Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(101,475)]
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([0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.l (of order \(9\), degree \(6\), 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: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 3 x^{17} + 15 x^{16} - 14 x^{15} + 72 x^{14} - 51 x^{13} + 231 x^{12} - 93 x^{11} + 438 x^{10} - 156 x^{9} + 582 x^{8} - 138 x^{7} + 437 x^{6} - 132 x^{5} + 198 x^{4} - 16 x^{3} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 176.3 | ||
Root | \(-0.791558 - 1.37102i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.176 |
Dual form | 475.2.l.c.251.3 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.42733 | − | 0.883478i | 1.71639 | − | 0.624713i | 0.718869 | − | 0.695146i | \(-0.244660\pi\) |
0.997517 | + | 0.0704330i | \(0.0224381\pi\) | |||||||
\(3\) | 0.0430161 | − | 0.243956i | 0.0248353 | − | 0.140848i | −0.969869 | − | 0.243628i | \(-0.921663\pi\) |
0.994704 | + | 0.102780i | \(0.0327736\pi\) | |||||||
\(4\) | 3.57933 | − | 3.00342i | 1.78967 | − | 1.50171i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.111115 | − | 0.630167i | −0.0453627 | − | 0.257265i | ||||
\(7\) | −0.200820 | − | 0.347830i | −0.0759028 | − | 0.131468i | 0.825576 | − | 0.564291i | \(-0.190851\pi\) |
−0.901479 | + | 0.432824i | \(0.857517\pi\) | |||||||
\(8\) | 3.45167 | − | 5.97847i | 1.22035 | − | 2.11371i | ||||
\(9\) | 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 | \(0.880604\pi\) | |||||||
\(12\) | −0.578733 | − | 1.00240i | −0.167066 | − | 0.289367i | ||||
\(13\) | −0.501737 | − | 2.84549i | −0.139157 | − | 0.789197i | −0.971875 | − | 0.235499i | \(-0.924327\pi\) |
0.832718 | − | 0.553698i | \(-0.186784\pi\) | |||||||
\(14\) | −0.794758 | − | 0.666881i | −0.212408 | − | 0.178231i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.47378 | − | 8.35823i | 0.368445 | − | 2.08956i | ||||
\(17\) | −3.89339 | + | 1.41708i | −0.944286 | + | 0.343692i | −0.767857 | − | 0.640621i | \(-0.778677\pi\) |
−0.176429 | + | 0.984313i | \(0.556455\pi\) | |||||||
\(18\) | 7.59083 | 1.78918 | ||||||||
\(19\) | 0.386682 | − | 4.34171i | 0.0887110 | − | 0.996057i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0934938 | + | 0.0340290i | −0.0204020 | + | 0.00742573i | ||||
\(22\) | −2.32827 | + | 13.2043i | −0.496388 | + | 2.81516i | ||||
\(23\) | −2.57278 | + | 2.15882i | −0.536462 | + | 0.450145i | −0.870326 | − | 0.492476i | \(-0.836092\pi\) |
0.333864 | + | 0.942621i | \(0.391647\pi\) | |||||||
\(24\) | −1.31001 | − | 1.09923i | −0.267404 | − | 0.224379i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.73181 | − | 6.46368i | −0.731868 | − | 1.26763i | ||||
\(27\) | 0.735558 | − | 1.27402i | 0.141558 | − | 0.245186i | ||||
\(28\) | −1.76348 | − | 0.641855i | −0.333267 | − | 0.121299i | ||||
\(29\) | −6.18683 | − | 2.25182i | −1.14887 | − | 0.418153i | −0.303758 | − | 0.952749i | \(-0.598241\pi\) |
−0.845107 | + | 0.534597i | \(0.820464\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.13119 | + | 5.42339i | 0.562379 | + | 0.974069i | 0.997288 | + | 0.0735948i | \(0.0234472\pi\) |
−0.434909 | + | 0.900474i | \(0.643220\pi\) | |||||||
\(32\) | −1.40944 | − | 7.99334i | −0.249156 | − | 1.41304i | ||||
\(33\) | 0.984992 | + | 0.826506i | 0.171465 | + | 0.143876i | ||||
\(34\) | −8.19861 | + | 6.87945i | −1.40605 | + | 1.17982i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 12.9027 | − | 4.69619i | 2.15045 | − | 0.782698i | ||||
\(37\) | −1.14106 | −0.187590 | −0.0937949 | − | 0.995592i | \(-0.529900\pi\) | ||||
−0.0937949 | + | 0.995592i | \(0.529900\pi\) | |||||||
\(38\) | −2.89720 | − | 10.8804i | −0.469988 | − | 1.76504i | ||||
\(39\) | −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 | \(-0.0161233\pi\) | |||||||
\(42\) | −0.196877 | + | 0.165199i | −0.0303788 | + | 0.0254908i | ||||
\(43\) | 9.52394 | + | 7.99153i | 1.45239 | + | 1.21870i | 0.930815 | + | 0.365491i | \(0.119099\pi\) |
0.521572 | + | 0.853207i | \(0.325346\pi\) | |||||||
\(44\) | 4.21150 | + | 23.8846i | 0.634908 | + | 3.60074i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.33773 | + | 7.51317i | −0.639564 | + | 1.10776i | ||||
\(47\) | 6.35381 | + | 2.31260i | 0.926798 | + | 0.337327i | 0.760940 | − | 0.648822i | \(-0.224738\pi\) |
0.165859 | + | 0.986150i | \(0.446960\pi\) | |||||||
\(48\) | −1.97565 | − | 0.719076i | −0.285160 | − | 0.103790i | ||||
\(49\) | 3.41934 | − | 5.92248i | 0.488478 | − | 0.846068i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.178227 | + | 1.01077i | 0.0249567 | + | 0.141537i | ||||
\(52\) | −10.3421 | − | 8.67803i | −1.43419 | − | 1.20343i | ||||
\(53\) | −9.42382 | + | 7.90752i | −1.29446 | + | 1.08618i | −0.303387 | + | 0.952867i | \(0.598117\pi\) |
−0.991074 | + | 0.133314i | \(0.957438\pi\) | |||||||
\(54\) | 0.659874 | − | 3.74233i | 0.0897975 | − | 0.509267i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.77266 | −0.370512 | ||||||||
\(57\) | −1.04255 | − | 0.281097i | −0.138090 | − | 0.0372322i | ||||
\(58\) | −17.0069 | −2.23312 | ||||||||
\(59\) | 1.42380 | − | 0.518220i | 0.185363 | − | 0.0674665i | −0.247671 | − | 0.968844i | \(-0.579665\pi\) |
0.433034 | + | 0.901378i | \(0.357443\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.35269 | + | 4.49144i | −0.685342 | + | 0.575070i | −0.917562 | − | 0.397593i | \(-0.869845\pi\) |
0.232220 | + | 0.972663i | \(0.425401\pi\) | |||||||
\(62\) | 12.3919 | + | 10.3980i | 1.57377 | + | 1.32055i | ||||
\(63\) | −0.204952 | − | 1.16234i | −0.0258216 | − | 0.146441i | ||||
\(64\) | −1.99595 | − | 3.45709i | −0.249494 | − | 0.432136i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.12111 | + | 1.13599i | 0.384182 | + | 0.139831i | ||||
\(67\) | −0.711451 | − | 0.258947i | −0.0869175 | − | 0.0316354i | 0.298195 | − | 0.954505i | \(-0.403615\pi\) |
−0.385113 | + | 0.922869i | \(0.625838\pi\) | |||||||
\(68\) | −9.67967 | + | 16.7657i | −1.17383 | + | 2.03314i | ||||
\(69\) | 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 | \(0.886928\pi\) | |||||||
\(72\) | 15.5403 | − | 13.0399i | 1.83144 | − | 1.53676i | ||||
\(73\) | 1.72232 | − | 9.76776i | 0.201582 | − | 1.14323i | −0.701146 | − | 0.713018i | \(-0.747328\pi\) |
0.902728 | − | 0.430212i | \(-0.141561\pi\) | |||||||
\(74\) | −2.76974 | + | 1.00810i | −0.321976 | + | 0.117190i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −11.6559 | − | 16.7018i | −1.33702 | − | 1.91583i | ||||
\(77\) | 2.08476 | 0.237580 | ||||||||
\(78\) | −1.73738 | + | 0.632356i | −0.196720 | + | 0.0716002i | ||||
\(79\) | 0.553655 | − | 3.13994i | 0.0622911 | − | 0.353270i | −0.937692 | − | 0.347467i | \(-0.887042\pi\) |
0.999983 | − | 0.00580301i | \(-0.00184717\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.47421 | + | 5.43251i | 0.719357 | + | 0.603612i | ||||
\(82\) | −1.28263 | − | 7.27414i | −0.141642 | − | 0.803294i | ||||
\(83\) | 2.75971 | + | 4.77995i | 0.302917 | + | 0.524668i | 0.976795 | − | 0.214174i | \(-0.0687061\pi\) |
−0.673878 | + | 0.738842i | \(0.735373\pi\) | |||||||
\(84\) | −0.232442 | + | 0.402602i | −0.0253615 | + | 0.0439275i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 30.1781 | + | 10.9839i | 3.25419 | + | 1.18443i | ||||
\(87\) | −0.815478 | + | 1.41245i | −0.0874285 | + | 0.151431i | ||||
\(88\) | 17.9163 | + | 31.0319i | 1.90988 | + | 3.30801i | ||||
\(89\) | −2.17478 | − | 12.3338i | −0.230527 | − | 1.30738i | −0.851833 | − | 0.523814i | \(-0.824509\pi\) |
0.621306 | − | 0.783568i | \(-0.286602\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.888989 | + | 0.745950i | −0.0931914 | + | 0.0781968i | ||||
\(92\) | −2.72500 | + | 15.4543i | −0.284101 | + | 1.61122i | ||||
\(93\) | 1.45776 | − | 0.530581i | 0.151163 | − | 0.0550187i | ||||
\(94\) | 17.4660 | 1.80148 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.01065 | −0.205211 | ||||||||
\(97\) | −8.35815 | + | 3.04212i | −0.848642 | + | 0.308880i | −0.729487 | − | 0.683995i | \(-0.760241\pi\) |
−0.119155 | + | 0.992876i | \(0.538019\pi\) | |||||||
\(98\) | 3.06752 | − | 17.3967i | 0.309866 | − | 1.75734i | ||||
\(99\) | −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 | \(0.923113\pi\) | |||||||
\(102\) | 1.32561 | + | 2.29603i | 0.131255 | + | 0.227341i | ||||
\(103\) | 6.21391 | − | 10.7628i | 0.612275 | − | 1.06049i | −0.378581 | − | 0.925568i | \(-0.623588\pi\) |
0.990856 | − | 0.134923i | \(-0.0430787\pi\) | |||||||
\(104\) | −18.7435 | − | 6.82208i | −1.83795 | − | 0.668960i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −15.8886 | + | 27.5199i | −1.54324 | + | 2.67297i | ||||
\(107\) | −7.28110 | − | 12.6112i | −0.703890 | − | 1.21917i | −0.967091 | − | 0.254432i | \(-0.918111\pi\) |
0.263200 | − | 0.964741i | \(-0.415222\pi\) | |||||||
\(108\) | −1.19362 | − | 6.76934i | −0.114856 | − | 0.651380i | ||||
\(109\) | 3.38582 | + | 2.84104i | 0.324303 | + | 0.272122i | 0.790374 | − | 0.612625i | \(-0.209886\pi\) |
