Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 7 x^{10} - 15 x^{9} + 59 x^{8} + 118 x^{7} + 266 x^{6} + 324 x^{5} + 1036 x^{4} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 729.3 | ||
Root | \(-0.965643 + 2.97194i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.729 |
Dual form | 847.2.f.t.323.3 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.71907 | − | 1.24898i | 1.21556 | − | 0.883160i | 0.219841 | − | 0.975536i | \(-0.429446\pi\) |
0.995724 | + | 0.0923762i | \(0.0294462\pi\) | |||||||
\(3\) | −0.965643 | − | 2.97194i | −0.557514 | − | 1.71585i | −0.689210 | − | 0.724562i | \(-0.742042\pi\) |
0.131696 | − | 0.991290i | \(-0.457958\pi\) | |||||||
\(4\) | 0.777220 | − | 2.39204i | 0.388610 | − | 1.19602i | ||||
\(5\) | −0.392262 | − | 0.284995i | −0.175425 | − | 0.127454i | 0.496608 | − | 0.867975i | \(-0.334579\pi\) |
−0.672033 | + | 0.740521i | \(0.734579\pi\) | |||||||
\(6\) | −5.37189 | − | 3.90291i | −2.19307 | − | 1.59336i | ||||
\(7\) | 0.309017 | − | 0.951057i | 0.116797 | − | 0.359466i | ||||
\(8\) | −0.338253 | − | 1.04104i | −0.119590 | − | 0.368062i | ||||
\(9\) | −5.47293 | + | 3.97631i | −1.82431 | + | 1.32544i | ||||
\(10\) | −1.03028 | −0.325802 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −7.85952 | −2.26885 | ||||||||
\(13\) | −4.53838 | + | 3.29733i | −1.25872 | + | 0.914514i | −0.998694 | − | 0.0510876i | \(-0.983731\pi\) |
−0.260026 | + | 0.965602i | \(0.583731\pi\) | |||||||
\(14\) | −0.656626 | − | 2.02089i | −0.175491 | − | 0.540105i | ||||
\(15\) | −0.468203 | + | 1.44098i | −0.120890 | + | 0.372060i | ||||
\(16\) | 2.18787 | + | 1.58958i | 0.546968 | + | 0.397395i | ||||
\(17\) | −4.53838 | − | 3.29733i | −1.10072 | − | 0.799719i | −0.119542 | − | 0.992829i | \(-0.538143\pi\) |
−0.981177 | + | 0.193110i | \(0.938143\pi\) | |||||||
\(18\) | −4.44201 | + | 13.6711i | −1.04699 | + | 3.22231i | ||||
\(19\) | −1.63162 | − | 5.02162i | −0.374320 | − | 1.15204i | −0.943936 | − | 0.330128i | \(-0.892908\pi\) |
0.569616 | − | 0.821911i | \(-0.307092\pi\) | |||||||
\(20\) | −0.986592 | + | 0.716801i | −0.220609 | + | 0.160282i | ||||
\(21\) | −3.12489 | −0.681906 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.48486 | 0.518130 | 0.259065 | − | 0.965860i | \(-0.416586\pi\) | ||||
0.259065 | + | 0.965860i | \(0.416586\pi\) | |||||||
\(24\) | −2.76727 | + | 2.01054i | −0.564866 | + | 0.410399i | ||||
\(25\) | −1.47244 | − | 4.53170i | −0.294488 | − | 0.906340i | ||||
\(26\) | −3.68350 | + | 11.3367i | −0.722395 | + | 2.22330i | ||||
\(27\) | 9.51801 | + | 6.91524i | 1.83174 | + | 1.33084i | ||||
\(28\) | −2.03479 | − | 1.47836i | −0.384539 | − | 0.279384i | ||||
\(29\) | 1.63162 | − | 5.02162i | 0.302985 | − | 0.932492i | −0.677436 | − | 0.735581i | \(-0.736909\pi\) |
0.980421 | − | 0.196911i | \(-0.0630909\pi\) | |||||||
\(30\) | 0.994879 | + | 3.06192i | 0.181639 | + | 0.559028i | ||||
\(31\) | 5.76415 | − | 4.18790i | 1.03527 | − | 0.752170i | 0.0659154 | − | 0.997825i | \(-0.479003\pi\) |
0.969357 | + | 0.245656i | \(0.0790033\pi\) | |||||||
\(32\) | 7.93567 | 1.40284 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −11.9201 | −2.04428 | ||||||||
\(35\) | −0.392262 | + | 0.284995i | −0.0663043 | + | 0.0481729i | ||||
\(36\) | 5.25783 | + | 16.1819i | 0.876304 | + | 2.69699i | ||||
\(37\) | −0.0726471 | + | 0.223585i | −0.0119431 | + | 0.0367571i | −0.956850 | − | 0.290581i | \(-0.906152\pi\) |
0.944907 | + | 0.327338i | \(0.106152\pi\) | |||||||
\(38\) | −9.07676 | − | 6.59465i | −1.47245 | − | 1.06979i | ||||
\(39\) | 14.1819 | + | 10.3038i | 2.27092 | + | 1.64992i | ||||
\(40\) | −0.164006 | + | 0.504758i | −0.0259316 | + | 0.0798093i | ||||
\(41\) | 0.738629 | + | 2.27327i | 0.115354 | + | 0.355024i | 0.992021 | − | 0.126074i | \(-0.0402378\pi\) |
−0.876666 | + | 0.481099i | \(0.840238\pi\) | |||||||
\(42\) | −5.37189 | + | 3.90291i | −0.828901 | + | 0.602232i | ||||
\(43\) | 1.03028 | 0.157116 | 0.0785578 | − | 0.996910i | \(-0.474968\pi\) | ||||
0.0785578 | + | 0.996910i | \(0.474968\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.28005 | 0.488961 | ||||||||
\(46\) | 4.27165 | − | 3.10353i | 0.629820 | − | 0.457591i | ||||
\(47\) | −0.497439 | − | 1.53096i | −0.0725590 | − | 0.223314i | 0.908200 | − | 0.418537i | \(-0.137457\pi\) |
−0.980759 | + | 0.195223i | \(0.937457\pi\) | |||||||
\(48\) | 2.61144 | − | 8.03719i | 0.376929 | − | 1.16007i | ||||
\(49\) | −0.809017 | − | 0.587785i | −0.115574 | − | 0.0839693i | ||||
\(50\) | −8.19120 | − | 5.95126i | −1.15841 | − | 0.841635i | ||||
\(51\) | −5.41701 | + | 16.6718i | −0.758533 | + | 2.33453i | ||||
\(52\) | 4.36001 | + | 13.4187i | 0.604625 | + | 1.86084i | ||||
\(53\) | 2.45154 | − | 1.78115i | 0.336746 | − | 0.244660i | −0.406542 | − | 0.913632i | \(-0.633265\pi\) |
0.743287 | + | 0.668972i | \(0.233265\pi\) | |||||||
\(54\) | 24.9991 | 3.40194 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.09461 | −0.146273 | ||||||||
\(57\) | −13.3484 | + | 9.69819i | −1.76804 | + | 1.28456i | ||||
\(58\) | −3.46701 | − | 10.6704i | −0.455241 | − | 1.40109i | ||||
\(59\) | 0.965643 | − | 2.97194i | 0.125716 | − | 0.386914i | −0.868315 | − | 0.496013i | \(-0.834797\pi\) |
0.994031 | + | 0.109099i | \(0.0347967\pi\) | |||||||
\(60\) | 3.08299 | + | 2.23992i | 0.398012 | + | 0.289173i | ||||
\(61\) | 1.93375 | + | 1.40496i | 0.247592 | + | 0.179886i | 0.704659 | − | 0.709546i | \(-0.251100\pi\) |
−0.457067 | + | 0.889432i | \(0.651100\pi\) | |||||||
\(62\) | 4.67838 | − | 14.3986i | 0.594155 | − | 1.82862i | ||||
\(63\) | 2.09047 | + | 6.43381i | 0.263375 | + | 0.810584i | ||||
\(64\) | 9.26621 | − | 6.73230i | 1.15828 | − | 0.841537i | ||||
\(65\) | 2.71995 | 0.337369 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.0147 | 1.22349 | 0.611744 | − | 0.791056i | \(-0.290468\pi\) | ||||
0.611744 | + | 0.791056i | \(0.290468\pi\) | |||||||
\(68\) | −11.4147 | + | 8.29323i | −1.38423 | + | 1.00570i | ||||
\(69\) | −2.39949 | − | 7.38487i | −0.288865 | − | 0.889034i | ||||
\(70\) | −0.318373 | + | 0.979851i | −0.0380528 | + | 0.117115i | ||||
\(71\) | −9.76907 | − | 7.09764i | −1.15938 | − | 0.842335i | −0.169676 | − | 0.985500i | \(-0.554272\pi\) |
−0.989699 | + | 0.143165i | \(0.954272\pi\) | |||||||
\(72\) | 5.99072 | + | 4.35251i | 0.706013 | + | 0.512948i | ||||
\(73\) | 0.738629 | − | 2.27327i | 0.0864499 | − | 0.266066i | −0.898481 | − | 0.439012i | \(-0.855329\pi\) |
0.984931 | + | 0.172946i | \(0.0553287\pi\) | |||||||
\(74\) | 0.154367 | + | 0.475092i | 0.0179448 | + | 0.0552284i | ||||
\(75\) | −12.0461 | + | 8.75200i | −1.39096 | + | 1.01059i | ||||
\(76\) | −13.2800 | −1.52333 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 37.2489 | 4.21760 | ||||||||
\(79\) | −7.30565 | + | 5.30786i | −0.821949 | + | 0.597181i | −0.917270 | − | 0.398265i | \(-0.869612\pi\) |
0.0953208 | + | 0.995447i | \(0.469612\pi\) | |||||||
\(80\) | −0.405195 | − | 1.24706i | −0.0453022 | − | 0.139426i | ||||
\(81\) | 5.08928 | − | 15.6632i | 0.565476 | − | 1.74036i | ||||
\(82\) | 4.10901 | + | 2.98537i | 0.453764 | + | 0.329679i | ||||
\(83\) | 2.60463 | + | 1.89237i | 0.285895 | + | 0.207715i | 0.721484 | − | 0.692431i | \(-0.243460\pi\) |
−0.435590 | + | 0.900145i | \(0.643460\pi\) | |||||||
\(84\) | −2.42872 | + | 7.47485i | −0.264996 | + | 0.815573i | ||||
\(85\) | 0.840512 | + | 2.58683i | 0.0911663 | + | 0.280581i | ||||
\(86\) | 1.77112 | − | 1.28679i | 0.190984 | − | 0.138758i | ||||
\(87\) | −16.4995 | −1.76894 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.26537 | −0.134129 | −0.0670643 | − | 0.997749i | \(-0.521363\pi\) | ||||
−0.0670643 | + | 0.997749i | \(0.521363\pi\) | |||||||
\(90\) | 5.63863 | − | 4.09670i | 0.594363 | − | 0.431830i | ||||
\(91\) | 1.73351 | + | 5.33519i | 0.181721 | + | 0.559280i | ||||
\(92\) | 1.93129 | − | 5.94389i | 0.201350 | − | 0.619693i | ||||
\(93\) | −18.0123 | − | 13.0867i | −1.86779 | − | 1.35703i | ||||
\(94\) | −2.76727 | − | 2.01054i | −0.285422 | − | 0.207371i | ||||
\(95\) | −0.791113 | + | 2.43479i | −0.0811664 | + | 0.249805i | ||||
\(96\) | −7.66302 | − | 23.5843i | −0.782104 | − | 2.40707i | ||||
\(97\) | 7.11545 | − | 5.16968i | 0.722465 | − | 0.524901i | −0.164706 | − | 0.986343i | \(-0.552667\pi\) |
0.887171 | + | 0.461441i | \(0.152667\pi\) | |||||||
\(98\) | −2.12489 | −0.214646 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −11.9844 | −1.19844 | ||||||||
\(101\) | 10.4771 | − | 7.61202i | 1.04251 | − | 0.757425i | 0.0717324 | − | 0.997424i | \(-0.477147\pi\) |
0.970773 | + | 0.239999i | \(0.0771472\pi\) | |||||||
\(102\) | 11.5105 | + | 35.4258i | 1.13971 | + | 3.50767i | ||||
\(103\) | 3.76069 | − | 11.5742i | 0.370552 | − | 1.14044i | −0.575880 | − | 0.817535i | \(-0.695340\pi\) |
0.946431 | − | 0.322906i | \(-0.104660\pi\) | |||||||
\(104\) | 4.96775 | + | 3.60928i | 0.487128 | + | 0.353919i | ||||
\(105\) | 1.22577 | + | 0.890576i | 0.119623 | + | 0.0869113i | ||||
\(106\) | 1.98976 | − | 6.12384i | 0.193262 | − | 0.594800i | ||||
\(107\) | 3.26325 | + | 10.0432i | 0.315470 | + | 0.970917i | 0.975560 | + | 0.219731i | \(0.0705180\pi\) |
−0.660090 | + | 0.751186i | \(0.729482\pi\) | |||||||
\(108\) | 23.9391 | − | 17.3928i | 2.30354 | − | 1.67362i | ||||
\(109\) | −7.34060 | −0.703102 | −0.351551 | − | 0.936169i | \(-0.614346\pi\) | ||||
−0.351551 | + | 0.936169i | \(0.614346\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.734633 | 0.0697283 | ||||||||
\(112\) | 2.18787 | − | 1.58958i | 0.206734 | − | 0.150201i | ||||
\(113\) | 4.25359 | + | 13.0912i | 0.400144 | + | 1.23152i | 0.924882 | + | 0.380253i | \(0.124163\pi\) |
−0.524738 | + | 0.851264i | \(0.675837\pi\) | |||||||
