) | 9.03414 | − | 4.32437i | 0.390945 | − | 0.187134i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −13.5269 | + | 4.39515i | −0.584272 | + | 0.189842i | ||||
\(537\) | −6.55630 | − | 2.31153i | −0.282925 | − | 0.0997501i | ||||
\(538\) | 9.20785 | + | 18.0714i | 0.396979 | + | 0.779114i | ||||
\(539\) | −5.84107 | − | 17.9770i | −0.251593 | − | 0.774323i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.576378 | − | 1.77391i | 0.0247804 | − | 0.0762663i | −0.937902 | − | 0.346902i | \(-0.887234\pi\) |
0.962682 | + | 0.270635i | \(0.0872338\pi\) | |||||||
\(542\) | −6.69064 | + | 1.05969i | −0.287387 | + | 0.0455177i | ||||
\(543\) | 0.175607 | − | 7.07940i | 0.00753604 | − | 0.303806i | ||||
\(544\) | −3.42531 | + | 4.71454i | −0.146859 | + | 0.202134i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4.83520 | + | 0.889254i | 0.206928 | + | 0.0380566i | ||||
\(547\) | 24.0199 | + | 3.80438i | 1.02702 | + | 0.162663i | 0.647138 | − | 0.762373i | \(-0.275966\pi\) |
0.379878 | + | 0.925036i | \(0.375966\pi\) | |||||||
\(548\) | 9.55034 | − | 18.7436i | 0.407970 | − | 0.800687i | ||||
\(549\) | −26.9462 | − | 1.33765i | −1.15004 | − | 0.0570894i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.4390i | 0.998535i | ||||||||
\(552\) | −0.345010 | − | 1.15886i | −0.0146846 | − | 0.0493244i | ||||
\(553\) | 1.04401 | − | 6.59162i | 0.0443958 | − | 0.280304i | ||||
\(554\) | 19.8071 | − | 14.3907i | 0.841524 | − | 0.611403i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.43519 | + | 6.85506i | 0.400141 | + | 0.290720i | ||||
\(557\) | 18.2820 | − | 18.2820i | 0.774632 | − | 0.774632i | −0.204281 | − | 0.978912i | \(-0.565485\pi\) |
0.978912 | + | 0.204281i | \(0.0654855\pi\) | |||||||
\(558\) | 17.7954 | − | 1.92003i | 0.753339 | − | 0.0812813i | ||||
\(559\) | −29.7107 | − | 9.65360i | −1.25663 | − | 0.408304i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −25.5291 | − | 13.8156i | −1.07784 | − | 0.583294i | ||||
\(562\) | −18.0340 | + | 9.18876i | −0.760717 | + | 0.387604i | ||||
\(563\) | −0.869364 | + | 0.442963i | −0.0366393 | + | 0.0186687i | −0.472214 | − | 0.881484i | \(-0.656545\pi\) |
0.435575 | + | 0.900153i | \(0.356545\pi\) | |||||||
\(564\) | 4.62502 | + | 2.50292i | 0.194748 | + | 0.105392i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.89740 | + | 2.56602i | 0.331952 | + | 0.107858i | ||||
\(567\) | 0.340335 | + | 5.87361i | 0.0142927 | + | 0.246669i | ||||
\(568\) | −8.60442 | + | 8.60442i | −0.361033 | + | 0.361033i | ||||
\(569\) | −22.6112 | − | 16.4280i | −0.947909 | − | 0.688696i | 0.00240243 | − | 0.999997i | \(-0.499235\pi\) |
−0.950311 | + | 0.311301i | \(0.899235\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.29121 | + | 3.11775i | −0.179582 | + | 0.130474i | −0.673945 | − | 0.738782i | \(-0.735401\pi\) |
0.494363 | + | 0.869256i | \(0.335401\pi\) | |||||||
\(572\) | 1.95339 | − | 12.3332i | 0.0816753 | − | 0.515678i | ||||
\(573\) | 6.01367 | + | 20.1994i | 0.251224 | + | 0.843843i | ||||
\(574\) | 4.36014i | 0.181989i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.148741 | − | 2.99631i | 0.00619754 | − | 0.124846i | ||||
\(577\) | 3.71857 | − | 7.29810i | 0.154806 | − | 0.303824i | −0.800558 | − | 0.599255i | \(-0.795463\pi\) |
0.955364 | + | 0.295432i | \(0.0954634\pi\) | |||||||
\(578\) | 16.7508 | + | 2.65307i | 0.696742 | + | 0.110353i | ||||
\(579\) | −21.7232 | − | 3.99516i | −0.902785 | − | 0.166033i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.82313 | + | 2.50933i | −0.0756364 | + | 0.104105i | ||||
\(582\) | −0.228869 | + | 9.22658i | −0.00948694 | + | 0.382454i | ||||
\(583\) | 6.42013 | − | 1.01685i | 0.265895 | − | 0.0421136i | ||||
\(584\) | 0.172991 | − | 0.532411i | 0.00715841 | − | 0.0220313i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.527935 | + | 1.62482i | 0.0218088 | + | 0.0671205i | ||||
\(587\) | 15.9900 | + | 31.3821i | 0.659978 | + | 1.29528i | 0.941917 | + | 0.335847i | \(0.109023\pi\) |
−0.281939 | + | 0.959432i | \(0.590977\pi\) | |||||||
\(588\) | −10.7364 | − | 3.78530i | −0.442763 | − | 0.156103i | ||||
\(589\) | −41.3460 | + | 13.4341i | −1.70363 | + | 0.553544i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.640605 | − | 0.306639i | 0.0263510 | − | 0.0126134i | ||||
\(592\) | 0.340567 | + | 2.15026i | 0.0139972 | + | 0.0883750i | ||||
\(593\) | 2.52481 | + | 2.52481i | 0.103681 | + | 0.103681i | 0.757045 | − | 0.653363i | \(-0.226643\pi\) |
−0.653363 | + | 0.757045i | \(0.726643\pi\) | |||||||