−0.466071 | + | 0.884747i | \(0.654331\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0490841 | + | 0.278370i | −0.00465885 | + | 0.0264217i | ||||
\(112\) | −3.20321 | + | 1.16587i | −0.302675 | + | 0.110165i | ||||
\(113\) | −8.08453 | −0.760528 | −0.380264 | − | 0.924878i | \(-0.624167\pi\) | ||||
−0.380264 | + | 0.924878i | \(0.624167\pi\) | |||||||
\(114\) | −2.77897 | + | 0.238757i | −0.260274 | + | 0.0223616i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −28.9079 | + | 10.5216i | −2.68403 | + | 0.976907i | ||||
\(117\) | 1.47442 | − | 8.36186i | 0.136310 | − | 0.773054i | ||||
\(118\) | 2.99820 | − | 2.51579i | 0.276006 | − | 0.231597i | ||||
\(119\) | 1.27477 | + | 1.06966i | 0.116858 | + | 0.0980557i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.97122 | − | 13.8065i | −0.724656 | − | 1.25514i | ||||
\(122\) | −9.02468 | + | 15.6312i | −0.817056 | + | 1.41518i | ||||
\(123\) | −0.665629 | − | 0.242269i | −0.0600178 | − | 0.0218447i | ||||
\(124\) | 27.4963 | + | 10.0078i | 2.46924 | + | 0.898730i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.52439 | − | 2.64032i | −0.135804 | − | 0.235219i | ||||
\(127\) | 0.0974458 | + | 0.552642i | 0.00864691 | + | 0.0490391i | 0.988826 | − | 0.149075i | \(-0.0476295\pi\) |
−0.980179 | + | 0.198114i | \(0.936518\pi\) | |||||||
\(128\) | 4.53632 | + | 3.80642i | 0.400958 | + | 0.336444i | ||||
\(129\) | 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 | \(0.246897\pi\) | |||||||
\(132\) | 6.00796 | 0.522926 | ||||||||
\(133\) | −1.58783 | + | 0.737403i | −0.137683 | + | 0.0639409i | ||||
\(134\) | −1.95570 | −0.168947 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.96675 | + | 28.1678i | −0.425895 | + | 2.41537i | ||||
\(137\) | 6.86600 | − | 5.76126i | 0.586602 | − | 0.492217i | −0.300506 | − | 0.953780i | \(-0.597155\pi\) |
0.887108 | + | 0.461563i | \(0.152711\pi\) | |||||||
\(138\) | 1.64629 | + | 1.38140i | 0.140142 | + | 0.117593i | ||||
\(139\) | −2.28639 | − | 12.9668i | −0.193929 | − | 1.09983i | −0.913935 | − | 0.405860i | \(-0.866972\pi\) |
0.720006 | − | 0.693968i | \(-0.244139\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.837488 | − | 1.45057i | 0.0705292 | − | 0.122160i | ||||
\(142\) | −20.2345 | − | 7.36475i | −1.69804 | − | 0.618036i | ||||
\(143\) | 14.0932 | + | 5.12951i | 1.17853 | + | 0.428951i | ||||
\(144\) | 12.4703 | − | 21.5993i | 1.03920 | − | 1.79994i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.44895 | − | 25.2313i | −0.368198 | − | 2.08815i | ||||
\(147\) | −1.29774 | − | 1.08893i | −0.107036 | − | 0.0898135i | ||||
\(148\) | −4.08425 | + | 3.42709i | −0.335723 | + | 0.281705i | ||||
\(149\) | −1.42107 | + | 8.05930i | −0.116419 | + | 0.660243i | 0.869619 | + | 0.493723i | \(0.164364\pi\) |
−0.986038 | + | 0.166520i | \(0.946747\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.60636 | 0.618997 | 0.309498 | − | 0.950900i | \(-0.399839\pi\) | ||||
0.309498 | + | 0.950900i | \(0.399839\pi\) | |||||||
\(152\) | −24.6221 | − | 17.2979i | −1.99712 | − | 1.40305i | ||||
\(153\) | −12.1755 | −0.984333 | ||||||||
\(154\) | 5.06040 | − | 1.84184i | 0.407779 | − | 0.148419i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.56193 | + | 2.14972i | −0.205119 | + | 0.172115i | ||||
\(157\) | 9.62566 | + | 8.07689i | 0.768212 | + | 0.644606i | 0.940250 | − | 0.340484i | \(-0.110591\pi\) |
−0.172039 | + | 0.985090i | \(0.555035\pi\) | |||||||
\(158\) | −1.43016 | − | 8.11082i | −0.113777 | − | 0.645262i | ||||
\(159\) | 1.52371 | + | 2.63915i | 0.120838 | + | 0.209298i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.26757 | + | 0.461357i | 0.0998984 | + | 0.0363600i | ||||
\(162\) | 20.5146 | + | 7.46669i | 1.61178 | + | 0.586639i | ||||
\(163\) | −1.64175 | + | 2.84359i | −0.128591 | + | 0.222727i | −0.923131 | − | 0.384485i | \(-0.874379\pi\) |
0.794540 | + | 0.607212i | \(0.207712\pi\) | |||||||
\(164\) | −6.68043 | − | 11.5708i | −0.521654 | − | 0.903531i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.9217 | + | 9.16441i | 0.847689 | + | 0.711296i | ||||
\(167\) | 4.00460 | − | 3.36026i | 0.309885 | − | 0.260025i | −0.474559 | − | 0.880224i | \(-0.657393\pi\) |
0.784445 | + | 0.620199i | \(0.212948\pi\) | |||||||
\(168\) | −0.119269 | + | 0.676407i | −0.00920179 | + | 0.0521860i | ||||
\(169\) | 4.37093 | − | 1.59089i | 0.336226 | − | 0.122376i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.43153 | − | 11.6006i | 0.415359 | − | 0.887122i | ||||
\(172\) | 58.0913 | 4.42942 | ||||||||
\(173\) | 4.23385 | − | 1.54100i | 0.321894 | − | 0.117160i | −0.176019 | − | 0.984387i | \(-0.556322\pi\) |
0.497913 | + | 0.867227i | \(0.334100\pi\) | |||||||
\(174\) | −0.731571 | + | 4.14895i | −0.0554603 | + | 0.314531i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 33.7470 | + | 28.3171i | 2.54378 | + | 2.13448i | ||||
\(177\) | −0.0651768 | − | 0.369636i | −0.00489899 | − | 0.0277835i | ||||
\(178\) | −16.1756 | − | 28.0169i | −1.21241 | − | 2.09996i | ||||
\(179\) | 1.88583 | − | 3.26636i | 0.140954 | − | 0.244139i | −0.786902 | − | 0.617078i | \(-0.788316\pi\) |
0.927856 | + | 0.372939i | \(0.121650\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.9437 | − | 6.53096i | −1.33374 | − | 0.485442i | −0.425906 | − | 0.904767i | \(-0.640045\pi\) |
−0.907836 | + | 0.419325i | \(0.862267\pi\) | |||||||
\(182\) | −1.49884 | + | 2.59607i | −0.111102 | + | 0.192434i | ||||
\(183\) | 0.865463 | + | 1.49903i | 0.0639768 | + | 0.110811i | ||||
\(184\) | 4.02605 | + | 22.8328i | 0.296804 | + | 1.68326i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.06972 | − | 2.57580i | 0.225082 | − | 0.188867i | ||||
\(187\) | 3.73449 | − | 21.1793i | 0.273093 | − | 1.54879i | ||||
\(188\) | 29.6881 | − | 10.8056i | 2.16523 | − | 0.788078i | ||||
\(189\) | −0.590859 | −0.0429787 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.89599 | 0.209547 | 0.104773 | − | 0.994496i | \(-0.466588\pi\) | ||||
0.104773 | + | 0.994496i | \(0.466588\pi\) | |||||||
\(192\) | −0.929236 | + | 0.338214i | −0.0670619 | + | 0.0244085i | ||||
\(193\) | −1.97618 | + | 11.2075i | −0.142249 | + | 0.806733i | 0.827286 | + | 0.561781i | \(0.189883\pi\) |
−0.969535 | + | 0.244952i | \(0.921228\pi\) | |||||||
\(194\) | −17.6004 | + | 14.7685i | −1.26363 | + | 1.06032i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.54870 | − | 31.4682i | −0.396336 | − | 2.24773i | ||||
\(197\) | −5.07545 | − | 8.79093i | −0.361610 | − | 0.626328i | 0.626616 | − | 0.779329i | \(-0.284440\pi\) |
−0.988226 | + | 0.153001i | \(0.951106\pi\) | |||||||
\(198\) | −19.7005 | + | 34.1223i | −1.40006 | + | 2.42497i | ||||
\(199\) | 2.75352 | + | 1.00220i | 0.195192 | + | 0.0710440i | 0.437766 | − | 0.899089i | \(-0.355770\pi\) |
−0.242575 | + | 0.970133i | \(0.577992\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.0937755 | + | 0.162424i | −0.00661441 | + | 0.0114565i | ||||
\(202\) | 1.73841 | + | 3.01101i | 0.122314 | + | 0.211854i | ||||
\(203\) | 0.459187 | + | 2.60418i | 0.0322286 | + | 0.182777i | ||||
\(204\) | 3.67371 | + | 3.08261i | 0.257211 | + | 0.215826i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.57454 | − | 31.6148i | 0.388397 | − | 2.20271i | ||||
\(207\) | −9.27428 | + | 3.37556i | −0.644607 | + | 0.234618i | ||||
\(208\) | −24.5227 | −1.70034 | ||||||||
\(209\) | 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 | \(0.328197\pi\) | |||||||
\(212\) | −9.98140 | + | 56.6073i | −0.685525 | + | 3.88781i | ||||
\(213\) | −1.58189 | + | 1.32737i | −0.108389 | + | 0.0909496i | ||||
\(214\) | −28.8154 | − | 24.1790i | −1.96978 | − | 1.65284i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.07781 | − | 8.79503i | −0.345501 | − | 0.598426i | ||||
\(217\) | 1.25761 | − | 2.17825i | 0.0853723 | − | 0.147869i | ||||
\(218\) | 10.7285 | + | 3.90486i | 0.726626 | + | 0.264470i | ||||
\(219\) | −2.30882 | − | 0.840341i | −0.156015 | − | 0.0567850i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.98574 | + | 10.3676i | 0.402644 | + | 0.697400i | ||||
\(222\) | 0.126790 | + | 0.719061i | 0.00850958 | + | 0.0482602i | ||||
\(223\) | −6.09836 | − | 5.11713i | −0.408376 | − | 0.342669i | 0.415344 | − | 0.909664i | \(-0.363661\pi\) |
−0.823721 | + | 0.566996i | \(0.808106\pi\) | |||||||
\(224\) | −2.49728 | + | 2.09547i | −0.166857 | + | 0.140009i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.6239 | + | 7.14250i | −1.30536 | + | 0.475112i | ||||
\(227\) | −8.02439 | −0.532597 | −0.266299 | − | 0.963891i | \(-0.585801\pi\) | ||||
−0.266299 | + | 0.963891i | \(0.585801\pi\) | |||||||
\(228\) | −4.57590 | + | 2.12509i | −0.303046 | + | 0.140737i | ||||
\(229\) | −28.2466 | −1.86659 | −0.933295 | − | 0.359111i | \(-0.883080\pi\) | ||||
−0.933295 | + | 0.359111i | \(0.883080\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0896780 | − | 0.508589i | 0.00590038 | − | 0.0334627i | ||||
\(232\) | −34.8174 | + | 29.2152i | −2.28587 | + | 1.91807i | ||||
\(233\) | −7.23338 | − | 6.06953i | −0.473875 | − | 0.397628i | 0.374331 | − | 0.927295i | \(-0.377872\pi\) |
−0.848206 | + | 0.529667i | \(0.822317\pi\) | |||||||