\(114\) | −10.8340 | + | 33.3437i | −1.01470 | + | 3.12292i | ||||
\(115\) | −0.974716 | − | 0.708172i | −0.0908927 | − | 0.0660374i | ||||
\(116\) | −10.7438 | − | 7.80582i | −0.997535 | − | 0.724752i | ||||
\(117\) | 11.7270 | − | 36.0921i | 1.08416 | − | 3.33671i | ||||
\(118\) | −2.05188 | − | 6.31504i | −0.188891 | − | 0.581346i | ||||
\(119\) | −4.53838 | + | 3.29733i | −0.416033 | + | 0.302265i | ||||
\(120\) | 1.65848 | 0.151398 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 5.07901 | 0.459832 | ||||||||
\(123\) | 6.04276 | − | 4.39032i | 0.544858 | − | 0.395862i | ||||
\(124\) | −5.53761 | − | 17.0430i | −0.497292 | − | 1.53051i | ||||
\(125\) | −1.46308 | + | 4.50290i | −0.130862 | + | 0.402752i | ||||
\(126\) | 11.6293 | + | 8.44921i | 1.03602 | + | 0.752716i | ||||
\(127\) | −2.07116 | − | 1.50479i | −0.183786 | − | 0.133528i | 0.492088 | − | 0.870545i | \(-0.336234\pi\) |
−0.675874 | + | 0.737017i | \(0.736234\pi\) | |||||||
\(128\) | 2.61626 | − | 8.05203i | 0.231247 | − | 0.711705i | ||||
\(129\) | −0.994879 | − | 3.06192i | −0.0875942 | − | 0.269587i | ||||
\(130\) | 4.67579 | − | 3.39716i | 0.410094 | − | 0.297950i | ||||
\(131\) | −2.71995 | −0.237643 | −0.118822 | − | 0.992916i | \(-0.537912\pi\) | ||||
−0.118822 | + | 0.992916i | \(0.537912\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.28005 | −0.457838 | ||||||||
\(134\) | 17.2159 | − | 12.5081i | 1.48723 | − | 1.08054i | ||||
\(135\) | −1.76274 | − | 5.42517i | −0.151713 | − | 0.466924i | ||||
\(136\) | −1.89751 | + | 5.83995i | −0.162710 | + | 0.500771i | ||||
\(137\) | 7.85099 | + | 5.70408i | 0.670755 | + | 0.487332i | 0.870278 | − | 0.492561i | \(-0.163939\pi\) |
−0.199523 | + | 0.979893i | \(0.563939\pi\) | |||||||
\(138\) | −13.3484 | − | 9.69819i | −1.13629 | − | 0.825565i | ||||
\(139\) | −6.09352 | + | 18.7539i | −0.516845 | + | 1.59069i | 0.263054 | + | 0.964781i | \(0.415270\pi\) |
−0.779899 | + | 0.625905i | \(0.784730\pi\) | |||||||
\(140\) | 0.376845 | + | 1.15981i | 0.0318492 | + | 0.0980217i | ||||
\(141\) | −4.06958 | + | 2.95672i | −0.342720 | + | 0.249001i | ||||
\(142\) | −25.6585 | −2.15321 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −18.2947 | −1.52456 | ||||||||
\(145\) | −2.07116 | + | 1.50479i | −0.172000 | + | 0.124966i | ||||
\(146\) | −1.56950 | − | 4.83043i | −0.129893 | − | 0.399769i | ||||
\(147\) | −0.965643 | + | 2.97194i | −0.0796449 | + | 0.245122i | ||||
\(148\) | 0.478361 | + | 0.347550i | 0.0393210 | + | 0.0285684i | ||||
\(149\) | −8.54330 | − | 6.20707i | −0.699894 | − | 0.508503i | 0.180004 | − | 0.983666i | \(-0.442389\pi\) |
−0.879898 | + | 0.475163i | \(0.842389\pi\) | |||||||
\(150\) | −9.77702 | + | 30.0906i | −0.798290 | + | 2.45689i | ||||
\(151\) | 4.78027 | + | 14.7121i | 0.389013 | + | 1.19726i | 0.933527 | + | 0.358506i | \(0.116714\pi\) |
−0.544515 | + | 0.838751i | \(0.683286\pi\) | |||||||
\(152\) | −4.67579 | + | 3.39716i | −0.379256 | + | 0.275546i | ||||
\(153\) | 37.9494 | 3.06803 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.45459 | −0.277479 | ||||||||
\(156\) | 35.6695 | − | 25.9154i | 2.85584 | − | 2.07489i | ||||
\(157\) | 2.81376 | + | 8.65985i | 0.224562 | + | 0.691131i | 0.998336 | + | 0.0576691i | \(0.0183668\pi\) |
−0.773774 | + | 0.633462i | \(0.781633\pi\) | |||||||
\(158\) | −5.92951 | + | 18.2492i | −0.471727 | + | 1.45183i | ||||
\(159\) | −7.66080 | − | 5.56589i | −0.607541 | − | 0.441404i | ||||
\(160\) | −3.11286 | − | 2.26162i | −0.246093 | − | 0.178797i | ||||
\(161\) | 0.767865 | − | 2.36324i | 0.0605162 | − | 0.186250i | ||||
\(162\) | −10.8141 | − | 33.2825i | −0.849639 | − | 2.61492i | ||||
\(163\) | 10.7438 | − | 7.80582i | 0.841518 | − | 0.611399i | −0.0812762 | − | 0.996692i | \(-0.525900\pi\) |
0.922794 | + | 0.385293i | \(0.125900\pi\) | |||||||
\(164\) | 6.01182 | 0.469444 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.84106 | 0.530969 | ||||||||
\(167\) | −8.13916 | + | 5.91344i | −0.629827 | + | 0.457596i | −0.856340 | − | 0.516412i | \(-0.827267\pi\) |
0.226513 | + | 0.974008i | \(0.427267\pi\) | |||||||
\(168\) | 1.05700 | + | 3.25312i | 0.0815494 | + | 0.250983i | ||||
\(169\) | 5.70732 | − | 17.5653i | 0.439024 | − | 1.35118i | ||||
\(170\) | 4.67579 | + | 3.39716i | 0.358616 | + | 0.260550i | ||||
\(171\) | 28.8973 | + | 20.9951i | 2.20983 | + | 1.60554i | ||||
\(172\) | 0.800752 | − | 2.46446i | 0.0610567 | − | 0.187913i | ||||
\(173\) | −2.52462 | − | 7.76998i | −0.191943 | − | 0.590741i | −0.999999 | − | 0.00163416i | \(-0.999480\pi\) |
0.808055 | − | 0.589107i | \(-0.200520\pi\) | |||||||
\(174\) | −28.3638 | + | 20.6075i | −2.15026 | + | 1.56225i | ||||
\(175\) | −4.76491 | −0.360193 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.76491 | −0.733975 | ||||||||
\(178\) | −2.17525 | + | 1.58041i | −0.163042 | + | 0.118457i | ||||
\(179\) | −3.78992 | − | 11.6642i | −0.283272 | − | 0.871822i | −0.986911 | − | 0.161265i | \(-0.948443\pi\) |
0.703639 | − | 0.710558i | \(-0.251557\pi\) | |||||||
\(180\) | 2.54932 | − | 7.84600i | 0.190015 | − | 0.584806i | ||||
\(181\) | 5.69949 | + | 4.14092i | 0.423640 | + | 0.307792i | 0.779101 | − | 0.626899i | \(-0.215676\pi\) |
−0.355461 | + | 0.934691i | \(0.615676\pi\) | |||||||
\(182\) | 9.64354 | + | 7.00644i | 0.714827 | + | 0.519352i | ||||
\(183\) | 2.30813 | − | 7.10369i | 0.170622 | − | 0.525120i | ||||
\(184\) | −0.840512 | − | 2.58683i | −0.0619633 | − | 0.190704i | ||||
\(185\) | 0.0922172 | − | 0.0669997i | 0.00677994 | − | 0.00492592i | ||||
\(186\) | −47.3094 | −3.46889 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −4.04874 | −0.295284 | ||||||||
\(189\) | 9.51801 | − | 6.91524i | 0.692333 | − | 0.503010i | ||||
\(190\) | 1.68102 | + | 5.17366i | 0.121954 | + | 0.375337i | ||||
\(191\) | 5.80803 | − | 17.8753i | 0.420254 | − | 1.29341i | −0.487211 | − | 0.873284i | \(-0.661986\pi\) |
0.907466 | − | 0.420126i | \(-0.138014\pi\) | |||||||
\(192\) | −28.9559 | − | 21.0377i | −2.08971 | − | 1.51826i | ||||
\(193\) | −13.3484 | − | 9.69819i | −0.960840 | − | 0.698091i | −0.00749397 | − | 0.999972i | \(-0.502385\pi\) |
−0.953346 | + | 0.301881i | \(0.902385\pi\) | |||||||
\(194\) | 5.77514 | − | 17.7741i | 0.414631 | − | 1.27610i | ||||
\(195\) | −2.62650 | − | 8.08354i | −0.188088 | − | 0.578875i | ||||
\(196\) | −2.03479 | + | 1.47836i | −0.145342 | + | 0.105597i | ||||
\(197\) | 24.4995 | 1.74552 | 0.872760 | − | 0.488149i | \(-0.162328\pi\) | ||||
0.872760 | + | 0.488149i | \(0.162328\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.3893 | −1.09092 | −0.545461 | − | 0.838136i | \(-0.683645\pi\) | ||||
−0.545461 | + | 0.838136i | \(0.683645\pi\) | |||||||
\(200\) | −4.21960 | + | 3.06572i | −0.298371 | + | 0.216779i | ||||
\(201\) | −9.67060 | − | 29.7631i | −0.682112 | − | 2.09932i | ||||
\(202\) | 8.50353 | − | 26.1712i | 0.598306 | − | 1.84140i | ||||
\(203\) | −4.27165 | − | 3.10353i | −0.299811 | − | 0.217825i | ||||
\(204\) | 35.6695 | + | 25.9154i | 2.49736 | + | 1.81444i | ||||
\(205\) | 0.358133 | − | 1.10222i | 0.0250131 | − | 0.0769824i | ||||
\(206\) | −7.99103 | − | 24.5939i | −0.556761 | − | 1.71354i | ||||
\(207\) | −13.5995 | + | 9.88059i | −0.945228 | + | 0.686749i | ||||
\(208\) | −15.1708 | −1.05190 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.21949 | 0.222166 | ||||||||
\(211\) | 11.6814 | − | 8.48703i | 0.804180 | − | 0.584271i | −0.107957 | − | 0.994156i | \(-0.534431\pi\) |
0.912137 | + | 0.409885i | \(0.134431\pi\) | |||||||
\(212\) | −2.35519 | − | 7.24854i | −0.161755 | − | 0.497832i | ||||
\(213\) | −11.6604 | + | 35.8869i | −0.798955 | + | 2.45893i | ||||
\(214\) | 18.1535 | + | 13.1893i | 1.24095 | + | 0.901602i | ||||
\(215\) | −0.404138 | − | 0.293623i | −0.0275620 | − | 0.0200249i | ||||
\(216\) | 3.97951 | − | 12.2477i | 0.270772 | − | 0.833349i | ||||
\(217\) | −2.20171 | − | 6.77617i | −0.149462 | − | 0.459996i | ||||
\(218\) | −12.6190 | + | 9.16823i | −0.854666 | + | 0.620951i | ||||
\(219\) | −7.46927 | −0.504726 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 31.4693 | 2.11685 | ||||||||
\(222\) | 1.26288 | − | 0.917539i | 0.0847592 | − | 0.0615812i | ||||
\(223\) | 5.33164 | + | 16.4091i | 0.357033 | + | 1.09883i | 0.954821 | + | 0.297181i | \(0.0960464\pi\) |
−0.597788 | + | 0.801654i | \(0.703954\pi\) | |||||||
\(224\) | 2.45226 | − | 7.54727i | 0.163848 | − | 0.504273i | ||||
\(225\) | 26.0780 | + | 18.9468i | 1.73853 | + | 1.26312i | ||||
\(226\) | 23.6628 | + | 17.1920i | 1.57403 | + | 1.14360i | ||||
\(227\) | 3.31265 | − | 10.1953i | 0.219868 | − | 0.676685i | −0.778904 | − | 0.627143i | \(-0.784224\pi\) |
0.998772 | − | 0.0495413i | \(-0.0157759\pi\) | |||||||
\(228\) | 12.8238 | + | 39.4675i | 0.849276 | + | 2.61380i | ||||
\(229\) | −4.41285 | + | 3.20613i | −0.291610 | + | 0.211867i | −0.723965 | − | 0.689836i | \(-0.757682\pi\) |
0.432356 | + | 0.901703i | \(0.357682\pi\) | |||||||
\(230\) | −2.56009 | −0.168808 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.77959 | −0.379449 | ||||||||
\(233\) | −24.0922 | + | 17.5040i | −1.57833 | + | 1.14673i | −0.659757 | + | 0.751479i | \(0.729341\pi\) |
−0.918575 | + | 0.395246i | \(0.870659\pi\) | |||||||
\(234\) | −24.9186 | − | 76.6915i | −1.62898 | − | 5.01348i | ||||
\(235\) | −0.241189 | + | 0.742305i | −0.0157335 | + | 0.0484226i | ||||
\(236\) | −6.35848 | − | 4.61971i | −0.413902 | − | 0.300717i | ||||
\(237\) | 22.8293 | + | 16.5865i | 1.48292 | + | 1.07741i | ||||
\(238\) | −3.68350 | + | 11.3367i | −0.238766 | + | 0.734847i | ||||
\(239\) | 0.791113 | + | 2.43479i | 0.0511728 | + | 0.157494i | 0.973377 | − | 0.229209i | \(-0.0736139\pi\) |