\(594\) | 14.8924 | − | 1.23410i | 0.611043 | − | 0.0506357i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.89486 | − | 8.11358i | −0.241463 | − | 0.332345i | ||||
\(597\) | 15.6795 | − | 10.8081i | 0.641719 | − | 0.442346i | ||||
\(598\) | −2.70072 | − | 1.37608i | −0.110441 | − | 0.0562723i | ||||
\(599\) | −39.4333 | −1.61120 | −0.805600 | − | 0.592460i | \(-0.798157\pi\) | ||||
−0.805600 | + | 0.592460i | \(0.798157\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.0191 | 1.14292 | 0.571462 | − | 0.820629i | \(-0.306376\pi\) | ||||
0.571462 | + | 0.820629i | \(0.306376\pi\) | |||||||
\(602\) | −4.19075 | − | 2.13529i | −0.170802 | − | 0.0870281i | ||||
\(603\) | −41.7609 | − | 8.75620i | −1.70064 | − | 0.356580i | ||||
\(604\) | 10.5317 | + | 14.4956i | 0.428527 | + | 0.589817i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 21.5628 | − | 2.86906i | 0.875928 | − | 0.116548i | ||||
\(607\) | 3.59236 | + | 3.59236i | 0.145809 | + | 0.145809i | 0.776243 | − | 0.630434i | \(-0.217123\pi\) |
−0.630434 | + | 0.776243i | \(0.717123\pi\) | |||||||
\(608\) | 1.13988 | + | 7.19694i | 0.0462284 | + | 0.291875i | ||||
\(609\) | −1.57254 | − | 3.28522i | −0.0637224 | − | 0.133124i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.5378 | − | 4.07379i | 0.507226 | − | 0.164808i | ||||
\(612\) | −15.9513 | + | 7.15480i | −0.644795 | + | 0.289216i | ||||
\(613\) | −6.96688 | − | 13.6733i | −0.281390 | − | 0.552258i | 0.706445 | − | 0.707768i | \(-0.250298\pi\) |
−0.987834 | + | 0.155510i | \(0.950298\pi\) | |||||||
\(614\) | −1.97818 | − | 6.08821i | −0.0798328 | − | 0.245700i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.580955 | − | 1.78800i | 0.0234074 | − | 0.0720404i | ||||
\(617\) | −7.10625 | + | 1.12552i | −0.286087 | + | 0.0453117i | −0.297829 | − | 0.954619i | \(-0.596262\pi\) |
0.0117417 | + | 0.999931i | \(0.496262\pi\) | |||||||
\(618\) | −10.6059 | − | 0.263084i | −0.426632 | − | 0.0105828i | ||||
\(619\) | −7.42133 | + | 10.2146i | −0.298288 | + | 0.410559i | −0.931684 | − | 0.363269i | \(-0.881661\pi\) |
0.633396 | + | 0.773828i | \(0.281661\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.832190 | − | 3.53063i | 0.0333946 | − | 0.141679i | ||||
\(622\) | 34.2051 | + | 5.41755i | 1.37150 | + | 0.217224i | ||||
\(623\) | 1.71618 | − | 3.36818i | 0.0687571 | − | 0.134943i | ||||
\(624\) | −5.18430 | − | 5.44804i | −0.207538 | − | 0.218096i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 26.1462i | 1.04501i | ||||||||
\(627\) | −34.7870 | + | 10.3566i | −1.38926 | + | 0.413603i | ||||
\(628\) | −1.42250 | + | 8.98132i | −0.0567640 | + | 0.358394i | ||||
\(629\) | 10.2638 | − | 7.45711i | 0.409246 | − | 0.297334i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.09574 | − | 1.52265i | −0.0834301 | − | 0.0606155i | 0.545288 | − | 0.838249i | \(-0.316420\pi\) |
−0.628718 | + | 0.777633i | \(0.716420\pi\) | |||||||
\(632\) | −7.21882 | + | 7.21882i | −0.287149 | + | 0.287149i | ||||
\(633\) | 22.6408 | − | 29.5905i | 0.899892 | − | 1.17612i | ||||
\(634\) | 12.9984 | + | 4.22343i | 0.516231 | + | 0.167734i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.86326 | − | 3.44301i | 0.0738829 | − | 0.136524i | ||||
\(637\) | −25.4278 | + | 12.9561i | −1.00748 | + | 0.513339i | ||||
\(638\) | −8.24255 | + | 4.19979i | −0.326326 | + | 0.166271i | ||||
\(639\) | −35.2354 | + | 9.54557i | −1.39389 | + | 0.377617i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.49095 | − | 1.13428i | −0.137884 | − | 0.0448012i | 0.239262 | − | 0.970955i | \(-0.423095\pi\) |
−0.377146 | + | 0.926154i | \(0.623095\pi\) | |||||||
\(642\) | −0.800574 | − | 0.612549i | −0.0315961 | − | 0.0241754i | ||||
\(643\) | −9.94703 | + | 9.94703i | −0.392273 | + | 0.392273i | −0.875497 | − | 0.483224i | \(-0.839466\pi\) |
0.483224 | + | 0.875497i | \(0.339466\pi\) | |||||||
\(644\) | −0.369198 | − | 0.268238i | −0.0145485 | − | 0.0105701i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 34.3532 | − | 24.9591i | 1.35161 | − | 0.982001i | ||||
\(647\) | 0.617590 | − | 3.89931i | 0.0242800 | − | 0.153298i | −0.972570 | − | 0.232612i | \(-0.925273\pi\) |
0.996850 | + | 0.0793138i | \(0.0252729\pi\) | |||||||
\(648\) | 4.86002 | − | 7.57497i | 0.190920 | − | 0.297573i | ||||
\(649\) | − | 24.7871i | − | 0.972979i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.89377 | − | 4.65686i | 0.191802 | − | 0.182517i | ||||
\(652\) | −4.21139 | + | 8.26532i | −0.164931 | + | 0.323695i | ||||
\(653\) | −14.3859 | − | 2.27850i | −0.562962 | − | 0.0891644i | −0.131534 | − | 0.991312i | \(-0.541990\pi\) |