\(234\) | −3.80860 | − | 21.5996i | −0.248976 | − | 1.41201i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.53981 | − | 6.13114i | 0.230422 | − | 0.399103i | ||||
\(237\) | −0.742191 | − | 0.270135i | −0.0482105 | − | 0.0175472i | ||||
\(238\) | 4.03932 | + | 1.47019i | 0.261831 | + | 0.0952985i | ||||
\(239\) | −5.89638 | + | 10.2128i | −0.381405 | + | 0.660613i | −0.991263 | − | 0.131897i | \(-0.957893\pi\) |
0.609858 | + | 0.792511i | \(0.291226\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.22273 | − | 12.6057i | −0.143179 | − | 0.812007i | −0.968811 | − | 0.247799i | \(-0.920293\pi\) |
0.825633 | − | 0.564208i | \(-0.190818\pi\) | |||||||
\(242\) | −31.5466 | − | 26.4707i | −2.02789 | − | 1.70160i | ||||
\(243\) | 4.98461 | − | 4.18258i | 0.319763 | − | 0.268313i | ||||
\(244\) | −5.66939 | + | 32.1527i | −0.362946 | + | 2.05837i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.82974 | −0.116660 | ||||||||
\(247\) | −12.5483 | + | 1.07810i | −0.798430 | + | 0.0685976i | ||||
\(248\) | 43.2314 | 2.74520 | ||||||||
\(249\) | 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 | \(0.253648\pi\) | |||||||
\(252\) | −4.22459 | − | 3.54485i | −0.266124 | − | 0.223305i | ||||
\(253\) | −3.02717 | − | 17.1680i | −0.190317 | − | 1.07934i | ||||
\(254\) | 0.724781 | + | 1.25536i | 0.0454768 | + | 0.0787681i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 21.8764 | + | 7.96235i | 1.36727 | + | 0.497647i | ||||
\(257\) | 16.1772 | + | 5.88802i | 1.00911 | + | 0.367285i | 0.793090 | − | 0.609105i | \(-0.208471\pi\) |
0.216017 | + | 0.976390i | \(0.430693\pi\) | |||||||
\(258\) | 3.97774 | − | 6.88966i | 0.247644 | − | 0.428931i | ||||
\(259\) | 0.229148 | + | 0.396897i | 0.0142386 | + | 0.0246620i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.8211 | − | 12.4364i | −0.917406 | − | 0.769795i | ||||
\(262\) | 19.5424 | − | 16.3980i | 1.20733 | − | 1.01307i | ||||
\(263\) | −2.54981 | + | 14.4607i | −0.157228 | + | 0.891685i | 0.799492 | + | 0.600677i | \(0.205102\pi\) |
−0.956720 | + | 0.291009i | \(0.906009\pi\) | |||||||
\(264\) | 8.34112 | − | 3.03592i | 0.513360 | − | 0.186848i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.20272 | + | 3.19274i | −0.196372 | + | 0.195759i | ||||
\(267\) | −3.10246 | −0.189868 | ||||||||
\(268\) | −3.32424 | + | 1.20993i | −0.203061 | + | 0.0739080i | ||||
\(269\) | −3.89891 | + | 22.1118i | −0.237721 | + | 1.34818i | 0.599086 | + | 0.800685i | \(0.295531\pi\) |
−0.836807 | + | 0.547498i | \(0.815580\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.1742 | + | 8.53716i | 0.618038 | + | 0.518596i | 0.897186 | − | 0.441652i | \(-0.145608\pi\) |
−0.279148 | + | 0.960248i | \(0.590052\pi\) | |||||||
\(272\) | 6.10626 | + | 34.6303i | 0.370246 | + | 2.09977i | ||||
\(273\) | 0.143738 | + | 0.248962i | 0.00869944 | + | 0.0150679i | ||||
\(274\) | 11.5761 | − | 20.0505i | 0.699340 | − | 1.21129i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.65294 | + | 1.32956i | 0.219881 | + | 0.0800303i | ||||
\(277\) | 1.67963 | − | 2.90921i | 0.100919 | − | 0.174797i | −0.811144 | − | 0.584846i | \(-0.801155\pi\) |
0.912064 | + | 0.410049i | \(0.134488\pi\) | |||||||
\(278\) | −17.0057 | − | 29.4548i | −1.01993 | − | 1.76658i | ||||
\(279\) | 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 | \(0.0740504\pi\) | |||||||
\(282\) | 0.751316 | − | 4.26093i | 0.0447402 | − | 0.253735i | ||||
\(283\) | 0.498021 | − | 0.181265i | 0.0296043 | − | 0.0107751i | −0.327176 | − | 0.944964i | \(-0.606097\pi\) |
0.356780 | + | 0.934188i | \(0.383875\pi\) | |||||||
\(284\) | −38.9503 | −2.31127 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 38.7407 | 2.29079 | ||||||||
\(287\) | −1.07922 | + | 0.392803i | −0.0637042 | + | 0.0231864i | ||||
\(288\) | 4.14183 | − | 23.4895i | 0.244060 | − | 1.38413i | ||||
\(289\) | 0.127626 | − | 0.107091i | 0.00750741 | − | 0.00629946i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.382609 | + | 2.16988i | 0.0224289 | + | 0.127201i | ||||
\(292\) | −23.1719 | − | 40.1349i | −1.35603 | − | 2.34872i | ||||
\(293\) | 15.8074 | − | 27.3793i | 0.923480 | − | 1.59951i | 0.129492 | − | 0.991580i | \(-0.458665\pi\) |
0.793988 | − | 0.607934i | \(-0.208001\pi\) | |||||||
\(294\) | −4.11209 | − | 1.49668i | −0.239822 | − | 0.0872881i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.93858 | + | 6.82182i | −0.228925 | + | 0.396510i | ||||
\(297\) | 3.81799 | + | 6.61296i | 0.221543 | + | 0.383723i | ||||
\(298\) | 3.67079 | + | 20.8181i | 0.212643 | + | 1.20596i | ||||
\(299\) | 7.43376 | + | 6.23766i | 0.429905 | + | 0.360733i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.867101 | − | 4.91757i | 0.0499789 | − | 0.283444i | ||||
\(302\) | 18.4632 | − | 6.72005i | 1.06244 | − | 0.386695i | ||||
\(303\) | 0.333425 | 0.0191548 | ||||||||
\(304\) | −35.7192 | − | 9.63072i | −2.04863 | − | 0.552359i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −29.5541 | + | 10.7568i | −1.68949 | + | 0.614926i | ||||
\(307\) | −1.59262 | + | 9.03222i | −0.0908958 | + | 0.515496i | 0.905032 | + | 0.425343i | \(0.139847\pi\) |
−0.995928 | + | 0.0901527i | \(0.971264\pi\) | |||||||
\(308\) | 7.46204 | − | 6.26139i | 0.425189 | − | 0.356776i | ||||
\(309\) | −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 | \(0.594485\pi\) | |||||||
\(312\) | −2.47056 | + | 4.27914i | −0.139868 | + | 0.242258i | ||||
\(313\) | −2.31124 | − | 0.841224i | −0.130639 | − | 0.0475488i | 0.275873 | − | 0.961194i | \(-0.411033\pi\) |
−0.406512 | + | 0.913645i | \(0.633255\pi\) | |||||||
\(314\) | 30.5005 | + | 11.1013i | 1.72124 | + | 0.626480i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.44882 | − | 12.9017i | −0.419029 | − | 0.725779i | ||||
\(317\) | −1.21940 | − | 6.91555i | −0.0684882 | − | 0.388416i | −0.999713 | − | 0.0239697i | \(-0.992369\pi\) |
0.931225 | − | 0.364446i | \(-0.118742\pi\) | |||||||
\(318\) | 6.03019 | + | 5.05993i | 0.338156 | + | 0.283747i | ||||
\(319\) | 26.1791 | − | 21.9669i | 1.46575 | − | 1.22991i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.38979 | + | 1.23378i | −0.189200 | + | 0.0688631i | ||||
\(322\) | 3.48441 | 0.194179 | ||||||||
\(323\) | 4.64704 | + | 17.4519i | 0.258568 | + | 0.971052i | ||||
\(324\) | 39.4894 | 2.19386 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.47282 | + | 8.35278i | −0.0815720 | + | 0.462618i | ||||
\(327\) | 0.838733 | − | 0.703781i | 0.0463821 | − | 0.0389192i | ||||
\(328\) | −15.1217 | − | 12.6886i | −0.834955 | − | 0.700610i | ||||
\(329\) | −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 | \(0.325480\pi\) | |||||||
\(332\) | 24.2341 | + | 8.82049i | 1.33002 | + | 0.484087i | ||||
\(333\) | −3.15095 | − | 1.14685i | −0.172671 | − | 0.0628471i | ||||
\(334\) | 6.75180 | − | 11.6945i | 0.369442 | − | 0.639892i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.146632 | + | 0.831594i | 0.00799946 | + | 0.0453672i | ||||
\(337\) | 25.0326 | + | 21.0048i | 1.36361 | + | 1.14420i | 0.974849 | + | 0.222866i | \(0.0715413\pi\) |
0.388761 | + | 0.921339i | \(0.372903\pi\) | |||||||
\(338\) | 9.20420 | − | 7.72324i | 0.500643 | − | 0.420089i | ||||
\(339\) | −0.347764 | + | 1.97227i | −0.0188880 | + | 0.107119i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −32.5056 | −1.76028 | ||||||||
\(342\) | 2.93524 | − | 32.9572i | 0.158720 | − | 1.78212i | ||||
\(343\) | −5.55817 | −0.300113 | ||||||||
\(344\) | 80.6507 | − | 29.3545i | 4.34839 | − | 1.58269i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.91554 | − | 7.48102i | 0.479302 | − | 0.402182i | ||||
\(347\) | −5.46153 | − | 4.58277i | −0.293191 | − | 0.246016i | 0.484313 | − | 0.874895i | \(-0.339070\pi\) |
−0.777503 | + | 0.628879i | \(0.783514\pi\) | |||||||
\(348\) | 1.32331 | + | 7.50485i | 0.0709368 | + | 0.402302i | ||||
\(349\) | −11.3504 | − | 19.6595i | −0.607575 | − | 1.05235i | −0.991639 | − | 0.129044i | \(-0.958809\pi\) |
0.384064 | − | 0.923307i | \(-0.374524\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.99428 | − | 1.45380i | −0.213199 | − | 0.0775980i | ||||
\(352\) | 39.5896 | + | 14.4094i | 2.11013 | + | 0.768025i | ||||
\(353\) | −2.24694 | + | 3.89182i | −0.119593 | + | 0.207141i | −0.919606 | − | 0.392841i | \(-0.871492\pi\) |
0.800014 | + | 0.599982i | \(0.204826\pi\) | |||||||
\(354\) | −0.484771 | − | 0.839648i | −0.0257653 | − | 0.0446268i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −44.8279 | − | 37.6151i | −2.37587 | − | 1.99359i | ||||
\(357\) | 0.315786 | − | 0.264976i | 0.0167132 | − | 0.0140240i | ||||
\(358\) | 1.69179 | − | 9.59464i | 0.0894140 | − | 0.507092i | ||||
\(359\) | −9.94626 | + | 3.62014i | −0.524943 | + | 0.191064i | −0.590879 | − | 0.806760i | \(-0.701219\pi\) |
0.0659357 | + | 0.997824i | \(0.478997\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7010 | − | 3.35773i | −0.984261 | − | 0.176723i | ||||
\(362\) | −49.3252 | −2.59248 | ||||||||
\(363\) | −3.71108 | + | 1.35072i | −0.194781 | + | 0.0708946i | ||||
