Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,2,Mod(107,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([10, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.l (of order \(20\), degree \(8\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.98878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{20})\) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 257.10 | ||
Character | \(\chi\) | \(=\) | 750.257 |
Dual form | 750.2.l.b.143.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{17}{20}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.453990 | + | 0.891007i | 0.321020 | + | 0.630037i | ||||
\(3\) | 1.12805 | + | 1.31434i | 0.651283 | + | 0.758835i | ||||
\(4\) | −0.587785 | + | 0.809017i | −0.293893 | + | 0.404508i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.658960 | + | 1.60180i | −0.269019 | + | 0.653933i | ||||
\(7\) | 1.51403 | + | 1.51403i | 0.572249 | + | 0.572249i | 0.932756 | − | 0.360507i | \(-0.117396\pi\) |
−0.360507 | + | 0.932756i | \(0.617396\pi\) | |||||||
\(8\) | −0.987688 | − | 0.156434i | −0.349201 | − | 0.0553079i | ||||
\(9\) | −0.454984 | + | 2.96530i | −0.151661 | + | 0.988433i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.62798 | − | 1.82864i | −1.69690 | − | 0.551357i | −0.708833 | − | 0.705376i | \(-0.750778\pi\) |
−0.988068 | + | 0.154020i | \(0.950778\pi\) | |||||||
\(12\) | −1.72638 | + | 0.140065i | −0.498362 | + | 0.0404334i | ||||
\(13\) | −0.941310 | − | 0.479621i | −0.261072 | − | 0.133023i | 0.318556 | − | 0.947904i | \(-0.396802\pi\) |
−0.579628 | + | 0.814881i | \(0.696802\pi\) | |||||||
\(14\) | −0.661655 | + | 2.03636i | −0.176835 | + | 0.544241i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.309017 | − | 0.951057i | −0.0772542 | − | 0.237764i | ||||
\(17\) | −0.899945 | + | 5.68203i | −0.218269 | + | 1.37809i | 0.598497 | + | 0.801125i | \(0.295765\pi\) |
−0.816766 | + | 0.576969i | \(0.804235\pi\) | |||||||
\(18\) | −2.84866 | + | 0.940823i | −0.671435 | + | 0.221754i | ||||
\(19\) | 3.16950 | + | 4.36244i | 0.727133 | + | 1.00081i | 0.999257 | + | 0.0385508i | \(0.0122742\pi\) |
−0.272123 | + | 0.962262i | \(0.587726\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.282042 | + | 3.69786i | −0.0615467 | + | 0.806939i | ||||
\(22\) | −0.925718 | − | 5.84476i | −0.197364 | − | 1.24611i | ||||
\(23\) | −1.37932 | + | 0.702799i | −0.287608 | + | 0.146544i | −0.591843 | − | 0.806054i | \(-0.701599\pi\) |
0.304235 | + | 0.952597i | \(0.401599\pi\) | |||||||
\(24\) | −0.908558 | − | 1.47463i | −0.185459 | − | 0.301007i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 1.05646i | − | 0.207188i | ||||||
\(27\) | −4.41066 | + | 2.74701i | −0.848832 | + | 0.528663i | ||||
\(28\) | −2.11480 | + | 0.334951i | −0.399659 | + | 0.0632998i | ||||
\(29\) | 3.67723 | + | 2.67167i | 0.682845 | + | 0.496116i | 0.874300 | − | 0.485386i | \(-0.161321\pi\) |
−0.191455 | + | 0.981501i | \(0.561321\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.62475 | − | 6.26624i | 1.54905 | − | 1.12545i | 0.604726 | − | 0.796433i | \(-0.293282\pi\) |
0.944324 | − | 0.329017i | \(-0.106718\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | −3.94521 | − | 9.45990i | −0.686774 | − | 1.64676i | ||||
\(34\) | −5.47129 | + | 1.77773i | −0.938319 | + | 0.304878i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.13154 | − | 2.11105i | −0.355257 | − | 0.351841i | ||||
