Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(24,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 16]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.24");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.u (of order \(18\), degree \(6\), 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: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 24.1 | ||
Character | \(\chi\) | \(=\) | 475.24 |
Dual form | 475.2.u.b.99.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{8}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.883478 | − | 2.42733i | −0.624713 | − | 1.71639i | −0.695146 | − | 0.718869i | \(-0.744660\pi\) |
0.0704330 | − | 0.997517i | \(-0.477562\pi\) | |||||||
\(3\) | 0.243956 | + | 0.0430161i | 0.140848 | + | 0.0248353i | 0.243628 | − | 0.969869i | \(-0.421663\pi\) |
−0.102780 | + | 0.994704i | \(0.532774\pi\) | |||||||
\(4\) | −3.57933 | + | 3.00342i | −1.78967 | + | 1.50171i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.111115 | − | 0.630167i | −0.0453627 | − | 0.257265i | ||||
\(7\) | −0.347830 | + | 0.200820i | −0.131468 | + | 0.0759028i | −0.564291 | − | 0.825576i | \(-0.690851\pi\) |
0.432824 | + | 0.901479i | \(0.357517\pi\) | |||||||
\(8\) | 5.97847 | + | 3.45167i | 2.11371 | + | 1.22035i | ||||
\(9\) | −2.76141 | − | 1.00507i | −0.920471 | − | 0.335024i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.59530 | + | 4.49520i | −0.782514 | + | 1.35535i | 0.147959 | + | 0.988993i | \(0.452730\pi\) |
−0.930473 | + | 0.366360i | \(0.880604\pi\) | |||||||
\(12\) | −1.00240 | + | 0.578733i | −0.289367 | + | 0.167066i | ||||
\(13\) | 2.84549 | − | 0.501737i | 0.789197 | − | 0.139157i | 0.235499 | − | 0.971875i | \(-0.424327\pi\) |
0.553698 | + | 0.832718i | \(0.313216\pi\) | |||||||
\(14\) | 0.794758 | + | 0.666881i | 0.212408 | + | 0.178231i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.47378 | − | 8.35823i | 0.368445 | − | 2.08956i | ||||
\(17\) | 1.41708 | + | 3.89339i | 0.343692 | + | 0.944286i | 0.984313 | + | 0.176429i | \(0.0564546\pi\) |
−0.640621 | + | 0.767857i | \(0.721323\pi\) | |||||||
\(18\) | 7.59083i | 1.78918i | ||||||||
\(19\) | −0.386682 | + | 4.34171i | −0.0887110 | + | 0.996057i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0934938 | + | 0.0340290i | −0.0204020 | + | 0.00742573i | ||||
\(22\) | 13.2043 | + | 2.32827i | 2.81516 | + | 0.496388i | ||||
\(23\) | −2.15882 | − | 2.57278i | −0.450145 | − | 0.536462i | 0.492476 | − | 0.870326i | \(-0.336092\pi\) |
−0.942621 | + | 0.333864i | \(0.891647\pi\) | |||||||
\(24\) | 1.31001 | + | 1.09923i | 0.267404 | + | 0.224379i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.73181 | − | 6.46368i | −0.731868 | − | 1.26763i | ||||
\(27\) | −1.27402 | − | 0.735558i | −0.245186 | − | 0.141558i | ||||
\(28\) | 0.641855 | − | 1.76348i | 0.121299 | − | 0.333267i | ||||
\(29\) | 6.18683 | + | 2.25182i | 1.14887 | + | 0.418153i | 0.845107 | − | 0.534597i | \(-0.179536\pi\) |
0.303758 | + | 0.952749i | \(0.401759\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.13119 | + | 5.42339i | 0.562379 | + | 0.974069i | 0.997288 | + | 0.0735948i | \(0.0234472\pi\) |
−0.434909 | + | 0.900474i | \(0.643220\pi\) | |||||||
\(32\) | −7.99334 | + | 1.40944i | −1.41304 | + | 0.249156i | ||||
\(33\) | −0.826506 | + | 0.984992i | −0.143876 | + | 0.171465i | ||||
\(34\) | 8.19861 | − | 6.87945i | 1.40605 | − | 1.17982i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 12.9027 | − | 4.69619i | 2.15045 | − | 0.782698i | ||||
\(37\) | 1.14106i | 0.187590i | 0.995592 | + | 0.0937949i | \(0.0298998\pi\) | ||||
−0.995592 | + | 0.0937949i | \(0.970100\pi\) | |||||||
\(38\) | 10.8804 | − | 2.89720i | 1.76504 | − | 0.469988i | ||||
\(39\) | 0.715757 | 0.114613 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.496543 | − | 2.81603i | 0.0775469 | − | 0.439790i | −0.921171 | − | 0.389159i | \(-0.872766\pi\) |
0.998717 | − | 0.0506312i | \(-0.0161233\pi\) | |||||||
\(42\) | 0.165199 | + | 0.196877i | 0.0254908 | + | 0.0303788i | ||||
\(43\) | −7.99153 | + | 9.52394i | −1.21870 | + | 1.45239i | −0.365491 | + | 0.930815i | \(0.619099\pi\) |
−0.853207 | + | 0.521572i | \(0.825346\pi\) | |||||||
\(44\) | −4.21150 | − | 23.8846i | −0.634908 | − | 3.60074i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.33773 | + | 7.51317i | −0.639564 | + | 1.10776i | ||||
\(47\) | 2.31260 | − | 6.35381i | 0.337327 | − | 0.926798i | −0.648822 | − | 0.760940i | \(-0.724738\pi\) |
0.986150 | − | 0.165859i | \(-0.0530395\pi\) | |||||||
\(48\) | 0.719076 | − | 1.97565i | 0.103790 | − | 0.285160i | ||||
\(49\) | −3.41934 | + | 5.92248i | −0.488478 | + | 0.846068i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.178227 | + | 1.01077i | 0.0249567 | + | 0.141537i | ||||
\(52\) | −8.67803 | + | 10.3421i | −1.20343 | + | 1.43419i | ||||
\(53\) | −7.90752 | − | 9.42382i | −1.08618 | − | 1.29446i | −0.952867 | − | 0.303387i | \(-0.901883\pi\) |
−0.133314 | − | 0.991074i | \(-0.542562\pi\) | |||||||
\(54\) | −0.659874 | + | 3.74233i | −0.0897975 | + | 0.509267i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.77266 | −0.370512 | ||||||||
\(57\) | −0.281097 | + | 1.04255i | −0.0372322 | + | 0.138090i | ||||
\(58\) | − | 17.0069i | − | 2.23312i | ||||||
\(59\) | −1.42380 | + | 0.518220i | −0.185363 | + | 0.0674665i | −0.433034 | − | 0.901378i | \(-0.642557\pi\) |
0.247671 | + | 0.968844i | \(0.420335\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.35269 | + | 4.49144i | −0.685342 | + | 0.575070i | −0.917562 | − | 0.397593i | \(-0.869845\pi\) |
0.232220 | + | 0.972663i | \(0.425401\pi\) | |||||||
\(62\) | 10.3980 | − | 12.3919i | 1.32055 | − | 1.57377i | ||||
\(63\) | 1.16234 | − | 0.204952i | 0.146441 | − | 0.0258216i | ||||
\(64\) | 1.99595 | + | 3.45709i | 0.249494 | + | 0.432136i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.12111 | + | 1.13599i | 0.384182 | + | 0.139831i | ||||
\(67\) | −0.258947 | + | 0.711451i | −0.0316354 | + | 0.0869175i | −0.954505 | − | 0.298195i | \(-0.903615\pi\) |
0.922869 | + | 0.385113i | \(0.125838\pi\) | |||||||
\(68\) | −16.7657 | − | 9.67967i | −2.03314 | − | 1.17383i | ||||
\(69\) | −0.415986 | − | 0.720510i | −0.0500789 | − | 0.0867392i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.38582 | − | 5.35834i | −0.757857 | − | 0.635918i | 0.179711 | − | 0.983719i | \(-0.442484\pi\) |
−0.937568 | + | 0.347802i | \(0.886928\pi\) | |||||||
\(72\) | −13.0399 | − | 15.5403i | −1.53676 | − | 1.83144i | ||||
\(73\) | 9.76776 | + | 1.72232i | 1.14323 | + | 0.201582i | 0.713018 | − | 0.701146i | \(-0.247328\pi\) |
0.430212 | + | 0.902728i | \(0.358439\pi\) | |||||||
\(74\) | 2.76974 | − | 1.00810i | 0.321976 | − | 0.117190i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −11.6559 | − | 16.7018i | −1.33702 | − | 1.91583i | ||||
\(77\) | − | 2.08476i | − | 0.237580i | ||||||
\(78\) | −0.632356 | − | 1.73738i | −0.0716002 | − | 0.196720i | ||||
\(79\) | −0.553655 | + | 3.13994i | −0.0622911 | + | 0.353270i | 0.937692 | + | 0.347467i | \(0.112958\pi\) |
−0.999983 | + | 0.00580301i | \(0.998153\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.47421 | + | 5.43251i | 0.719357 | + | 0.603612i | ||||
\(82\) | −7.27414 | + | 1.28263i | −0.803294 | + | 0.141642i | ||||
\(83\) | −4.77995 | + | 2.75971i | −0.524668 | + | 0.302917i | −0.738842 | − | 0.673878i | \(-0.764627\pi\) |
0.214174 | + | 0.976795i | \(0.431294\pi\) | |||||||
\(84\) | 0.232442 | − | 0.402602i | 0.0253615 | − | 0.0439275i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 30.1781 | + | 10.9839i | 3.25419 | + | 1.18443i | ||||
\(87\) | 1.41245 | + | 0.815478i | 0.151431 | + | 0.0874285i | ||||
\(88\) | −31.0319 | + | 17.9163i | −3.30801 | + | 1.90988i | ||||
\(89\) | 2.17478 | + | 12.3338i | 0.230527 | + | 1.30738i | 0.851833 | + | 0.523814i | \(0.175491\pi\) |
−0.621306 | + | 0.783568i | \(0.713398\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.888989 | + | 0.745950i | −0.0931914 | + | 0.0781968i | ||||
\(92\) | 15.4543 | + | 2.72500i | 1.61122 | + | 0.284101i | ||||
\(93\) | 0.530581 | + | 1.45776i | 0.0550187 | + | 0.151163i | ||||
\(94\) | −17.4660 | −1.80148 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.01065 | −0.205211 | ||||||||
\(97\) | 3.04212 | + | 8.35815i | 0.308880 | + | 0.848642i | 0.992876 | + | 0.119155i | \(0.0380187\pi\) |
−0.683995 | + | 0.729487i | \(0.739759\pi\) | |||||||
\(98\) | 17.3967 | + | 3.06752i | 1.75734 | + | 0.309866i | ||||
\(99\) | 11.6847 | − | 9.80464i | 1.17436 | − | 0.985403i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.233727 | + | 1.32553i | 0.0232567 | + | 0.131895i | 0.994226 | − | 0.107311i | \(-0.0342240\pi\) |
−0.970969 | + | 0.239206i | \(0.923113\pi\) | |||||||
\(102\) | 2.29603 | − | 1.32561i | 0.227341 | − | 0.131255i | ||||
\(103\) | 10.7628 | + | 6.21391i | 1.06049 | + | 0.612275i | 0.925568 | − | 0.378581i | \(-0.123588\pi\) |
0.134923 | + | 0.990856i | \(0.456921\pi\) | |||||||
\(104\) | 18.7435 | + | 6.82208i | 1.83795 | + | 0.668960i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −15.8886 | + | 27.5199i | −1.54324 | + | 2.67297i | ||||
\(107\) | −12.6112 | + | 7.28110i | −1.21917 | + | 0.703890i | −0.964741 | − | 0.263200i | \(-0.915222\pi\) |
−0.254432 | + | 0.967091i | \(0.581889\pi\) | |||||||
\(108\) | 6.76934 | − | 1.19362i | 0.651380 | − | 0.114856i | ||||
\(109\) | −3.38582 | − | 2.84104i | −0.324303 | − | 0.272122i | 0.466071 | − | 0.884747i | \(-0.345669\pi\) |
−0.790374 | + | 0.612625i | \(0.790114\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0490841 | + | 0.278370i | −0.00465885 | + | 0.0264217i | ||||