−0.922204 | + | 0.386703i | \(0.873614\pi\) | |||||||
\(240\) | −3.31493 | + | 2.40843i | −0.213978 | + | 0.155464i | ||||
\(241\) | 27.3893 | 1.76430 | 0.882151 | − | 0.470966i | \(-0.156095\pi\) | ||||
0.882151 | + | 0.470966i | \(0.156095\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.1698 | −1.03730 | ||||||||
\(244\) | 4.86366 | − | 3.53366i | 0.311364 | − | 0.226219i | ||||
\(245\) | 0.149831 | + | 0.461131i | 0.00957232 | + | 0.0294606i | ||||
\(246\) | 4.90451 | − | 15.0945i | 0.312700 | − | 0.962392i | ||||
\(247\) | 23.9629 | + | 17.4100i | 1.52472 | + | 1.10777i | ||||
\(248\) | −6.30950 | − | 4.58412i | −0.400653 | − | 0.291092i | ||||
\(249\) | 3.10888 | − | 9.56815i | 0.197017 | − | 0.606357i | ||||
\(250\) | 3.10888 | + | 9.56815i | 0.196623 | + | 0.605143i | ||||
\(251\) | −7.96464 | + | 5.78665i | −0.502724 | + | 0.365250i | −0.810056 | − | 0.586352i | \(-0.800564\pi\) |
0.307333 | + | 0.951602i | \(0.400564\pi\) | |||||||
\(252\) | 17.0147 | 1.07182 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −5.43991 | −0.341330 | ||||||||
\(255\) | 6.87627 | − | 4.99591i | 0.430609 | − | 0.312856i | ||||
\(256\) | 1.51950 | + | 4.67654i | 0.0949688 | + | 0.292284i | ||||
\(257\) | −6.95274 | + | 21.3983i | −0.433700 | + | 1.33479i | 0.460713 | + | 0.887549i | \(0.347594\pi\) |
−0.894413 | + | 0.447242i | \(0.852406\pi\) | |||||||
\(258\) | −5.53453 | − | 4.02107i | −0.344565 | − | 0.250341i | ||||
\(259\) | 0.190193 | + | 0.138183i | 0.0118180 | + | 0.00858628i | ||||
\(260\) | 2.11400 | − | 6.50623i | 0.131105 | − | 0.403499i | ||||
\(261\) | 11.0378 | + | 33.9708i | 0.683222 | + | 2.10274i | ||||
\(262\) | −4.67579 | + | 3.39716i | −0.288871 | + | 0.209877i | ||||
\(263\) | −16.0000 | −0.986602 | −0.493301 | − | 0.869859i | \(-0.664210\pi\) | ||||
−0.493301 | + | 0.869859i | \(0.664210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.46927 | −0.0902563 | ||||||||
\(266\) | −9.07676 | + | 6.59465i | −0.556532 | + | 0.404344i | ||||
\(267\) | 1.22189 | + | 3.76060i | 0.0747786 | + | 0.230145i | ||||
\(268\) | 7.78361 | − | 23.9555i | 0.475460 | − | 1.46331i | ||||
\(269\) | −7.45873 | − | 5.41908i | −0.454767 | − | 0.330407i | 0.336708 | − | 0.941609i | \(-0.390686\pi\) |
−0.791475 | + | 0.611202i | \(0.790686\pi\) | |||||||
\(270\) | −9.80618 | − | 7.12461i | −0.596785 | − | 0.433590i | ||||
\(271\) | 3.26325 | − | 10.0432i | 0.198228 | − | 0.610084i | −0.801695 | − | 0.597733i | \(-0.796068\pi\) |
0.999924 | − | 0.0123511i | \(-0.00393157\pi\) | |||||||
\(272\) | −4.68802 | − | 14.4282i | −0.284253 | − | 0.874841i | ||||
\(273\) | 14.1819 | − | 10.3038i | 0.858329 | − | 0.623612i | ||||
\(274\) | 20.6206 | 1.24574 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −19.5298 | −1.17556 | ||||||||
\(277\) | 15.0154 | − | 10.9093i | 0.902190 | − | 0.655479i | −0.0368377 | − | 0.999321i | \(-0.511728\pi\) |
0.939028 | + | 0.343842i | \(0.111728\pi\) | |||||||
\(278\) | 12.9480 | + | 39.8499i | 0.776571 | + | 2.39004i | ||||
\(279\) | −14.8944 | + | 45.8402i | −0.891703 | + | 2.74438i | ||||
\(280\) | 0.429373 | + | 0.311958i | 0.0256600 | + | 0.0186430i | ||||
\(281\) | −20.7581 | − | 15.0817i | −1.23833 | − | 0.899698i | −0.240842 | − | 0.970564i | \(-0.577423\pi\) |
−0.997486 | + | 0.0708669i | \(0.977423\pi\) | |||||||
\(282\) | −3.30301 | + | 10.1656i | −0.196691 | + | 0.605354i | ||||
\(283\) | 9.35677 | + | 28.7972i | 0.556202 | + | 1.71181i | 0.692748 | + | 0.721180i | \(0.256400\pi\) |
−0.136546 | + | 0.990634i | \(0.543600\pi\) | |||||||
\(284\) | −24.5706 | + | 17.8516i | −1.45799 | + | 1.05929i | ||||
\(285\) | 8.00000 | 0.473879 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.39025 | 0.141092 | ||||||||
\(288\) | −43.4313 | + | 31.5547i | −2.55922 | + | 1.85938i | ||||
\(289\) | 4.47125 | + | 13.7611i | 0.263015 | + | 0.809476i | ||||
\(290\) | −1.68102 | + | 5.17366i | −0.0987131 | + | 0.303808i | ||||
\(291\) | −22.2350 | − | 16.1547i | −1.30344 | − | 0.947003i | ||||
\(292\) | −4.86366 | − | 3.53366i | −0.284624 | − | 0.206792i | ||||
\(293\) | 0.942395 | − | 2.90039i | 0.0550553 | − | 0.169443i | −0.919748 | − | 0.392510i | \(-0.871607\pi\) |
0.974803 | + | 0.223067i | \(0.0716069\pi\) | |||||||
\(294\) | 2.05188 | + | 6.31504i | 0.119668 | + | 0.368300i | ||||
\(295\) | −1.22577 | + | 0.890576i | −0.0713672 | + | 0.0518513i | ||||
\(296\) | 0.257333 | 0.0149572 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −22.4390 | −1.29986 | ||||||||
\(299\) | −11.2773 | + | 8.19340i | −0.652180 | + | 0.473837i | ||||
\(300\) | 11.5727 | + | 35.6170i | 0.668147 | + | 2.05635i | ||||
\(301\) | 0.318373 | − | 0.979851i | 0.0183507 | − | 0.0564777i | ||||
\(302\) | 26.5927 | + | 19.3207i | 1.53024 | + | 1.11178i | ||||
\(303\) | −32.7396 | − | 23.7867i | −1.88084 | − | 1.36651i | ||||
\(304\) | 4.41249 | − | 13.5803i | 0.253074 | − | 0.778881i | ||||
\(305\) | −0.358133 | − | 1.10222i | −0.0205066 | − | 0.0631129i | ||||
\(306\) | 65.2377 | − | 47.3979i | 3.72939 | − | 2.70956i | ||||
\(307\) | 3.71904 | 0.212257 | 0.106128 | − | 0.994352i | \(-0.466155\pi\) | ||||
0.106128 | + | 0.994352i | \(0.466155\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −38.0294 | −2.16341 | ||||||||
\(310\) | −5.93867 | + | 4.31470i | −0.337294 | + | 0.245058i | ||||
\(311\) | 1.28855 | + | 3.96575i | 0.0730671 | + | 0.224877i | 0.980920 | − | 0.194411i | \(-0.0622796\pi\) |
−0.907853 | + | 0.419288i | \(0.862280\pi\) | |||||||
\(312\) | 5.92951 | − | 18.2492i | 0.335692 | − | 1.03316i | ||||
\(313\) | 9.46902 | + | 6.87965i | 0.535221 | + | 0.388861i | 0.822307 | − | 0.569044i | \(-0.192687\pi\) |
−0.287086 | + | 0.957905i | \(0.592687\pi\) | |||||||
\(314\) | 15.6530 | + | 11.3726i | 0.883349 | + | 0.641791i | ||||
\(315\) | 1.01359 | − | 3.11951i | 0.0571093 | − | 0.175764i | ||||
\(316\) | 7.01851 | + | 21.6008i | 0.394822 | + | 1.21514i | ||||
\(317\) | 1.80823 | − | 1.31375i | 0.101560 | − | 0.0737878i | −0.535846 | − | 0.844316i | \(-0.680007\pi\) |
0.637406 | + | 0.770528i | \(0.280007\pi\) | |||||||
\(318\) | −20.1211 | −1.12834 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −5.55345 | −0.310447 | ||||||||
\(321\) | 26.6968 | − | 19.3964i | 1.49007 | − | 1.08260i | ||||
\(322\) | −1.63162 | − | 5.02162i | −0.0909269 | − | 0.279844i | ||||
\(323\) | −9.15300 | + | 28.1700i | −0.509287 | + | 1.56742i | ||||
\(324\) | −33.5115 | − | 24.3475i | −1.86175 | − | 1.35264i | ||||
\(325\) | 21.6250 | + | 15.7115i | 1.19954 | + | 0.871515i | ||||
\(326\) | 8.72002 | − | 26.8375i | 0.482957 | − | 1.48639i | ||||
\(327\) | 7.08840 | + | 21.8158i | 0.391989 | + | 1.20642i | ||||
\(328\) | 2.11671 | − | 1.53788i | 0.116876 | − | 0.0849151i | ||||
\(329\) | −1.60975 | −0.0887482 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.3250 | 1.22709 | 0.613547 | − | 0.789659i | \(-0.289742\pi\) | ||||
0.613547 | + | 0.789659i | \(0.289742\pi\) | |||||||
\(332\) | 6.55099 | − | 4.75958i | 0.359532 | − | 0.261216i | ||||
\(333\) | −0.491451 | − | 1.51253i | −0.0269314 | − | 0.0828862i | ||||
\(334\) | −6.60602 | + | 20.3312i | −0.361465 | + | 1.11248i | ||||
\(335\) | −3.92837 | − | 2.85413i | −0.214630 | − | 0.155938i | ||||
\(336\) | −6.83684 | − | 4.96726i | −0.372980 | − | 0.270986i | ||||
\(337\) | −4.10376 | + | 12.6301i | −0.223546 | + | 0.688004i | 0.774890 | + | 0.632096i | \(0.217805\pi\) |
−0.998436 | + | 0.0559078i | \(0.982195\pi\) | |||||||
\(338\) | −12.1274 | − | 37.3243i | −0.659643 | − | 2.03017i | ||||
\(339\) | 34.7989 | − | 25.2829i | 1.89001 | − | 1.37318i | ||||
\(340\) | 6.84106 | 0.371008 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 75.8989 | 4.10414 | ||||||||
\(343\) | −0.809017 | + | 0.587785i | −0.0436828 | + | 0.0317374i | ||||
\(344\) | −0.348494 | − | 1.07255i | −0.0187895 | − | 0.0578282i | ||||
\(345\) | −1.16342 | + | 3.58064i | −0.0626365 | + | 0.192775i | ||||
\(346\) | −14.0445 | − | 10.2039i | −0.755038 | − | 0.548567i | ||||
\(347\) | 14.5861 | + | 10.5974i | 0.783021 | + | 0.568898i | 0.905884 | − | 0.423526i | \(-0.139208\pi\) |
−0.122863 | + | 0.992424i | \(0.539208\pi\) | |||||||
\(348\) | −12.8238 | + | 39.4675i | −0.687427 | + | 2.11568i | ||||
\(349\) | −6.78275 | − | 20.8751i | −0.363072 | − | 1.11742i | −0.951180 | − | 0.308638i | \(-0.900127\pi\) |
0.588107 | − | 0.808783i | \(-0.299873\pi\) | |||||||
\(350\) | −8.19120 | + | 5.95126i | −0.437838 | + | 0.318108i | ||||
\(351\) | −65.9982 | −3.52272 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.8557 | 1.00359 | 0.501795 | − | 0.864987i | \(-0.332673\pi\) | ||||
0.501795 | + | 0.864987i | \(0.332673\pi\) | |||||||
\(354\) | −16.7865 | + | 12.1961i | −0.892195 | + | 0.648218i | ||||
\(355\) | 1.80924 | + | 5.56827i | 0.0960244 | + | 0.295533i | ||||
\(356\) | −0.983469 | + | 3.02681i | −0.0521238 | + | 0.160420i | ||||
\(357\) | 14.1819 | + | 10.3038i | 0.750587 | + | 0.545333i | ||||
\(358\) | −21.0834 | − | 15.3180i | −1.11429 | − | 0.809582i | ||||
\(359\) | 0.472740 | − | 1.45494i | 0.0249502 | − | 0.0767890i | −0.937806 | − | 0.347160i | \(-0.887146\pi\) |
0.962756 | + | 0.270371i | \(0.0871462\pi\) | |||||||
\(360\) | −1.10949 | − | 3.41464i | −0.0584750 | − | 0.179968i | ||||
\(361\) | −7.18318 | + | 5.21888i | −0.378062 | + | 0.274678i | ||||
\(362\) | 14.9697 | 0.786791 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 14.1093 | 0.739528 | ||||||||
\(365\) | −0.937604 | + | 0.681209i | −0.0490764 | + | 0.0356561i | ||||
\(366\) | −4.90451 | − | 15.0945i | −0.256363 | − | 0.789004i | ||||
\(367\) | 4.52855 | − | 13.9375i | 0.236389 | − | 0.727529i | −0.760546 | − | 0.649284i | \(-0.775068\pi\) |
0.996934 | − | 0.0782446i | \(-0.0249315\pi\) | |||||||