\(37\) | −0.100380 | + | 0.197006i | −0.0165023 | + | 0.0323876i | −0.899111 | − | 0.437722i | \(-0.855786\pi\) |
0.882608 | + | 0.470109i | \(0.155786\pi\) | |||||||
\(38\) | −2.44804 | + | 4.80455i | −0.397125 | + | 0.779402i | ||||
\(39\) | −0.431463 | − | 1.77824i | −0.0690894 | − | 0.284747i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.54235 | − | 0.501139i | 0.240874 | − | 0.0782648i | −0.186092 | − | 0.982532i | \(-0.559582\pi\) |
0.426966 | + | 0.904268i | \(0.359582\pi\) | |||||||
\(42\) | −3.42286 | + | 1.42749i | −0.528159 | + | 0.220267i | ||||
\(43\) | −1.33532 | + | 1.33532i | −0.203634 | + | 0.203634i | −0.801555 | − | 0.597921i | \(-0.795994\pi\) |
0.597921 | + | 0.801555i | \(0.295994\pi\) | |||||||
\(44\) | 4.78745 | − | 3.47829i | 0.721735 | − | 0.524371i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.25240 | − | 0.909919i | −0.184656 | − | 0.134160i | ||||
\(47\) | 4.75083 | − | 0.752458i | 0.692980 | − | 0.109757i | 0.199998 | − | 0.979796i | \(-0.435907\pi\) |
0.492983 | + | 0.870039i | \(0.335907\pi\) | |||||||
\(48\) | 0.901424 | − | 1.47900i | 0.130109 | − | 0.213475i | ||||
\(49\) | − | 2.41543i | − | 0.345062i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.48331 | + | 5.22681i | −1.18790 | + | 0.731899i | ||||
\(52\) | 0.941310 | − | 0.479621i | 0.130536 | − | 0.0665115i | ||||
\(53\) | −0.949805 | − | 5.99683i | −0.130466 | − | 0.823728i | −0.962950 | − | 0.269680i | \(-0.913082\pi\) |
0.832484 | − | 0.554049i | \(-0.186918\pi\) | |||||||
\(54\) | −4.45000 | − | 2.68281i | −0.605569 | − | 0.365084i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.25854 | − | 1.73224i | −0.168180 | − | 0.231480i | ||||
\(57\) | −2.15837 | + | 9.08688i | −0.285883 | + | 1.20359i | ||||
\(58\) | −0.711043 | + | 4.48935i | −0.0933645 | + | 0.589480i | ||||
\(59\) | 2.24119 | + | 6.89769i | 0.291779 | + | 0.898002i | 0.984285 | + | 0.176590i | \(0.0565066\pi\) |
−0.692506 | + | 0.721412i | \(0.743493\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.30934 | + | 4.02973i | −0.167644 | + | 0.515954i | −0.999221 | − | 0.0394543i | \(-0.987438\pi\) |
0.831578 | + | 0.555408i | \(0.187438\pi\) | |||||||
\(62\) | 9.49882 | + | 4.83989i | 1.20635 | + | 0.614667i | ||||
\(63\) | −5.17841 | + | 3.80069i | −0.652418 | + | 0.478842i | ||||
\(64\) | 0.951057 | + | 0.309017i | 0.118882 | + | 0.0386271i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.63774 | − | 7.80992i | 0.817050 | − | 0.961334i | ||||
\(67\) | 1.28043 | + | 0.202800i | 0.156429 | + | 0.0247759i | 0.234158 | − | 0.972199i | \(-0.424767\pi\) |
−0.0777287 | + | 0.996975i | \(0.524767\pi\) | |||||||
\(68\) | −4.06788 | − | 4.06788i | −0.493303 | − | 0.493303i | ||||
\(69\) | −2.47967 | − | 1.02010i | −0.298517 | − | 0.122806i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.39892 | − | 3.30183i | 0.284700 | − | 0.391856i | −0.642584 | − | 0.766215i | \(-0.722138\pi\) |
0.927283 | + | 0.374360i | \(0.122138\pi\) | |||||||
\(72\) | 0.913257 | − | 2.85761i | 0.107628 | − | 0.336773i | ||||
\(73\) | −0.141918 | − | 0.278530i | −0.0166102 | − | 0.0325994i | 0.882552 | − | 0.470214i | \(-0.155823\pi\) |
−0.899163 | + | 0.437615i | \(0.855823\pi\) | |||||||
\(74\) | −0.221105 | −0.0257030 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.39228 | −0.618537 | ||||||||