−0.431428 | + | 0.902147i | \(0.641990\pi\) | |||||||
\(654\) | −3.63999 | + | 19.7920i | −0.142335 | + | 0.773927i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.92038 | − | 5.39594i | 0.153065 | − | 0.210676i | ||||
\(657\) | 1.24495 | − | 1.12720i | 0.0485703 | − | 0.0439761i | ||||
\(658\) | 1.96038 | − | 0.310493i | 0.0764235 | − | 0.0121043i | ||||
\(659\) | 4.21526 | − | 12.9732i | 0.164203 | − | 0.505365i | −0.834774 | − | 0.550593i | \(-0.814402\pi\) |
0.998977 | + | 0.0452283i | \(0.0144015\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.48143 | − | 7.63705i | −0.0965164 | − | 0.297047i | 0.891130 | − | 0.453749i | \(-0.149914\pi\) |
−0.987646 | + | 0.156702i | \(0.949914\pi\) | |||||||
\(662\) | −4.79834 | − | 9.41728i | −0.186493 | − | 0.366013i | ||||
\(663\) | −14.5723 | + | 41.3321i | −0.565942 | + | 1.60520i | ||||
\(664\) | 4.51248 | − | 1.46619i | 0.175118 | − | 0.0568994i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.32373 | + | 6.10382i | −0.0900428 | + | 0.236518i | ||||
\(667\) | 0.351281 | + | 2.21790i | 0.0136017 | + | 0.0858775i | ||||
\(668\) | 3.59263 | + | 3.59263i | 0.139003 | + | 0.139003i | ||||
\(669\) | 1.45004 | + | 10.8979i | 0.0560616 | + | 0.421338i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.2019 | + | 20.9237i | 0.586865 | + | 0.807750i | ||||
\(672\) | −0.642614 | − | 0.932251i | −0.0247894 | − | 0.0359623i | ||||
\(673\) | 24.0809 | + | 12.2698i | 0.928251 | + | 0.472967i | 0.851660 | − | 0.524095i | \(-0.175596\pi\) |
0.0765912 | + | 0.997063i | \(0.475596\pi\) | |||||||
\(674\) | 31.5318 | 1.21456 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.85270 | −0.225104 | ||||||||
\(677\) | 16.4613 | + | 8.38747i | 0.632660 | + | 0.322357i | 0.740746 | − | 0.671785i | \(-0.234472\pi\) |
−0.108086 | + | 0.994142i | \(0.534472\pi\) | |||||||
\(678\) | 13.9268 | + | 20.2038i | 0.534855 | + | 0.775924i | ||||
\(679\) | 2.04750 | + | 2.81814i | 0.0785757 | + | 0.108150i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.22654 | + | 24.2494i | 0.123641 | + | 0.929241i | ||||
\(682\) | −12.1326 | − | 12.1326i | −0.464581 | − | 0.464581i | ||||
\(683\) | 5.94046 | + | 37.5066i | 0.227305 | + | 1.43515i | 0.792338 | + | 0.610082i | \(0.208863\pi\) |
−0.565033 | + | 0.825068i | \(0.691137\pi\) | |||||||
\(684\) | −7.77757 | + | 20.4296i | −0.297383 | + | 0.781144i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.43843 | + | 2.74181i | −0.322181 | + | 0.104683i | ||||
\(687\) | −8.76231 | + | 24.8529i | −0.334303 | + | 0.948198i | ||||
\(688\) | 3.26638 | + | 6.41064i | 0.124530 | + | 0.244403i | ||||
\(689\) | −3.03266 | − | 9.33356i | −0.115535 | − | 0.355580i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.65184 | + | 8.16151i | −0.100881 | + | 0.310479i | −0.988742 | − | 0.149633i | \(-0.952191\pi\) |
0.887861 | + | 0.460112i | \(0.152191\pi\) | |||||||
\(692\) | −18.8394 | + | 2.98388i | −0.716168 | + | 0.113430i | ||||
\(693\) | 4.18093 | − | 3.78547i | 0.158820 | − | 0.143798i | ||||
\(694\) | 7.68036 | − | 10.5711i | 0.291542 | − | 0.401274i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.00777 | + | 5.47959i | −0.0381992 | + | 0.207703i | ||||
\(697\) | −38.3894 | − | 6.08028i | −1.45410 | − | 0.230307i | ||||
\(698\) | −13.8161 | + | 27.1156i | −0.522947 | + | 1.02634i | ||||
\(699\) | 9.52861 | − | 9.06733i | 0.360405 | − | 0.342958i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 52.4507i | 1.98104i | 0.137384 | + | 0.990518i | \(0.456131\pi\) | ||||
−0.137384 | + | 0.990518i | \(0.543869\pi\) | |||||||
\(702\) | −5.35764 | − | 21.9162i | −0.202211 | − | 0.827173i | ||||
\(703\) | 2.48160 | − | 15.6682i | 0.0935951 | − | 0.590937i | ||||
\(704\) | −2.32663 | + | 1.69040i | −0.0876881 | + | 0.0637092i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.35718 | + | 1.71259i | 0.0887136 | + | 0.0644542i | ||||
\(707\) | 5.80538 | − | 5.80538i | 0.218334 | − | 0.218334i | ||||
\(708\) | −11.8561 | − | 9.07156i | −0.445580 | − | 0.340930i | ||||
\(709\) | 5.89184 | + | 1.91438i | 0.221273 | + | 0.0718959i | 0.417555 | − | 0.908652i | \(-0.362887\pi\) |
−0.196283 | + | 0.980547i | \(0.562887\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −29.5613 | + | 8.00841i | −1.10863 | + | 0.300339i | ||||
\(712\) | −5.15235 | + | 2.62525i | −0.193092 | + | 0.0983855i | ||||
\(713\) | −3.71101 | + | 1.89085i | −0.138978 | + | 0.0708130i | ||||