\(112\) | 1.16587 | + | 3.20321i | 0.110165 | + | 0.302675i | ||||
\(113\) | − | 8.08453i | − | 0.760528i | −0.924878 | − | 0.380264i | \(-0.875833\pi\) | ||
0.924878 | − | 0.380264i | \(-0.124167\pi\) | |||||||
\(114\) | 2.77897 | − | 0.238757i | 0.260274 | − | 0.0223616i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −28.9079 | + | 10.5216i | −2.68403 | + | 0.976907i | ||||
\(117\) | −8.36186 | − | 1.47442i | −0.773054 | − | 0.136310i | ||||
\(118\) | 2.51579 | + | 2.99820i | 0.231597 | + | 0.276006i | ||||
\(119\) | −1.27477 | − | 1.06966i | −0.116858 | − | 0.0980557i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.97122 | − | 13.8065i | −0.724656 | − | 1.25514i | ||||
\(122\) | 15.6312 | + | 9.02468i | 1.41518 | + | 0.817056i | ||||
\(123\) | 0.242269 | − | 0.665629i | 0.0218447 | − | 0.0600178i | ||||
\(124\) | −27.4963 | − | 10.0078i | −2.46924 | − | 0.898730i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.52439 | − | 2.64032i | −0.135804 | − | 0.235219i | ||||
\(127\) | 0.552642 | − | 0.0974458i | 0.0490391 | − | 0.00864691i | −0.149075 | − | 0.988826i | \(-0.547630\pi\) |
0.198114 | + | 0.980179i | \(0.436518\pi\) | |||||||
\(128\) | −3.80642 | + | 4.53632i | −0.336444 | + | 0.400958i | ||||
\(129\) | −2.35927 | + | 1.97966i | −0.207722 | + | 0.174299i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.28037 | − | 3.37778i | 0.810830 | − | 0.295118i | 0.0968634 | − | 0.995298i | \(-0.469119\pi\) |
0.713967 | + | 0.700180i | \(0.246897\pi\) | |||||||
\(132\) | − | 6.00796i | − | 0.522926i | ||||||
\(133\) | −0.737403 | − | 1.58783i | −0.0639409 | − | 0.137683i | ||||
\(134\) | 1.95570 | 0.168947 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.96675 | + | 28.1678i | −0.425895 | + | 2.41537i | ||||
\(137\) | −5.76126 | − | 6.86600i | −0.492217 | − | 0.586602i | 0.461563 | − | 0.887108i | \(-0.347289\pi\) |
−0.953780 | + | 0.300506i | \(0.902845\pi\) | |||||||
\(138\) | −1.38140 | + | 1.64629i | −0.117593 | + | 0.140142i | ||||
\(139\) | 2.28639 | + | 12.9668i | 0.193929 | + | 1.09983i | 0.913935 | + | 0.405860i | \(0.133028\pi\) |
−0.720006 | + | 0.693968i | \(0.755861\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.837488 | − | 1.45057i | 0.0705292 | − | 0.122160i | ||||
\(142\) | −7.36475 | + | 20.2345i | −0.618036 | + | 1.69804i | ||||
\(143\) | −5.12951 | + | 14.0932i | −0.428951 | + | 1.17853i | ||||
\(144\) | −12.4703 | + | 21.5993i | −1.03920 | + | 1.79994i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.44895 | − | 25.2313i | −0.368198 | − | 2.08815i | ||||
\(147\) | −1.08893 | + | 1.29774i | −0.0898135 | + | 0.107036i | ||||
\(148\) | −3.42709 | − | 4.08425i | −0.281705 | − | 0.335723i | ||||
\(149\) | 1.42107 | − | 8.05930i | 0.116419 | − | 0.660243i | −0.869619 | − | 0.493723i | \(-0.835636\pi\) |
0.986038 | − | 0.166520i | \(-0.0532532\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.60636 | 0.618997 | 0.309498 | − | 0.950900i | \(-0.399839\pi\) | ||||
0.309498 | + | 0.950900i | \(0.399839\pi\) | |||||||
\(152\) | −17.2979 | + | 24.6221i | −1.40305 | + | 1.99712i | ||||
\(153\) | − | 12.1755i | − | 0.984333i | ||||||
\(154\) | −5.06040 | + | 1.84184i | −0.407779 | + | 0.148419i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.56193 | + | 2.14972i | −0.205119 | + | 0.172115i | ||||
\(157\) | 8.07689 | − | 9.62566i | 0.644606 | − | 0.768212i | −0.340484 | − | 0.940250i | \(-0.610591\pi\) |
0.985090 | + | 0.172039i | \(0.0550354\pi\) | |||||||
\(158\) | 8.11082 | − | 1.43016i | 0.645262 | − | 0.113777i | ||||
\(159\) | −1.52371 | − | 2.63915i | −0.120838 | − | 0.209298i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.26757 | + | 0.461357i | 0.0998984 | + | 0.0363600i | ||||
\(162\) | 7.46669 | − | 20.5146i | 0.586639 | − | 1.61178i | ||||
\(163\) | −2.84359 | − | 1.64175i | −0.222727 | − | 0.128591i | 0.384485 | − | 0.923131i | \(-0.374379\pi\) |
−0.607212 | + | 0.794540i | \(0.707712\pi\) | |||||||
\(164\) | 6.68043 | + | 11.5708i | 0.521654 | + | 0.903531i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.9217 | + | 9.16441i | 0.847689 | + | 0.711296i | ||||
\(167\) | −3.36026 | − | 4.00460i | −0.260025 | − | 0.309885i | 0.620199 | − | 0.784445i | \(-0.287052\pi\) |
−0.880224 | + | 0.474559i | \(0.842607\pi\) | |||||||
\(168\) | −0.676407 | − | 0.119269i | −0.0521860 | − | 0.00920179i | ||||
\(169\) | −4.37093 | + | 1.59089i | −0.336226 | + | 0.122376i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.43153 | − | 11.6006i | 0.415359 | − | 0.887122i | ||||
\(172\) | − | 58.0913i | − | 4.42942i | ||||||
\(173\) | 1.54100 | + | 4.23385i | 0.117160 | + | 0.321894i | 0.984387 | − | 0.176019i | \(-0.0563221\pi\) |
−0.867227 | + | 0.497913i | \(0.834100\pi\) | |||||||
\(174\) | 0.731571 | − | 4.14895i | 0.0554603 | − | 0.314531i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 33.7470 | + | 28.3171i | 2.54378 | + | 2.13448i | ||||
\(177\) | −0.369636 | + | 0.0651768i | −0.0277835 | + | 0.00489899i | ||||
\(178\) | 28.0169 | − | 16.1756i | 2.09996 | − | 1.21241i | ||||
\(179\) | −1.88583 | + | 3.26636i | −0.140954 | + | 0.244139i | −0.927856 | − | 0.372939i | \(-0.878350\pi\) |
0.786902 | + | 0.617078i | \(0.211684\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.9437 | − | 6.53096i | −1.33374 | − | 0.485442i | −0.425906 | − | 0.904767i | \(-0.640045\pi\) |
−0.907836 | + | 0.419325i | \(0.862267\pi\) | |||||||
\(182\) | 2.59607 | + | 1.49884i | 0.192434 | + | 0.111102i | ||||
\(183\) | −1.49903 | + | 0.865463i | −0.110811 | + | 0.0639768i | ||||
\(184\) | −4.02605 | − | 22.8328i | −0.296804 | − | 1.68326i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.06972 | − | 2.57580i | 0.225082 | − | 0.188867i | ||||
\(187\) | −21.1793 | − | 3.73449i | −1.54879 | − | 0.273093i | ||||
\(188\) | 10.8056 | + | 29.6881i | 0.788078 | + | 2.16523i | ||||
\(189\) | 0.590859 | 0.0429787 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.89599 | 0.209547 | 0.104773 | − | 0.994496i | \(-0.466588\pi\) | ||||
0.104773 | + | 0.994496i | \(0.466588\pi\) | |||||||
\(192\) | 0.338214 | + | 0.929236i | 0.0244085 | + | 0.0670619i | ||||
\(193\) | −11.2075 | − | 1.97618i | −0.806733 | − | 0.142249i | −0.244952 | − | 0.969535i | \(-0.578772\pi\) |
−0.561781 | + | 0.827286i | \(0.689883\pi\) | |||||||
\(194\) | 17.6004 | − | 14.7685i | 1.26363 | − | 1.06032i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.54870 | − | 31.4682i | −0.396336 | − | 2.24773i | ||||
\(197\) | −8.79093 | + | 5.07545i | −0.626328 | + | 0.361610i | −0.779329 | − | 0.626616i | \(-0.784440\pi\) |
0.153001 | + | 0.988226i | \(0.451106\pi\) | |||||||
\(198\) | −34.1223 | − | 19.7005i | −2.42497 | − | 1.40006i | ||||
\(199\) | −2.75352 | − | 1.00220i | −0.195192 | − | 0.0710440i | 0.242575 | − | 0.970133i | \(-0.422008\pi\) |
−0.437766 | + | 0.899089i | \(0.644230\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.0937755 | + | 0.162424i | −0.00661441 | + | 0.0114565i | ||||
\(202\) | 3.01101 | − | 1.73841i | 0.211854 | − | 0.122314i | ||||
\(203\) | −2.60418 | + | 0.459187i | −0.182777 | + | 0.0322286i | ||||
\(204\) | −3.67371 | − | 3.08261i | −0.257211 | − | 0.215826i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.57454 | − | 31.6148i | 0.388397 | − | 2.20271i | ||||
\(207\) | 3.37556 | + | 9.27428i | 0.234618 | + | 0.644607i | ||||
\(208\) | − | 24.5227i | − | 1.70034i | ||||||
\(209\) | −18.5133 | − | 13.0063i | −1.28059 | − | 0.899664i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.17374 | − | 1.88309i | 0.356175 | − | 0.129637i | −0.157734 | − | 0.987482i | \(-0.550419\pi\) |
0.513909 | + | 0.857845i | \(0.328197\pi\) | |||||||
\(212\) | 56.6073 | + | 9.98140i | 3.88781 | + | 0.685525i | ||||
\(213\) | −1.32737 | − | 1.58189i | −0.0909496 | − | 0.108389i | ||||
\(214\) | 28.8154 | + | 24.1790i | 1.96978 | + | 1.65284i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.07781 | − | 8.79503i | −0.345501 | − | 0.598426i | ||||
\(217\) | −2.17825 | − | 1.25761i | −0.147869 | − | 0.0853723i | ||||
\(218\) | −3.90486 | + | 10.7285i | −0.264470 | + | 0.726626i | ||||
\(219\) | 2.30882 | + | 0.840341i | 0.156015 | + | 0.0567850i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.98574 | + | 10.3676i | 0.402644 | + | 0.697400i | ||||
\(222\) | 0.719061 | − | 0.126790i | 0.0482602 | − | 0.00850958i | ||||
\(223\) | 5.11713 | − | 6.09836i | 0.342669 | − | 0.408376i | −0.566996 | − | 0.823721i | \(-0.691894\pi\) |
0.909664 | + | 0.415344i | \(0.136339\pi\) | |||||||
\(224\) | 2.49728 | − | 2.09547i | 0.166857 | − | 0.140009i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.6239 | + | 7.14250i | −1.30536 | + | 0.475112i | ||||
\(227\) | 8.02439i | 0.532597i | 0.963891 | + | 0.266299i | \(0.0858008\pi\) | ||||
−0.963891 | + | 0.266299i | \(0.914199\pi\) | |||||||
\(228\) | −2.12509 | − | 4.57590i | −0.140737 | − | 0.303046i | ||||
\(229\) | 28.2466 | 1.86659 | 0.933295 | − | 0.359111i | \(-0.116920\pi\) | ||||
0.933295 | + | 0.359111i | \(0.116920\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0896780 | − | 0.508589i | 0.00590038 | − | 0.0334627i | ||||
\(232\) | 29.2152 | + | 34.8174i | 1.91807 | + | 2.28587i | ||||
\(233\) | 6.06953 | − | 7.23338i | 0.397628 | − | 0.473875i | −0.529667 | − | 0.848206i | \(-0.677683\pi\) |
0.927295 | + | 0.374331i | \(0.122128\pi\) | |||||||
\(234\) | 3.80860 | + | 21.5996i | 0.248976 | + | 1.41201i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.53981 | − | 6.13114i | 0.230422 | − | 0.399103i | ||||
\(237\) | −0.270135 | + | 0.742191i | −0.0175472 | + | 0.0482105i | ||||
\(238\) | −1.47019 | + | 4.03932i | −0.0952985 | + | 0.261831i | ||||