\(368\) | 5.43656 | + | 3.94989i | 0.283400 | + | 0.205902i | ||||
\(369\) | −13.0817 | − | 9.50439i | −0.681005 | − | 0.494779i | ||||
\(370\) | 0.0748466 | − | 0.230354i | 0.00389109 | − | 0.0119755i | ||||
\(371\) | −0.936407 | − | 2.88196i | −0.0486158 | − | 0.149624i | ||||
\(372\) | −45.3035 | + | 32.9149i | −2.34888 | + | 1.70656i | ||||
\(373\) | 10.0606 | 0.520916 | 0.260458 | − | 0.965485i | \(-0.416127\pi\) | ||||
0.260458 | + | 0.965485i | \(0.416127\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.7952 | 0.764020 | ||||||||
\(376\) | −1.42552 | + | 1.03570i | −0.0735158 | + | 0.0534123i | ||||
\(377\) | 9.15300 | + | 28.1700i | 0.471403 | + | 1.45083i | ||||
\(378\) | 7.72514 | − | 23.7755i | 0.397338 | − | 1.22288i | ||||
\(379\) | 14.4762 | + | 10.5176i | 0.743593 | + | 0.540252i | 0.893834 | − | 0.448398i | \(-0.148005\pi\) |
−0.150241 | + | 0.988649i | \(0.548005\pi\) | |||||||
\(380\) | 5.20925 | + | 3.78474i | 0.267229 | + | 0.194153i | ||||
\(381\) | −2.47214 | + | 7.60845i | −0.126651 | + | 0.389793i | ||||
\(382\) | −12.3414 | − | 37.9829i | −0.631441 | − | 1.94338i | ||||
\(383\) | 15.3430 | − | 11.1474i | 0.783992 | − | 0.569604i | −0.122182 | − | 0.992508i | \(-0.538989\pi\) |
0.906174 | + | 0.422904i | \(0.138989\pi\) | |||||||
\(384\) | −26.4565 | −1.35010 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −35.0596 | −1.78449 | ||||||||
\(387\) | −5.63863 | + | 4.09670i | −0.286627 | + | 0.208247i | ||||
\(388\) | −6.83580 | − | 21.0384i | −0.347035 | − | 1.06806i | ||||
\(389\) | 10.5883 | − | 32.5874i | 0.536848 | − | 1.65225i | −0.202774 | − | 0.979226i | \(-0.564996\pi\) |
0.739622 | − | 0.673023i | \(-0.235004\pi\) | |||||||
\(390\) | −14.6113 | − | 10.6157i | −0.739872 | − | 0.537548i | ||||
\(391\) | −11.2773 | − | 8.19340i | −0.570315 | − | 0.414358i | ||||
\(392\) | −0.338253 | + | 1.04104i | −0.0170844 | + | 0.0525802i | ||||
\(393\) | 2.62650 | + | 8.08354i | 0.132490 | + | 0.407761i | ||||
\(394\) | 42.1164 | − | 30.5993i | 2.12179 | − | 1.54157i | ||||
\(395\) | 4.37844 | 0.220303 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.2791 | 0.817026 | 0.408513 | − | 0.912752i | \(-0.366047\pi\) | ||||
0.408513 | + | 0.912752i | \(0.366047\pi\) | |||||||
\(398\) | −26.4553 | + | 19.2209i | −1.32609 | + | 0.963457i | ||||
\(399\) | 5.09864 | + | 15.6920i | 0.255251 | + | 0.785582i | ||||
\(400\) | 3.98200 | − | 12.2553i | 0.199100 | − | 0.612766i | ||||
\(401\) | −23.4118 | − | 17.0096i | −1.16913 | − | 0.849421i | −0.178223 | − | 0.983990i | \(-0.557035\pi\) |
−0.990904 | + | 0.134569i | \(0.957035\pi\) | |||||||
\(402\) | −53.7978 | − | 39.0864i | −2.68319 | − | 1.94945i | ||||
\(403\) | −12.3510 | + | 38.0126i | −0.615249 | + | 1.89354i | ||||
\(404\) | −10.0653 | − | 30.9777i | −0.500766 | − | 1.54120i | ||||
\(405\) | −6.46026 | + | 4.69365i | −0.321013 | + | 0.233230i | ||||
\(406\) | −11.2195 | −0.556814 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 19.1883 | 0.949963 | ||||||||
\(409\) | −12.5482 | + | 9.11681i | −0.620469 | + | 0.450797i | −0.853085 | − | 0.521771i | \(-0.825271\pi\) |
0.232616 | + | 0.972569i | \(0.425271\pi\) | |||||||
\(410\) | −0.760991 | − | 2.34209i | −0.0375827 | − | 0.115668i | ||||
\(411\) | 9.37094 | − | 28.8408i | 0.462234 | − | 1.42261i | ||||
\(412\) | −24.7631 | − | 17.9914i | −1.21999 | − | 0.886374i | ||||
\(413\) | −2.52809 | − | 1.83676i | −0.124399 | − | 0.0903811i | ||||
\(414\) | −11.0378 | + | 33.9708i | −0.542478 | + | 1.66957i | ||||
\(415\) | −0.482379 | − | 1.48461i | −0.0236790 | − | 0.0728766i | ||||
\(416\) | −36.0151 | + | 26.1665i | −1.76578 | + | 1.28292i | ||||
\(417\) | 61.6197 | 3.01753 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.9503 | −0.632666 | −0.316333 | − | 0.948648i | \(-0.602452\pi\) | ||||
−0.316333 | + | 0.948648i | \(0.602452\pi\) | |||||||
\(420\) | 3.08299 | − | 2.23992i | 0.150434 | − | 0.109297i | ||||
\(421\) | −5.28136 | − | 16.2543i | −0.257398 | − | 0.792188i | −0.993348 | − | 0.115153i | \(-0.963264\pi\) |
0.735950 | − | 0.677036i | \(-0.236736\pi\) | |||||||
\(422\) | 9.48101 | − | 29.1796i | 0.461528 | − | 1.42044i | ||||
\(423\) | 8.81003 | + | 6.40086i | 0.428358 | + | 0.311220i | ||||
\(424\) | −2.68348 | − | 1.94967i | −0.130321 | − | 0.0946841i | ||||
\(425\) | −8.26000 | + | 25.4217i | −0.400669 | + | 1.23313i | ||||
\(426\) | 24.7769 | + | 76.2555i | 1.20045 | + | 3.69459i | ||||
\(427\) | 1.93375 | − | 1.40496i | 0.0935810 | − | 0.0679905i | ||||
\(428\) | 26.5601 | 1.28383 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.06147 | −0.0511886 | ||||||||
\(431\) | −15.6530 | + | 11.3726i | −0.753978 | + | 0.547797i | −0.897057 | − | 0.441914i | \(-0.854300\pi\) |
0.143079 | + | 0.989711i | \(0.454300\pi\) | |||||||
\(432\) | 9.83184 | + | 30.2593i | 0.473035 | + | 1.45585i | ||||
\(433\) | 4.89034 | − | 15.0509i | 0.235015 | − | 0.723300i | −0.762105 | − | 0.647454i | \(-0.775834\pi\) |
0.997119 | − | 0.0758469i | \(-0.0241660\pi\) | |||||||
\(434\) | −12.2482 | − | 8.89881i | −0.587931 | − | 0.427157i | ||||
\(435\) | 6.47214 | + | 4.70228i | 0.310315 | + | 0.225457i | ||||
\(436\) | −5.70526 | + | 17.5590i | −0.273233 | + | 0.840923i | ||||
\(437\) | −4.05436 | − | 12.4780i | −0.193946 | − | 0.596906i | ||||
\(438\) | −12.8402 | + | 9.32894i | −0.613527 | + | 0.445754i | ||||
\(439\) | −11.0596 | −0.527848 | −0.263924 | − | 0.964544i | \(-0.585017\pi\) | ||||
−0.263924 | + | 0.964544i | \(0.585017\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.76491 | 0.322139 | ||||||||
\(442\) | 54.0978 | − | 39.3044i | 2.57317 | − | 1.86952i | ||||
\(443\) | −10.7240 | − | 33.0049i | −0.509510 | − | 1.56811i | −0.793053 | − | 0.609152i | \(-0.791510\pi\) |
0.283543 | − | 0.958960i | \(-0.408490\pi\) | |||||||
\(444\) | 0.570972 | − | 1.75727i | 0.0270971 | − | 0.0833963i | ||||
\(445\) | 0.496355 | + | 0.360623i | 0.0235295 | + | 0.0170952i | ||||
\(446\) | 29.6600 | + | 21.5493i | 1.40444 | + | 1.02039i | ||||
\(447\) | −10.1973 | + | 31.3840i | −0.482315 | + | 1.48441i | ||||
\(448\) | −3.53938 | − | 10.8931i | −0.167220 | − | 0.514650i | ||||
\(449\) | 29.3623 | − | 21.3330i | 1.38569 | − | 1.00676i | 0.389371 | − | 0.921081i | \(-0.372693\pi\) |
0.996322 | − | 0.0856838i | \(-0.0273075\pi\) | |||||||
\(450\) | 68.4939 | 3.22883 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 34.6206 | 1.62842 | ||||||||
\(453\) | 39.1076 | − | 28.4134i | 1.83744 | − | 1.33498i | ||||
\(454\) | −7.03900 | − | 21.6638i | −0.330356 | − | 1.01673i | ||||
\(455\) | 0.840512 | − | 2.58683i | 0.0394038 | − | 0.121272i | ||||
\(456\) | 14.6113 | + | 10.6157i | 0.684237 | + | 0.497127i | ||||
\(457\) | 1.66702 | + | 1.21116i | 0.0779800 | + | 0.0566558i | 0.626092 | − | 0.779749i | \(-0.284653\pi\) |
−0.548112 | + | 0.836405i | \(0.684653\pi\) | |||||||
\(458\) | −3.58162 | + | 11.0231i | −0.167358 | + | 0.515075i | ||||
\(459\) | −20.3946 | − | 62.7680i | −0.951936 | − | 2.92976i | ||||
\(460\) | −2.45154 | + | 1.78115i | −0.114304 | + | 0.0830466i | ||||
\(461\) | −7.17076 | −0.333975 | −0.166988 | − | 0.985959i | \(-0.553404\pi\) | ||||
−0.166988 | + | 0.985959i | \(0.553404\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.45459 | 0.160548 | 0.0802741 | − | 0.996773i | \(-0.474420\pi\) | ||||
0.0802741 | + | 0.996773i | \(0.474420\pi\) | |||||||
\(464\) | 11.5521 | − | 8.39306i | 0.536291 | − | 0.389638i | ||||
\(465\) | 3.33590 | + | 10.2668i | 0.154698 | + | 0.476113i | ||||
\(466\) | −19.5540 | + | 60.1812i | −0.905824 | + | 2.78784i | ||||
\(467\) | 10.9183 | + | 7.93261i | 0.505239 | + | 0.367077i | 0.811014 | − | 0.585026i | \(-0.198916\pi\) |
−0.305776 | + | 0.952104i | \(0.598916\pi\) | |||||||
\(468\) | −77.2191 | − | 56.1030i | −3.56945 | − | 2.59336i | ||||
\(469\) | 3.09471 | − | 9.52453i | 0.142900 | − | 0.439802i | ||||
\(470\) | 0.512500 | + | 1.57731i | 0.0236399 | + | 0.0727560i | ||||
\(471\) | 23.0195 | − | 16.7246i | 1.06068 | − | 0.770631i | ||||
\(472\) | −3.42053 | −0.157443 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 59.9612 | 2.75411 | ||||||||
\(475\) | −20.3540 | + | 14.7881i | −0.933906 | + | 0.678523i | ||||
\(476\) | 4.36001 | + | 13.4187i | 0.199841 | + | 0.615047i | ||||
\(477\) | −6.33471 | + | 19.4962i | −0.290046 | + | 0.892671i | ||||
\(478\) | 4.40098 | + | 3.19750i | 0.201296 | + | 0.146250i | ||||
\(479\) | −28.3638 | − | 20.6075i | −1.29598 | − | 0.941582i | −0.296069 | − | 0.955166i | \(-0.595676\pi\) |
−0.999908 | + | 0.0135841i | \(0.995676\pi\) | |||||||
\(480\) | −3.71551 | + | 11.4352i | −0.169589 | + | 0.521941i | ||||
\(481\) | −0.407532 | − | 1.25426i | −0.0185819 | − | 0.0571891i | ||||
\(482\) | 47.0841 | − | 34.2086i | 2.14462 | − | 1.55816i | ||||
\(483\) | −7.76491 | −0.353316 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.26445 | −0.193639 | ||||||||
\(486\) | −27.7971 | + | 20.1957i | −1.26090 | + | 0.916098i | ||||
\(487\) | 9.16718 | + | 28.2137i | 0.415404 | + | 1.27848i | 0.911889 | + | 0.410437i | \(0.134624\pi\) |
−0.496484 | + | 0.868046i | \(0.665376\pi\) | |||||||
\(488\) | 0.808510 | − | 2.48834i | 0.0365995 | − | 0.112642i | ||||
\(489\) | −33.5731 | − | 24.3923i | −1.51823 | − | 1.10306i | ||||
\(490\) | 0.833511 | + | 0.605581i | 0.0376542 | + | 0.0273574i | ||||
\(491\) | 7.88915 | − | 24.2803i | 0.356032 | − | 1.09575i | −0.599376 | − | 0.800467i | \(-0.704585\pi\) |
0.955409 | − | 0.295287i | \(-0.0954153\pi\) | |||||||
\(492\) | −5.80527 | − | 17.8668i | −0.261722 | − | 0.805496i | ||||
\(493\) | −23.9629 | + | 17.4100i | −1.07923 | + | 0.784109i | ||||
\(494\) | 62.9385 | 2.83174 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 19.2682 | 0.865169 | ||||||||