\(364\) | −0.941588 | + | 5.34001i | −0.0493526 | + | 0.279893i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.42512 | + | 2.87402i | 0.179034 | + | 0.150227i | ||||
\(367\) | 0.313391 | + | 1.77733i | 0.0163589 | + | 0.0927759i | 0.991894 | − | 0.127067i | \(-0.0405565\pi\) |
−0.975535 | + | 0.219843i | \(0.929445\pi\) | |||||||
\(368\) | 14.2522 | + | 24.6855i | 0.742947 | + | 1.28682i | ||||
\(369\) | 4.20148 | − | 7.27717i | 0.218720 | − | 0.378834i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.64297 | + | 1.68990i | 0.241051 | + | 0.0877353i | ||||
\(372\) | 3.62425 | − | 6.27739i | 0.187909 | − | 0.325468i | ||||
\(373\) | −6.48193 | − | 11.2270i | −0.335622 | − | 0.581314i | 0.647982 | − | 0.761655i | \(-0.275613\pi\) |
−0.983604 | + | 0.180342i | \(0.942280\pi\) | |||||||
\(374\) | −9.64661 | − | 54.7086i | −0.498814 | − | 2.82892i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 35.7571 | − | 30.0038i | 1.84403 | − | 1.54733i | ||||
\(377\) | −3.30338 | + | 18.7344i | −0.170132 | + | 0.964869i | ||||
\(378\) | −1.43421 | + | 0.522011i | −0.0737679 | + | 0.0268493i | ||||
\(379\) | 33.1372 | 1.70214 | 0.851071 | − | 0.525051i | \(-0.175954\pi\) | ||||
0.851071 | + | 0.525051i | \(0.175954\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.139012 | 0.00712181 | ||||||||
\(382\) | 7.02955 | − | 2.55855i | 0.359663 | − | 0.130907i | ||||
\(383\) | −3.50654 | + | 19.8866i | −0.179176 | + | 1.01616i | 0.754037 | + | 0.656832i | \(0.228104\pi\) |
−0.933213 | + | 0.359324i | \(0.883007\pi\) | |||||||
\(384\) | 1.12374 | − | 0.942926i | 0.0573454 | − | 0.0481185i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.10471 | + | 28.9503i | 0.259823 | + | 1.47353i | ||||
\(387\) | 18.2675 | + | 31.6402i | 0.928588 | + | 1.60836i | ||||
\(388\) | −20.7799 | + | 35.9918i | −1.05494 | + | 1.82721i | ||||
\(389\) | 1.90648 | + | 0.693903i | 0.0966625 | + | 0.0351823i | 0.389899 | − | 0.920858i | \(-0.372510\pi\) |
−0.293236 | + | 0.956040i | \(0.594732\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.95762 | − | 12.0510i | 0.351862 | − | 0.609443i | ||||
\(392\) | −23.6049 | − | 40.8849i | −1.19223 | − | 2.06500i | ||||
\(393\) | −0.424825 | − | 2.40930i | −0.0214296 | − | 0.121533i | ||||
\(394\) | −20.0864 | − | 16.8545i | −1.01194 | − | 0.849117i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −12.3761 | + | 70.1881i | −0.621920 | + | 3.52709i | ||||
\(397\) | 7.54838 | − | 2.74738i | 0.378842 | − | 0.137887i | −0.145578 | − | 0.989347i | \(-0.546504\pi\) |
0.524420 | + | 0.851459i | \(0.324282\pi\) | |||||||
\(398\) | 7.56914 | 0.379406 | ||||||||
\(399\) | 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 | \(0.271989\pi\) | |||||||
\(402\) | −0.0841266 | + | 0.477106i | −0.00419585 | + | 0.0237959i | ||||
\(403\) | 13.8612 | − | 11.6309i | 0.690473 | − | 0.579376i | ||||
\(404\) | 4.81770 | + | 4.04253i | 0.239690 | + | 0.201124i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.41533 | + | 5.91553i | 0.169500 | + | 0.293583i | ||||
\(407\) | 2.96141 | − | 5.12931i | 0.146792 | − | 0.254250i | ||||
\(408\) | 6.65806 | + | 2.42334i | 0.329623 | + | 0.119973i | ||||
\(409\) | −0.227020 | − | 0.0826284i | −0.0112254 | − | 0.00408571i | 0.336401 | − | 0.941719i | \(-0.390790\pi\) |
−0.347627 | + | 0.937633i | \(0.613012\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.11015 | − | 1.92283i | −0.0547595 | − | 0.0948462i | ||||
\(412\) | −10.0835 | − | 57.1867i | −0.496781 | − | 2.81738i | ||||
\(413\) | −0.466179 | − | 0.391171i | −0.0229392 | − | 0.0192483i | ||||
\(414\) | −19.5296 | + | 16.3872i | −0.959825 | + | 0.805389i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −22.0378 | + | 8.02110i | −1.08049 | + | 0.393267i | ||||
\(417\) | −3.26168 | −0.159725 | ||||||||
\(418\) | 56.4288 | + | 15.2145i | 2.76002 | + | 0.744166i | ||||
\(419\) | −22.7086 | −1.10939 | −0.554693 | − | 0.832055i | \(-0.687164\pi\) | ||||
−0.554693 | + | 0.832055i | \(0.687164\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.33685 | + | 24.5955i | −0.211365 | + | 1.19871i | 0.675738 | + | 0.737142i | \(0.263825\pi\) |
−0.887103 | + | 0.461571i | \(0.847286\pi\) | |||||||
\(422\) | 10.8947 | − | 9.14177i | 0.530347 | − | 0.445014i | ||||
\(423\) | 15.2212 | + | 12.7721i | 0.740079 | + | 0.621000i | ||||
\(424\) | 14.7470 | + | 83.6342i | 0.716176 | + | 4.06164i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.66708 | + | 4.61953i | −0.129221 | + | 0.223817i | ||||
\(427\) | 2.63719 | + | 0.959857i | 0.127622 | + | 0.0464507i | ||||
\(428\) | −63.9383 | − | 23.2716i | −3.09057 | − | 1.12488i | ||||
\(429\) | 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 | \(0.802911\pi\) | |||||||
\(432\) | −9.56453 | − | 8.02560i | −0.460174 | − | 0.386132i | ||||
\(433\) | 29.9613 | − | 25.1405i | 1.43985 | − | 1.20818i | 0.500257 | − | 0.865877i | \(-0.333239\pi\) |
0.939591 | − | 0.342299i | \(-0.111206\pi\) | |||||||
\(434\) | 1.12821 | − | 6.39841i | 0.0541559 | − | 0.307134i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 20.6518 | 0.989042 | ||||||||
\(437\) | 8.37813 | + | 12.0051i | 0.400780 | + | 0.574280i | ||||
\(438\) | −6.34670 | −0.303257 | ||||||||
\(439\) | −17.6050 | + | 6.40768i | −0.840239 | + | 0.305822i | −0.726054 | − | 0.687638i | \(-0.758648\pi\) |
−0.114185 | + | 0.993460i | \(0.536426\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.3947 | − | 12.9177i | 0.733083 | − | 0.615129i | ||||
\(442\) | 23.6889 | + | 19.8774i | 1.12677 | + | 0.945471i | ||||
\(443\) | −2.96093 | − | 16.7923i | −0.140678 | − | 0.797826i | −0.970736 | − | 0.240149i | \(-0.922804\pi\) |
0.830058 | − | 0.557677i | \(-0.188307\pi\) | |||||||
\(444\) | 0.660372 | + | 1.14380i | 0.0313399 | + | 0.0542822i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −19.3236 | − | 7.03323i | −0.915001 | − | 0.333033i | ||||
\(447\) | 1.90499 | + | 0.693358i | 0.0901028 | + | 0.0327947i | ||||
\(448\) | −0.801654 | + | 1.38851i | −0.0378746 | + | 0.0656007i | ||||
\(449\) | −6.10161 | − | 10.5683i | −0.287953 | − | 0.498749i | 0.685368 | − | 0.728197i | \(-0.259641\pi\) |
−0.973321 | + | 0.229448i | \(0.926308\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.3700 | + | 9.54052i | 0.535390 | + | 0.449246i | ||||
\(452\) | −28.9372 | + | 24.2812i | −1.36109 | + | 1.14209i | ||||
\(453\) | 0.327195 | − | 1.85562i | 0.0153730 | − | 0.0871845i | ||||
\(454\) | −19.4779 | + | 7.08937i | −0.914142 | + | 0.332721i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.27909 | + | 5.26263i | −0.247216 | + | 0.246445i | ||||
\(457\) | 13.4079 | 0.627193 | 0.313596 | − | 0.949556i | \(-0.398466\pi\) | ||||
0.313596 | + | 0.949556i | \(0.398466\pi\) | |||||||
\(458\) | −68.5640 | + | 24.9553i | −3.20379 | + | 1.16608i | ||||
\(459\) | −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 | \(0.828058\pi\) | |||||||
\(462\) | −0.231649 | − | 1.31374i | −0.0107773 | − | 0.0611209i | ||||
\(463\) | 13.0889 | + | 22.6706i | 0.608292 | + | 1.05359i | 0.991522 | + | 0.129940i | \(0.0414785\pi\) |
−0.383230 | + | 0.923653i | \(0.625188\pi\) | |||||||
\(464\) | −27.9393 | + | 48.3922i | −1.29705 | + | 2.24655i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −22.9201 | − | 8.34225i | −1.06175 | − | 0.386447i | ||||
\(467\) | −19.7941 | + | 34.2843i | −0.915960 | + | 1.58649i | −0.110470 | + | 0.993879i | \(0.535236\pi\) |
−0.805490 | + | 0.592609i | \(0.798098\pi\) | |||||||
\(468\) | −19.8367 | − | 34.3582i | −0.916952 | − | 1.58821i | ||||
\(469\) | 0.0528039 | + | 0.299466i | 0.00243826 | + | 0.0138280i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.38447 | − | 2.00080i | 0.109870 | − | 0.0921922i | ||||
\(472\) | 1.81632 | − | 10.3009i | 0.0836029 | − | 0.474135i | ||||
\(473\) | −60.6411 | + | 22.0715i | −2.78828 | + | 1.01485i | ||||
\(474\) | −2.04020 | −0.0937097 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.77548 | 0.356389 | ||||||||
\(477\) | −33.9707 | + | 12.3643i | −1.55541 | + | 0.566123i | ||||
\(478\) | −5.28968 | + | 29.9993i | −0.241944 | + | 1.37214i | ||||
\(479\) | 2.89476 | − | 2.42899i | 0.132265 | − | 0.110983i | −0.574255 | − | 0.818676i | \(-0.694708\pi\) |
0.706520 | + | 0.707693i | \(0.250264\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.572514 | + | 3.24689i | 0.0261044 | + | 0.148045i | ||||
\(482\) | −16.5322 | − | 28.6346i | −0.753022 | − | 1.30427i | ||||
\(483\) | 0.167077 | − | 0.289385i | 0.00760225 | − | 0.0131675i | ||||
\(484\) | −69.9985 | − | 25.4774i | −3.18175 | − | 1.15806i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8.40410 | − | 14.5563i | 0.381218 | − | 0.660288i | ||||
\(487\) | 3.49493 | + | 6.05339i | 0.158370 | + | 0.274305i | 0.934281 | − | 0.356537i | \(-0.116043\pi\) |
−0.775911 | + | 0.630843i | \(0.782709\pi\) | |||||||
\(488\) | 8.37622 | + | 47.5039i | 0.379174 | + | 2.15040i | ||||
\(489\) | 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 | \(0.792041\pi\) | |||||||
\(492\) | −3.11014 | + | 1.13200i | −0.140216 | + | 0.0510345i | ||||
\(493\) | 27.2787 | 1.22857 | ||||||||