\(714\) | −3.14044 | + | 5.80305i | −0.117528 | + | 0.217174i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.81721 | + | 1.24029i | 0.142656 | + | 0.0463517i | ||||
\(717\) | −13.1432 | + | 17.1776i | −0.490842 | + | 0.641508i | ||||
\(718\) | −5.59498 | + | 5.59498i | −0.208803 | + | 0.208803i | ||||
\(719\) | −3.26095 | − | 2.36922i | −0.121613 | − | 0.0883570i | 0.525316 | − | 0.850907i | \(-0.323947\pi\) |
−0.646929 | + | 0.762550i | \(0.723947\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.23943 | + | 2.35359i | −0.120643 | + | 0.0876521i | ||||
\(722\) | 5.33368 | − | 33.6756i | 0.198499 | − | 1.25327i | ||||
\(723\) | −37.6772 | + | 11.2171i | −1.40123 | + | 0.417167i | ||||
\(724\) | 4.08855i | 0.151950i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.25885 | + | 3.42464i | 0.120947 | + | 0.127100i | ||||
\(727\) | 13.8279 | − | 27.1388i | 0.512850 | − | 1.00652i | −0.478844 | − | 0.877900i | \(-0.658944\pi\) |
0.991693 | − | 0.128624i | \(-0.0410560\pi\) | |||||||
\(728\) | −2.80348 | − | 0.444028i | −0.103904 | − | 0.0164568i | ||||
\(729\) | 23.9549 | − | 12.4565i | 0.887218 | − | 0.461350i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.6445 | − | 33.9203i | 0.911510 | − | 1.25459i | ||||
\(732\) | 15.5718 | + | 0.386264i | 0.575549 | + | 0.0142767i | ||||
\(733\) | 13.6402 | − | 2.16039i | 0.503812 | − | 0.0797960i | 0.100645 | − | 0.994922i | \(-0.467909\pi\) |
0.403167 | + | 0.915126i | \(0.367909\pi\) | |||||||
\(734\) | 6.80279 | − | 20.9368i | 0.251096 | − | 0.772793i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.215722 | + | 0.663923i | 0.00795161 | + | 0.0244725i | ||||
\(737\) | 18.5698 | + | 36.4453i | 0.684028 | + | 1.34248i | ||||
\(738\) | 18.2568 | − | 8.18890i | 0.672043 | − | 0.301438i | ||||
\(739\) | −25.2888 | + | 8.21683i | −0.930264 | + | 0.302261i | −0.734671 | − | 0.678424i | \(-0.762663\pi\) |
−0.195593 | + | 0.980685i | \(0.562663\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 23.6599 | + | 49.4285i | 0.869170 | + | 1.81580i | ||||
\(742\) | −0.231141 | − | 1.45937i | −0.00848547 | − | 0.0535751i | ||||
\(743\) | −19.0708 | − | 19.0708i | −0.699641 | − | 0.699641i | 0.264692 | − | 0.964333i | \(-0.414730\pi\) |
−0.964333 | + | 0.264692i | \(0.914730\pi\) | |||||||
\(744\) | −10.2435 | + | 1.36297i | −0.375546 | + | 0.0499687i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −12.5568 | − | 17.2829i | −0.459736 | − | 0.632772i | ||||
\(747\) | 13.9312 | + | 2.92101i | 0.509715 | + | 0.106874i | ||||
\(748\) | 14.9325 | + | 7.60848i | 0.545985 | + | 0.278193i | ||||
\(749\) | −0.380457 | −0.0139016 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.8529 | −1.01637 | −0.508183 | − | 0.861249i | \(-0.669683\pi\) | ||||
−0.508183 | + | 0.861249i | \(0.669683\pi\) | |||||||
\(752\) | −2.70527 | − | 1.37840i | −0.0986509 | − | 0.0502652i | ||||
\(753\) | −11.9847 | + | 8.26123i | −0.436747 | + | 0.301056i | ||||
\(754\) | 8.20949 | + | 11.2994i | 0.298972 | + | 0.411500i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.280525 | − | 3.38522i | −0.0102026 | − | 0.123119i | ||||
\(757\) | 14.2550 | + | 14.2550i | 0.518108 | + | 0.518108i | 0.916998 | − | 0.398891i | \(-0.130605\pi\) |
−0.398891 | + | 0.916998i | \(0.630605\pi\) | |||||||
\(758\) | −0.154776 | − | 0.977218i | −0.00562172 | − | 0.0354942i | ||||
\(759\) | −3.13649 | + | 1.50134i | −0.113847 | + | 0.0544953i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.4602 | + | 6.64792i | −0.741681 | + | 0.240987i | −0.655398 | − | 0.755284i | \(-0.727499\pi\) |
−0.0862835 | + | 0.996271i | \(0.527499\pi\) | |||||||
\(762\) | 23.6767 | + | 8.34763i | 0.857717 | + | 0.302403i | ||||
\(763\) | 3.44817 | + | 6.76742i | 0.124832 | + | 0.244997i | ||||
\(764\) | −3.76012 | − | 11.5725i | −0.136036 | − | 0.418677i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.90822 | + | 12.0283i | −0.141210 | + | 0.434599i | ||||
\(767\) | −36.9626 | + | 5.85431i | −1.33464 | + | 0.211387i | ||||
\(768\) | −0.0429510 | + | 1.73152i | −0.00154986 | + | 0.0624808i | ||||
\(769\) | 5.35630 | − | 7.37231i | 0.193153 | − | 0.265852i | −0.701446 | − | 0.712723i | \(-0.747462\pi\) |
0.894599 | + | 0.446871i | \(0.147462\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 51.1431 | + | 9.40586i | 1.84188 | + | 0.338744i | ||||
\(772\) | 12.5952 | + | 1.99489i | 0.453312 | + | 0.0717976i | ||||
\(773\) | −20.4388 | + | 40.1134i | −0.735132 | + | 1.44278i | 0.155397 | + | 0.987852i | \(0.450334\pi\) |
−0.890529 | + | 0.454926i | \(0.849666\pi\) | |||||||