\(497\) | −9.76907 | + | 7.09764i | −0.438203 | + | 0.318373i | ||||
\(498\) | −6.60602 | − | 20.3312i | −0.296023 | − | 0.911064i | ||||
\(499\) | −7.92891 | + | 24.4027i | −0.354947 | + | 1.09241i | 0.601094 | + | 0.799179i | \(0.294732\pi\) |
−0.956040 | + | 0.293235i | \(0.905268\pi\) | |||||||
\(500\) | 9.63398 | + | 6.99950i | 0.430845 | + | 0.313027i | ||||
\(501\) | 25.4339 | + | 18.4788i | 1.13630 | + | 0.825573i | ||||
\(502\) | −6.46437 | + | 19.8953i | −0.288519 | + | 0.887971i | ||||
\(503\) | 0.791113 | + | 2.43479i | 0.0352740 | + | 0.108562i | 0.967143 | − | 0.254232i | \(-0.0818228\pi\) |
−0.931869 | + | 0.362794i | \(0.881823\pi\) | |||||||
\(504\) | 5.99072 | − | 4.35251i | 0.266848 | − | 0.193876i | ||||
\(505\) | −6.27913 | −0.279418 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −57.7143 | −2.56318 | ||||||||
\(508\) | −5.20925 | + | 3.78474i | −0.231123 | + | 0.167921i | ||||
\(509\) | 4.15770 | + | 12.7961i | 0.184287 | + | 0.567176i | 0.999935 | − | 0.0113716i | \(-0.00361976\pi\) |
−0.815649 | + | 0.578547i | \(0.803620\pi\) | |||||||
\(510\) | 5.58102 | − | 17.1766i | 0.247132 | − | 0.760593i | ||||
\(511\) | −1.93375 | − | 1.40496i | −0.0855443 | − | 0.0621516i | ||||
\(512\) | 22.1519 | + | 16.0943i | 0.978987 | + | 0.711275i | ||||
\(513\) | 19.1959 | − | 59.0789i | 0.847520 | − | 2.60840i | ||||
\(514\) | 14.7738 | + | 45.4690i | 0.651643 | + | 2.00555i | ||||
\(515\) | −4.77376 | + | 3.46834i | −0.210357 | + | 0.152833i | ||||
\(516\) | −8.09747 | −0.356471 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0.499542 | 0.0219486 | ||||||||
\(519\) | −20.6541 | + | 15.0061i | −0.906612 | + | 0.658693i | ||||
\(520\) | −0.920032 | − | 2.83157i | −0.0403461 | − | 0.124172i | ||||
\(521\) | −9.96062 | + | 30.6556i | −0.436383 | + | 1.34305i | 0.455280 | + | 0.890348i | \(0.349539\pi\) |
−0.891663 | + | 0.452700i | \(0.850461\pi\) | |||||||
\(522\) | 61.4035 | + | 44.6122i | 2.68756 | + | 1.95262i | ||||
\(523\) | 26.1634 | + | 19.0088i | 1.14404 | + | 0.831196i | 0.987678 | − | 0.156503i | \(-0.0500221\pi\) |
0.156366 | + | 0.987699i | \(0.450022\pi\) | |||||||
\(524\) | −2.11400 | + | 6.50623i | −0.0923507 | + | 0.284226i | ||||
\(525\) | 4.60120 | + | 14.1610i | 0.200813 | + | 0.618038i | ||||
\(526\) | −27.5051 | + | 19.9836i | −1.19928 | + | 0.871327i | ||||
\(527\) | −39.9688 | −1.74107 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8255 | −0.731542 | ||||||||
\(530\) | −2.52577 | + | 1.83508i | −0.109712 | + | 0.0797107i | ||||
\(531\) | 6.53248 | + | 20.1049i | 0.283486 | + | 0.872479i | ||||
\(532\) | −4.10376 | + | 12.6301i | −0.177921 | + | 0.547583i | ||||
\(533\) | −10.8479 | − | 7.88144i | −0.469874 | − | 0.341383i | ||||
\(534\) | 6.79742 | + | 4.93861i | 0.294153 | + | 0.213715i | ||||
\(535\) | 1.58223 | − | 4.86959i | 0.0684056 | − | 0.210531i | ||||
\(536\) | −3.38749 | − | 10.4256i | −0.146317 | − | 0.450319i | ||||
\(537\) | −31.0056 | + | 22.5269i | −1.33799 | + | 0.972106i | ||||
\(538\) | −19.5904 | −0.844601 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −14.3472 | −0.617407 | ||||||||
\(541\) | 19.0123 | − | 13.8132i | 0.817401 | − | 0.593877i | −0.0985656 | − | 0.995131i | \(-0.531425\pi\) |
0.915967 | + | 0.401254i | \(0.131425\pi\) | |||||||
\(542\) | −6.93403 | − | 21.3407i | −0.297842 | − | 0.916664i | ||||
\(543\) | 6.80291 | − | 20.9372i | 0.291941 | − | 0.898501i | ||||
\(544\) | −36.0151 | − | 26.1665i | −1.54413 | − | 1.12188i | ||||
\(545\) | 2.87943 | + | 2.09203i | 0.123341 | + | 0.0896128i | ||||
\(546\) | 11.5105 | − | 35.4258i | 0.492605 | − | 1.51608i | ||||
\(547\) | −1.27349 | − | 3.91940i | −0.0544506 | − | 0.167582i | 0.920133 | − | 0.391606i | \(-0.128080\pi\) |
−0.974583 | + | 0.224025i | \(0.928080\pi\) | |||||||
\(548\) | 19.7463 | − | 14.3465i | 0.843521 | − | 0.612854i | ||||
\(549\) | −16.1698 | −0.690112 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.8789 | −1.18768 | ||||||||
\(552\) | −6.87627 | + | 4.99591i | −0.292674 | + | 0.212640i | ||||
\(553\) | 2.79051 | + | 8.58830i | 0.118665 | + | 0.365212i | ||||
\(554\) | 12.1870 | − | 37.5078i | 0.517777 | − | 1.59356i | ||||
\(555\) | −0.288168 | − | 0.209366i | −0.0122321 | − | 0.00888711i | ||||
\(556\) | 40.1241 | + | 29.1519i | 1.70164 | + | 1.23631i | ||||
\(557\) | −4.30753 | + | 13.2572i | −0.182516 | + | 0.561726i | −0.999897 | − | 0.0143718i | \(-0.995425\pi\) |
0.817381 | + | 0.576098i | \(0.195425\pi\) | |||||||
\(558\) | 31.6488 | + | 97.4051i | 1.33980 | + | 4.12349i | ||||
\(559\) | −4.67579 | + | 3.39716i | −0.197765 | + | 0.143684i | ||||
\(560\) | −1.31124 | −0.0554100 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −54.5213 | −2.29984 | ||||||||
\(563\) | −2.20049 | + | 1.59875i | −0.0927395 | + | 0.0673792i | −0.633189 | − | 0.773997i | \(-0.718254\pi\) |
0.540449 | + | 0.841377i | \(0.318254\pi\) | |||||||
\(564\) | 3.90963 | + | 12.0326i | 0.164625 | + | 0.506664i | ||||
\(565\) | 2.06240 | − | 6.34743i | 0.0867660 | − | 0.267038i | ||||
\(566\) | 52.0519 | + | 37.8179i | 2.18790 | + | 1.58961i | ||||
\(567\) | −13.3239 | − | 9.68039i | −0.559552 | − | 0.406538i | ||||
\(568\) | −4.08448 | + | 12.5707i | −0.171381 | + | 0.527457i | ||||
\(569\) | −8.56565 | − | 26.3624i | −0.359091 | − | 1.10517i | −0.953599 | − | 0.301079i | \(-0.902653\pi\) |
0.594508 | − | 0.804089i | \(-0.297347\pi\) | |||||||
\(570\) | 13.7525 | − | 9.99181i | 0.576031 | − | 0.418511i | ||||
\(571\) | 38.1193 | 1.59524 | 0.797621 | − | 0.603159i | \(-0.206092\pi\) | ||||
0.797621 | + | 0.603159i | \(0.206092\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −58.7328 | −2.45360 | ||||||||
\(574\) | 4.10901 | − | 2.98537i | 0.171507 | − | 0.124607i | ||||
\(575\) | −3.65880 | − | 11.2606i | −0.152583 | − | 0.469601i | ||||
\(576\) | −23.9436 | + | 73.6907i | −0.997649 | + | 3.07045i | ||||
\(577\) | −18.7731 | − | 13.6394i | −0.781534 | − | 0.567818i | 0.123905 | − | 0.992294i | \(-0.460458\pi\) |
−0.905439 | + | 0.424476i | \(0.860458\pi\) | |||||||
\(578\) | 24.8737 | + | 18.0718i | 1.03461 | + | 0.751687i | ||||
\(579\) | −15.9327 | + | 49.0357i | −0.662139 | + | 2.03785i | ||||
\(580\) | 1.98976 | + | 6.12384i | 0.0826202 | + | 0.254279i | ||||
\(581\) | 2.60463 | − | 1.89237i | 0.108058 | − | 0.0785088i | ||||
\(582\) | −58.4002 | −2.42077 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −2.61639 | −0.108267 | ||||||||
\(585\) | −14.8861 | + | 10.8154i | −0.615465 | + | 0.447161i | ||||
\(586\) | −2.00248 | − | 6.16300i | −0.0827217 | − | 0.254591i | ||||
\(587\) | −3.41453 | + | 10.5088i | −0.140933 | + | 0.433746i | −0.996466 | − | 0.0840022i | \(-0.973230\pi\) |
0.855533 | + | 0.517749i | \(0.173230\pi\) | |||||||
\(588\) | 6.35848 | + | 4.61971i | 0.262219 | + | 0.190514i | ||||
\(589\) | −30.4350 | − | 22.1123i | −1.25405 | − | 0.911122i | ||||
\(590\) | −0.994879 | + | 3.06192i | −0.0409585 | + | 0.126057i | ||||
\(591\) | −23.6578 | − | 72.8112i | −0.973152 | − | 2.99505i | ||||
\(592\) | −0.514349 | + | 0.373696i | −0.0211396 | + | 0.0153588i | ||||
\(593\) | −36.3884 | −1.49429 | −0.747147 | − | 0.664659i | \(-0.768577\pi\) | ||||
−0.747147 | + | 0.664659i | \(0.768577\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.71995 | 0.111507 | ||||||||
\(596\) | −21.4876 | + | 15.6116i | −0.880165 | + | 0.639477i | ||||
\(597\) | 14.8606 | + | 45.7362i | 0.608204 | + | 1.87186i | ||||
\(598\) | −9.15300 | + | 28.1700i | −0.374294 | + | 1.15196i | ||||
\(599\) | −23.9942 | − | 17.4328i | −0.980377 | − | 0.712286i | −0.0225843 | − | 0.999745i | \(-0.507189\pi\) |
−0.957793 | + | 0.287459i | \(0.907189\pi\) | |||||||
\(600\) | 13.1858 | + | 9.58002i | 0.538307 | + | 0.391103i | ||||
\(601\) | 0.429895 | − | 1.32308i | 0.0175358 | − | 0.0539696i | −0.941906 | − | 0.335877i | \(-0.890967\pi\) |
0.959442 | + | 0.281908i | \(0.0909672\pi\) | |||||||
\(602\) | −0.676506 | − | 2.08207i | −0.0275723 | − | 0.0848589i | ||||
\(603\) | −54.8096 | + | 39.8215i | −2.23202 | + | 1.62166i | ||||
\(604\) | 38.9073 | 1.58312 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −85.9906 | −3.49313 | ||||||||
\(607\) | −25.0298 | + | 18.1852i | −1.01593 | + | 0.738115i | −0.965444 | − | 0.260610i | \(-0.916076\pi\) |
−0.0504839 | + | 0.998725i | \(0.516076\pi\) | |||||||
\(608\) | −12.9480 | − | 39.8499i | −0.525112 | − | 1.61613i | ||||
\(609\) | −5.09864 | + | 15.6920i | −0.206607 | + | 0.635872i | ||||
\(610\) | −1.99230 | − | 1.44749i | −0.0806659 | − | 0.0586072i | ||||
\(611\) | 7.30565 | + | 5.30786i | 0.295555 | + | 0.214733i | ||||
\(612\) | 29.4951 | − | 90.7765i | 1.19227 | − | 3.66942i | ||||
\(613\) | 2.52154 | + | 7.76049i | 0.101844 | + | 0.313443i | 0.988977 | − | 0.148071i | \(-0.0473064\pi\) |
−0.887133 | + | 0.461514i | \(0.847306\pi\) | |||||||
\(614\) | 6.39328 | − | 4.64499i | 0.258012 | − | 0.187456i | ||||
\(615\) | −3.62156 | −0.146036 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.5298 | −1.10831 | −0.554154 | − | 0.832414i | \(-0.686958\pi\) | ||||
−0.554154 | + | 0.832414i | \(0.686958\pi\) | |||||||
\(618\) | −65.3751 | + | 47.4978i | −2.62977 | + | 1.91064i | ||||
\(619\) | 6.17215 | + | 18.9959i | 0.248080 | + | 0.763511i | 0.995115 | + | 0.0987261i | \(0.0314768\pi\) |
−0.747035 | + | 0.664785i | \(0.768523\pi\) | |||||||
\(620\) | −2.68497 | + | 8.26350i | −0.107831 | + | 0.331870i | ||||
\(621\) | 23.6509 | + | 17.1834i | 0.949080 | + | 0.689547i | ||||
\(622\) | 7.16824 | + | 5.20803i | 0.287420 | + | 0.208823i | ||||
\(623\) | −0.391020 | + | 1.20344i | −0.0156659 | + | 0.0482146i | ||||
\(624\) | 14.6495 | + | 45.0866i | 0.586451 | + | 1.80491i | ||||