\(494\) | −29.5065 | + | 13.7031i | −1.32756 | + | 0.616530i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 49.9446 | − | 18.1784i | 2.24258 | − | 0.816232i | ||||
\(497\) | −0.581393 | + | 3.29724i | −0.0260790 | + | 0.147902i | ||||
\(498\) | 2.70552 | − | 2.27020i | 0.121237 | − | 0.101730i | ||||
\(499\) | 21.2906 | + | 17.8650i | 0.953100 | + | 0.799746i | 0.979817 | − | 0.199897i | \(-0.0640608\pi\) |
−0.0267168 | + | 0.999643i | \(0.508505\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.647494 | − | 1.12149i | −0.0289279 | − | 0.0501046i | ||||
\(502\) | 3.09927 | − | 5.36809i | 0.138327 | − | 0.239590i | ||||
\(503\) | 15.3827 | + | 5.59886i | 0.685883 | + | 0.249641i | 0.661371 | − | 0.750059i | \(-0.269975\pi\) |
0.0245113 | + | 0.999700i | \(0.492197\pi\) | |||||||
\(504\) | −7.65646 | − | 2.78672i | −0.341046 | − | 0.124131i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −22.5155 | − | 38.9979i | −1.00093 | − | 1.73367i | ||||
\(507\) | −0.200087 | − | 1.13475i | −0.00888618 | − | 0.0503960i | ||||
\(508\) | 2.00861 | + | 1.68542i | 0.0891175 | + | 0.0747785i | ||||
\(509\) | −27.2953 | + | 22.9034i | −1.20984 | + | 1.01518i | −0.210548 | + | 0.977584i | \(0.567525\pi\) |
−0.999293 | + | 0.0375938i | \(0.988031\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.74340 | + | 1.36249i | −0.165598 | + | 0.0602728i | ||||
\(512\) | 48.2924 | 2.13424 | ||||||||
\(513\) | −5.24702 | − | 3.68622i | −0.231662 | − | 0.162751i | ||||
\(514\) | 44.4694 | 1.96146 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.49886 | − | 14.1717i | 0.110006 | − | 0.623875i | ||||
\(517\) | −26.8857 | + | 22.5598i | −1.18243 | + | 0.992177i | ||||
\(518\) | 0.906869 | + | 0.760954i | 0.0398455 | + | 0.0334344i | ||||
\(519\) | −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 | \(0.889310\pi\) | |||||||
\(522\) | −46.9632 | − | 17.0932i | −2.05552 | − | 0.748149i | ||||
\(523\) | −12.7730 | − | 4.64899i | −0.558524 | − | 0.203286i | 0.0473057 | − | 0.998880i | \(-0.484936\pi\) |
−0.605830 | + | 0.795594i | \(0.707159\pi\) | |||||||
\(524\) | 23.0727 | − | 39.9630i | 1.00793 | − | 1.74579i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.58646 | + | 37.3537i | 0.287183 | + | 1.62870i | ||||
\(527\) | −19.8763 | − | 16.6782i | −0.865826 | − | 0.726515i | ||||
\(528\) | 8.35979 | − | 7.01470i | 0.363813 | − | 0.305276i | ||||
\(529\) | −2.03521 | + | 11.5422i | −0.0884873 | + | 0.501837i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.45254 | 0.193224 | ||||||||
\(532\) | −3.46866 | + | 7.40834i | −0.150385 | + | 0.321192i | ||||
\(533\) | −8.26213 | −0.357872 | ||||||||
\(534\) | −7.53071 | + | 2.74096i | −0.325886 | + | 0.118613i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.00380 | + | 3.35959i | −0.172938 | + | 0.145112i | ||||
\(537\) | −0.715727 | − | 0.600566i | −0.0308859 | − | 0.0259163i | ||||
\(538\) | 10.0713 | + | 57.1174i | 0.434206 | + | 2.46251i | ||||
\(539\) | 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 | \(0.557050\pi\) | |||||||
\(542\) | 32.2386 | + | 11.7339i | 1.38476 | + | 0.504013i | ||||
\(543\) | −2.36513 | + | 4.09653i | −0.101498 | + | 0.175799i | ||||
\(544\) | 16.8147 | + | 29.1239i | 0.720924 | + | 1.24868i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.568854 | + | 0.477325i | 0.0243447 | + | 0.0204276i | ||||
\(547\) | −20.3369 | + | 17.0647i | −0.869544 | + | 0.729634i | −0.964002 | − | 0.265895i | \(-0.914333\pi\) |
0.0944579 | + | 0.995529i | \(0.469888\pi\) | |||||||
\(548\) | 7.27224 | − | 41.2429i | 0.310655 | − | 1.76181i | ||||
\(549\) | −19.2952 | + | 7.02288i | −0.823500 | + | 0.299729i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.1691 | + | 25.9907i | −0.518421 | + | 1.10724i | ||||
\(552\) | 5.74340 | 0.244455 | ||||||||
\(553\) | −1.20335 | + | 0.437984i | −0.0511717 | + | 0.0186250i | ||||
\(554\) | 1.50681 | − | 8.54554i | 0.0640182 | − | 0.363065i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −47.1284 | − | 39.5455i | −1.99869 | − | 1.67710i | ||||
\(557\) | −0.661630 | − | 3.75229i | −0.0280342 | − | 0.158990i | 0.967577 | − | 0.252576i | \(-0.0812779\pi\) |
−0.995611 | + | 0.0935867i | \(0.970167\pi\) | |||||||
\(558\) | 23.7684 | + | 41.1680i | 1.00620 | + | 1.74278i | ||||
\(559\) | 17.9613 | − | 31.1099i | 0.759683 | − | 1.31581i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.00618 | − | 1.82210i | −0.211361 | − | 0.0769292i | ||||
\(562\) | 25.8601 | − | 44.7910i | 1.09084 | − | 1.88939i | ||||
\(563\) | −6.08960 | − | 10.5475i | −0.256646 | − | 0.444524i | 0.708695 | − | 0.705515i | \(-0.249284\pi\) |
−0.965341 | + | 0.260991i | \(0.915951\pi\) | |||||||
\(564\) | −1.35902 | − | 7.70741i | −0.0572252 | − | 0.324540i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.04872 | − | 0.879981i | 0.0440810 | − | 0.0369884i | ||||
\(567\) | 0.589440 | − | 3.34288i | 0.0247542 | − | 0.140388i | ||||
\(568\) | −54.0764 | + | 19.6822i | −2.26900 | + | 0.825847i | ||||
\(569\) | 22.8626 | 0.958451 | 0.479226 | − | 0.877692i | \(-0.340918\pi\) | ||||
0.479226 | + | 0.877692i | \(0.340918\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.3908 | 1.69030 | 0.845152 | − | 0.534527i | \(-0.179510\pi\) | ||||
0.845152 | + | 0.534527i | \(0.179510\pi\) | |||||||
\(572\) | 65.8503 | − | 23.9676i | 2.75334 | − | 1.00213i | ||||
\(573\) | 0.124574 | − | 0.706496i | 0.00520416 | − | 0.0295143i | ||||
\(574\) | −2.27259 | + | 1.90693i | −0.0948560 | + | 0.0795937i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.03702 | − | 11.5525i | −0.0848760 | − | 0.481355i | ||||
\(577\) | −3.93190 | − | 6.81026i | −0.163687 | − | 0.283515i | 0.772501 | − | 0.635013i | \(-0.219005\pi\) |
−0.936188 | + | 0.351499i | \(0.885672\pi\) | |||||||
\(578\) | 0.215179 | − | 0.372700i | 0.00895025 | − | 0.0155023i | ||||
\(579\) | 2.64913 | + | 0.964204i | 0.110094 | + | 0.0400710i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.10841 | − | 1.91982i | 0.0459845 | − | 0.0796475i | ||||
\(582\) | 2.84576 | + | 4.92901i | 0.117961 | + | 0.204314i | ||||
\(583\) | −11.0882 | − | 62.8844i | −0.459227 | − | 2.60440i | ||||
\(584\) | −52.4514 | − | 44.0120i | −2.17045 | − | 1.82123i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.1810 | − | 80.4242i | 0.585810 | − | 3.32229i | ||||
\(587\) | 37.7961 | − | 13.7566i | 1.56001 | − | 0.567797i | 0.589271 | − | 0.807935i | \(-0.299415\pi\) |
0.970739 | + | 0.240138i | \(0.0771927\pi\) | |||||||
\(588\) | −7.91555 | −0.326432 | ||||||||
\(589\) | 24.7576 | − | 11.4976i | 1.02012 | − | 0.473751i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.36293 | + | 0.860035i | −0.0971978 | + | 0.0353771i | ||||
\(592\) | −1.68168 | + | 9.53727i | −0.0691166 | + | 0.391980i | ||||
\(593\) | −26.1035 | + | 21.9034i | −1.07194 | + | 0.899466i | −0.995227 | − | 0.0975874i | \(-0.968887\pi\) |
−0.0767145 | + | 0.997053i | \(0.524443\pi\) | |||||||
\(594\) | 15.1100 | + | 12.6788i | 0.619969 | + | 0.520216i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.1189 | + | 33.1150i | 0.783142 | + | 1.35644i | ||||
\(597\) | 0.362938 | − | 0.628627i | 0.0148541 | − | 0.0257280i | ||||
\(598\) | 23.5551 | + | 8.57334i | 0.963238 | + | 0.350590i | ||||
\(599\) | −16.8047 | − | 6.11643i | −0.686623 | − | 0.249910i | −0.0249346 | − | 0.999689i | \(-0.507938\pi\) |
−0.661689 | + | 0.749779i | \(0.730160\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.355966 | − | 0.616551i | −0.0145201 | − | 0.0251496i | 0.858674 | − | 0.512522i | \(-0.171289\pi\) |
−0.873194 | + | 0.487372i | \(0.837955\pi\) | |||||||
\(602\) | −2.23982 | − | 12.7027i | −0.0912884 | − | 0.517722i | ||||
\(603\) | −1.70435 | − | 1.43012i | −0.0694065 | − | 0.0582389i | ||||
\(604\) | 27.2257 | − | 22.8451i | 1.10780 | − | 0.929553i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.809335 | − | 0.294574i | 0.0328770 | − | 0.0119662i | ||||
\(607\) | 34.3415 | 1.39388 | 0.696940 | − | 0.717129i | \(-0.254544\pi\) | ||||
0.696940 | + | 0.717129i | \(0.254544\pi\) | |||||||
\(608\) | −35.2498 | + | 3.02851i | −1.42957 | + | 0.122822i | ||||
\(609\) | 0.655057 | 0.0265443 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.39253 | − | 19.2400i | 0.137247 | − | 0.778368i | ||||
\(612\) | −43.5803 | + | 36.5682i | −1.76163 | + | 1.47818i | ||||
\(613\) | −22.9647 | − | 19.2696i | −0.927534 | − | 0.778293i | 0.0478390 | − | 0.998855i | \(-0.484767\pi\) |
−0.975373 | + | 0.220562i | \(0.929211\pi\) | |||||||
\(614\) | 4.11393 | + | 23.3313i | 0.166025 | + | 0.941573i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.19590 | − | 12.4637i | 0.289931 | − | 0.502175i | ||||
\(617\) | 20.7677 | + | 7.55883i | 0.836076 | + | 0.304307i | 0.724350 | − | 0.689432i | \(-0.242140\pi\) |
0.111726 | + | 0.993739i | \(0.464362\pi\) | |||||||
\(618\) | −7.47283 | − | 2.71989i | −0.300601 | − | 0.109410i | ||||
\(619\) | −9.72359 | + | 16.8417i | −0.390824 | + | 0.676927i | −0.992558 | − | 0.121769i | \(-0.961143\pi\) |