\(239\) | 5.89638 | − | 10.2128i | 0.381405 | − | 0.660613i | −0.609858 | − | 0.792511i | \(-0.708774\pi\) |
0.991263 | + | 0.131897i | \(0.0421069\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.22273 | − | 12.6057i | −0.143179 | − | 0.812007i | −0.968811 | − | 0.247799i | \(-0.920293\pi\) |
0.825633 | − | 0.564208i | \(-0.190818\pi\) | |||||||
\(242\) | −26.4707 | + | 31.5466i | −1.70160 | + | 2.02789i | ||||
\(243\) | 4.18258 | + | 4.98461i | 0.268313 | + | 0.319763i | ||||
\(244\) | 5.66939 | − | 32.1527i | 0.362946 | − | 2.05837i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.82974 | −0.116660 | ||||||||
\(247\) | 1.07810 | + | 12.5483i | 0.0685976 | + | 0.798430i | ||||
\(248\) | 43.2314i | 2.74520i | ||||||||
\(249\) | −1.28481 | + | 0.467633i | −0.0814216 | + | 0.0296350i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.83823 | − | 1.54246i | 0.116028 | − | 0.0973590i | −0.582928 | − | 0.812524i | \(-0.698093\pi\) |
0.698956 | + | 0.715165i | \(0.253648\pi\) | |||||||
\(252\) | −3.54485 | + | 4.22459i | −0.223305 | + | 0.266124i | ||||
\(253\) | 17.1680 | − | 3.02717i | 1.07934 | − | 0.190317i | ||||
\(254\) | −0.724781 | − | 1.25536i | −0.0454768 | − | 0.0787681i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 21.8764 | + | 7.96235i | 1.36727 | + | 0.497647i | ||||
\(257\) | 5.88802 | − | 16.1772i | 0.367285 | − | 1.00911i | −0.609105 | − | 0.793090i | \(-0.708471\pi\) |
0.976390 | − | 0.216017i | \(-0.0693066\pi\) | |||||||
\(258\) | 6.88966 | + | 3.97774i | 0.428931 | + | 0.247644i | ||||
\(259\) | −0.229148 | − | 0.396897i | −0.0142386 | − | 0.0246620i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.8211 | − | 12.4364i | −0.917406 | − | 0.769795i | ||||
\(262\) | −16.3980 | − | 19.5424i | −1.01307 | − | 1.20733i | ||||
\(263\) | −14.4607 | − | 2.54981i | −0.891685 | − | 0.157228i | −0.291009 | − | 0.956720i | \(-0.593991\pi\) |
−0.600677 | + | 0.799492i | \(0.705102\pi\) | |||||||
\(264\) | −8.34112 | + | 3.03592i | −0.513360 | + | 0.186848i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.20272 | + | 3.19274i | −0.196372 | + | 0.195759i | ||||
\(267\) | 3.10246i | 0.189868i | ||||||||
\(268\) | −1.20993 | − | 3.32424i | −0.0739080 | − | 0.203061i | ||||
\(269\) | 3.89891 | − | 22.1118i | 0.237721 | − | 1.34818i | −0.599086 | − | 0.800685i | \(-0.704469\pi\) |
0.836807 | − | 0.547498i | \(-0.184420\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.1742 | + | 8.53716i | 0.618038 | + | 0.518596i | 0.897186 | − | 0.441652i | \(-0.145608\pi\) |
−0.279148 | + | 0.960248i | \(0.590052\pi\) | |||||||
\(272\) | 34.6303 | − | 6.10626i | 2.09977 | − | 0.370246i | ||||
\(273\) | −0.248962 | + | 0.143738i | −0.0150679 | + | 0.00869944i | ||||
\(274\) | −11.5761 | + | 20.0505i | −0.699340 | + | 1.21129i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.65294 | + | 1.32956i | 0.219881 | + | 0.0800303i | ||||
\(277\) | −2.90921 | − | 1.67963i | −0.174797 | − | 0.100919i | 0.410049 | − | 0.912064i | \(-0.365512\pi\) |
−0.584846 | + | 0.811144i | \(0.698845\pi\) | |||||||
\(278\) | 29.4548 | − | 17.0057i | 1.76658 | − | 1.01993i | ||||
\(279\) | −3.19563 | − | 18.1233i | −0.191317 | − | 1.08501i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.3380 | − | 12.8702i | 0.914991 | − | 0.767769i | −0.0580707 | − | 0.998312i | \(-0.518495\pi\) |
0.973062 | + | 0.230544i | \(0.0740504\pi\) | |||||||
\(282\) | −4.26093 | − | 0.751316i | −0.253735 | − | 0.0447402i | ||||
\(283\) | 0.181265 | + | 0.498021i | 0.0107751 | + | 0.0296043i | 0.944964 | − | 0.327176i | \(-0.106097\pi\) |
−0.934188 | + | 0.356780i | \(0.883875\pi\) | |||||||
\(284\) | 38.9503 | 2.31127 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 38.7407 | 2.29079 | ||||||||
\(287\) | 0.392803 | + | 1.07922i | 0.0231864 | + | 0.0637042i | ||||
\(288\) | 23.4895 | + | 4.14183i | 1.38413 | + | 0.244060i | ||||
\(289\) | −0.127626 | + | 0.107091i | −0.00750741 | + | 0.00629946i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.382609 | + | 2.16988i | 0.0224289 | + | 0.127201i | ||||
\(292\) | −40.1349 | + | 23.1719i | −2.34872 | + | 1.35603i | ||||
\(293\) | 27.3793 | + | 15.8074i | 1.59951 | + | 0.923480i | 0.991580 | + | 0.129492i | \(0.0413348\pi\) |
0.607934 | + | 0.793988i | \(0.291999\pi\) | |||||||
\(294\) | 4.11209 | + | 1.49668i | 0.239822 | + | 0.0872881i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.93858 | + | 6.82182i | −0.228925 | + | 0.396510i | ||||
\(297\) | 6.61296 | − | 3.81799i | 0.383723 | − | 0.221543i | ||||
\(298\) | −20.8181 | + | 3.67079i | −1.20596 | + | 0.212643i | ||||
\(299\) | −7.43376 | − | 6.23766i | −0.429905 | − | 0.360733i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.867101 | − | 4.91757i | 0.0499789 | − | 0.283444i | ||||
\(302\) | −6.72005 | − | 18.4632i | −0.386695 | − | 1.06244i | ||||
\(303\) | 0.333425i | 0.0191548i | ||||||||
\(304\) | 35.7192 | + | 9.63072i | 2.04863 | + | 0.552359i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −29.5541 | + | 10.7568i | −1.68949 | + | 0.614926i | ||||
\(307\) | 9.03222 | + | 1.59262i | 0.515496 | + | 0.0908958i | 0.425343 | − | 0.905032i | \(-0.360153\pi\) |
0.0901527 | + | 0.995928i | \(0.471264\pi\) | |||||||
\(308\) | 6.26139 | + | 7.46204i | 0.356776 | + | 0.425189i | ||||
\(309\) | 2.35836 | + | 1.97890i | 0.134162 | + | 0.112575i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0255 | + | 20.8288i | 0.681906 | + | 1.18110i | 0.974399 | + | 0.224828i | \(0.0721819\pi\) |
−0.292493 | + | 0.956268i | \(0.594485\pi\) | |||||||
\(312\) | 4.27914 | + | 2.47056i | 0.242258 | + | 0.139868i | ||||
\(313\) | 0.841224 | − | 2.31124i | 0.0475488 | − | 0.130639i | −0.913645 | − | 0.406512i | \(-0.866745\pi\) |
0.961194 | + | 0.275873i | \(0.0889670\pi\) | |||||||
\(314\) | −30.5005 | − | 11.1013i | −1.72124 | − | 0.626480i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.44882 | − | 12.9017i | −0.419029 | − | 0.725779i | ||||
\(317\) | −6.91555 | + | 1.21940i | −0.388416 | + | 0.0684882i | −0.364446 | − | 0.931225i | \(-0.618742\pi\) |
−0.0239697 | + | 0.999713i | \(0.507631\pi\) | |||||||
\(318\) | −5.05993 | + | 6.03019i | −0.283747 | + | 0.338156i | ||||
\(319\) | −26.1791 | + | 21.9669i | −1.46575 | + | 1.22991i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.38979 | + | 1.23378i | −0.189200 | + | 0.0688631i | ||||
\(322\) | − | 3.48441i | − | 0.194179i | ||||||
\(323\) | −17.4519 | + | 4.64704i | −0.971052 | + | 0.258568i | ||||
\(324\) | −39.4894 | −2.19386 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.47282 | + | 8.35278i | −0.0815720 | + | 0.462618i | ||||
\(327\) | −0.703781 | − | 0.838733i | −0.0389192 | − | 0.0463821i | ||||
\(328\) | 12.6886 | − | 15.1217i | 0.700610 | − | 0.834955i | ||||
\(329\) | 0.471580 | + | 2.67446i | 0.0259991 | + | 0.147448i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.70524 | + | 15.0779i | −0.478483 | + | 0.828758i | −0.999696 | − | 0.0246694i | \(-0.992147\pi\) |
0.521212 | + | 0.853427i | \(0.325480\pi\) | |||||||
\(332\) | 8.82049 | − | 24.2341i | 0.484087 | − | 1.33002i | ||||
\(333\) | 1.14685 | − | 3.15095i | 0.0628471 | − | 0.172671i | ||||
\(334\) | −6.75180 | + | 11.6945i | −0.369442 | + | 0.639892i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.146632 | + | 0.831594i | 0.00799946 | + | 0.0453672i | ||||
\(337\) | 21.0048 | − | 25.0326i | 1.14420 | − | 1.36361i | 0.222866 | − | 0.974849i | \(-0.428459\pi\) |
0.921339 | − | 0.388761i | \(-0.127097\pi\) | |||||||
\(338\) | 7.72324 | + | 9.20420i | 0.420089 | + | 0.500643i | ||||
\(339\) | 0.347764 | − | 1.97227i | 0.0188880 | − | 0.107119i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −32.5056 | −1.76028 | ||||||||
\(342\) | −32.9572 | − | 2.93524i | −1.78212 | − | 0.158720i | ||||
\(343\) | − | 5.55817i | − | 0.300113i | ||||||
\(344\) | −80.6507 | + | 29.3545i | −4.34839 | + | 1.58269i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.91554 | − | 7.48102i | 0.479302 | − | 0.402182i | ||||
\(347\) | −4.58277 | + | 5.46153i | −0.246016 | + | 0.293191i | −0.874895 | − | 0.484313i | \(-0.839070\pi\) |
0.628879 | + | 0.777503i | \(0.283514\pi\) | |||||||
\(348\) | −7.50485 | + | 1.32331i | −0.402302 | + | 0.0709368i | ||||
\(349\) | 11.3504 | + | 19.6595i | 0.607575 | + | 1.05235i | 0.991639 | + | 0.129044i | \(0.0411909\pi\) |
−0.384064 | + | 0.923307i | \(0.625476\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.99428 | − | 1.45380i | −0.213199 | − | 0.0775980i | ||||
\(352\) | 14.4094 | − | 39.5896i | 0.768025 | − | 2.11013i | ||||
\(353\) | −3.89182 | − | 2.24694i | −0.207141 | − | 0.119593i | 0.392841 | − | 0.919606i | \(-0.371492\pi\) |
−0.599982 | + | 0.800014i | \(0.704826\pi\) | |||||||
\(354\) | 0.484771 | + | 0.839648i | 0.0257653 | + | 0.0446268i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −44.8279 | − | 37.6151i | −2.37587 | − | 1.99359i | ||||
\(357\) | −0.264976 | − | 0.315786i | −0.0140240 | − | 0.0167132i | ||||
\(358\) | 9.59464 | + | 1.69179i | 0.507092 | + | 0.0894140i | ||||
\(359\) | 9.94626 | − | 3.62014i | 0.524943 | − | 0.191064i | −0.0659357 | − | 0.997824i | \(-0.521003\pi\) |
0.590879 | + | 0.806760i | \(0.298781\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7010 | − | 3.35773i | −0.984261 | − | 0.176723i | ||||
\(362\) | 49.3252i | 2.59248i | ||||||||
\(363\) | −1.35072 | − | 3.71108i | −0.0708946 | − | 0.194781i | ||||
\(364\) | 0.941588 | − | 5.34001i | 0.0493526 | − | 0.279893i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.42512 | + | 2.87402i | 0.179034 | + | 0.150227i | ||||