\(774\) | −1.07017 | + | 21.5579i | −0.0384663 | + | 0.774884i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 5.32861i | − | 0.191286i | ||||||
\(777\) | 0.703366 | + | 2.36255i | 0.0252331 | + | 0.0847560i | ||||
\(778\) | −4.28069 | + | 27.0272i | −0.153470 | + | 0.968973i | ||||
\(779\) | −39.3184 | + | 28.5665i | −1.40873 | + | 1.02350i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.3116 | + | 20.5695i | 1.01307 | + | 0.736036i | ||||
\(782\) | 2.87659 | − | 2.87659i | 0.102867 | − | 0.102867i | ||||
\(783\) | −10.8025 | + | 12.7546i | −0.386049 | + | 0.455813i | ||||
\(784\) | 6.25096 | + | 2.03106i | 0.223249 | + | 0.0725379i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.37310 | + | 4.53128i | 0.298659 | + | 0.161625i | ||||
\(787\) | −22.6577 | + | 11.5447i | −0.807659 | + | 0.411523i | −0.808514 | − | 0.588477i | \(-0.799728\pi\) |
0.000855029 | 1.00000i | \(0.499728\pi\) | ||||||||
\(788\) | −0.365350 | + | 0.186155i | −0.0130150 | + | 0.00663150i | ||||
\(789\) | 6.42014 | + | 3.47439i | 0.228563 | + | 0.123692i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.80823 | + | 2.86197i | 0.313185 | + | 0.101760i | ||||
\(792\) | −8.57783 | + | 0.925503i | −0.304800 | + | 0.0328863i | ||||
\(793\) | 27.6110 | − | 27.6110i | 0.980497 | − | 0.980497i | ||||
\(794\) | −2.87697 | − | 2.09024i | −0.102100 | − | 0.0741798i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.89504 | + | 6.46262i | −0.315276 | + | 0.229062i | ||||
\(797\) | 1.71644 | − | 10.8372i | 0.0607996 | − | 0.383874i | −0.938460 | − | 0.345389i | \(-0.887747\pi\) |
0.999259 | − | 0.0384845i | \(-0.0122530\pi\) | |||||||
\(798\) | 2.35418 | + | 7.90749i | 0.0833369 | + | 0.279922i | ||||
\(799\) | 17.6934i | 0.625946i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.3265 | − | 0.860112i | −0.612202 | − | 0.0303906i | ||||
\(802\) | −7.55891 | + | 14.8352i | −0.266914 | + | 0.523849i | ||||
\(803\) | −1.59012 | − | 0.251850i | −0.0561141 | − | 0.00888760i | ||||
\(804\) | 24.2286 | + | 4.45595i | 0.854478 | + | 0.157149i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −15.2267 | + | 20.9577i | −0.536337 | + | 0.738204i | ||||
\(807\) | 0.871135 | − | 35.1187i | 0.0306654 | − | 1.23624i | ||||
\(808\) | −12.4044 | + | 1.96466i | −0.436384 | + | 0.0691165i | ||||
\(809\) | −13.0207 | + | 40.0735i | −0.457782 | + | 1.40891i | 0.410056 | + | 0.912060i | \(0.365509\pi\) |
−0.867838 | + | 0.496848i | \(0.834491\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.38556 | + | 13.4974i | 0.153998 | + | 0.473957i | 0.998058 | − | 0.0622916i | \(-0.0198409\pi\) |
−0.844060 | + | 0.536249i | \(0.819841\pi\) | |||||||
\(812\) | 0.954659 | + | 1.87362i | 0.0335020 | + | 0.0657513i | ||||
\(813\) | 11.0654 | + | 3.90128i | 0.388080 | + | 0.136824i | ||||
\(814\) | 5.95451 | − | 1.93474i | 0.208706 | − | 0.0678126i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 9.10425 | − | 4.35793i | 0.318712 | − | 0.152558i | ||||
\(817\) | −8.20127 | − | 51.7808i | −0.286926 | − | 1.81158i | ||||
\(818\) | −3.04402 | − | 3.04402i | −0.106432 | − | 0.106432i | ||||
\(819\) | −6.63237 | − | 5.34056i | −0.231754 | − | 0.186614i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.28341 | + | 12.7775i | 0.323993 | + | 0.445939i | 0.939681 | − | 0.342052i | \(-0.111122\pi\) |
−0.615688 | + | 0.787990i | \(0.711122\pi\) | |||||||
\(822\) | −29.9995 | + | 20.6791i | −1.04635 | + | 0.721266i | ||||
\(823\) | −21.3898 | − | 10.8987i | −0.745603 | − | 0.379904i | 0.0395404 | − | 0.999218i | \(-0.487411\pi\) |
−0.785143 | + | 0.619314i | \(0.787411\pi\) | |||||||
\(824\) | 6.12520 | 0.213382 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.63439 | −0.196046 | ||||||||
\(827\) | 23.7234 | + | 12.0877i | 0.824944 | + | 0.420330i | 0.814887 | − | 0.579619i | \(-0.196799\pi\) |
0.0100569 | + | 0.999949i | \(0.496799\pi\) | |||||||
\(828\) | −0.429769 | + | 2.04970i | −0.0149355 | + | 0.0712320i | ||||
\(829\) | −9.16301 | − | 12.6118i | −0.318245 | − | 0.438026i | 0.619686 | − | 0.784850i | \(-0.287260\pi\) |
−0.937930 | + | 0.346824i | \(0.887260\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −42.0352 | + | 5.59305i | −1.45819 | + | 0.194021i | ||||
\(832\) | 3.07024 | + | 3.07024i | 0.106441 | + | 0.106441i | ||||
\(833\) | −5.99176 | − | 37.8305i | −0.207602 | − | 1.31075i | ||||
\(834\) | −8.72151 | − | 18.2203i | −0.302001 | − | 0.630917i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 19.9298 | − | 6.47560i | 0.689288 | − | 0.223963i | ||||