0.601734 | + | 0.798696i | \(0.294477\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.857958 | + | 4.86572i | 0.0344287 | + | 0.195255i | ||||
\(622\) | 47.5918 | + | 39.9343i | 1.90826 | + | 1.60122i | ||||
\(623\) | −3.85334 | + | 3.23333i | −0.154381 | + | 0.129541i | ||||
\(624\) | −1.05487 | + | 5.98246i | −0.0422286 | + | 0.239490i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6.35337 | −0.253932 | ||||||||
\(627\) | 3.96933 | − | 3.95696i | 0.158520 | − | 0.158026i | ||||
\(628\) | 58.7117 | 2.34285 | ||||||||
\(629\) | 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 | \(0.249672\pi\) | |||||||
\(632\) | −16.8610 | − | 14.1480i | −0.670694 | − | 0.562779i | ||||
\(633\) | −0.236837 | − | 1.34317i | −0.00941342 | − | 0.0533862i | ||||
\(634\) | −9.06962 | − | 15.7090i | −0.360201 | − | 0.623886i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 13.3803 | + | 4.87005i | 0.530565 | + | 0.193110i | ||||
\(637\) | −18.5680 | − | 6.75818i | −0.735689 | − | 0.267769i | ||||
\(638\) | 44.1382 | − | 76.4496i | 1.74745 | − | 3.02667i | ||||
\(639\) | −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 | \(0.553042\pi\) | |||||||
\(642\) | −7.13814 | + | 5.98961i | −0.281720 | + | 0.236391i | ||||
\(643\) | −6.45413 | + | 36.6032i | −0.254526 | + | 1.44349i | 0.542761 | + | 0.839887i | \(0.317379\pi\) |
−0.797287 | + | 0.603601i | \(0.793732\pi\) | |||||||
\(644\) | 5.92270 | − | 2.15569i | 0.233387 | − | 0.0849459i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 26.6983 | + | 38.2562i | 1.05043 | + | 1.50517i | ||||
\(647\) | −20.6750 | −0.812819 | −0.406409 | − | 0.913691i | \(-0.633219\pi\) | ||||
−0.406409 | + | 0.913691i | \(0.633219\pi\) | |||||||
\(648\) | 54.8250 | − | 19.9547i | 2.15373 | − | 0.783893i | ||||
\(649\) | −1.36569 | + | 7.74519i | −0.0536079 | + | 0.304025i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.477300 | − | 0.400502i | −0.0187068 | − | 0.0156969i | ||||
\(652\) | 2.66412 | + | 15.1090i | 0.104335 | + | 0.591714i | ||||
\(653\) | 17.0168 | + | 29.4740i | 0.665919 | + | 1.15341i | 0.979035 | + | 0.203691i | \(0.0652939\pi\) |
−0.313116 | + | 0.949715i | \(0.601373\pi\) | |||||||
\(654\) | 1.41411 | − | 2.44931i | 0.0552962 | − | 0.0957758i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −22.8053 | − | 8.30043i | −0.890395 | − | 0.324077i | ||||
\(657\) | 14.5733 | − | 25.2418i | 0.568560 | − | 0.984775i | ||||
\(658\) | −3.50751 | − | 6.07519i | −0.136737 | − | 0.236836i | ||||
\(659\) | −5.38526 | − | 30.5413i | −0.209780 | − | 1.18972i | −0.889739 | − | 0.456470i | \(-0.849114\pi\) |
0.679959 | − | 0.733250i | \(-0.261998\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.9912 | + | 11.7400i | −0.544195 | + | 0.456634i | −0.872970 | − | 0.487775i | \(-0.837809\pi\) |
0.328775 | + | 0.944408i | \(0.393364\pi\) | |||||||
\(662\) | −7.80953 | + | 44.2901i | −0.303526 | + | 1.72138i | ||||
\(663\) | 2.78672 | − | 1.01428i | 0.108227 | − | 0.0393915i | ||||
\(664\) | 38.1024 | 1.47866 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.66163 | −0.335631 | ||||||||
\(667\) | 20.7786 | − | 7.56280i | 0.804552 | − | 0.292833i | ||||
\(668\) | 4.24154 | − | 24.0550i | 0.164110 | − | 0.930715i | ||||
\(669\) | −1.51068 | + | 1.26761i | −0.0584064 | + | 0.0490088i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.29806 | − | 35.7181i | −0.243134 | − | 1.37888i | ||||
\(672\) | 0.403779 | + | 0.699366i | 0.0155761 | + | 0.0269786i | ||||
\(673\) | 13.0160 | − | 22.5444i | 0.501731 | − | 0.869023i | −0.498267 | − | 0.867024i | \(-0.666030\pi\) |
0.999998 | − | 0.00199979i | \(-0.000636552\pi\) | |||||||
\(674\) | 79.3197 | + | 28.8700i | 3.05528 | + | 1.11203i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.8669 | − | 18.8221i | 0.417958 | − | 0.723925i | ||||
\(677\) | −0.0300638 | − | 0.0520720i | −0.00115545 | − | 0.00200129i | 0.865447 | − | 0.501000i | \(-0.167034\pi\) |
−0.866603 | + | 0.498999i | \(0.833701\pi\) | |||||||
\(678\) | 0.898316 | + | 5.09460i | 0.0344996 | + | 0.195657i | ||||
\(679\) | 2.73663 | + | 2.29630i | 0.105022 | + | 0.0881240i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.345178 | + | 1.95760i | −0.0132272 | + | 0.0750154i | ||||
\(682\) | −78.9020 | + | 28.7180i | −3.02131 | + | 1.09967i | ||||
\(683\) | 31.5145 | 1.20587 | 0.602935 | − | 0.797790i | \(-0.293998\pi\) | ||||
0.602935 | + | 0.797790i | \(0.293998\pi\) | |||||||
\(684\) | −15.4003 | − | 57.8356i | −0.588844 | − | 2.21140i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −13.4915 | + | 4.91052i | −0.515109 | + | 0.187484i | ||||
\(687\) | −1.21506 | + | 6.89094i | −0.0463574 | + | 0.262906i | ||||
\(688\) | 80.8313 | − | 67.8255i | 3.08166 | − | 2.58582i | ||||
\(689\) | 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 | \(0.890525\pi\) | |||||||
\(692\) | 10.5261 | − | 18.2318i | 0.400143 | − | 0.693067i | ||||
\(693\) | 5.75687 | + | 2.09533i | 0.218686 | + | 0.0795950i | ||||
\(694\) | −17.3057 | − | 6.29878i | −0.656917 | − | 0.239098i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.62953 | + | 9.75063i | 0.213387 | + | 0.369597i | ||||
\(697\) | 2.05730 | + | 11.6676i | 0.0779260 | + | 0.441940i | ||||
\(698\) | −44.9201 | − | 37.6924i | −1.70025 | − | 1.42668i | ||||
\(699\) | −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 | \(0.344267\pi\) | |||||||
\(702\) | −10.9798 | −0.414408 | ||||||||
\(703\) | −0.441229 | + | 4.95417i | −0.0166413 | + | 0.186850i | ||||
\(704\) | 20.7204 | 0.780930 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.01575 | + | 11.4319i | −0.0758637 | + | 0.430245i | ||||
\(707\) | 0.414122 | − | 0.347490i | 0.0155747 | − | 0.0130687i | ||||
\(708\) | −1.34346 | − | 1.12730i | −0.0504903 | − | 0.0423664i | ||||
\(709\) | −7.51502 | − | 42.6198i | −0.282233 | − | 1.60062i | −0.715006 | − | 0.699118i | \(-0.753576\pi\) |
0.432774 | − | 0.901502i | \(-0.357535\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.68474 | − | 8.11420i | 0.175691 | − | 0.304306i | ||||
\(712\) | −81.2440 | − | 29.5704i | −3.04475 | − | 1.10820i | ||||
\(713\) | −19.7640 | − | 7.19350i | −0.740167 | − | 0.269399i | ||||
\(714\) | 0.532419 | − | 0.922176i | 0.0199253 | − | 0.0345116i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.06021 | − | 17.3553i | −0.114366 | − | 0.648599i | ||||
\(717\) | 2.23784 | + | 1.87777i | 0.0835738 | + | 0.0701268i | ||||
\(718\) | −20.9446 | + | 17.5746i | −0.781645 | + | 0.655878i | ||||
\(719\) | 5.61767 | − | 31.8594i | 0.209504 | − | 1.18815i | −0.680690 | − | 0.732572i | \(-0.738320\pi\) |
0.890193 | − | 0.455583i | \(-0.150569\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.99151 | −0.185894 | ||||||||
\(722\) | −48.3600 | + | 8.37154i | −1.79977 | + | 0.311557i | ||||
\(723\) | −3.17086 | −0.117926 | ||||||||
\(724\) | −83.8416 | + | 30.5158i | −3.11595 | + | 1.13411i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −7.81471 | + | 6.55732i | −0.290031 | + | 0.243365i | ||||
\(727\) | −38.0516 | − | 31.9291i | −1.41125 | − | 1.18418i | −0.955834 | − | 0.293907i | \(-0.905044\pi\) |
−0.455421 | − | 0.890276i | \(-0.650511\pi\) | |||||||
\(728\) | 1.39114 | + | 7.88957i | 0.0515592 | + | 0.292407i | ||||
\(729\) | 11.8713 | + | 20.5616i | 0.439677 | + | 0.761542i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −48.4051 | − | 17.6180i | −1.79033 | − | 0.651625i | ||||
\(732\) | 7.59998 | + | 2.76617i | 0.280903 | + | 0.102240i | ||||
\(733\) | 0.684201 | − | 1.18507i | 0.0252715 | − | 0.0437716i | −0.853113 | − | 0.521726i | \(-0.825288\pi\) |
0.878385 | + | 0.477955i | \(0.158622\pi\) | |||||||
\(734\) | 2.33094 | + | 4.03730i | 0.0860365 | + | 0.149020i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.8824 | + | 17.5224i | 0.769734 | + | 0.645883i | ||||
\(737\) | 3.01045 | − | 2.52607i | 0.110891 | − | 0.0930489i | ||||
\(738\) | 3.76917 | − | 21.3760i | 0.138745 | − | 0.786863i | ||||
\(739\) | −16.6998 | + | 6.07823i | −0.614312 | + | 0.223591i | −0.630389 | − | 0.776279i | \(-0.717105\pi\) |
0.0160769 | + | 0.999871i | \(0.494882\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.276771 | + | 3.10761i | −0.0101674 | + | 0.114161i | ||||
\(742\) | 12.7630 | 0.468545 | ||||||||
\(743\) | 36.2978 | − | 13.2113i | 1.33164 | − | 0.484676i | 0.424469 | − | 0.905443i | \(-0.360461\pi\) |
0.907169 | + | 0.420766i | \(0.138239\pi\) | |||||||
\(744\) | 1.85965 | − | 10.5466i | 0.0681779 | − | 0.386656i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −25.6526 | − | 21.5251i | −0.939210 | − | 0.788091i | ||||
\(747\) | 2.81649 | + | 15.9731i | 0.103050 | + | 0.584426i | ||||
\(748\) | −50.2434 | − | 87.0241i | −1.83708 | − | 3.18192i | ||||
\(749\) | −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 | \(0.705284\pi\) | |||||||
\(752\) | 28.6933 | − | 49.6983i | 1.04634 | − | 1.81231i | ||||
\(753\) | −0.297218 | − | 0.514797i | −0.0108312 | − | 0.0187603i | ||||
\(754\) | 8.53300 | + | 48.3931i | 0.310754 | + | 1.76237i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.11488 | + | 1.77460i | −0.0769175 | + | 0.0645414i | ||||