\(367\) | 1.77733 | − | 0.313391i | 0.0927759 | − | 0.0163589i | −0.127067 | − | 0.991894i | \(-0.540556\pi\) |
0.219843 | + | 0.975535i | \(0.429445\pi\) | |||||||
\(368\) | −24.6855 | + | 14.2522i | −1.28682 | + | 0.742947i | ||||
\(369\) | −4.20148 | + | 7.27717i | −0.218720 | + | 0.378834i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.64297 | + | 1.68990i | 0.241051 | + | 0.0877353i | ||||
\(372\) | −6.27739 | − | 3.62425i | −0.325468 | − | 0.187909i | ||||
\(373\) | 11.2270 | − | 6.48193i | 0.581314 | − | 0.335622i | −0.180342 | − | 0.983604i | \(-0.557720\pi\) |
0.761655 | + | 0.647982i | \(0.224387\pi\) | |||||||
\(374\) | 9.64661 | + | 54.7086i | 0.498814 | + | 2.82892i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 35.7571 | − | 30.0038i | 1.84403 | − | 1.54733i | ||||
\(377\) | 18.7344 | + | 3.30338i | 0.964869 | + | 0.170132i | ||||
\(378\) | −0.522011 | − | 1.43421i | −0.0268493 | − | 0.0737679i | ||||
\(379\) | −33.1372 | −1.70214 | −0.851071 | − | 0.525051i | \(-0.824046\pi\) | ||||
−0.851071 | + | 0.525051i | \(0.824046\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.139012 | 0.00712181 | ||||||||
\(382\) | −2.55855 | − | 7.02955i | −0.130907 | − | 0.359663i | ||||
\(383\) | −19.8866 | − | 3.50654i | −1.01616 | − | 0.179176i | −0.359324 | − | 0.933213i | \(-0.616993\pi\) |
−0.656832 | + | 0.754037i | \(0.728104\pi\) | |||||||
\(384\) | −1.12374 | + | 0.942926i | −0.0573454 | + | 0.0481185i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.10471 | + | 28.9503i | 0.259823 | + | 1.47353i | ||||
\(387\) | 31.6402 | − | 18.2675i | 1.60836 | − | 0.928588i | ||||
\(388\) | −35.9918 | − | 20.7799i | −1.82721 | − | 1.05494i | ||||
\(389\) | −1.90648 | − | 0.693903i | −0.0966625 | − | 0.0351823i | 0.293236 | − | 0.956040i | \(-0.405268\pi\) |
−0.389899 | + | 0.920858i | \(0.627490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.95762 | − | 12.0510i | 0.351862 | − | 0.609443i | ||||
\(392\) | −40.8849 | + | 23.6049i | −2.06500 | + | 1.19223i | ||||
\(393\) | 2.40930 | − | 0.424825i | 0.121533 | − | 0.0214296i | ||||
\(394\) | 20.0864 | + | 16.8545i | 1.01194 | + | 0.849117i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −12.3761 | + | 70.1881i | −0.621920 | + | 3.52709i | ||||
\(397\) | −2.74738 | − | 7.54838i | −0.137887 | − | 0.378842i | 0.851459 | − | 0.524420i | \(-0.175718\pi\) |
−0.989347 | + | 0.145578i | \(0.953496\pi\) | |||||||
\(398\) | 7.56914i | 0.379406i | ||||||||
\(399\) | −0.111592 | − | 0.419082i | −0.00558657 | − | 0.0209803i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.5128 | − | 4.91825i | 0.674796 | − | 0.245606i | 0.0181845 | − | 0.999835i | \(-0.494211\pi\) |
0.656611 | + | 0.754229i | \(0.271989\pi\) | |||||||
\(402\) | 0.477106 | + | 0.0841266i | 0.0237959 | + | 0.00419585i | ||||
\(403\) | 11.6309 | + | 13.8612i | 0.579376 | + | 0.690473i | ||||
\(404\) | −4.81770 | − | 4.04253i | −0.239690 | − | 0.201124i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.41533 | + | 5.91553i | 0.169500 | + | 0.293583i | ||||
\(407\) | −5.12931 | − | 2.96141i | −0.254250 | − | 0.146792i | ||||
\(408\) | −2.42334 | + | 6.65806i | −0.119973 | + | 0.329623i | ||||
\(409\) | 0.227020 | + | 0.0826284i | 0.0112254 | + | 0.00408571i | 0.347627 | − | 0.937633i | \(-0.386988\pi\) |
−0.336401 | + | 0.941719i | \(0.609210\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.11015 | − | 1.92283i | −0.0547595 | − | 0.0948462i | ||||
\(412\) | −57.1867 | + | 10.0835i | −2.81738 | + | 0.496781i | ||||
\(413\) | 0.391171 | − | 0.466179i | 0.0192483 | − | 0.0229392i | ||||
\(414\) | 19.5296 | − | 16.3872i | 0.959825 | − | 0.805389i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −22.0378 | + | 8.02110i | −1.08049 | + | 0.393267i | ||||
\(417\) | 3.26168i | 0.159725i | ||||||||
\(418\) | −15.2145 | + | 56.4288i | −0.744166 | + | 2.76002i | ||||
\(419\) | 22.7086 | 1.10939 | 0.554693 | − | 0.832055i | \(-0.312836\pi\) | ||||
0.554693 | + | 0.832055i | \(0.312836\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.33685 | + | 24.5955i | −0.211365 | + | 1.19871i | 0.675738 | + | 0.737142i | \(0.263825\pi\) |
−0.887103 | + | 0.461571i | \(0.847286\pi\) | |||||||
\(422\) | −9.14177 | − | 10.8947i | −0.445014 | − | 0.530347i | ||||
\(423\) | −12.7721 | + | 15.2212i | −0.621000 | + | 0.740079i | ||||
\(424\) | −14.7470 | − | 83.6342i | −0.716176 | − | 4.06164i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.66708 | + | 4.61953i | −0.129221 | + | 0.223817i | ||||
\(427\) | 0.959857 | − | 2.63719i | 0.0464507 | − | 0.127622i | ||||
\(428\) | 23.2716 | − | 63.9383i | 1.12488 | − | 3.09057i | ||||
\(429\) | −1.85761 | + | 3.21747i | −0.0896862 | + | 0.155341i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.10128 | + | 17.5883i | 0.149384 | + | 0.847196i | 0.963742 | + | 0.266835i | \(0.0859777\pi\) |
−0.814359 | + | 0.580362i | \(0.802911\pi\) | |||||||
\(432\) | −8.02560 | + | 9.56453i | −0.386132 | + | 0.460174i | ||||
\(433\) | 25.1405 | + | 29.9613i | 1.20818 | + | 1.43985i | 0.865877 | + | 0.500257i | \(0.166761\pi\) |
0.342299 | + | 0.939591i | \(0.388794\pi\) | |||||||
\(434\) | −1.12821 | + | 6.39841i | −0.0541559 | + | 0.307134i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 20.6518 | 0.989042 | ||||||||
\(437\) | 12.0051 | − | 8.37813i | 0.574280 | − | 0.400780i | ||||
\(438\) | − | 6.34670i | − | 0.303257i | ||||||
\(439\) | 17.6050 | − | 6.40768i | 0.840239 | − | 0.305822i | 0.114185 | − | 0.993460i | \(-0.463574\pi\) |
0.726054 | + | 0.687638i | \(0.241352\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.3947 | − | 12.9177i | 0.733083 | − | 0.615129i | ||||
\(442\) | 19.8774 | − | 23.6889i | 0.945471 | − | 1.12677i | ||||
\(443\) | 16.7923 | − | 2.96093i | 0.797826 | − | 0.140678i | 0.240149 | − | 0.970736i | \(-0.422804\pi\) |
0.557677 | + | 0.830058i | \(0.311693\pi\) | |||||||
\(444\) | −0.660372 | − | 1.14380i | −0.0313399 | − | 0.0542822i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −19.3236 | − | 7.03323i | −0.915001 | − | 0.333033i | ||||
\(447\) | 0.693358 | − | 1.90499i | 0.0327947 | − | 0.0901028i | ||||
\(448\) | −1.38851 | − | 0.801654i | −0.0656007 | − | 0.0378746i | ||||
\(449\) | 6.10161 | + | 10.5683i | 0.287953 | + | 0.498749i | 0.973321 | − | 0.229448i | \(-0.0736920\pi\) |
−0.685368 | + | 0.728197i | \(0.740359\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.3700 | + | 9.54052i | 0.535390 | + | 0.449246i | ||||
\(452\) | 24.2812 | + | 28.9372i | 1.14209 | + | 1.36109i | ||||
\(453\) | 1.85562 | + | 0.327195i | 0.0871845 | + | 0.0153730i | ||||
\(454\) | 19.4779 | − | 7.08937i | 0.914142 | − | 0.332721i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.27909 | + | 5.26263i | −0.247216 | + | 0.246445i | ||||
\(457\) | − | 13.4079i | − | 0.627193i | −0.949556 | − | 0.313596i | \(-0.898466\pi\) | ||
0.949556 | − | 0.313596i | \(-0.101534\pi\) | |||||||
\(458\) | −24.9553 | − | 68.5640i | −1.16608 | − | 3.20379i | ||||
\(459\) | 1.05842 | − | 6.00262i | 0.0494030 | − | 0.280178i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.7371 | − | 9.00946i | −0.500075 | − | 0.419613i | 0.357546 | − | 0.933896i | \(-0.383614\pi\) |
−0.857621 | + | 0.514283i | \(0.828058\pi\) | |||||||
\(462\) | −1.31374 | + | 0.231649i | −0.0611209 | + | 0.0107773i | ||||
\(463\) | −22.6706 | + | 13.0889i | −1.05359 | + | 0.608292i | −0.923653 | − | 0.383230i | \(-0.874812\pi\) |
−0.129940 | + | 0.991522i | \(0.541478\pi\) | |||||||
\(464\) | 27.9393 | − | 48.3922i | 1.29705 | − | 2.24655i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −22.9201 | − | 8.34225i | −1.06175 | − | 0.386447i | ||||
\(467\) | 34.2843 | + | 19.7941i | 1.58649 | + | 0.915960i | 0.993879 | + | 0.110470i | \(0.0352355\pi\) |
0.592609 | + | 0.805490i | \(0.298098\pi\) | |||||||
\(468\) | 34.3582 | − | 19.8367i | 1.58821 | − | 0.916952i | ||||
\(469\) | −0.0528039 | − | 0.299466i | −0.00243826 | − | 0.0138280i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.38447 | − | 2.00080i | 0.109870 | − | 0.0921922i | ||||
\(472\) | −10.3009 | − | 1.81632i | −0.474135 | − | 0.0836029i | ||||
\(473\) | −22.0715 | − | 60.6411i | −1.01485 | − | 2.78828i | ||||
\(474\) | 2.04020 | 0.0937097 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.77548 | 0.356389 | ||||||||
\(477\) | 12.3643 | + | 33.9707i | 0.566123 | + | 1.55541i | ||||
\(478\) | −29.9993 | − | 5.28968i | −1.37214 | − | 0.241944i | ||||
\(479\) | −2.89476 | + | 2.42899i | −0.132265 | + | 0.110983i | −0.706520 | − | 0.707693i | \(-0.749736\pi\) |
0.574255 | + | 0.818676i | \(0.305292\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.572514 | + | 3.24689i | 0.0261044 | + | 0.148045i | ||||
\(482\) | −28.6346 | + | 16.5322i | −1.30427 | + | 0.753022i | ||||
\(483\) | 0.289385 | + | 0.167077i | 0.0131675 | + | 0.00760225i | ||||
\(484\) | 69.9985 | + | 25.4774i | 3.18175 | + | 1.15806i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8.40410 | − | 14.5563i | 0.381218 | − | 0.660288i | ||||
\(487\) | 6.05339 | − | 3.49493i | 0.274305 | − | 0.158370i | −0.356537 | − | 0.934281i | \(-0.616043\pi\) |
0.630843 | + | 0.775911i | \(0.282709\pi\) | |||||||
\(488\) | −47.5039 | + | 8.37622i | −2.15040 | + | 0.379174i | ||||
\(489\) | −0.623089 | − | 0.522834i | −0.0281771 | − | 0.0236434i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.66765 | + | 32.1428i | −0.255777 | + | 1.45059i | 0.538292 | + | 0.842758i | \(0.319070\pi\) |
−0.794069 | + | 0.607827i | \(0.792041\pi\) | |||||||
\(492\) | 1.13200 | + | 3.11014i | 0.0510345 | + | 0.140216i | ||||
\(493\) | 27.2787i | 1.22857i | ||||||||