\(837\) | −28.6904 | − | 11.7451i | −0.991686 | − | 0.405969i | ||||
\(838\) | 3.27974 | + | 6.43686i | 0.113297 | + | 0.222358i | ||||
\(839\) | 4.03893 | + | 12.4305i | 0.139439 | + | 0.429150i | 0.996254 | − | 0.0864743i | \(-0.0275600\pi\) |
−0.856815 | + | 0.515624i | \(0.827560\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.76404 | + | 17.7399i | −0.198760 | + | 0.611720i | ||||
\(842\) | −14.3608 | + | 2.27453i | −0.494907 | + | 0.0783856i | ||||
\(843\) | 35.0459 | + | 0.869329i | 1.20705 | + | 0.0299413i | ||||
\(844\) | −12.6440 | + | 17.4030i | −0.435225 | + | 0.599036i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.98194 | − | 7.62538i | −0.171283 | − | 0.262166i | ||||
\(847\) | 1.76227 | + | 0.279116i | 0.0605522 | + | 0.00959053i | ||||
\(848\) | −1.02613 | + | 2.01389i | −0.0352374 | + | 0.0691572i | ||||
\(849\) | −9.91473 | − | 10.4191i | −0.340273 | − | 0.357583i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.51978i | − | 0.0520975i | ||||||
\(852\) | 20.2002 | − | 6.01391i | 0.692048 | − | 0.206033i | ||||
\(853\) | −6.36392 | + | 40.1802i | −0.217897 | + | 1.37574i | 0.599825 | + | 0.800131i | \(0.295237\pi\) |
−0.817722 | + | 0.575614i | \(0.804763\pi\) | |||||||
\(854\) | 4.75619 | − | 3.45558i | 0.162754 | − | 0.118247i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.470839 | + | 0.342085i | 0.0160930 | + | 0.0116922i | ||||
\(857\) | −24.0957 | + | 24.0957i | −0.823093 | + | 0.823093i | −0.986550 | − | 0.163457i | \(-0.947735\pi\) |
0.163457 | + | 0.986550i | \(0.447735\pi\) | |||||||
\(858\) | −13.1426 | + | 17.1768i | −0.448682 | + | 0.586407i | ||||
\(859\) | −17.4179 | − | 5.65942i | −0.594291 | − | 0.193097i | −0.00359858 | − | 0.999994i | \(-0.501145\pi\) |
−0.590693 | + | 0.806897i | \(0.701145\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.59434 | − | 6.64178i | 0.122495 | − | 0.226351i | ||||
\(862\) | 3.69822 | − | 1.88434i | 0.125962 | − | 0.0641808i | ||||
\(863\) | 7.06405 | − | 3.59931i | 0.240463 | − | 0.122522i | −0.329607 | − | 0.944118i | \(-0.606916\pi\) |
0.570070 | + | 0.821596i | \(0.306916\pi\) | |||||||
\(864\) | −2.69662 | + | 4.44165i | −0.0917410 | + | 0.151108i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −27.7975 | − | 9.03196i | −0.944598 | − | 0.306918i | ||||
\(867\) | −23.3293 | − | 17.8501i | −0.792306 | − | 0.606223i | ||||
\(868\) | −2.75788 | + | 2.75788i | −0.0936085 | + | 0.0936085i | ||||
\(869\) | 23.7524 | + | 17.2572i | 0.805747 | + | 0.585409i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 49.9615 | − | 36.2992i | 1.69288 | − | 1.22995i | ||||
\(872\) | 1.81754 | − | 11.4755i | 0.0615497 | − | 0.388609i | ||||
\(873\) | 7.95468 | − | 13.8661i | 0.269225 | − | 0.469297i | ||||
\(874\) | − | 5.08674i | − | 0.172062i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.702415 | + | 0.668411i | −0.0237324 | + | 0.0225835i | ||||
\(877\) | −23.3612 | + | 45.8490i | −0.788853 | + | 1.54821i | 0.0467683 | + | 0.998906i | \(0.485108\pi\) |
−0.835621 | + | 0.549306i | \(0.814892\pi\) | |||||||
\(878\) | 11.1570 | + | 1.76709i | 0.376530 | + | 0.0596365i | ||||
\(879\) | 0.535237 | − | 2.91028i | 0.0180531 | − | 0.0981614i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.69050 | − | 2.32677i | 0.0569544 | − | 0.0783909i | −0.779590 | − | 0.626290i | \(-0.784572\pi\) |
0.836544 | + | 0.547900i | \(0.184572\pi\) | |||||||
\(882\) | 13.2343 | + | 14.6168i | 0.445621 | + | 0.492175i | ||||
\(883\) | 36.4793 | − | 5.77775i | 1.22763 | − | 0.194437i | 0.491255 | − | 0.871016i | \(-0.336538\pi\) |
0.736370 | + | 0.676579i | \(0.236538\pi\) | |||||||
\(884\) | 7.81899 | − | 24.0644i | 0.262981 | − | 0.809372i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.38779 | − | 16.5819i | −0.181006 | − | 0.557081i | ||||
\(887\) | −2.57475 | − | 5.05323i | −0.0864515 | − | 0.169671i | 0.843733 | − | 0.536763i | \(-0.180353\pi\) |
−0.930184 | + | 0.367093i | \(0.880353\pi\) | |||||||
\(888\) | 1.25381 | − | 3.55623i | 0.0420750 | − | 0.119339i | ||||
\(889\) | 9.01156 | − | 2.92803i | 0.302238 | − | 0.0982031i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −23.7029 | − | 10.3969i | −0.794077 | − | 0.348308i | ||||
\(892\) | −0.992947 | − | 6.26922i | −0.0332463 | − | 0.209909i | ||||
\(893\) | 15.6438 | + | 15.6438i | 0.523500 | + | 0.523500i | ||||
\(894\) | 2.29108 | + | 17.2189i | 0.0766251 | + | 0.575885i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.384246 | + | 0.528869i | 0.0128368 | + | 0.0176683i | ||||
\(897\) | 2.97960 | + | 4.32255i | 0.0994858 | + | 0.144326i | ||||