\(625\) | −17.4172 | + | 12.6544i | −0.696690 | + | 0.506175i | ||||
\(626\) | 24.8704 | 0.994022 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22.9016 | 0.913874 | ||||||||
\(629\) | 1.06693 | − | 0.775172i | 0.0425414 | − | 0.0309081i | ||||
\(630\) | −2.15376 | − | 6.62860i | −0.0858080 | − | 0.264090i | ||||
\(631\) | −5.32565 | + | 16.3907i | −0.212011 | + | 0.652502i | 0.787341 | + | 0.616517i | \(0.211457\pi\) |
−0.999352 | + | 0.0359852i | \(0.988543\pi\) | |||||||
\(632\) | 7.99683 | + | 5.81004i | 0.318097 | + | 0.231111i | ||||
\(633\) | −36.5030 | − | 26.5210i | −1.45086 | − | 1.05411i | ||||
\(634\) | 1.46762 | − | 4.51686i | 0.0582866 | − | 0.179388i | ||||
\(635\) | 0.383580 | + | 1.18054i | 0.0152219 | + | 0.0468483i | ||||
\(636\) | −19.2680 | + | 13.9990i | −0.764024 | + | 0.555096i | ||||
\(637\) | 5.60975 | 0.222266 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 81.6878 | 3.23152 | ||||||||
\(640\) | −3.32104 | + | 2.41288i | −0.131276 | + | 0.0953774i | ||||
\(641\) | −13.7250 | − | 42.2411i | −0.542103 | − | 1.66842i | −0.727779 | − | 0.685812i | \(-0.759447\pi\) |
0.185675 | − | 0.982611i | \(-0.440553\pi\) | |||||||
\(642\) | 21.6680 | − | 66.6874i | 0.855170 | − | 2.63194i | ||||
\(643\) | 18.2301 | + | 13.2449i | 0.718924 | + | 0.522329i | 0.886040 | − | 0.463609i | \(-0.153446\pi\) |
−0.167117 | + | 0.985937i | \(0.553446\pi\) | |||||||
\(644\) | −5.05617 | − | 3.67352i | −0.199241 | − | 0.144757i | ||||
\(645\) | −0.482379 | + | 1.48461i | −0.0189936 | + | 0.0584564i | ||||
\(646\) | 19.4491 | + | 59.8581i | 0.765214 | + | 2.35509i | ||||
\(647\) | 15.1899 | − | 11.0361i | 0.597178 | − | 0.433876i | −0.247698 | − | 0.968837i | \(-0.579674\pi\) |
0.844876 | + | 0.534962i | \(0.179674\pi\) | |||||||
\(648\) | −18.0274 | −0.708184 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 56.7980 | 2.22780 | ||||||||
\(651\) | −18.0123 | + | 13.0867i | −0.705958 | + | 0.512909i | ||||
\(652\) | −10.3215 | − | 31.7664i | −0.404222 | − | 1.24407i | ||||
\(653\) | 9.76883 | − | 30.0654i | 0.382284 | − | 1.17655i | −0.556147 | − | 0.831084i | \(-0.687721\pi\) |
0.938431 | − | 0.345466i | \(-0.112279\pi\) | |||||||
\(654\) | 39.4329 | + | 28.6497i | 1.54195 | + | 1.12029i | ||||
\(655\) | 1.06693 | + | 0.775172i | 0.0416885 | + | 0.0302885i | ||||
\(656\) | −1.99752 | + | 6.14772i | −0.0779899 | + | 0.240028i | ||||
\(657\) | 4.99676 | + | 15.3784i | 0.194942 | + | 0.599970i | ||||
\(658\) | −2.76727 | + | 2.01054i | −0.107879 | + | 0.0783789i | ||||
\(659\) | 19.8477 | 0.773157 | 0.386578 | − | 0.922257i | \(-0.373657\pi\) | ||||
0.386578 | + | 0.922257i | \(0.373657\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.4234 | 1.22223 | 0.611114 | − | 0.791542i | \(-0.290722\pi\) | ||||
0.611114 | + | 0.791542i | \(0.290722\pi\) | |||||||
\(662\) | 38.3782 | − | 27.8834i | 1.49161 | − | 1.08372i | ||||
\(663\) | −30.3881 | − | 93.5249i | −1.18017 | − | 3.63220i | ||||
\(664\) | 1.08900 | − | 3.35161i | 0.0422615 | − | 0.130068i | ||||
\(665\) | 2.07116 | + | 1.50479i | 0.0803161 | + | 0.0583531i | ||||
\(666\) | −2.73395 | − | 1.98633i | −0.105939 | − | 0.0769689i | ||||
\(667\) | 4.05436 | − | 12.4780i | 0.156985 | − | 0.483152i | ||||
\(668\) | 7.81927 | + | 24.0652i | 0.302536 | + | 0.931112i | ||||
\(669\) | 43.6185 | − | 31.6907i | 1.68639 | − | 1.22523i | ||||
\(670\) | −10.3179 | −0.398615 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −24.7980 | −0.956606 | ||||||||
\(673\) | 15.5489 | − | 11.2969i | 0.599366 | − | 0.435465i | −0.246288 | − | 0.969197i | \(-0.579211\pi\) |
0.845654 | + | 0.533732i | \(0.179211\pi\) | |||||||
\(674\) | 8.72002 | + | 26.8375i | 0.335883 | + | 1.03374i | ||||
\(675\) | 17.3231 | − | 53.3150i | 0.666766 | − | 2.05210i | ||||
\(676\) | −37.5811 | − | 27.3042i | −1.44543 | − | 1.05016i | ||||
\(677\) | −20.8167 | − | 15.1242i | −0.800051 | − | 0.581271i | 0.110878 | − | 0.993834i | \(-0.464634\pi\) |
−0.910929 | + | 0.412563i | \(0.864634\pi\) | |||||||
\(678\) | 28.2439 | − | 86.9259i | 1.08470 | − | 3.33837i | ||||
\(679\) | −2.71786 | − | 8.36472i | −0.104302 | − | 0.321008i | ||||
\(680\) | 2.40867 | − | 1.75000i | 0.0923685 | − | 0.0671096i | ||||
\(681\) | −33.4986 | −1.28367 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.0596 | −0.423185 | −0.211593 | − | 0.977358i | \(-0.567865\pi\) | ||||
−0.211593 | + | 0.977358i | \(0.567865\pi\) | |||||||
\(684\) | 72.6807 | − | 52.8056i | 2.77902 | − | 2.01907i | ||||
\(685\) | −1.45401 | − | 4.47498i | −0.0555548 | − | 0.170980i | ||||
\(686\) | −0.656626 | + | 2.02089i | −0.0250701 | + | 0.0771578i | ||||
\(687\) | 13.7897 | + | 10.0188i | 0.526108 | + | 0.382240i | ||||
\(688\) | 2.25411 | + | 1.63771i | 0.0859372 | + | 0.0624370i | ||||
\(689\) | −5.25301 | + | 16.1671i | −0.200124 | + | 0.615917i | ||||
\(690\) | 2.47214 | + | 7.60845i | 0.0941126 | + | 0.289649i | ||||
\(691\) | −36.4265 | + | 26.4654i | −1.38573 | + | 1.00679i | −0.389409 | + | 0.921065i | \(0.627321\pi\) |
−0.996319 | + | 0.0857252i | \(0.972679\pi\) | |||||||
\(692\) | −20.5483 | −0.781128 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 38.3103 | 1.45424 | ||||||||
\(695\) | 7.73502 | − | 5.61982i | 0.293406 | − | 0.213172i | ||||
\(696\) | 5.58102 | + | 17.1766i | 0.211548 | + | 0.651078i | ||||
\(697\) | 4.14352 | − | 12.7524i | 0.156947 | − | 0.483033i | ||||
\(698\) | −37.7326 | − | 27.4143i | −1.42820 | − | 1.03765i | ||||
\(699\) | 75.2853 | + | 54.6980i | 2.84755 | + | 2.06887i | ||||
\(700\) | −3.70338 | + | 11.3978i | −0.139975 | + | 0.430798i | ||||
\(701\) | 14.4554 | + | 44.4892i | 0.545973 | + | 1.68033i | 0.718665 | + | 0.695357i | \(0.244754\pi\) |
−0.172692 | + | 0.984976i | \(0.555246\pi\) | |||||||
\(702\) | −113.455 | + | 82.4301i | −4.28210 | + | 3.11113i | ||||
\(703\) | 1.24129 | 0.0468162 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.43899 | 0.0918577 | ||||||||
\(706\) | 32.4143 | − | 23.5504i | 1.21993 | − | 0.886330i | ||||
\(707\) | −4.00188 | − | 12.3165i | −0.150506 | − | 0.463210i | ||||
\(708\) | −7.58949 | + | 23.3580i | −0.285230 | + | 0.877849i | ||||
\(709\) | 7.39786 | + | 5.37486i | 0.277833 | + | 0.201857i | 0.717972 | − | 0.696072i | \(-0.245071\pi\) |
−0.440139 | + | 0.897930i | \(0.645071\pi\) | |||||||
\(710\) | 10.0648 | + | 7.31253i | 0.377727 | + | 0.274434i | ||||
\(711\) | 18.8775 | − | 58.0991i | 0.707963 | − | 2.17889i | ||||
\(712\) | 0.428014 | + | 1.31729i | 0.0160405 | + | 0.0493676i | ||||
\(713\) | 14.3231 | − | 10.4064i | 0.536405 | − | 0.389721i | ||||
\(714\) | 37.2489 | 1.39400 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −30.8468 | −1.15280 | ||||||||
\(717\) | 6.47214 | − | 4.70228i | 0.241706 | − | 0.175610i | ||||
\(718\) | −1.00452 | − | 3.09159i | −0.0374883 | − | 0.115377i | ||||
\(719\) | −9.41435 | + | 28.9744i | −0.351096 | + | 1.08056i | 0.607143 | + | 0.794593i | \(0.292316\pi\) |
−0.958239 | + | 0.285970i | \(0.907684\pi\) | |||||||
\(720\) | 7.17632 | + | 5.21390i | 0.267446 | + | 0.194311i | ||||
\(721\) | −9.84561 | − | 7.15325i | −0.366670 | − | 0.266401i | ||||
\(722\) | −5.83011 | + | 17.9432i | −0.216974 | + | 0.667778i | ||||
\(723\) | −26.4483 | − | 81.3995i | −0.983623 | − | 3.02728i | ||||
\(724\) | 14.3350 | − | 10.4150i | 0.532756 | − | 0.387070i | ||||
\(725\) | −25.1589 | −0.934380 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.12580 | −0.227193 | −0.113597 | − | 0.993527i | \(-0.536237\pi\) | ||||
−0.113597 | + | 0.993527i | \(0.536237\pi\) | |||||||
\(728\) | 4.96775 | − | 3.60928i | 0.184117 | − | 0.133769i | ||||
\(729\) | 0.346440 | + | 1.06623i | 0.0128311 | + | 0.0394901i | ||||
\(730\) | −0.760991 | + | 2.34209i | −0.0281656 | + | 0.0866847i | ||||
\(731\) | −4.67579 | − | 3.39716i | −0.172940 | − | 0.125648i | ||||
\(732\) | −15.1984 | − | 11.0423i | −0.561748 | − | 0.408134i | ||||
\(733\) | −13.0005 | + | 40.0115i | −0.480185 | + | 1.47786i | 0.358651 | + | 0.933472i | \(0.383237\pi\) |
−0.838835 | + | 0.544385i | \(0.816763\pi\) | |||||||
\(734\) | −9.62265 | − | 29.6155i | −0.355179 | − | 1.09313i | ||||
\(735\) | 1.22577 | − | 0.890576i | 0.0452133 | − | 0.0328494i | ||||
\(736\) | 19.7190 | 0.726853 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −34.3591 | −1.26477 | ||||||||
\(739\) | 23.3628 | − | 16.9741i | 0.859414 | − | 0.624401i | −0.0683118 | − | 0.997664i | \(-0.521761\pi\) |
0.927725 | + | 0.373263i | \(0.121761\pi\) | |||||||
\(740\) | −0.0885928 | − | 0.272661i | −0.00325674 | − | 0.0100232i | ||||
\(741\) | 28.6021 | − | 88.0281i | 1.05072 | − | 3.23379i | ||||
\(742\) | −5.20925 | − | 3.78474i | −0.191238 | − | 0.138942i | ||||
\(743\) | 11.8773 | + | 8.62939i | 0.435737 | + | 0.316582i | 0.783939 | − | 0.620838i | \(-0.213208\pi\) |
−0.348202 | + | 0.937420i | \(0.613208\pi\) | |||||||
\(744\) | −7.53101 | + | 23.1781i | −0.276100 | + | 0.849750i | ||||
\(745\) | 1.58223 | + | 4.86959i | 0.0579682 | + | 0.178408i | ||||
\(746\) | 17.2948 | − | 12.5654i | 0.633207 | − | 0.460052i | ||||
\(747\) | −21.7796 | −0.796873 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.5601 | 0.385857 | ||||||||
\(750\) | 25.4339 | − | 18.4788i | 0.928716 | − | 0.674752i | ||||
\(751\) | −2.04136 | − | 6.28265i | −0.0744901 | − | 0.229257i | 0.906878 | − | 0.421393i | \(-0.138459\pi\) |
−0.981368 | + | 0.192136i | \(0.938459\pi\) | |||||||
\(752\) | 1.34525 | − | 4.14026i | 0.0490563 | − | 0.150980i | ||||
\(753\) | 24.8886 | + | 18.0826i | 0.906991 | + | 0.658967i | ||||
\(754\) | 50.9183 | + | 36.9943i | 1.85434 | + | 1.34725i | ||||
\(755\) | 2.31777 | − | 7.13336i | 0.0843523 | − | 0.259610i | ||||