\(494\) | 29.5065 | − | 13.7031i | 1.32756 | − | 0.616530i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 49.9446 | − | 18.1784i | 2.24258 | − | 0.816232i | ||||
\(497\) | 3.29724 | + | 0.581393i | 0.147902 | + | 0.0260790i | ||||
\(498\) | 2.27020 | + | 2.70552i | 0.101730 | + | 0.121237i | ||||
\(499\) | −21.2906 | − | 17.8650i | −0.953100 | − | 0.799746i | 0.0267168 | − | 0.999643i | \(-0.491495\pi\) |
−0.979817 | + | 0.199897i | \(0.935939\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.647494 | − | 1.12149i | −0.0289279 | − | 0.0501046i | ||||
\(502\) | −5.36809 | − | 3.09927i | −0.239590 | − | 0.138327i | ||||
\(503\) | −5.59886 | + | 15.3827i | −0.249641 | + | 0.685883i | 0.750059 | + | 0.661371i | \(0.230025\pi\) |
−0.999700 | + | 0.0245113i | \(0.992197\pi\) | |||||||
\(504\) | 7.65646 | + | 2.78672i | 0.341046 | + | 0.124131i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −22.5155 | − | 38.9979i | −1.00093 | − | 1.73367i | ||||
\(507\) | −1.13475 | + | 0.200087i | −0.0503960 | + | 0.00888618i | ||||
\(508\) | −1.68542 | + | 2.00861i | −0.0747785 | + | 0.0891175i | ||||
\(509\) | 27.2953 | − | 22.9034i | 1.20984 | − | 1.01518i | 0.210548 | − | 0.977584i | \(-0.432475\pi\) |
0.999293 | − | 0.0375938i | \(-0.0119693\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.74340 | + | 1.36249i | −0.165598 | + | 0.0602728i | ||||
\(512\) | − | 48.2924i | − | 2.13424i | ||||||
\(513\) | 3.68622 | − | 5.24702i | 0.162751 | − | 0.231662i | ||||
\(514\) | −44.4694 | −1.96146 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.49886 | − | 14.1717i | 0.110006 | − | 0.623875i | ||||
\(517\) | 22.5598 | + | 26.8857i | 0.992177 | + | 1.18243i | ||||
\(518\) | −0.760954 | + | 0.906869i | −0.0334344 | + | 0.0398455i | ||||
\(519\) | 0.193812 | + | 1.09916i | 0.00850739 | + | 0.0482478i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.4659 | + | 30.2518i | −0.765194 | + | 1.32536i | 0.174950 | + | 0.984577i | \(0.444024\pi\) |
−0.940144 | + | 0.340778i | \(0.889310\pi\) | |||||||
\(522\) | −17.0932 | + | 46.9632i | −0.748149 | + | 2.05552i | ||||
\(523\) | 4.64899 | − | 12.7730i | 0.203286 | − | 0.558524i | −0.795594 | − | 0.605830i | \(-0.792841\pi\) |
0.998880 | + | 0.0473057i | \(0.0150635\pi\) | |||||||
\(524\) | −23.0727 | + | 39.9630i | −1.00793 | + | 1.74579i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.58646 | + | 37.3537i | 0.287183 | + | 1.62870i | ||||
\(527\) | −16.6782 | + | 19.8763i | −0.726515 | + | 0.865826i | ||||
\(528\) | 7.01470 | + | 8.35979i | 0.305276 | + | 0.363813i | ||||
\(529\) | 2.03521 | − | 11.5422i | 0.0884873 | − | 0.501837i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.45254 | 0.193224 | ||||||||
\(532\) | 7.40834 | + | 3.46866i | 0.321192 | + | 0.150385i | ||||
\(533\) | − | 8.26213i | − | 0.357872i | ||||||
\(534\) | 7.53071 | − | 2.74096i | 0.325886 | − | 0.118613i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.00380 | + | 3.35959i | −0.172938 | + | 0.145112i | ||||
\(537\) | −0.600566 | + | 0.715727i | −0.0259163 | + | 0.0308859i | ||||
\(538\) | −57.1174 | + | 10.0713i | −2.46251 | + | 0.434206i | ||||
\(539\) | −17.7485 | − | 30.7413i | −0.764481 | − | 1.32412i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.38859 | + | 2.68923i | 0.317660 | + | 0.115619i | 0.495929 | − | 0.868363i | \(-0.334828\pi\) |
−0.178269 | + | 0.983982i | \(0.557050\pi\) | |||||||
\(542\) | 11.7339 | − | 32.2386i | 0.504013 | − | 1.38476i | ||||
\(543\) | −4.09653 | − | 2.36513i | −0.175799 | − | 0.101498i | ||||
\(544\) | −16.8147 | − | 29.1239i | −0.720924 | − | 1.24868i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.568854 | + | 0.477325i | 0.0243447 | + | 0.0204276i | ||||
\(547\) | 17.0647 | + | 20.3369i | 0.729634 | + | 0.869544i | 0.995529 | − | 0.0944579i | \(-0.0301118\pi\) |
−0.265895 | + | 0.964002i | \(0.585667\pi\) | |||||||
\(548\) | 41.2429 | + | 7.27224i | 1.76181 | + | 0.310655i | ||||
\(549\) | 19.2952 | − | 7.02288i | 0.823500 | − | 0.299729i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.1691 | + | 25.9907i | −0.518421 | + | 1.10724i | ||||
\(552\) | − | 5.74340i | − | 0.244455i | ||||||
\(553\) | −0.437984 | − | 1.20335i | −0.0186250 | − | 0.0511717i | ||||
\(554\) | −1.50681 | + | 8.54554i | −0.0640182 | + | 0.363065i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −47.1284 | − | 39.5455i | −1.99869 | − | 1.67710i | ||||
\(557\) | −3.75229 | + | 0.661630i | −0.158990 | + | 0.0280342i | −0.252576 | − | 0.967577i | \(-0.581278\pi\) |
0.0935867 | + | 0.995611i | \(0.470167\pi\) | |||||||
\(558\) | −41.1680 | + | 23.7684i | −1.74278 | + | 1.00620i | ||||
\(559\) | −17.9613 | + | 31.1099i | −0.759683 | + | 1.31581i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.00618 | − | 1.82210i | −0.211361 | − | 0.0769292i | ||||
\(562\) | −44.7910 | − | 25.8601i | −1.88939 | − | 1.09084i | ||||
\(563\) | 10.5475 | − | 6.08960i | 0.444524 | − | 0.256646i | −0.260991 | − | 0.965341i | \(-0.584049\pi\) |
0.705515 | + | 0.708695i | \(0.250716\pi\) | |||||||
\(564\) | 1.35902 | + | 7.70741i | 0.0572252 | + | 0.324540i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.04872 | − | 0.879981i | 0.0440810 | − | 0.0369884i | ||||
\(567\) | −3.34288 | − | 0.589440i | −0.140388 | − | 0.0247542i | ||||
\(568\) | −19.6822 | − | 54.0764i | −0.825847 | − | 2.26900i | ||||
\(569\) | −22.8626 | −0.958451 | −0.479226 | − | 0.877692i | \(-0.659082\pi\) | ||||
−0.479226 | + | 0.877692i | \(0.659082\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.3908 | 1.69030 | 0.845152 | − | 0.534527i | \(-0.179510\pi\) | ||||
0.845152 | + | 0.534527i | \(0.179510\pi\) | |||||||
\(572\) | −23.9676 | − | 65.8503i | −1.00213 | − | 2.75334i | ||||
\(573\) | 0.706496 | + | 0.124574i | 0.0295143 | + | 0.00520416i | ||||
\(574\) | 2.27259 | − | 1.90693i | 0.0948560 | − | 0.0795937i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.03702 | − | 11.5525i | −0.0848760 | − | 0.481355i | ||||
\(577\) | −6.81026 | + | 3.93190i | −0.283515 | + | 0.163687i | −0.635013 | − | 0.772501i | \(-0.719005\pi\) |
0.351499 | + | 0.936188i | \(0.385672\pi\) | |||||||
\(578\) | 0.372700 | + | 0.215179i | 0.0155023 | + | 0.00895025i | ||||
\(579\) | −2.64913 | − | 0.964204i | −0.110094 | − | 0.0400710i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.10841 | − | 1.91982i | 0.0459845 | − | 0.0796475i | ||||
\(582\) | 4.92901 | − | 2.84576i | 0.204314 | − | 0.117961i | ||||
\(583\) | 62.8844 | − | 11.0882i | 2.60440 | − | 0.459227i | ||||
\(584\) | 52.4514 | + | 44.0120i | 2.17045 | + | 1.82123i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.1810 | − | 80.4242i | 0.585810 | − | 3.32229i | ||||
\(587\) | −13.7566 | − | 37.7961i | −0.567797 | − | 1.56001i | −0.807935 | − | 0.589271i | \(-0.799415\pi\) |
0.240138 | − | 0.970739i | \(-0.422807\pi\) | |||||||
\(588\) | − | 7.91555i | − | 0.326432i | ||||||
\(589\) | −24.7576 | + | 11.4976i | −1.02012 | + | 0.473751i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.36293 | + | 0.860035i | −0.0971978 | + | 0.0353771i | ||||
\(592\) | 9.53727 | + | 1.68168i | 0.391980 | + | 0.0691166i | ||||
\(593\) | −21.9034 | − | 26.1035i | −0.899466 | − | 1.07194i | −0.997053 | − | 0.0767145i | \(-0.975557\pi\) |
0.0975874 | − | 0.995227i | \(-0.468887\pi\) | |||||||
\(594\) | −15.1100 | − | 12.6788i | −0.619969 | − | 0.520216i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.1189 | + | 33.1150i | 0.783142 | + | 1.35644i | ||||
\(597\) | −0.628627 | − | 0.362938i | −0.0257280 | − | 0.0148541i | ||||
\(598\) | −8.57334 | + | 23.5551i | −0.350590 | + | 0.963238i | ||||
\(599\) | 16.8047 | + | 6.11643i | 0.686623 | + | 0.249910i | 0.661689 | − | 0.749779i | \(-0.269840\pi\) |
0.0249346 | + | 0.999689i | \(0.492062\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.355966 | − | 0.616551i | −0.0145201 | − | 0.0251496i | 0.858674 | − | 0.512522i | \(-0.171289\pi\) |
−0.873194 | + | 0.487372i | \(0.837955\pi\) | |||||||
\(602\) | −12.7027 | + | 2.23982i | −0.517722 | + | 0.0912884i | ||||
\(603\) | 1.43012 | − | 1.70435i | 0.0582389 | − | 0.0694065i | ||||
\(604\) | −27.2257 | + | 22.8451i | −1.10780 | + | 0.929553i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.809335 | − | 0.294574i | 0.0328770 | − | 0.0119662i | ||||
\(607\) | − | 34.3415i | − | 1.39388i | −0.717129 | − | 0.696940i | \(-0.754544\pi\) | ||
0.717129 | − | 0.696940i | \(-0.245456\pi\) | |||||||
\(608\) | −3.02851 | − | 35.2498i | −0.122822 | − | 1.42957i | ||||
\(609\) | −0.655057 | −0.0265443 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.39253 | − | 19.2400i | 0.137247 | − | 0.778368i | ||||
\(612\) | 36.5682 | + | 43.5803i | 1.47818 | + | 1.76163i | ||||
\(613\) | 19.2696 | − | 22.9647i | 0.778293 | − | 0.927534i | −0.220562 | − | 0.975373i | \(-0.570789\pi\) |
0.998855 | + | 0.0478390i | \(0.0152334\pi\) | |||||||
\(614\) | −4.11393 | − | 23.3313i | −0.166025 | − | 0.941573i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.19590 | − | 12.4637i | 0.289931 | − | 0.502175i | ||||
\(617\) | 7.55883 | − | 20.7677i | 0.304307 | − | 0.836076i | −0.689432 | − | 0.724350i | \(-0.742140\pi\) |
0.993739 | − | 0.111726i | \(-0.0356379\pi\) | |||||||
\(618\) | 2.71989 | − | 7.47283i | 0.109410 | − | 0.300601i | ||||
\(619\) | 9.72359 | − | 16.8417i | 0.390824 | − | 0.676927i | −0.601734 | − | 0.798696i | \(-0.705523\pi\) |
0.992558 | + | 0.121769i | \(0.0388568\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.857958 | + | 4.86572i | 0.0344287 | + | 0.195255i | ||||
\(622\) | 39.9343 | − | 47.5918i | 1.60122 | − | 1.90826i | ||||
\(623\) | −3.23333 | − | 3.85334i | −0.129541 | − | 0.154381i | ||||