\(898\) | 10.1628 | + | 5.17823i | 0.339138 | + | 0.172800i | ||||
\(899\) | 19.1916 | 0.640075 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.1715 | 0.438807 | ||||||||
\(902\) | −17.0907 | − | 8.70815i | −0.569058 | − | 0.289950i | ||||
\(903\) | 4.62349 | + | 6.70738i | 0.153860 | + | 0.223208i | ||||
\(904\) | −8.32742 | − | 11.4617i | −0.276966 | − | 0.381211i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.09320 | − | 30.7629i | −0.135988 | − | 1.02203i | ||||
\(907\) | 23.6056 | + | 23.6056i | 0.783811 | + | 0.783811i | 0.980472 | − | 0.196661i | \(-0.0630097\pi\) |
−0.196661 | + | 0.980472i | \(0.563010\pi\) | |||||||
\(908\) | −2.20945 | − | 13.9499i | −0.0733232 | − | 0.462944i | ||||
\(909\) | −35.2116 | − | 13.4051i | −1.16790 | − | 0.444620i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.8162 | + | 13.2620i | −1.35230 | + | 0.439390i | −0.893466 | − | 0.449131i | \(-0.851734\pi\) |
−0.458837 | + | 0.888521i | \(0.651734\pi\) | |||||||
\(912\) | 4.19651 | − | 11.9027i | 0.138960 | − | 0.394139i | ||||
\(913\) | −6.19478 | − | 12.1579i | −0.205017 | − | 0.402369i | ||||
\(914\) | 1.98641 | + | 6.11354i | 0.0657046 | + | 0.202218i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.70155 | − | 14.4699i | 0.155344 | − | 0.478098i | ||||
\(917\) | 3.54906 | − | 0.562115i | 0.117200 | − | 0.0185627i | ||||
\(918\) | 30.1967 | + | 2.25082i | 0.996641 | + | 0.0742882i | ||||
\(919\) | 7.08527 | − | 9.75204i | 0.233722 | − | 0.321690i | −0.676006 | − | 0.736896i | \(-0.736291\pi\) |
0.909727 | + | 0.415206i | \(0.136291\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.00554 | + | 10.9049i | −0.0660848 | + | 0.359328i | ||||
\(922\) | 19.0727 | + | 3.02082i | 0.628126 | + | 0.0994854i | ||||
\(923\) | 23.9867 | − | 47.0765i | 0.789531 | − | 1.54954i | ||||
\(924\) | −2.35892 | + | 2.24473i | −0.0776029 | + | 0.0738461i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 4.47523i | − | 0.147065i | ||||||
\(927\) | 15.9390 | + | 9.14386i | 0.523507 | + | 0.300324i | ||||
\(928\) | 0.503203 | − | 3.17710i | 0.0165185 | − | 0.104293i | ||||
\(929\) | 15.3269 | − | 11.1356i | 0.502859 | − | 0.365349i | −0.307249 | − | 0.951629i | \(-0.599408\pi\) |
0.810108 | + | 0.586280i | \(0.199408\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −38.7460 | − | 28.1506i | −1.26985 | − | 0.922598i | ||||
\(932\) | −5.36984 | + | 5.36984i | −0.175895 | + | 0.175895i | ||||
\(933\) | −47.6384 | − | 36.4499i | −1.55961 | − | 1.19332i | ||||
\(934\) | −1.67753 | − | 0.545064i | −0.0548906 | − | 0.0178350i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.40606 | + | 12.5727i | 0.111330 | + | 0.410952i | ||||
\(937\) | −34.7728 | + | 17.7176i | −1.13598 | + | 0.578809i | −0.917778 | − | 0.397095i | \(-0.870018\pi\) |
−0.218199 | + | 0.975904i | \(0.570018\pi\) | |||||||
\(938\) | 8.28444 | − | 4.22113i | 0.270497 | − | 0.137825i | ||||
\(939\) | 21.5540 | − | 39.8284i | 0.703387 | − | 1.29975i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.0266 | + | 8.45656i | 0.848443 | + | 0.275676i | 0.700794 | − | 0.713364i | \(-0.252829\pi\) |
0.147649 | + | 0.989040i | \(0.452829\pi\) | |||||||
\(942\) | 9.57075 | − | 12.5085i | 0.311832 | − | 0.407550i | ||||
\(943\) | −3.29235 | + | 3.29235i | −0.107214 | + | 0.107214i | ||||
\(944\) | 6.97291 | + | 5.06611i | 0.226949 | + | 0.164888i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.7397 | − | 12.1621i | 0.544254 | − | 0.395424i | ||||
\(947\) | 4.63200 | − | 29.2453i | 0.150520 | − | 0.950344i | −0.790615 | − | 0.612313i | \(-0.790239\pi\) |
0.941135 | − | 0.338031i | \(-0.109761\pi\) | |||||||
\(948\) | 16.9473 | − | 5.04547i | 0.550423 | − | 0.163869i | ||||
\(949\) | 2.43068i | 0.0789031i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.3187 | − | 17.1489i | −0.529171 | − | 0.556091i | ||||
\(952\) | 1.72949 | − | 3.39432i | 0.0560532 | − | 0.110011i | ||||
\(953\) | 8.50033 | + | 1.34632i | 0.275353 | + | 0.0436116i | 0.292584 | − | 0.956240i | \(-0.405485\pi\) |
−0.0172309 | + | 0.999852i | \(0.505485\pi\) | |||||||
\(954\) | −5.67658 | + | 3.70872i | −0.183786 | + | 0.120074i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7.33996 | − | 10.1026i | 0.237391 | − | 0.326741i | ||||
\(957\) | 16.0180 | + | 0.397333i | 0.517788 | + | 0.0128439i | ||||
\(958\) | 16.8163 | − | 2.66344i | 0.543311 | − | 0.0860519i | ||||
\(959\) | −4.24957 | + | 13.0788i | −0.137226 | + | 0.422338i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.42019 | + | 4.37089i | 0.0458125 | + | 0.140996i | ||||