\(756\) | −9.14393 | − | 28.1421i | −0.332561 | − | 1.02352i | ||||
\(757\) | −2.02217 | + | 1.46919i | −0.0734971 | + | 0.0533988i | −0.623927 | − | 0.781483i | \(-0.714464\pi\) |
0.550430 | + | 0.834881i | \(0.314464\pi\) | |||||||
\(758\) | 38.0218 | 1.38101 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.80230 | 0.101650 | ||||||||
\(761\) | 9.74763 | − | 7.08207i | 0.353351 | − | 0.256725i | −0.396922 | − | 0.917852i | \(-0.629922\pi\) |
0.750274 | + | 0.661127i | \(0.229922\pi\) | |||||||
\(762\) | 5.25301 | + | 16.1671i | 0.190296 | + | 0.585672i | ||||
\(763\) | −2.26837 | + | 6.98132i | −0.0821205 | + | 0.252741i | ||||
\(764\) | −38.2442 | − | 27.7861i | −1.38363 | − | 1.00526i | ||||
\(765\) | −14.8861 | − | 10.8154i | −0.538208 | − | 0.391031i | ||||
\(766\) | 12.4529 | − | 38.3262i | 0.449942 | − | 1.38478i | ||||
\(767\) | 5.41701 | + | 16.6718i | 0.195597 | + | 0.601986i | ||||
\(768\) | 12.4311 | − | 9.03173i | 0.448569 | − | 0.325905i | ||||
\(769\) | 0.489560 | 0.0176540 | 0.00882699 | − | 0.999961i | \(-0.497190\pi\) | ||||
0.00882699 | + | 0.999961i | \(0.497190\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 70.3085 | 2.53210 | ||||||||
\(772\) | −33.5731 | + | 24.3923i | −1.20832 | + | 0.877897i | ||||
\(773\) | −14.4367 | − | 44.4316i | −0.519252 | − | 1.59809i | −0.775410 | − | 0.631458i | \(-0.782457\pi\) |
0.256159 | − | 0.966635i | \(-0.417543\pi\) | |||||||
\(774\) | −4.57650 | + | 14.0850i | −0.164499 | + | 0.506276i | ||||
\(775\) | −27.4657 | − | 19.9550i | −0.986596 | − | 0.716804i | ||||
\(776\) | −7.78864 | − | 5.65878i | −0.279596 | − | 0.203138i | ||||
\(777\) | 0.227014 | − | 0.698677i | 0.00814408 | − | 0.0250649i | ||||
\(778\) | −22.4989 | − | 69.2446i | −0.806625 | − | 2.48254i | ||||
\(779\) | 10.2103 | − | 7.41823i | 0.365823 | − | 0.265786i | ||||
\(780\) | −21.3775 | −0.765438 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −29.6197 | −1.05920 | ||||||||
\(783\) | 50.2555 | − | 36.5128i | 1.79599 | − | 1.30486i | ||||
\(784\) | −0.835692 | − | 2.57200i | −0.0298461 | − | 0.0918570i | ||||
\(785\) | 1.36428 | − | 4.19883i | 0.0486934 | − | 0.149863i | ||||
\(786\) | 14.6113 | + | 10.6157i | 0.521168 | + | 0.378650i | ||||
\(787\) | 6.74694 | + | 4.90194i | 0.240503 | + | 0.174735i | 0.701507 | − | 0.712662i | \(-0.252511\pi\) |
−0.461005 | + | 0.887398i | \(0.652511\pi\) | |||||||
\(788\) | 19.0415 | − | 58.6038i | 0.678327 | − | 2.08768i | ||||
\(789\) | 15.4503 | + | 47.5511i | 0.550045 | + | 1.69286i | ||||
\(790\) | 7.52683 | − | 5.46856i | 0.267793 | − | 0.194563i | ||||
\(791\) | 13.7649 | 0.489424 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.4087 | −0.476157 | ||||||||
\(794\) | 27.9849 | − | 20.3322i | 0.993148 | − | 0.721564i | ||||
\(795\) | 1.41879 | + | 4.36657i | 0.0503191 | + | 0.154866i | ||||
\(796\) | −11.9609 | + | 36.8119i | −0.423943 | + | 1.30476i | ||||
\(797\) | 25.4963 | + | 18.5241i | 0.903125 | + | 0.656158i | 0.939267 | − | 0.343188i | \(-0.111507\pi\) |
−0.0361420 | + | 0.999347i | \(0.511507\pi\) | |||||||
\(798\) | 28.3638 | + | 20.6075i | 1.00407 | + | 0.729499i | ||||
\(799\) | −2.79051 | + | 8.58830i | −0.0987211 | + | 0.303832i | ||||
\(800\) | −11.6848 | − | 35.9620i | −0.413119 | − | 1.27145i | ||||
\(801\) | 6.92526 | − | 5.03150i | 0.244692 | − | 0.177779i | ||||
\(802\) | −61.4911 | −2.17132 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −78.7106 | −2.77591 | ||||||||
\(805\) | −0.974716 | + | 0.708172i | −0.0343542 | + | 0.0249598i | ||||
\(806\) | 26.2445 | + | 80.7724i | 0.924425 | + | 2.84509i | ||||
\(807\) | −8.90274 | + | 27.3998i | −0.313391 | + | 0.964519i | ||||
\(808\) | −11.4683 | − | 8.33219i | −0.403453 | − | 0.293125i | ||||
\(809\) | −12.5401 | − | 9.11094i | −0.440888 | − | 0.320324i | 0.345100 | − | 0.938566i | \(-0.387845\pi\) |
−0.785988 | + | 0.618242i | \(0.787845\pi\) | |||||||
\(810\) | −5.24337 | + | 16.1374i | −0.184233 | + | 0.567011i | ||||
\(811\) | −14.9378 | − | 45.9738i | −0.524537 | − | 1.61436i | −0.765231 | − | 0.643756i | \(-0.777375\pi\) |
0.240694 | − | 0.970601i | \(-0.422625\pi\) | |||||||
\(812\) | −10.7438 | + | 7.80582i | −0.377033 | + | 0.273930i | ||||
\(813\) | −32.9991 | −1.15733 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.43899 | −0.225548 | ||||||||
\(816\) | −38.3530 | + | 27.8651i | −1.34262 | + | 0.975472i | ||||
\(817\) | −1.68102 | − | 5.17366i | −0.0588116 | − | 0.181003i | ||||
\(818\) | −10.1846 | + | 31.3448i | −0.356095 | + | 1.09595i | ||||
\(819\) | −30.7017 | − | 22.3061i | −1.07281 | − | 0.779439i | ||||
\(820\) | −2.35820 | − | 1.71334i | −0.0823521 | − | 0.0598323i | ||||
\(821\) | −3.26325 | + | 10.0432i | −0.113888 | + | 0.350512i | −0.991714 | − | 0.128469i | \(-0.958994\pi\) |
0.877825 | + | 0.478981i | \(0.158994\pi\) | |||||||
\(822\) | −19.9122 | − | 61.2834i | −0.694517 | − | 2.13750i | ||||
\(823\) | −15.6335 | + | 11.3584i | −0.544950 | + | 0.395929i | −0.825920 | − | 0.563787i | \(-0.809344\pi\) |
0.280970 | + | 0.959717i | \(0.409344\pi\) | |||||||
\(824\) | −13.3212 | −0.464067 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.64002 | −0.231036 | ||||||||
\(827\) | 0.429373 | − | 0.311958i | 0.0149308 | − | 0.0108478i | −0.580295 | − | 0.814406i | \(-0.697063\pi\) |
0.595226 | + | 0.803559i | \(0.297063\pi\) | |||||||
\(828\) | 13.0650 | + | 40.2098i | 0.454039 | + | 1.39739i | ||||
\(829\) | −14.5842 | + | 44.8855i | −0.506530 | + | 1.55894i | 0.291654 | + | 0.956524i | \(0.405794\pi\) |
−0.798184 | + | 0.602414i | \(0.794206\pi\) | |||||||
\(830\) | −2.68348 | − | 1.94967i | −0.0931451 | − | 0.0676739i | ||||
\(831\) | −46.9215 | − | 34.0905i | −1.62769 | − | 1.18259i | ||||
\(832\) | −19.8550 | + | 61.1075i | −0.688349 | + | 2.11852i | ||||
\(833\) | 1.73351 | + | 5.33519i | 0.0600625 | + | 0.184853i | ||||
\(834\) | 105.929 | − | 76.9616i | 3.66801 | − | 2.66496i | ||||
\(835\) | 4.87798 | 0.168809 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 83.8236 | 2.89737 | ||||||||
\(838\) | −22.2625 | + | 16.1747i | −0.769046 | + | 0.558745i | ||||
\(839\) | −11.7128 | − | 36.0484i | −0.404372 | − | 1.24453i | −0.921418 | − | 0.388572i | \(-0.872968\pi\) |
0.517046 | − | 0.855958i | \(-0.327032\pi\) | |||||||
\(840\) | 0.512500 | − | 1.57731i | 0.0176829 | − | 0.0544224i | ||||
\(841\) | 0.906992 | + | 0.658969i | 0.0312756 | + | 0.0227231i | ||||
\(842\) | −29.3803 | − | 21.3460i | −1.01251 | − | 0.735633i | ||||
\(843\) | −24.7769 | + | 76.2555i | −0.853363 | + | 2.62638i | ||||
\(844\) | −11.2223 | − | 34.5386i | −0.386287 | − | 1.18887i | ||||
\(845\) | −7.24478 | + | 5.26364i | −0.249228 | + | 0.181075i | ||||
\(846\) | 23.1396 | 0.795555 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.19495 | 0.281416 | ||||||||
\(849\) | 76.5482 | − | 55.6155i | 2.62713 | − | 1.90872i | ||||
\(850\) | 17.5516 | + | 54.0182i | 0.602014 | + | 1.85281i | ||||
\(851\) | −0.180518 | + | 0.555578i | −0.00618808 | + | 0.0190450i | ||||
\(852\) | 76.7802 | + | 55.7841i | 2.63045 | + | 1.91113i | ||||
\(853\) | 5.07185 | + | 3.68491i | 0.173657 | + | 0.126169i | 0.671219 | − | 0.741260i | \(-0.265771\pi\) |
−0.497562 | + | 0.867429i | \(0.665771\pi\) | |||||||
\(854\) | 1.56950 | − | 4.83043i | 0.0537072 | − | 0.165294i | ||||
\(855\) | −5.35180 | − | 16.4712i | −0.183028 | − | 0.563302i | ||||
\(856\) | 9.35157 | − | 6.79431i | 0.319630 | − | 0.232225i | ||||
\(857\) | 36.9503 | 1.26220 | 0.631100 | − | 0.775702i | \(-0.282604\pi\) | ||||
0.631100 | + | 0.775702i | \(0.282604\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.90447 | 0.303817 | 0.151908 | − | 0.988395i | \(-0.451458\pi\) | ||||
0.151908 | + | 0.988395i | \(0.451458\pi\) | |||||||
\(860\) | −1.01646 | + | 0.738503i | −0.0346611 | + | 0.0251827i | ||||
\(861\) | −2.30813 | − | 7.10369i | −0.0786609 | − | 0.242093i | ||||
\(862\) | −12.7045 | + | 39.1004i | −0.432717 | + | 1.33177i | ||||
\(863\) | 34.0752 | + | 24.7571i | 1.15993 | + | 0.842741i | 0.989770 | − | 0.142675i | \(-0.0455703\pi\) |
0.170164 | + | 0.985416i | \(0.445570\pi\) | |||||||
\(864\) | 75.5318 | + | 54.8770i | 2.56964 | + | 1.86695i | ||||
\(865\) | −1.22409 | + | 3.76737i | −0.0416204 | + | 0.128094i | ||||
\(866\) | −10.3914 | − | 31.9815i | −0.353114 | − | 1.08677i | ||||
\(867\) | 36.5795 | − | 26.5766i | 1.24231 | − | 0.902588i | ||||
\(868\) | −17.9201 | −0.608247 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 16.9991 | 0.576323 | ||||||||
\(871\) | −45.4504 | + | 33.0217i | −1.54003 | + | 1.11890i | ||||
\(872\) | 2.48298 | + | 7.64182i | 0.0840843 | + | 0.258785i | ||||
\(873\) | −18.3861 | + | 56.5866i | −0.622275 | + | 1.91516i | ||||
\(874\) | −22.5545 | − | 16.3868i | −0.762917 | − | 0.554292i | ||||
\(875\) | 3.83040 | + | 2.78295i | 0.129491 | + | 0.0940808i | ||||
\(876\) | −5.80527 | + | 17.8668i | −0.196142 | + | 0.603662i | ||||
\(877\) | 7.52138 | + | 23.1484i | 0.253979 | + | 0.781666i | 0.994029 | + | 0.109115i | \(0.0348016\pi\) |
−0.740050 | + | 0.672551i | \(0.765198\pi\) | |||||||
\(878\) | −19.0123 | + | 13.8132i | −0.641633 | + | 0.466174i | ||||
\(879\) | −9.52982 | −0.321433 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.64380 | 0.190145 | 0.0950723 | − | 0.995470i | \(-0.469692\pi\) | ||||
0.0950723 | + | 0.995470i | \(0.469692\pi\) | |||||||
\(882\) | 11.6293 | − | 8.44921i | 0.391580 | − | 0.284500i | ||||
\(883\) | 4.69111 | + | 14.4377i | 0.157868 | + | 0.485869i | 0.998440 | − | 0.0558313i | \(-0.0177809\pi\) |
−0.840572 | + | 0.541700i | \(0.817781\pi\) | |||||||
\(884\) | 24.4586 | − | 75.2757i | 0.822630 | − | 2.53180i | ||||
\(885\) | 3.83040 | + | 2.78295i | 0.128757 | + | 0.0935478i | ||||