\(624\) | 1.05487 | − | 5.98246i | 0.0422286 | − | 0.239490i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6.35337 | −0.253932 | ||||||||
\(627\) | −3.95696 | − | 3.96933i | −0.158026 | − | 0.158520i | ||||
\(628\) | 58.7117i | 2.34285i | ||||||||
\(629\) | −4.44261 | + | 1.61698i | −0.177138 | + | 0.0644731i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.39379 | − | 2.84773i | 0.135105 | − | 0.113366i | −0.572731 | − | 0.819743i | \(-0.694116\pi\) |
0.707836 | + | 0.706377i | \(0.249672\pi\) | |||||||
\(632\) | −14.1480 | + | 16.8610i | −0.562779 | + | 0.670694i | ||||
\(633\) | 1.34317 | − | 0.236837i | 0.0533862 | − | 0.00941342i | ||||
\(634\) | 9.06962 | + | 15.7090i | 0.360201 | + | 0.623886i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 13.3803 | + | 4.87005i | 0.530565 | + | 0.193110i | ||||
\(637\) | −6.75818 | + | 18.5680i | −0.267769 | + | 0.735689i | ||||
\(638\) | 76.4496 | + | 44.1382i | 3.02667 | + | 1.74745i | ||||
\(639\) | 12.2484 | + | 21.2148i | 0.484538 | + | 0.839244i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.6593 | + | 16.4961i | 0.776496 | + | 0.651558i | 0.942364 | − | 0.334590i | \(-0.108598\pi\) |
−0.165867 | + | 0.986148i | \(0.553042\pi\) | |||||||
\(642\) | 5.98961 | + | 7.13814i | 0.236391 | + | 0.281720i | ||||
\(643\) | −36.6032 | − | 6.45413i | −1.44349 | − | 0.254526i | −0.603601 | − | 0.797287i | \(-0.706268\pi\) |
−0.839887 | + | 0.542761i | \(0.817379\pi\) | |||||||
\(644\) | −5.92270 | + | 2.15569i | −0.233387 | + | 0.0849459i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 26.6983 | + | 38.2562i | 1.05043 | + | 1.50517i | ||||
\(647\) | 20.6750i | 0.812819i | 0.913691 | + | 0.406409i | \(0.133219\pi\) | ||||
−0.913691 | + | 0.406409i | \(0.866781\pi\) | |||||||
\(648\) | 19.9547 | + | 54.8250i | 0.783893 | + | 2.15373i | ||||
\(649\) | 1.36569 | − | 7.74519i | 0.0536079 | − | 0.304025i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.477300 | − | 0.400502i | −0.0187068 | − | 0.0156969i | ||||
\(652\) | 15.1090 | − | 2.66412i | 0.591714 | − | 0.104335i | ||||
\(653\) | −29.4740 | + | 17.0168i | −1.15341 | + | 0.665919i | −0.949715 | − | 0.313116i | \(-0.898627\pi\) |
−0.203691 | + | 0.979035i | \(0.565294\pi\) | |||||||
\(654\) | −1.41411 | + | 2.44931i | −0.0552962 | + | 0.0957758i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −22.8053 | − | 8.30043i | −0.890395 | − | 0.324077i | ||||
\(657\) | −25.2418 | − | 14.5733i | −0.984775 | − | 0.568560i | ||||
\(658\) | 6.07519 | − | 3.50751i | 0.236836 | − | 0.136737i | ||||
\(659\) | 5.38526 | + | 30.5413i | 0.209780 | + | 1.18972i | 0.889739 | + | 0.456470i | \(0.150886\pi\) |
−0.679959 | + | 0.733250i | \(0.738002\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.9912 | + | 11.7400i | −0.544195 | + | 0.456634i | −0.872970 | − | 0.487775i | \(-0.837809\pi\) |
0.328775 | + | 0.944408i | \(0.393364\pi\) | |||||||
\(662\) | 44.2901 | + | 7.80953i | 1.72138 | + | 0.303526i | ||||
\(663\) | 1.01428 | + | 2.78672i | 0.0393915 | + | 0.108227i | ||||
\(664\) | −38.1024 | −1.47866 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.66163 | −0.335631 | ||||||||
\(667\) | −7.56280 | − | 20.7786i | −0.292833 | − | 0.804552i | ||||
\(668\) | 24.0550 | + | 4.24154i | 0.930715 | + | 0.164110i | ||||
\(669\) | 1.51068 | − | 1.26761i | 0.0584064 | − | 0.0490088i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.29806 | − | 35.7181i | −0.243134 | − | 1.37888i | ||||
\(672\) | 0.699366 | − | 0.403779i | 0.0269786 | − | 0.0155761i | ||||
\(673\) | 22.5444 | + | 13.0160i | 0.869023 | + | 0.501731i | 0.867024 | − | 0.498267i | \(-0.166030\pi\) |
0.00199979 | + | 0.999998i | \(0.499363\pi\) | |||||||
\(674\) | −79.3197 | − | 28.8700i | −3.05528 | − | 1.11203i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.8669 | − | 18.8221i | 0.417958 | − | 0.723925i | ||||
\(677\) | −0.0520720 | + | 0.0300638i | −0.00200129 | + | 0.00115545i | −0.501000 | − | 0.865447i | \(-0.667034\pi\) |
0.498999 | + | 0.866603i | \(0.333701\pi\) | |||||||
\(678\) | −5.09460 | + | 0.898316i | −0.195657 | + | 0.0344996i | ||||
\(679\) | −2.73663 | − | 2.29630i | −0.105022 | − | 0.0881240i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.345178 | + | 1.95760i | −0.0132272 | + | 0.0750154i | ||||
\(682\) | 28.7180 | + | 78.9020i | 1.09967 | + | 3.02131i | ||||
\(683\) | 31.5145i | 1.20587i | 0.797790 | + | 0.602935i | \(0.206002\pi\) | ||||
−0.797790 | + | 0.602935i | \(0.793998\pi\) | |||||||
\(684\) | 15.4003 | + | 57.8356i | 0.588844 | + | 2.21140i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −13.4915 | + | 4.91052i | −0.515109 | + | 0.187484i | ||||
\(687\) | 6.89094 | + | 1.21506i | 0.262906 | + | 0.0463574i | ||||
\(688\) | 67.8255 | + | 80.8313i | 2.58582 | + | 3.08166i | ||||
\(689\) | −27.2290 | − | 22.8479i | −1.03734 | − | 0.870435i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.69765 | − | 8.13657i | −0.178707 | − | 0.309530i | 0.762731 | − | 0.646716i | \(-0.223858\pi\) |
−0.941438 | + | 0.337186i | \(0.890525\pi\) | |||||||
\(692\) | −18.2318 | − | 10.5261i | −0.693067 | − | 0.400143i | ||||
\(693\) | −2.09533 | + | 5.75687i | −0.0795950 | + | 0.218686i | ||||
\(694\) | 17.3057 | + | 6.29878i | 0.656917 | + | 0.239098i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.62953 | + | 9.75063i | 0.213387 | + | 0.369597i | ||||
\(697\) | 11.6676 | − | 2.05730i | 0.441940 | − | 0.0779260i | ||||
\(698\) | 37.6924 | − | 44.9201i | 1.42668 | − | 1.70025i | ||||
\(699\) | 1.79185 | − | 1.50354i | 0.0677740 | − | 0.0568691i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.95262 | − | 2.53055i | 0.262597 | − | 0.0955775i | −0.207367 | − | 0.978263i | \(-0.566489\pi\) |
0.469964 | + | 0.882686i | \(0.344267\pi\) | |||||||
\(702\) | 10.9798i | 0.414408i | ||||||||
\(703\) | −4.95417 | − | 0.441229i | −0.186850 | − | 0.0166413i | ||||
\(704\) | −20.7204 | −0.780930 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.01575 | + | 11.4319i | −0.0758637 | + | 0.430245i | ||||
\(707\) | −0.347490 | − | 0.414122i | −0.0130687 | − | 0.0155747i | ||||
\(708\) | 1.12730 | − | 1.34346i | 0.0423664 | − | 0.0504903i | ||||
\(709\) | 7.51502 | + | 42.6198i | 0.282233 | + | 1.60062i | 0.715006 | + | 0.699118i | \(0.246424\pi\) |
−0.432774 | + | 0.901502i | \(0.642465\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.68474 | − | 8.11420i | 0.175691 | − | 0.304306i | ||||
\(712\) | −29.5704 | + | 81.2440i | −1.10820 | + | 3.04475i | ||||
\(713\) | 7.19350 | − | 19.7640i | 0.269399 | − | 0.740167i | ||||
\(714\) | −0.532419 | + | 0.922176i | −0.0199253 | + | 0.0345116i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.06021 | − | 17.3553i | −0.114366 | − | 0.648599i | ||||
\(717\) | 1.87777 | − | 2.23784i | 0.0701268 | − | 0.0835738i | ||||
\(718\) | −17.5746 | − | 20.9446i | −0.655878 | − | 0.781645i | ||||
\(719\) | −5.61767 | + | 31.8594i | −0.209504 | + | 1.18815i | 0.680690 | + | 0.732572i | \(0.261680\pi\) |
−0.890193 | + | 0.455583i | \(0.849431\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.99151 | −0.185894 | ||||||||
\(722\) | 8.37154 | + | 48.3600i | 0.311557 | + | 1.79977i | ||||
\(723\) | − | 3.17086i | − | 0.117926i | ||||||
\(724\) | 83.8416 | − | 30.5158i | 3.11595 | − | 1.13411i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −7.81471 | + | 6.55732i | −0.290031 | + | 0.243365i | ||||
\(727\) | −31.9291 | + | 38.0516i | −1.18418 | + | 1.41125i | −0.293907 | + | 0.955834i | \(0.594956\pi\) |
−0.890276 | + | 0.455421i | \(0.849489\pi\) | |||||||
\(728\) | −7.88957 | + | 1.39114i | −0.292407 | + | 0.0515592i | ||||
\(729\) | −11.8713 | − | 20.5616i | −0.439677 | − | 0.761542i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −48.4051 | − | 17.6180i | −1.79033 | − | 0.651625i | ||||
\(732\) | 2.76617 | − | 7.59998i | 0.102240 | − | 0.280903i | ||||
\(733\) | 1.18507 | + | 0.684201i | 0.0437716 | + | 0.0252715i | 0.521726 | − | 0.853113i | \(-0.325288\pi\) |
−0.477955 | + | 0.878385i | \(0.658622\pi\) | |||||||
\(734\) | −2.33094 | − | 4.03730i | −0.0860365 | − | 0.149020i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.8824 | + | 17.5224i | 0.769734 | + | 0.645883i | ||||
\(737\) | −2.52607 | − | 3.01045i | −0.0930489 | − | 0.110891i | ||||
\(738\) | 21.3760 | + | 3.76917i | 0.786863 | + | 0.138745i | ||||
\(739\) | 16.6998 | − | 6.07823i | 0.614312 | − | 0.223591i | −0.0160769 | − | 0.999871i | \(-0.505118\pi\) |
0.630389 | + | 0.776279i | \(0.282895\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.276771 | + | 3.10761i | −0.0101674 | + | 0.114161i | ||||
\(742\) | − | 12.7630i | − | 0.468545i | ||||||
\(743\) | 13.2113 | + | 36.2978i | 0.484676 | + | 1.33164i | 0.905443 | + | 0.424469i | \(0.139539\pi\) |
−0.420766 | + | 0.907169i | \(0.638239\pi\) | |||||||
\(744\) | −1.85965 | + | 10.5466i | −0.0681779 | + | 0.386656i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −25.6526 | − | 21.5251i | −0.939210 | − | 0.788091i | ||||
\(747\) | 15.9731 | − | 2.81649i | 0.584426 | − | 0.103050i | ||||
\(748\) | 87.0241 | − | 50.2434i | 3.18192 | − | 1.83708i | ||||
\(749\) | 2.92438 | − | 5.06517i | 0.106854 | − | 0.185077i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.0160 | − | 5.46539i | −0.547943 | − | 0.199435i | 0.0531894 | − | 0.998584i | \(-0.483061\pi\) |
−0.601132 | + | 0.799150i | \(0.705284\pi\) | |||||||
\(752\) | −49.6983 | − | 28.6933i | −1.81231 | − | 1.04634i | ||||
\(753\) | 0.514797 | − | 0.297218i | 0.0187603 | − | 0.0108312i | ||||
\(754\) | −8.53300 | − | 48.3931i | −0.310754 | − | 1.76237i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.11488 | + | 1.77460i | −0.0769175 | + | 0.0645414i | ||||