\(962\) | −4.29145 | − | 8.42244i | −0.138362 | − | 0.271550i | ||||
\(963\) | 0.714547 | + | 1.59306i | 0.0230260 | + | 0.0513355i | ||||
\(964\) | 21.5856 | − | 7.01360i | 0.695227 | − | 0.225893i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.341272 | + | 0.712959i | 0.0109803 | + | 0.0229391i | ||||
\(967\) | 4.89692 | + | 30.9179i | 0.157474 | + | 0.994254i | 0.932197 | + | 0.361952i | \(0.117890\pi\) |
−0.774722 | + | 0.632302i | \(0.782110\pi\) | |||||||
\(968\) | −1.92995 | − | 1.92995i | −0.0620309 | − | 0.0620309i | ||||
\(969\) | −72.9053 | + | 9.70051i | −2.34206 | + | 0.311625i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.9971 | − | 23.3945i | −0.545463 | − | 0.750765i | 0.443925 | − | 0.896064i | \(-0.353586\pi\) |
−0.989388 | + | 0.145299i | \(0.953586\pi\) | |||||||
\(972\) | −13.6478 | + | 7.53249i | −0.437752 | + | 0.241605i | ||||
\(973\) | −6.79305 | − | 3.46123i | −0.217775 | − | 0.110962i | ||||
\(974\) | −28.1581 | −0.902245 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.99313 | −0.287863 | ||||||||
\(977\) | 1.82021 | + | 0.927445i | 0.0582338 | + | 0.0296716i | 0.482865 | − | 0.875695i | \(-0.339596\pi\) |
−0.424631 | + | 0.905366i | \(0.639596\pi\) | |||||||
\(978\) | 13.2288 | − | 9.11881i | 0.423011 | − | 0.291587i | ||||
\(979\) | 9.77490 | + | 13.4540i | 0.312407 | + | 0.429992i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21.8605 | − | 27.1483i | 0.697953 | − | 0.866780i | ||||
\(982\) | 6.46512 | + | 6.46512i | 0.206310 | + | 0.206310i | ||||
\(983\) | −4.54655 | − | 28.7058i | −0.145012 | − | 0.915572i | −0.947698 | − | 0.319169i | \(-0.896596\pi\) |
0.802685 | − | 0.596403i | \(-0.203404\pi\) | |||||||
\(984\) | −10.4201 | + | 4.98779i | −0.332181 | + | 0.159005i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −17.8278 | + | 5.79262i | −0.567754 | + | 0.184474i | ||||
\(987\) | −3.24219 | − | 1.14309i | −0.103200 | − | 0.0363849i | ||||
\(988\) | −14.3635 | − | 28.1900i | −0.456965 | − | 0.896845i | ||||
\(989\) | −1.55208 | − | 4.77681i | −0.0493533 | − | 0.151894i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.33291 | + | 13.3353i | −0.137640 | + | 0.423611i | −0.995991 | − | 0.0894508i | \(-0.971489\pi\) |
0.858352 | + | 0.513062i | \(0.171489\pi\) | |||||||
\(992\) | 5.89277 | − | 0.933323i | 0.187096 | − | 0.0296330i | ||||
\(993\) | −0.453961 | + | 18.3009i | −0.0144060 | + | 0.580760i | ||||
\(994\) | 4.67569 | − | 6.43554i | 0.148304 | − | 0.204123i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.08252 | − | 1.48648i | −0.256104 | − | 0.0471008i | ||||
\(997\) | 35.5407 | + | 5.62909i | 1.12558 | + | 0.178275i | 0.691347 | − | 0.722523i | \(-0.257018\pi\) |
0.434238 | + | 0.900798i | \(0.357018\pi\) | |||||||
\(998\) | 5.86715 | − | 11.5149i | 0.185722 | − | 0.364499i | ||||
\(999\) | 8.57149 | − | 7.38231i | 0.271190 | − | 0.233566i |
(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 | 750.2.l.b.107.7 | 80 | ||
3.2 | odd | 2 | inner | 750.2.l.b.107.4 | 80 | ||
5.2 | odd | 4 | 750.2.l.c.143.2 | 80 | |||
5.3 | odd | 4 | 750.2.l.a.143.9 | 80 | |||
5.4 | even | 2 | 150.2.l.a.17.4 | ✓ | 80 | ||
15.2 | even | 4 | 750.2.l.c.143.7 | 80 | |||
15.8 | even | 4 | 750.2.l.a.143.4 | 80 | |||
15.14 | odd | 2 | 150.2.l.a.17.7 | yes | 80 | ||
25.3 | odd | 20 | inner | 750.2.l.b.743.4 | 80 | ||
25.4 | even | 10 | 750.2.l.c.257.7 | 80 | |||
25.21 | even | 5 | 750.2.l.a.257.4 | 80 | |||
25.22 | odd | 20 | 150.2.l.a.53.7 | yes | 80 | ||
75.29 | odd | 10 | 750.2.l.c.257.2 | 80 | |||
75.47 | even | 20 | 150.2.l.a.53.4 | yes | 80 | ||
75.53 | even | 20 | inner | 750.2.l.b.743.7 | 80 | ||
75.71 | odd | 10 | 750.2.l.a.257.9 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.l.a.17.4 | ✓ | 80 | 5.4 | even | 2 | ||
150.2.l.a.17.7 | yes | 80 | 15.14 | odd | 2 | ||
150.2.l.a.53.4 | yes | 80 | 75.47 | even | 20 | ||
150.2.l.a.53.7 | yes | 80 | 25.22 | odd | 20 | ||
750.2.l.a.143.4 | 80 | 15.8 | even | 4 | |||
750.2.l.a.143.9 | 80 | 5.3 | odd | 4 | |||
750.2.l.a.257.4 | 80 | 25.21 | even | 5 | |||
750.2.l.a.257.9 | 80 | 75.71 | odd | 10 | |||
750.2.l.b.107.4 | 80 | 3.2 | odd | 2 | inner | ||
750.2.l.b.107.7 | 80 | 1.1 | even | 1 | trivial | ||
750.2.l.b.743.4 | 80 | 25.3 | odd | 20 | inner | ||
750.2.l.b.743.7 | 80 | 75.53 | even | 20 | inner | ||
750.2.l.c.143.2 | 80 | 5.2 | odd | 4 | |||
750.2.l.c.143.7 | 80 | 15.2 | even | 4 | |||
750.2.l.c.257.2 | 80 | 75.29 | odd | 10 | |||
750.2.l.c.257.7 | 80 | 25.4 | even | 10 |