\(757\) | −0.338466 | + | 1.91954i | −0.0123018 | + | 0.0697668i | −0.990341 | − | 0.138656i | \(-0.955722\pi\) |
0.978039 | + | 0.208423i | \(0.0668329\pi\) | |||||||
\(758\) | 80.4350 | − | 29.2759i | 2.92153 | − | 1.06335i | ||||
\(759\) | −4.31845 | −0.156750 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −48.1168 | −1.74423 | −0.872115 | − | 0.489300i | \(-0.837252\pi\) | ||||
−0.872115 | + | 0.489300i | \(0.837252\pi\) | |||||||
\(762\) | 0.337429 | − | 0.122814i | 0.0122238 | − | 0.00444909i | ||||
\(763\) | 0.308260 | − | 1.74823i | 0.0111597 | − | 0.0632901i | ||||
\(764\) | 10.3657 | − | 8.69788i | 0.375019 | − | 0.314678i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.05780 | + | 51.3693i | 0.327272 | + | 1.85605i | ||||
\(767\) | −2.18896 | − | 3.79139i | −0.0790388 | − | 0.136899i | ||||
\(768\) | 2.88350 | − | 4.99437i | 0.104049 | − | 0.180219i | ||||
\(769\) | 6.00593 | + | 2.18598i | 0.216579 | + | 0.0788284i | 0.448031 | − | 0.894018i | \(-0.352125\pi\) |
−0.231452 | + | 0.972846i | \(0.574348\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.13230 | − | 3.69325i | 0.0767929 | − | 0.133009i | ||||
\(772\) | 26.5874 | + | 46.0507i | 0.956900 | + | 1.65740i | ||||
\(773\) | 6.20576 | + | 35.1946i | 0.223206 | + | 1.26586i | 0.866086 | + | 0.499895i | \(0.166628\pi\) |
−0.642880 | + | 0.765967i | \(0.722261\pi\) | |||||||
\(774\) | 72.2947 | + | 60.6624i | 2.59858 | + | 2.18047i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −10.6624 | + | 60.4694i | −0.382757 | + | 2.17073i | ||||
\(777\) | 0.106682 | − | 0.0388292i | 0.00382721 | − | 0.00139299i | ||||
\(778\) | 5.24072 | 0.187889 | ||||||||
\(779\) | −12.0344 | − | 3.24476i | −0.431177 | − | 0.116255i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.6599 | − | 14.7990i | 1.45493 | − | 0.529550i | ||||
\(782\) | 6.24173 | − | 35.3986i | 0.223204 | − | 1.26585i | ||||
\(783\) | −7.41964 | + | 6.22582i | −0.265156 | + | 0.222493i | ||||
\(784\) | −44.4620 | − | 37.3081i | −1.58793 | − | 1.33243i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.15976 | − | 5.47286i | −0.112705 | − | 0.195211i | ||||
\(787\) | 0.970153 | − | 1.68035i | 0.0345822 | − | 0.0598982i | −0.848216 | − | 0.529650i | \(-0.822323\pi\) |
0.882799 | + | 0.469752i | \(0.155657\pi\) | |||||||
\(788\) | −44.5695 | − | 16.2220i | −1.58772 | − | 0.577884i | ||||
\(789\) | 3.41810 | + | 1.24409i | 0.121687 | + | 0.0442906i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.62353 | + | 2.81204i | 0.0577262 | + | 0.0999848i | ||||
\(792\) | 18.2850 | + | 103.699i | 0.649728 | + | 3.68479i | ||||
\(793\) | 15.4660 | + | 12.9775i | 0.549213 | + | 0.460845i | ||||
\(794\) | 15.8952 | − | 13.3376i | 0.564099 | − | 0.473335i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.8658 | − | 4.68276i | 0.456016 | − | 0.165976i | ||||
\(797\) | −44.3436 | −1.57073 | −0.785365 | − | 0.619033i | \(-0.787525\pi\) | ||||
−0.785365 | + | 0.619033i | \(0.787525\pi\) | |||||||
\(798\) | 0.641120 | + | 0.918663i | 0.0226954 | + | 0.0325203i | ||||
\(799\) | −28.0150 | −0.991099 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.39090 | − | 36.2446i | 0.225811 | − | 1.28064i | ||||
\(802\) | 28.4549 | − | 23.8765i | 1.00478 | − | 0.843108i | ||||
\(803\) | 39.4381 | + | 33.0925i | 1.39174 | + | 1.16781i | ||||
\(804\) | 0.152173 | + | 0.863016i | 0.00536673 | + | 0.0304362i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 23.3700 | − | 40.4781i | 0.823175 | − | 1.42578i | ||||
\(807\) | 5.22660 | + | 1.90233i | 0.183985 | + | 0.0669651i | ||||
\(808\) | 8.73139 | + | 3.17797i | 0.307169 | + | 0.111800i | ||||
\(809\) | 13.9319 | − | 24.1307i | 0.489819 | − | 0.848392i | −0.510112 | − | 0.860108i | \(-0.670396\pi\) |
0.999931 | + | 0.0117160i | \(0.00372940\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.29449 | + | 30.0265i | 0.185915 | + | 1.05437i | 0.924775 | + | 0.380515i | \(0.124253\pi\) |
−0.738860 | + | 0.673859i | \(0.764636\pi\) | |||||||
\(812\) | 9.46501 | + | 7.94209i | 0.332157 | + | 0.278713i | ||||
\(813\) | 2.52035 | − | 2.11482i | 0.0883924 | − | 0.0741700i | ||||
\(814\) | 2.65670 | − | 15.0669i | 0.0931173 | − | 0.528094i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8.71095 | 0.304944 | ||||||||
\(817\) | 38.3797 | − | 38.2600i | 1.34274 | − | 1.33855i | ||||
\(818\) | −0.624053 | −0.0218195 | ||||||||
\(819\) | −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 | \(-0.0622609\pi\) | |||||||
\(822\) | −4.39347 | − | 3.68656i | −0.153240 | − | 0.128584i | ||||
\(823\) | −7.55147 | − | 42.8265i | −0.263228 | − | 1.49284i | −0.774035 | − | 0.633143i | \(-0.781765\pi\) |
0.510807 | − | 0.859695i | \(-0.329347\pi\) | |||||||
\(824\) | −42.8968 | − | 74.2994i | −1.49438 | − | 2.58834i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.47716 | − | 0.537644i | −0.0513971 | − | 0.0187070i | ||||
\(827\) | −0.559803 | − | 0.203752i | −0.0194663 | − | 0.00708514i | 0.332269 | − | 0.943185i | \(-0.392186\pi\) |
−0.351735 | + | 0.936100i | \(0.614408\pi\) | |||||||
\(828\) | −23.0575 | + | 39.9368i | −0.801304 | + | 1.38790i | ||||
\(829\) | −9.62397 | − | 16.6692i | −0.334254 | − | 0.578946i | 0.649087 | − | 0.760714i | \(-0.275151\pi\) |
−0.983341 | + | 0.181769i | \(0.941818\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.637468 | − | 0.534900i | −0.0221135 | − | 0.0185555i | ||||
\(832\) | −8.83567 | + | 7.41401i | −0.306322 | + | 0.257035i | ||||
\(833\) | −4.92023 | + | 27.9040i | −0.170476 | + | 0.966816i | ||||
\(834\) | −7.91719 | + | 2.88162i | −0.274150 | + | 0.0997824i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 105.329 | − | 9.04937i | 3.64287 | − | 0.312979i | ||||
\(837\) | 9.21270 | 0.318438 | ||||||||
\(838\) | −55.1213 | + | 20.0625i | −1.90413 | + | 0.693048i | ||||
\(839\) | −8.84381 | + | 50.1557i | −0.305322 | + | 1.73157i | 0.316662 | + | 0.948539i | \(0.397438\pi\) |
−0.621984 | + | 0.783030i | \(0.713673\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.9908 | + | 9.22242i | 0.378995 | + | 0.318014i | ||||
\(842\) | 11.2026 | + | 63.5331i | 0.386067 | + | 2.18949i | ||||
\(843\) | −2.47997 | − | 4.29543i | −0.0854147 | − | 0.147943i | ||||
\(844\) | 12.8628 | − | 22.2791i | 0.442757 | − | 0.766878i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 48.2307 | + | 17.5545i | 1.65821 | + | 0.603538i | ||||
\(847\) | −3.20156 | + | 5.54526i | −0.110007 | + | 0.190537i | ||||
\(848\) | 52.2042 | + | 90.4204i | 1.79270 | + | 3.10505i | ||||
\(849\) | −0.0227978 | − | 0.129293i | −0.000782418 | − | 0.00443731i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.93571 | − | 2.46335i | 0.100635 | − | 0.0844426i | ||||
\(852\) | −1.67549 | + | 9.50216i | −0.0574013 | + | 0.325539i | ||||
\(853\) | −2.44273 | + | 0.889082i | −0.0836375 | + | 0.0304416i | −0.383500 | − | 0.923541i | \(-0.625281\pi\) |
0.299863 | + | 0.953982i | \(0.403059\pi\) | |||||||
\(854\) | 7.24935 | 0.248067 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −100.528 | −3.43597 | ||||||||
\(857\) | 37.7972 | − | 13.7570i | 1.29113 | − | 0.469932i | 0.397030 | − | 0.917806i | \(-0.370041\pi\) |
0.894097 | + | 0.447874i | \(0.147819\pi\) | |||||||
\(858\) | 1.66647 | − | 9.45104i | 0.0568925 | − | 0.322653i | ||||
\(859\) | −21.5150 | + | 18.0532i | −0.734083 | + | 0.615969i | −0.931241 | − | 0.364403i | \(-0.881273\pi\) |
0.197159 | + | 0.980372i | \(0.436829\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.0494030 | + | 0.280179i | 0.00168365 | + | 0.00954846i | ||||
\(862\) | 23.0667 | + | 39.9527i | 0.785654 | + | 1.36079i | ||||
\(863\) | −14.9698 | + | 25.9284i | −0.509577 | + | 0.882613i | 0.490362 | + | 0.871519i | \(0.336865\pi\) |
−0.999938 | + | 0.0110937i | \(0.996469\pi\) | |||||||
\(864\) | −11.2204 | − | 4.08390i | −0.381727 | − | 0.138937i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 50.5150 | − | 87.4946i | 1.71657 | − | 2.97319i | ||||
\(867\) | −0.0206355 | − | 0.0357418i | −0.000700819 | − | 0.00121385i | ||||
\(868\) | −2.04078 | − | 11.5738i | −0.0692684 | − | 0.392841i | ||||
\(869\) | 12.6777 | + | 10.6379i | 0.430063 | + | 0.360866i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.379870 | + | 2.15435i | −0.0128714 | + | 0.0729973i | ||||
\(872\) | 28.6718 | − | 10.4357i | 0.970950 | − | 0.353397i | ||||
\(873\) | −26.1379 | −0.884633 | ||||||||
\(874\) | 30.9427 | + | 21.7384i | 1.04665 | + | 0.735312i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.7879 | + | 3.92648i | −0.364490 | + | 0.132664i | ||||
\(877\) | 1.40747 | − | 7.98213i | 0.0475267 | − | 0.269537i | −0.951779 | − | 0.306783i | \(-0.900747\pi\) |
0.999306 | + | 0.0372458i | \(0.0118584\pi\) | |||||||
\(878\) | −37.0721 | + | 31.1072i | −1.25112 | + | 1.04982i | ||||
\(879\) | −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 | \(0.881410\pi\) | |||||||
\(882\) | 25.9557 | − | 44.9565i | 0.873973 | − | 1.51377i | ||||
\(883\) | −1.42061 | − | 0.517061i | −0.0478074 | − | 0.0174005i | 0.318006 | − | 0.948089i | \(-0.396987\pi\) |