\(757\) | 1.91954 | + | 0.338466i | 0.0697668 | + | 0.0123018i | 0.208423 | − | 0.978039i | \(-0.433167\pi\) |
−0.138656 | + | 0.990341i | \(0.544278\pi\) | |||||||
\(758\) | 29.2759 | + | 80.4350i | 1.06335 | + | 2.92153i | ||||
\(759\) | 4.31845 | 0.156750 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −48.1168 | −1.74423 | −0.872115 | − | 0.489300i | \(-0.837252\pi\) | ||||
−0.872115 | + | 0.489300i | \(0.837252\pi\) | |||||||
\(762\) | −0.122814 | − | 0.337429i | −0.00444909 | − | 0.0122238i | ||||
\(763\) | 1.74823 | + | 0.308260i | 0.0632901 | + | 0.0111597i | ||||
\(764\) | −10.3657 | + | 8.69788i | −0.375019 | + | 0.314678i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.05780 | + | 51.3693i | 0.327272 | + | 1.85605i | ||||
\(767\) | −3.79139 | + | 2.18896i | −0.136899 | + | 0.0790388i | ||||
\(768\) | 4.99437 | + | 2.88350i | 0.180219 | + | 0.104049i | ||||
\(769\) | −6.00593 | − | 2.18598i | −0.216579 | − | 0.0788284i | 0.231452 | − | 0.972846i | \(-0.425652\pi\) |
−0.448031 | + | 0.894018i | \(0.647875\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.13230 | − | 3.69325i | 0.0767929 | − | 0.133009i | ||||
\(772\) | 46.0507 | − | 26.5874i | 1.65740 | − | 0.956900i | ||||
\(773\) | −35.1946 | + | 6.20576i | −1.26586 | + | 0.223206i | −0.765967 | − | 0.642880i | \(-0.777739\pi\) |
−0.499895 | + | 0.866086i | \(0.666628\pi\) | |||||||
\(774\) | −72.2947 | − | 60.6624i | −2.59858 | − | 2.18047i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −10.6624 | + | 60.4694i | −0.382757 | + | 2.17073i | ||||
\(777\) | −0.0388292 | − | 0.106682i | −0.00139299 | − | 0.00382721i | ||||
\(778\) | 5.24072i | 0.187889i | ||||||||
\(779\) | 12.0344 | + | 3.24476i | 0.431177 | + | 0.116255i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.6599 | − | 14.7990i | 1.45493 | − | 0.529550i | ||||
\(782\) | −35.3986 | − | 6.24173i | −1.26585 | − | 0.223204i | ||||
\(783\) | −6.22582 | − | 7.41964i | −0.222493 | − | 0.265156i | ||||
\(784\) | 44.4620 | + | 37.3081i | 1.58793 | + | 1.33243i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.15976 | − | 5.47286i | −0.112705 | − | 0.195211i | ||||
\(787\) | −1.68035 | − | 0.970153i | −0.0598982 | − | 0.0345822i | 0.469752 | − | 0.882799i | \(-0.344343\pi\) |
−0.529650 | + | 0.848216i | \(0.677677\pi\) | |||||||
\(788\) | 16.2220 | − | 44.5695i | 0.577884 | − | 1.58772i | ||||
\(789\) | −3.41810 | − | 1.24409i | −0.121687 | − | 0.0442906i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.62353 | + | 2.81204i | 0.0577262 | + | 0.0999848i | ||||
\(792\) | 103.699 | − | 18.2850i | 3.68479 | − | 0.649728i | ||||
\(793\) | −12.9775 | + | 15.4660i | −0.460845 | + | 0.549213i | ||||
\(794\) | −15.8952 | + | 13.3376i | −0.564099 | + | 0.473335i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.8658 | − | 4.68276i | 0.456016 | − | 0.165976i | ||||
\(797\) | 44.3436i | 1.57073i | 0.619033 | + | 0.785365i | \(0.287525\pi\) | ||||
−0.619033 | + | 0.785365i | \(0.712475\pi\) | |||||||
\(798\) | −0.918663 | + | 0.641120i | −0.0325203 | + | 0.0226954i | ||||
\(799\) | 28.0150 | 0.991099 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.39090 | − | 36.2446i | 0.225811 | − | 1.28064i | ||||
\(802\) | −23.8765 | − | 28.4549i | −0.843108 | − | 1.00478i | ||||
\(803\) | −33.0925 | + | 39.4381i | −1.16781 | + | 1.39174i | ||||
\(804\) | −0.152173 | − | 0.863016i | −0.00536673 | − | 0.0304362i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 23.3700 | − | 40.4781i | 0.823175 | − | 1.42578i | ||||
\(807\) | 1.90233 | − | 5.22660i | 0.0669651 | − | 0.183985i | ||||
\(808\) | −3.17797 | + | 8.73139i | −0.111800 | + | 0.307169i | ||||
\(809\) | −13.9319 | + | 24.1307i | −0.489819 | + | 0.848392i | −0.999931 | − | 0.0117160i | \(-0.996271\pi\) |
0.510112 | + | 0.860108i | \(0.329604\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.29449 | + | 30.0265i | 0.185915 | + | 1.05437i | 0.924775 | + | 0.380515i | \(0.124253\pi\) |
−0.738860 | + | 0.673859i | \(0.764636\pi\) | |||||||
\(812\) | 7.94209 | − | 9.46501i | 0.278713 | − | 0.332157i | ||||
\(813\) | 2.11482 | + | 2.52035i | 0.0741700 | + | 0.0883924i | ||||
\(814\) | −2.65670 | + | 15.0669i | −0.0931173 | + | 0.528094i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8.71095 | 0.304944 | ||||||||
\(817\) | −38.2600 | − | 38.3797i | −1.33855 | − | 1.34274i | ||||
\(818\) | − | 0.624053i | − | 0.0218195i | ||||||
\(819\) | 3.20460 | − | 1.16638i | 0.111978 | − | 0.0407566i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.4716 | − | 32.2815i | 1.34267 | − | 1.12663i | 0.361738 | − | 0.932280i | \(-0.382184\pi\) |
0.980932 | − | 0.194354i | \(-0.0622609\pi\) | |||||||
\(822\) | −3.68656 | + | 4.39347i | −0.128584 | + | 0.153240i | ||||
\(823\) | 42.8265 | − | 7.55147i | 1.49284 | − | 0.263228i | 0.633143 | − | 0.774035i | \(-0.281765\pi\) |
0.859695 | + | 0.510807i | \(0.170653\pi\) | |||||||
\(824\) | 42.8968 | + | 74.2994i | 1.49438 | + | 2.58834i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.47716 | − | 0.537644i | −0.0513971 | − | 0.0187070i | ||||
\(827\) | −0.203752 | + | 0.559803i | −0.00708514 | + | 0.0194663i | −0.943185 | − | 0.332269i | \(-0.892186\pi\) |
0.936100 | + | 0.351735i | \(0.114408\pi\) | |||||||
\(828\) | −39.9368 | − | 23.0575i | −1.38790 | − | 0.801304i | ||||
\(829\) | 9.62397 | + | 16.6692i | 0.334254 | + | 0.578946i | 0.983341 | − | 0.181769i | \(-0.0581822\pi\) |
−0.649087 | + | 0.760714i | \(0.724849\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.637468 | − | 0.534900i | −0.0221135 | − | 0.0185555i | ||||
\(832\) | 7.41401 | + | 8.83567i | 0.257035 | + | 0.306322i | ||||
\(833\) | −27.9040 | − | 4.92023i | −0.966816 | − | 0.170476i | ||||
\(834\) | 7.91719 | − | 2.88162i | 0.274150 | − | 0.0997824i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 105.329 | − | 9.04937i | 3.64287 | − | 0.312979i | ||||
\(837\) | − | 9.21270i | − | 0.318438i | ||||||
\(838\) | −20.0625 | − | 55.1213i | −0.693048 | − | 1.90413i | ||||
\(839\) | 8.84381 | − | 50.1557i | 0.305322 | − | 1.73157i | −0.316662 | − | 0.948539i | \(-0.602562\pi\) |
0.621984 | − | 0.783030i | \(-0.286327\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.9908 | + | 9.22242i | 0.378995 | + | 0.318014i | ||||
\(842\) | 63.5331 | − | 11.2026i | 2.18949 | − | 0.386067i | ||||
\(843\) | 4.29543 | − | 2.47997i | 0.147943 | − | 0.0854147i | ||||
\(844\) | −12.8628 | + | 22.2791i | −0.442757 | + | 0.766878i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 48.2307 | + | 17.5545i | 1.65821 | + | 0.603538i | ||||
\(847\) | 5.54526 | + | 3.20156i | 0.190537 | + | 0.110007i | ||||
\(848\) | −90.4204 | + | 52.2042i | −3.10505 | + | 1.79270i | ||||
\(849\) | 0.0227978 | + | 0.129293i | 0.000782418 | + | 0.00443731i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.93571 | − | 2.46335i | 0.100635 | − | 0.0844426i | ||||
\(852\) | 9.50216 | + | 1.67549i | 0.325539 | + | 0.0574013i | ||||
\(853\) | −0.889082 | − | 2.44273i | −0.0304416 | − | 0.0836375i | 0.923541 | − | 0.383500i | \(-0.125281\pi\) |
−0.953982 | + | 0.299863i | \(0.903059\pi\) | |||||||
\(854\) | −7.24935 | −0.248067 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −100.528 | −3.43597 | ||||||||
\(857\) | −13.7570 | − | 37.7972i | −0.469932 | − | 1.29113i | −0.917806 | − | 0.397030i | \(-0.870041\pi\) |
0.447874 | − | 0.894097i | \(-0.352181\pi\) | |||||||
\(858\) | 9.45104 | + | 1.66647i | 0.322653 | + | 0.0568925i | ||||
\(859\) | 21.5150 | − | 18.0532i | 0.734083 | − | 0.615969i | −0.197159 | − | 0.980372i | \(-0.563171\pi\) |
0.931241 | + | 0.364403i | \(0.118727\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.0494030 | + | 0.280179i | 0.00168365 | + | 0.00954846i | ||||
\(862\) | 39.9527 | − | 23.0667i | 1.36079 | − | 0.785654i | ||||
\(863\) | −25.9284 | − | 14.9698i | −0.882613 | − | 0.509577i | −0.0110937 | − | 0.999938i | \(-0.503531\pi\) |
−0.871519 | + | 0.490362i | \(0.836865\pi\) | |||||||
\(864\) | 11.2204 | + | 4.08390i | 0.381727 | + | 0.138937i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 50.5150 | − | 87.4946i | 1.71657 | − | 2.97319i | ||||
\(867\) | −0.0357418 | + | 0.0206355i | −0.00121385 | + | 0.000700819i | ||||
\(868\) | 11.5738 | − | 2.04078i | 0.392841 | − | 0.0692684i | ||||
\(869\) | −12.6777 | − | 10.6379i | −0.430063 | − | 0.360866i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.379870 | + | 2.15435i | −0.0128714 | + | 0.0729973i | ||||
\(872\) | −10.4357 | − | 28.6718i | −0.353397 | − | 0.970950i | ||||
\(873\) | − | 26.1379i | − | 0.884633i | ||||||
\(874\) | −30.9427 | − | 21.7384i | −1.04665 | − | 0.735312i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.7879 | + | 3.92648i | −0.364490 | + | 0.132664i | ||||
\(877\) | −7.98213 | − | 1.40747i | −0.269537 | − | 0.0475267i | 0.0372458 | − | 0.999306i | \(-0.488142\pi\) |
−0.306783 | + | 0.951779i | \(0.599253\pi\) | |||||||
\(878\) | −31.1072 | − | 37.0721i | −1.04982 | − | 1.25112i | ||||
\(879\) | 5.99937 | + | 5.03407i | 0.202354 | + | 0.169795i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.46598 | − | 7.73530i | −0.150463 | − | 0.260609i | 0.780935 | − | 0.624612i | \(-0.214743\pi\) |
−0.931398 | + | 0.364003i | \(0.881410\pi\) | |||||||
\(882\) | −44.9565 | − | 25.9557i | −1.51377 | − | 0.873973i | ||||
\(883\) | 0.517061 | − | 1.42061i | 0.0174005 | − | 0.0478074i | −0.930688 | − | 0.365813i | \(-0.880791\pi\) |
0.948089 | + | 0.318006i | \(0.103013\pi\) | |||||||