\(886\) | −59.6576 | − | 43.3438i | −2.00424 | − | 1.45616i | ||||
\(887\) | 8.28704 | − | 25.5049i | 0.278252 | − | 0.856370i | −0.710089 | − | 0.704112i | \(-0.751345\pi\) |
0.988341 | − | 0.152259i | \(-0.0486546\pi\) | |||||||
\(888\) | −0.248492 | − | 0.764779i | −0.00833883 | − | 0.0256643i | ||||
\(889\) | −2.07116 | + | 1.50479i | −0.0694645 | + | 0.0504689i | ||||
\(890\) | 1.30368 | 0.0436994 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 43.3951 | 1.45297 | ||||||||
\(893\) | −6.87627 | + | 4.99591i | −0.230106 | + | 0.167182i | ||||
\(894\) | 21.6680 | + | 66.6874i | 0.724688 | + | 2.23036i | ||||
\(895\) | −1.83759 | + | 5.65552i | −0.0614239 | + | 0.189043i | ||||
\(896\) | −6.84946 | − | 4.97643i | −0.228824 | − | 0.166251i | ||||
\(897\) | 35.2401 | + | 25.6034i | 1.17663 | + | 0.854874i | ||||
\(898\) | 23.8314 | − | 73.3457i | 0.795266 | − | 2.44758i | ||||
\(899\) | −11.6251 | − | 35.7785i | −0.387720 | − | 1.19328i | ||||
\(900\) | 65.5898 | − | 47.6537i | 2.18633 | − | 1.58846i | ||||
\(901\) | −16.9991 | −0.566322 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.21949 | −0.107138 | ||||||||
\(904\) | 12.1896 | − | 8.85628i | 0.405421 | − | 0.294555i | ||||
\(905\) | −1.05555 | − | 3.24865i | −0.0350877 | − | 0.107989i | ||||
\(906\) | 31.7411 | − | 97.6890i | 1.05453 | − | 3.24550i | ||||
\(907\) | −25.9674 | − | 18.8664i | −0.862233 | − | 0.626449i | 0.0662582 | − | 0.997803i | \(-0.478894\pi\) |
−0.928492 | + | 0.371353i | \(0.878894\pi\) | |||||||
\(908\) | −21.8128 | − | 15.8480i | −0.723885 | − | 0.525933i | ||||
\(909\) | −27.0723 | + | 83.3201i | −0.897933 | + | 2.76355i | ||||
\(910\) | −1.78599 | − | 5.49672i | −0.0592050 | − | 0.182214i | ||||
\(911\) | −9.83753 | + | 7.14739i | −0.325932 | + | 0.236803i | −0.738703 | − | 0.674032i | \(-0.764561\pi\) |
0.412771 | + | 0.910835i | \(0.364561\pi\) | |||||||
\(912\) | −44.6206 | −1.47754 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 4.37844 | 0.144826 | ||||||||
\(915\) | −2.92991 | + | 2.12870i | −0.0968597 | + | 0.0703727i | ||||
\(916\) | 4.23942 | + | 13.0476i | 0.140074 | + | 0.431104i | ||||
\(917\) | −0.840512 | + | 2.58683i | −0.0277561 | + | 0.0854246i | ||||
\(918\) | −113.455 | − | 82.4301i | −3.74458 | − | 2.72060i | ||||
\(919\) | 32.3607 | + | 23.5114i | 1.06748 | + | 0.775570i | 0.975458 | − | 0.220187i | \(-0.0706668\pi\) |
0.0920227 | + | 0.995757i | \(0.470667\pi\) | |||||||
\(920\) | −0.407532 | + | 1.25426i | −0.0134359 | + | 0.0413516i | ||||
\(921\) | −3.59126 | − | 11.0528i | −0.118336 | − | 0.364201i | ||||
\(922\) | −12.3270 | + | 8.95611i | −0.405969 | + | 0.294954i | ||||
\(923\) | 67.7390 | 2.22966 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.12019 | 0.0368315 | ||||||||
\(926\) | 5.93867 | − | 4.31470i | 0.195157 | − | 0.141790i | ||||
\(927\) | 25.4407 | + | 78.2985i | 0.835583 | + | 2.57166i | ||||
\(928\) | 12.9480 | − | 39.8499i | 0.425040 | − | 1.30814i | ||||
\(929\) | 17.2963 | + | 12.5665i | 0.567472 | + | 0.412292i | 0.834186 | − | 0.551483i | \(-0.185938\pi\) |
−0.266714 | + | 0.963776i | \(0.585938\pi\) | |||||||
\(930\) | 18.5577 | + | 13.4829i | 0.608530 | + | 0.442123i | ||||
\(931\) | −1.63162 | + | 5.02162i | −0.0534743 | + | 0.164577i | ||||
\(932\) | 23.1453 | + | 71.2339i | 0.758150 | + | 2.33334i | ||||
\(933\) | 10.5417 | − | 7.65900i | 0.345120 | − | 0.250745i | ||||
\(934\) | 28.6769 | 0.938338 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −41.5398 | −1.35777 | ||||||||
\(937\) | 25.4925 | − | 18.5214i | 0.832803 | − | 0.605067i | −0.0875479 | − | 0.996160i | \(-0.527903\pi\) |
0.920351 | + | 0.391093i | \(0.127903\pi\) | |||||||
\(938\) | −6.57590 | − | 20.2385i | −0.214711 | − | 0.660811i | ||||
\(939\) | 11.3022 | − | 34.7847i | 0.368834 | − | 1.13516i | ||||
\(940\) | 1.58816 | + | 1.15387i | 0.0518002 | + | 0.0376350i | ||||
\(941\) | −34.5692 | − | 25.1160i | −1.12693 | − | 0.818759i | −0.141681 | − | 0.989912i | \(-0.545251\pi\) |
−0.985244 | + | 0.171153i | \(0.945251\pi\) | |||||||
\(942\) | 18.6834 | − | 57.5016i | 0.608738 | − | 1.87350i | ||||
\(943\) | 1.83539 | + | 5.64875i | 0.0597685 | + | 0.183949i | ||||
\(944\) | 6.83684 | − | 4.96726i | 0.222520 | − | 0.161670i | ||||
\(945\) | −5.70436 | −0.185563 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.29473 | 0.107064 | 0.0535321 | − | 0.998566i | \(-0.482952\pi\) | ||||
0.0535321 | + | 0.998566i | \(0.482952\pi\) | |||||||
\(948\) | 57.4189 | − | 41.7172i | 1.86488 | − | 1.35491i | ||||
\(949\) | 4.14352 | + | 12.7524i | 0.134504 | + | 0.413962i | ||||
\(950\) | −16.5200 | + | 50.8434i | −0.535980 | + | 1.64958i | ||||
\(951\) | −5.65050 | − | 4.10533i | −0.183230 | − | 0.133124i | ||||
\(952\) | 4.96775 | + | 3.60928i | 0.161006 | + | 0.116978i | ||||
\(953\) | 11.9531 | − | 36.7880i | 0.387200 | − | 1.19168i | −0.547671 | − | 0.836694i | \(-0.684485\pi\) |
0.934871 | − | 0.354987i | \(-0.115515\pi\) | |||||||
\(954\) | 13.4605 | + | 41.4272i | 0.435801 | + | 1.34126i | ||||
\(955\) | −7.37263 | + | 5.35653i | −0.238573 | + | 0.173333i | ||||
\(956\) | 6.43899 | 0.208252 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −74.4977 | −2.40691 | ||||||||
\(959\) | 7.85099 | − | 5.70408i | 0.253522 | − | 0.184194i | ||||
\(960\) | 5.36265 | + | 16.5045i | 0.173079 | + | 0.532681i | ||||
\(961\) | 6.10741 | − | 18.7967i | 0.197013 | − | 0.606344i | ||||
\(962\) | −2.26711 | − | 1.64715i | −0.0730946 | − | 0.0531063i | ||||
\(963\) | −57.7946 | − | 41.9902i | −1.86241 | − | 1.35312i | ||||
\(964\) | 21.2876 | − | 65.5163i | 0.685626 | − | 2.11014i | ||||
\(965\) | 2.47214 | + | 7.60845i | 0.0795809 | + | 0.244925i | ||||
\(966\) | −13.3484 | + | 9.69819i | −0.429478 | + | 0.312034i | ||||
\(967\) | −3.34816 | −0.107670 | −0.0538348 | − | 0.998550i | \(-0.517144\pi\) | ||||
−0.0538348 | + | 0.998550i | \(0.517144\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 92.5583 | 2.97340 | ||||||||
\(970\) | −7.33088 | + | 5.32620i | −0.235380 | + | 0.171014i | ||||
\(971\) | 18.1434 | + | 55.8398i | 0.582251 | + | 1.79198i | 0.610041 | + | 0.792370i | \(0.291153\pi\) |
−0.0277898 | + | 0.999614i | \(0.508847\pi\) | |||||||
\(972\) | −12.5675 | + | 38.6789i | −0.403104 | + | 1.24063i | ||||
\(973\) | 15.9530 | + | 11.5906i | 0.511431 | + | 0.371576i | ||||
\(974\) | 50.9972 | + | 37.0516i | 1.63406 | + | 1.18721i | ||||
\(975\) | 25.8116 | − | 79.4398i | 0.826632 | − | 2.54411i | ||||
\(976\) | 1.99752 | + | 6.14772i | 0.0639389 | + | 0.196784i | ||||
\(977\) | −11.1360 | + | 8.09081i | −0.356274 | + | 0.258848i | −0.751496 | − | 0.659737i | \(-0.770667\pi\) |
0.395223 | + | 0.918585i | \(0.370667\pi\) | |||||||
\(978\) | −88.1798 | −2.81968 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.21949 | 0.0389553 | ||||||||
\(981\) | 40.1746 | − | 29.1885i | 1.28267 | − | 0.931918i | ||||
\(982\) | −16.7635 | − | 51.5929i | −0.534946 | − | 1.64639i | ||||
\(983\) | 15.5169 | − | 47.7562i | 0.494914 | − | 1.52319i | −0.322178 | − | 0.946679i | \(-0.604415\pi\) |
0.817091 | − | 0.576508i | \(-0.195585\pi\) | |||||||
\(984\) | −6.61446 | − | 4.80569i | −0.210861 | − | 0.153200i | ||||
\(985\) | −9.61023 | − | 6.98224i | −0.306207 | − | 0.222473i | ||||
\(986\) | −19.4491 | + | 59.8581i | −0.619385 | + | 1.90627i | ||||
\(987\) | 1.55444 | + | 4.78408i | 0.0494784 | + | 0.152279i | ||||
\(988\) | 60.2699 | − | 43.7887i | 1.91744 | − | 1.39310i | ||||
\(989\) | 2.56009 | 0.0814062 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.65940 | −0.148011 | −0.0740054 | − | 0.997258i | \(-0.523578\pi\) | ||||
−0.0740054 | + | 0.997258i | \(0.523578\pi\) | |||||||
\(992\) | 45.7424 | − | 33.2338i | 1.45232 | − | 1.05517i | ||||
\(993\) | −21.5580 | − | 66.3486i | −0.684122 | − | 2.10551i | ||||
\(994\) | −7.92891 | + | 24.4027i | −0.251490 | + | 0.774006i | ||||
\(995\) | 6.03664 | + | 4.38588i | 0.191375 | + | 0.139042i | ||||
\(996\) | −20.4711 | − | 14.8731i | −0.648652 | − | 0.471273i | ||||
\(997\) | 1.04736 | − | 3.22345i | 0.0331703 | − | 0.102088i | −0.933101 | − | 0.359615i | \(-0.882908\pi\) |
0.966271 | + | 0.257528i | \(0.0829079\pi\) | |||||||
\(998\) | 16.8480 | + | 51.8529i | 0.533315 | + | 1.64137i | ||||
\(999\) | −2.23760 | + | 1.62571i | −0.0707945 | + | 0.0514352i |
(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 | 847.2.f.t.729.3 | 12 | ||
11.2 | odd | 10 | 847.2.a.i.1.3 | ✓ | 3 | ||
11.3 | even | 5 | inner | 847.2.f.t.148.1 | 12 | ||
11.4 | even | 5 | inner | 847.2.f.t.323.3 | 12 | ||
11.5 | even | 5 | inner | 847.2.f.t.372.1 | 12 | ||
11.6 | odd | 10 | 847.2.f.u.372.3 | 12 | |||
11.7 | odd | 10 | 847.2.f.u.323.1 | 12 | |||
11.8 | odd | 10 | 847.2.f.u.148.3 | 12 | |||
11.9 | even | 5 | 847.2.a.j.1.1 | yes | 3 | ||
11.10 | odd | 2 | 847.2.f.u.729.1 | 12 | |||
33.2 | even | 10 | 7623.2.a.ce.1.1 | 3 | |||
33.20 | odd | 10 | 7623.2.a.bz.1.3 | 3 | |||
77.13 | even | 10 | 5929.2.a.t.1.3 | 3 | |||
77.20 | odd | 10 | 5929.2.a.y.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.i.1.3 | ✓ | 3 | 11.2 | odd | 10 | ||
847.2.a.j.1.1 | yes | 3 | 11.9 | even | 5 | ||
847.2.f.t.148.1 | 12 | 11.3 | even | 5 | inner | ||
847.2.f.t.323.3 | 12 | 11.4 | even | 5 | inner | ||
847.2.f.t.372.1 | 12 | 11.5 | even | 5 | inner | ||
847.2.f.t.729.3 | 12 | 1.1 | even | 1 | trivial | ||
847.2.f.u.148.3 | 12 | 11.8 | odd | 10 | |||
847.2.f.u.323.1 | 12 | 11.7 | odd | 10 | |||
847.2.f.u.372.3 | 12 | 11.6 | odd | 10 | |||
847.2.f.u.729.1 | 12 | 11.10 | odd | 2 | |||
5929.2.a.t.1.3 | 3 | 77.13 | even | 10 | |||
5929.2.a.y.1.1 | 3 | 77.20 | odd | 10 | |||
7623.2.a.bz.1.3 | 3 | 33.20 | odd | 10 | |||
7623.2.a.ce.1.1 | 3 | 33.2 | even | 10 |