−0.365813 | + | 0.930688i | \(0.619209\pi\) | |||||||
\(884\) | 52.5632 | + | 19.1314i | 1.76789 | + | 0.643460i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −22.0228 | − | 38.1446i | −0.739870 | − | 1.28149i | ||||
\(887\) | −4.83393 | − | 27.4146i | −0.162307 | − | 0.920491i | −0.951797 | − | 0.306728i | \(-0.900766\pi\) |
0.789490 | − | 0.613764i | \(-0.210345\pi\) | |||||||
\(888\) | 1.49480 | + | 1.25429i | 0.0501623 | + | 0.0420912i | ||||
\(889\) | 0.172657 | − | 0.144876i | 0.00579072 | − | 0.00485899i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −41.2228 | + | 15.0039i | −1.38101 | + | 0.502648i | ||||
\(892\) | −37.1970 | −1.24545 | ||||||||
\(893\) | 12.4975 | − | 26.6922i | 0.418214 | − | 0.893220i | ||||
\(894\) | 5.23661 | 0.175138 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.413006 | − | 2.34228i | 0.0137976 | − | 0.0782499i | ||||
\(897\) | 1.84149 | − | 1.54519i | 0.0614855 | − | 0.0515924i | ||||
\(898\) | −24.1475 | − | 20.2622i | −0.805813 | − | 0.676157i | ||||
\(899\) | −7.15966 | − | 40.6045i | −0.238788 | − | 1.35423i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.4850 | − | 44.1414i | 0.849029 | − | 1.47056i | ||||
\(902\) | 36.0275 | + | 13.1129i | 1.19959 | + | 0.436613i | ||||
\(903\) | −1.16237 | − | 0.423069i | −0.0386814 | − | 0.0140789i | ||||
\(904\) | −27.9051 | + | 48.3331i | −0.928111 | + | 1.60754i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.845184 | − | 4.79328i | −0.0280794 | − | 0.159246i | ||||
\(907\) | −24.2585 | − | 20.3553i | −0.805492 | − | 0.675888i | 0.144036 | − | 0.989573i | \(-0.453992\pi\) |
−0.949527 | + | 0.313685i | \(0.898436\pi\) | |||||||
\(908\) | −28.7220 | + | 24.1006i | −0.953172 | + | 0.799806i | ||||
\(909\) | −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 | \(0.444476\pi\) | |||||||
\(912\) | −3.88597 | + | 8.29963i | −0.128677 | + | 0.274828i | ||||
\(913\) | −28.6491 | −0.948148 | ||||||||
\(914\) | 32.5454 | − | 11.8455i | 1.07650 | − | 0.391816i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −101.104 | + | 84.8364i | −3.34057 | + | 2.80307i | ||||
\(917\) | −3.03858 | − | 2.54967i | −0.100343 | − | 0.0841975i | ||||
\(918\) | 2.73403 | + | 15.5055i | 0.0902364 | + | 0.511756i | ||||
\(919\) | 5.30464 | + | 9.18791i | 0.174984 | + | 0.303081i | 0.940156 | − | 0.340745i | \(-0.110679\pi\) |
−0.765172 | + | 0.643826i | \(0.777346\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.13496 | + | 0.777061i | 0.0703492 | + | 0.0256050i | ||||
\(922\) | −34.0221 | − | 12.3830i | −1.12046 | − | 0.407814i | ||||
\(923\) | −12.0431 | + | 20.8593i | −0.396403 | + | 0.686591i | ||||
\(924\) | −1.20652 | − | 2.08975i | −0.0396915 | − | 0.0687477i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 51.8001 | + | 43.4655i | 1.70226 | + | 1.42836i | ||||
\(927\) | 27.9766 | − | 23.4751i | 0.918871 | − | 0.771025i | ||||
\(928\) | −9.27960 | + | 52.6272i | −0.304618 | + | 1.72757i | ||||
\(929\) | 13.3285 | − | 4.85116i | 0.437293 | − | 0.159162i | −0.113987 | − | 0.993482i | \(-0.536362\pi\) |
0.551279 | + | 0.834321i | \(0.314140\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.3915 | − | 17.1359i | −0.799399 | − | 0.561607i | ||||
\(932\) | −44.1200 | −1.44520 | ||||||||
\(933\) | 5.59862 | − | 2.03773i | 0.183290 | − | 0.0667123i | ||||
\(934\) | −17.7574 | + | 100.707i | −0.581039 | + | 3.29524i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −44.9019 | − | 37.6772i | −1.46766 | − | 1.23152i | ||||
\(937\) | −7.73465 | − | 43.8654i | −0.252680 | − | 1.43302i | −0.801958 | − | 0.597380i | \(-0.796208\pi\) |
0.549278 | − | 0.835640i | \(-0.314903\pi\) | |||||||
\(938\) | 0.392744 | + | 0.680253i | 0.0128235 | + | 0.0222110i | ||||
\(939\) | −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 | \(0.446141\pi\) | |||||||
\(942\) | 4.02023 | − | 6.96324i | 0.130986 | − | 0.226875i | ||||
\(943\) | 4.80181 | + | 8.31698i | 0.156368 | + | 0.270838i | ||||
\(944\) | −2.23303 | − | 12.6642i | −0.0726791 | − | 0.412183i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −127.696 | + | 107.150i | −4.15177 | + | 3.48375i | ||||
\(947\) | 5.37877 | − | 30.5045i | 0.174787 | − | 0.991264i | −0.763603 | − | 0.645686i | \(-0.776572\pi\) |
0.938390 | − | 0.345578i | \(-0.112317\pi\) | |||||||
\(948\) | −3.46788 | + | 1.26220i | −0.112631 | + | 0.0409945i | ||||
\(949\) | −28.6582 | −0.930285 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.73954 | −0.0564086 | ||||||||
\(952\) | 10.7950 | − | 3.92908i | 0.349869 | − | 0.127342i | ||||
\(953\) | 3.86599 | − | 21.9251i | 0.125232 | − | 0.710224i | −0.855938 | − | 0.517078i | \(-0.827020\pi\) |
0.981170 | − | 0.193146i | \(-0.0618691\pi\) | |||||||
\(954\) | −71.5346 | + | 60.0247i | −2.31602 | + | 1.94337i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.56828 | + | 54.2644i | 0.309460 | + | 1.75504i | ||||
\(957\) | −4.23283 | − | 7.33148i | −0.136828 | − | 0.236993i | ||||
\(958\) | 4.88059 | − | 8.45343i | 0.157685 | − | 0.273118i | ||||
\(959\) | −3.38277 | − | 1.23123i | −0.109235 | − | 0.0397584i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.10876 | + | 7.11657i | −0.132540 | + | 0.229567i | ||||
\(962\) | 4.25823 | + | 7.37548i | 0.137291 | + | 0.237795i | ||||
\(963\) | −7.43092 | − | 42.1428i | −0.239458 | − | 1.35803i | ||||
\(964\) | −45.8162 | − | 38.4444i | −1.47564 | − | 1.23821i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.149886 | − | 0.850044i | 0.00482249 | − | 0.0273497i | ||||
\(967\) | −16.4816 | + | 5.99883i | −0.530014 | + | 0.192909i | −0.593145 | − | 0.805096i | \(-0.702114\pi\) |
0.0631307 | + | 0.998005i | \(0.479892\pi\) | |||||||
\(968\) | −110.056 | −3.53734 | ||||||||
\(969\) | 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 | \(0.302160\pi\) | |||||||
\(972\) | 5.27953 | − | 29.9417i | 0.169341 | − | 0.960381i | ||||
\(973\) | −4.05109 | + | 3.39927i | −0.129872 | + | 0.108975i | ||||
\(974\) | 13.8314 | + | 11.6059i | 0.443187 | + | 0.371878i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 29.6518 | + | 51.3584i | 0.949131 | + | 1.64394i | ||||
\(977\) | −14.3920 | + | 24.9276i | −0.460440 | + | 0.797506i | −0.998983 | − | 0.0450925i | \(-0.985642\pi\) |
0.538543 | + | 0.842598i | \(0.318975\pi\) | |||||||
\(978\) | 1.97436 | + | 0.718608i | 0.0631330 | + | 0.0229785i | ||||
\(979\) | 61.0872 | + | 22.2339i | 1.95236 | + | 0.710599i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.49419 | + | 11.2483i | 0.207344 | + | 0.359130i | ||||
\(982\) | 14.6402 | + | 83.0287i | 0.467187 | + | 2.64955i | ||||
\(983\) | 22.9176 | + | 19.2302i | 0.730959 | + | 0.613348i | 0.930393 | − | 0.366564i | \(-0.119466\pi\) |
−0.199434 | + | 0.979911i | \(0.563910\pi\) | |||||||
\(984\) | −3.74593 | + | 3.14321i | −0.119416 | + | 0.100202i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 66.2147 | − | 24.1002i | 2.10870 | − | 0.767506i | ||||
\(987\) | −0.672737 | −0.0214135 | ||||||||
\(988\) | −41.6766 | + | 41.5467i | −1.32591 | + | 1.32178i | ||||
\(989\) | −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 | \(-0.204570\pi\) | |||||||
\(992\) | 38.9377 | − | 32.6726i | 1.23627 | − | 1.03736i | ||||
\(993\) | 3.30389 | + | 2.77229i | 0.104846 | + | 0.0879760i | ||||
\(994\) | 1.50181 | + | 8.51716i | 0.0476344 | + | 0.270148i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.19427 | − | 5.53264i | 0.101214 | − | 0.175308i | ||||
\(997\) | −50.6964 | − | 18.4520i | −1.60557 | − | 0.584380i | −0.625014 | − | 0.780614i | \(-0.714907\pi\) |
−0.980557 | + | 0.196234i | \(0.937129\pi\) | |||||||
\(998\) | 67.4628 | + | 24.5545i | 2.13550 | + | 0.777258i | ||||
\(999\) | −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.l.c.176.3 | 18 | ||
5.2 | odd | 4 | 475.2.u.b.24.6 | 36 | |||
5.3 | odd | 4 | 475.2.u.b.24.1 | 36 | |||
5.4 | even | 2 | 95.2.k.a.81.1 | yes | 18 | ||
15.14 | odd | 2 | 855.2.bs.c.271.3 | 18 | |||
19.2 | odd | 18 | 9025.2.a.cf.1.9 | 9 | |||
19.4 | even | 9 | inner | 475.2.l.c.251.3 | 18 | ||
19.17 | even | 9 | 9025.2.a.cc.1.1 | 9 | |||
95.4 | even | 18 | 95.2.k.a.61.1 | ✓ | 18 | ||
95.23 | odd | 36 | 475.2.u.b.99.6 | 36 | |||
95.42 | odd | 36 | 475.2.u.b.99.1 | 36 | |||
95.59 | odd | 18 | 1805.2.a.s.1.1 | 9 | |||
95.74 | even | 18 | 1805.2.a.v.1.9 | 9 | |||
285.194 | odd | 18 | 855.2.bs.c.631.3 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.k.a.61.1 | ✓ | 18 | 95.4 | even | 18 | ||
95.2.k.a.81.1 | yes | 18 | 5.4 | even | 2 | ||
475.2.l.c.176.3 | 18 | 1.1 | even | 1 | trivial | ||
475.2.l.c.251.3 | 18 | 19.4 | even | 9 | inner | ||
475.2.u.b.24.1 | 36 | 5.3 | odd | 4 | |||
475.2.u.b.24.6 | 36 | 5.2 | odd | 4 | |||
475.2.u.b.99.1 | 36 | 95.42 | odd | 36 | |||
475.2.u.b.99.6 | 36 | 95.23 | odd | 36 | |||
855.2.bs.c.271.3 | 18 | 15.14 | odd | 2 | |||
855.2.bs.c.631.3 | 18 | 285.194 | odd | 18 | |||
1805.2.a.s.1.1 | 9 | 95.59 | odd | 18 | |||
1805.2.a.v.1.9 | 9 | 95.74 | even | 18 | |||
9025.2.a.cc.1.1 | 9 | 19.17 | even | 9 | |||
9025.2.a.cf.1.9 | 9 | 19.2 | odd | 18 |