\(884\) | −52.5632 | − | 19.1314i | −1.76789 | − | 0.643460i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −22.0228 | − | 38.1446i | −0.739870 | − | 1.28149i | ||||
\(887\) | −27.4146 | + | 4.83393i | −0.920491 | + | 0.162307i | −0.613764 | − | 0.789490i | \(-0.710345\pi\) |
−0.306728 | + | 0.951797i | \(0.599234\pi\) | |||||||
\(888\) | −1.25429 | + | 1.49480i | −0.0420912 | + | 0.0501623i | ||||
\(889\) | −0.172657 | + | 0.144876i | −0.00579072 | + | 0.00485899i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −41.2228 | + | 15.0039i | −1.38101 | + | 0.502648i | ||||
\(892\) | 37.1970i | 1.24545i | ||||||||
\(893\) | 26.6922 | + | 12.4975i | 0.893220 | + | 0.418214i | ||||
\(894\) | −5.23661 | −0.175138 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.413006 | − | 2.34228i | 0.0137976 | − | 0.0782499i | ||||
\(897\) | −1.54519 | − | 1.84149i | −0.0515924 | − | 0.0614855i | ||||
\(898\) | 20.2622 | − | 24.1475i | 0.676157 | − | 0.805813i | ||||
\(899\) | 7.15966 | + | 40.6045i | 0.238788 | + | 1.35423i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.4850 | − | 44.1414i | 0.849029 | − | 1.47056i | ||||
\(902\) | 13.1129 | − | 36.0275i | 0.436613 | − | 1.19959i | ||||
\(903\) | 0.423069 | − | 1.16237i | 0.0140789 | − | 0.0386814i | ||||
\(904\) | 27.9051 | − | 48.3331i | 0.928111 | − | 1.60754i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.845184 | − | 4.79328i | −0.0280794 | − | 0.159246i | ||||
\(907\) | −20.3553 | + | 24.2585i | −0.675888 | + | 0.805492i | −0.989573 | − | 0.144036i | \(-0.953992\pi\) |
0.313685 | + | 0.949527i | \(0.398436\pi\) | |||||||
\(908\) | −24.1006 | − | 28.7220i | −0.799806 | − | 0.953172i | ||||
\(909\) | 0.686837 | − | 3.89525i | 0.0227810 | − | 0.129197i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.4766 | 0.347104 | 0.173552 | − | 0.984825i | \(-0.444476\pi\) | ||||
0.173552 | + | 0.984825i | \(0.444476\pi\) | |||||||
\(912\) | 8.29963 | + | 3.88597i | 0.274828 | + | 0.128677i | ||||
\(913\) | − | 28.6491i | − | 0.948148i | ||||||
\(914\) | −32.5454 | + | 11.8455i | −1.07650 | + | 0.391816i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −101.104 | + | 84.8364i | −3.34057 | + | 2.80307i | ||||
\(917\) | −2.54967 | + | 3.03858i | −0.0841975 | + | 0.100343i | ||||
\(918\) | −15.5055 | + | 2.73403i | −0.511756 | + | 0.0902364i | ||||
\(919\) | −5.30464 | − | 9.18791i | −0.174984 | − | 0.303081i | 0.765172 | − | 0.643826i | \(-0.222654\pi\) |
−0.940156 | + | 0.340745i | \(0.889321\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.13496 | + | 0.777061i | 0.0703492 | + | 0.0256050i | ||||
\(922\) | −12.3830 | + | 34.0221i | −0.407814 | + | 1.12046i | ||||
\(923\) | −20.8593 | − | 12.0431i | −0.686591 | − | 0.396403i | ||||
\(924\) | 1.20652 | + | 2.08975i | 0.0396915 | + | 0.0687477i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 51.8001 | + | 43.4655i | 1.70226 | + | 1.42836i | ||||
\(927\) | −23.4751 | − | 27.9766i | −0.771025 | − | 0.918871i | ||||
\(928\) | −52.6272 | − | 9.27960i | −1.72757 | − | 0.304618i | ||||
\(929\) | −13.3285 | + | 4.85116i | −0.437293 | + | 0.159162i | −0.551279 | − | 0.834321i | \(-0.685860\pi\) |
0.113987 | + | 0.993482i | \(0.463638\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.3915 | − | 17.1359i | −0.799399 | − | 0.561607i | ||||
\(932\) | 44.1200i | 1.44520i | ||||||||
\(933\) | 2.03773 | + | 5.59862i | 0.0667123 | + | 0.183290i | ||||
\(934\) | 17.7574 | − | 100.707i | 0.581039 | − | 3.29524i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −44.9019 | − | 37.6772i | −1.46766 | − | 1.23152i | ||||
\(937\) | −43.8654 | + | 7.73465i | −1.43302 | + | 0.252680i | −0.835640 | − | 0.549278i | \(-0.814903\pi\) |
−0.597380 | + | 0.801958i | \(0.703792\pi\) | |||||||
\(938\) | −0.680253 | + | 0.392744i | −0.0222110 | + | 0.0128235i | ||||
\(939\) | 0.304642 | − | 0.527656i | 0.00994163 | − | 0.0172194i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.5593 | + | 10.3947i | 0.931006 | + | 0.338859i | 0.762608 | − | 0.646860i | \(-0.223918\pi\) |
0.168398 | + | 0.985719i | \(0.446141\pi\) | |||||||
\(942\) | −6.96324 | − | 4.02023i | −0.226875 | − | 0.130986i | ||||
\(943\) | −8.31698 | + | 4.80181i | −0.270838 | + | 0.156368i | ||||
\(944\) | 2.23303 | + | 12.6642i | 0.0726791 | + | 0.412183i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −127.696 | + | 107.150i | −4.15177 | + | 3.48375i | ||||
\(947\) | −30.5045 | − | 5.37877i | −0.991264 | − | 0.174787i | −0.345578 | − | 0.938390i | \(-0.612317\pi\) |
−0.645686 | + | 0.763603i | \(0.723428\pi\) | |||||||
\(948\) | −1.26220 | − | 3.46788i | −0.0409945 | − | 0.112631i | ||||
\(949\) | 28.6582 | 0.930285 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.73954 | −0.0564086 | ||||||||
\(952\) | −3.92908 | − | 10.7950i | −0.127342 | − | 0.349869i | ||||
\(953\) | 21.9251 | + | 3.86599i | 0.710224 | + | 0.125232i | 0.517078 | − | 0.855938i | \(-0.327020\pi\) |
0.193146 | + | 0.981170i | \(0.438131\pi\) | |||||||
\(954\) | 71.5346 | − | 60.0247i | 2.31602 | − | 1.94337i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.56828 | + | 54.2644i | 0.309460 | + | 1.75504i | ||||
\(957\) | −7.33148 | + | 4.23283i | −0.236993 | + | 0.136828i | ||||
\(958\) | 8.45343 | + | 4.88059i | 0.273118 | + | 0.157685i | ||||
\(959\) | 3.38277 | + | 1.23123i | 0.109235 | + | 0.0397584i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.10876 | + | 7.11657i | −0.132540 | + | 0.229567i | ||||
\(962\) | 7.37548 | − | 4.25823i | 0.237795 | − | 0.137291i | ||||
\(963\) | 42.1428 | − | 7.43092i | 1.35803 | − | 0.239458i | ||||
\(964\) | 45.8162 | + | 38.4444i | 1.47564 | + | 1.23821i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.149886 | − | 0.850044i | 0.00482249 | − | 0.0273497i | ||||
\(967\) | 5.99883 | + | 16.4816i | 0.192909 | + | 0.530014i | 0.998005 | − | 0.0631307i | \(-0.0201085\pi\) |
−0.805096 | + | 0.593145i | \(0.797886\pi\) | |||||||
\(968\) | − | 110.056i | − | 3.53734i | ||||||
\(969\) | −4.45741 | + | 0.382961i | −0.143193 | + | 0.0123025i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.7599 | − | 5.73614i | 0.505759 | − | 0.184081i | −0.0765232 | − | 0.997068i | \(-0.524382\pi\) |
0.582283 | + | 0.812986i | \(0.302160\pi\) | |||||||
\(972\) | −29.9417 | − | 5.27953i | −0.960381 | − | 0.169341i | ||||
\(973\) | −3.39927 | − | 4.05109i | −0.108975 | − | 0.129872i | ||||
\(974\) | −13.8314 | − | 11.6059i | −0.443187 | − | 0.371878i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 29.6518 | + | 51.3584i | 0.949131 | + | 1.64394i | ||||
\(977\) | 24.9276 | + | 14.3920i | 0.797506 | + | 0.460440i | 0.842598 | − | 0.538543i | \(-0.181025\pi\) |
−0.0450925 | + | 0.998983i | \(0.514358\pi\) | |||||||
\(978\) | −0.718608 | + | 1.97436i | −0.0229785 | + | 0.0631330i | ||||
\(979\) | −61.0872 | − | 22.2339i | −1.95236 | − | 0.710599i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.49419 | + | 11.2483i | 0.207344 | + | 0.359130i | ||||
\(982\) | 83.0287 | − | 14.6402i | 2.64955 | − | 0.467187i | ||||
\(983\) | −19.2302 | + | 22.9176i | −0.613348 | + | 0.730959i | −0.979911 | − | 0.199434i | \(-0.936090\pi\) |
0.366564 | + | 0.930393i | \(0.380534\pi\) | |||||||
\(984\) | 3.74593 | − | 3.14321i | 0.119416 | − | 0.100202i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 66.2147 | − | 24.1002i | 2.10870 | − | 0.767506i | ||||
\(987\) | 0.672737i | 0.0214135i | ||||||||
\(988\) | −41.5467 | − | 41.6766i | −1.32178 | − | 1.32591i | ||||
\(989\) | 41.7553 | 1.32774 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.97273 | − | 45.2156i | 0.253262 | − | 1.43632i | −0.547232 | − | 0.836981i | \(-0.684319\pi\) |
0.800495 | − | 0.599340i | \(-0.204570\pi\) | |||||||
\(992\) | −32.6726 | − | 38.9377i | −1.03736 | − | 1.23627i | ||||
\(993\) | −2.77229 | + | 3.30389i | −0.0879760 | + | 0.104846i | ||||
\(994\) | −1.50181 | − | 8.51716i | −0.0476344 | − | 0.270148i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.19427 | − | 5.53264i | 0.101214 | − | 0.175308i | ||||
\(997\) | −18.4520 | + | 50.6964i | −0.584380 | + | 1.60557i | 0.196234 | + | 0.980557i | \(0.437129\pi\) |
−0.780614 | + | 0.625014i | \(0.785093\pi\) | |||||||
\(998\) | −24.5545 | + | 67.4628i | −0.777258 | + | 2.13550i | ||||
\(999\) | 0.839319 | − | 1.45374i | 0.0265549 | − | 0.0459944i |
(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 | 475.2.u.b.24.1 | 36 | ||
5.2 | odd | 4 | 475.2.l.c.176.3 | 18 | |||
5.3 | odd | 4 | 95.2.k.a.81.1 | yes | 18 | ||
5.4 | even | 2 | inner | 475.2.u.b.24.6 | 36 | ||
15.8 | even | 4 | 855.2.bs.c.271.3 | 18 | |||
19.4 | even | 9 | inner | 475.2.u.b.99.6 | 36 | ||
95.2 | even | 36 | 9025.2.a.cf.1.9 | 9 | |||
95.4 | even | 18 | inner | 475.2.u.b.99.1 | 36 | ||
95.17 | odd | 36 | 9025.2.a.cc.1.1 | 9 | |||
95.23 | odd | 36 | 95.2.k.a.61.1 | ✓ | 18 | ||
95.42 | odd | 36 | 475.2.l.c.251.3 | 18 | |||
95.78 | even | 36 | 1805.2.a.s.1.1 | 9 | |||
95.93 | odd | 36 | 1805.2.a.v.1.9 | 9 | |||
285.23 | even | 36 | 855.2.bs.c.631.3 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.k.a.61.1 | ✓ | 18 | 95.23 | odd | 36 | ||
95.2.k.a.81.1 | yes | 18 | 5.3 | odd | 4 | ||
475.2.l.c.176.3 | 18 | 5.2 | odd | 4 | |||
475.2.l.c.251.3 | 18 | 95.42 | odd | 36 | |||
475.2.u.b.24.1 | 36 | 1.1 | even | 1 | trivial | ||
475.2.u.b.24.6 | 36 | 5.4 | even | 2 | inner | ||
475.2.u.b.99.1 | 36 | 95.4 | even | 18 | inner | ||
475.2.u.b.99.6 | 36 | 19.4 | even | 9 | inner | ||
855.2.bs.c.271.3 | 18 | 15.8 | even | 4 | |||
855.2.bs.c.631.3 | 18 | 285.23 | even | 36 | |||
1805.2.a.s.1.1 | 9 | 95.78 | even | 36 | |||
1805.2.a.v.1.9 | 9 | 95.93 | odd | 36 | |||
9025.2.a.cc.1.1 | 9 | 95.17 | odd | 36 | |||
9025.2.a.cf.1.9 | 9 | 95.2 | even | 36 |