\(77\) | −5.75231 | − | 11.2895i | −0.655537 | − | 1.28656i | ||||
\(78\) | 1.38854 | − | 1.19174i | 0.157222 | − | 0.134938i | ||||
\(79\) | 0.555462 | − | 0.764528i | 0.0624944 | − | 0.0860162i | −0.776626 | − | 0.629962i | \(-0.783070\pi\) |
0.839120 | + | 0.543946i | \(0.183070\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.58598 | − | 2.69833i | −0.953998 | − | 0.299814i | ||||
\(82\) | 1.14673 | + | 1.14673i | 0.126635 | + | 0.126635i | ||||
\(83\) | 7.47149 | + | 1.18337i | 0.820102 | + | 0.129891i | 0.552367 | − | 0.833601i | \(-0.313725\pi\) |
0.267735 | + | 0.963493i | \(0.413725\pi\) | |||||||
\(84\) | −2.82585 | − | 2.40172i | −0.308325 | − | 0.262050i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.79600 | − | 0.583556i | −0.193668 | − | 0.0629264i | ||||
\(87\) | 0.636640 | + | 7.84692i | 0.0682550 | + | 0.841278i | ||||
\(88\) | 5.27263 | + | 2.68654i | 0.562064 | + | 0.286386i | ||||
\(89\) | 2.67429 | − | 8.23061i | 0.283474 | − | 0.872443i | −0.703378 | − | 0.710816i | \(-0.748326\pi\) |
0.986852 | − | 0.161627i | \(-0.0516741\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.699010 | − | 2.15133i | −0.0732762 | − | 0.225521i | ||||
\(92\) | 0.242168 | − | 1.52899i | 0.0252477 | − | 0.159408i | ||||
\(93\) | 17.9652 | + | 4.26719i | 1.86290 | + | 0.442487i | ||||
\(94\) | 2.82728 | + | 3.89142i | 0.291612 | + | 0.401369i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.72703 | + | 0.131724i | 0.176265 | + | 0.0134440i | ||||
\(97\) | −1.88725 | − | 11.9156i | −0.191621 | − | 1.20985i | −0.876577 | − | 0.481262i | \(-0.840179\pi\) |
0.684956 | − | 0.728584i | \(-0.259821\pi\) | |||||||
\(98\) | 2.15217 | − | 1.09658i | 0.217402 | − | 0.110772i | ||||
\(99\) | 7.98311 | − | 15.8566i | 0.802333 | − | 1.59365i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 0.310282i | − | 0.0308742i | −0.999881 | − | 0.0154371i | \(-0.995086\pi\) | ||
0.999881 | − | 0.0154371i | \(-0.00491398\pi\) | |||||||
\(102\) | −8.50846 | − | 5.18576i | −0.842463 | − | 0.513467i | ||||
\(103\) | 8.72553 | − | 1.38199i | 0.859752 | − | 0.136171i | 0.289035 | − | 0.957318i | \(-0.406665\pi\) |
0.570717 | + | 0.821147i | \(0.306665\pi\) | |||||||
\(104\) | 0.854692 | + | 0.620970i | 0.0838094 | + | 0.0608911i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.91201 | − | 3.56879i | 0.477097 | − | 0.346631i | ||||
\(107\) | −4.19190 | + | 4.19190i | −0.405246 | + | 0.405246i | −0.880077 | − | 0.474831i | \(-0.842509\pi\) |
0.474831 | + | 0.880077i | \(0.342509\pi\) | |||||||
\(108\) | 0.370140 | − | 5.18295i | 0.0356167 | − | 0.498730i | ||||
\(109\) | 1.79521 | − | 0.583300i | 0.171950 | − | 0.0558700i | −0.221777 | − | 0.975098i | \(-0.571186\pi\) |
0.393727 | + | 0.919227i | \(0.371186\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.372167 | + | 0.0903007i | −0.0353245 | + | 0.00857096i | ||||
\(112\) | 0.972066 | − | 1.90779i | 0.0918516 | − | 0.180269i | ||||
\(113\) | 3.85086 | − | 7.55774i | 0.362258 | − | 0.710972i | −0.635891 | − | 0.771779i | \(-0.719367\pi\) |
0.998150 | + | 0.0608066i | \(0.0193673\pi\) | |||||||
\(114\) | −9.07635 | + | 2.20224i | −0.850078 | + | 0.206258i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.32285 | + | 1.40458i | −0.401366 | + | 0.130412i | ||||
\(117\) | 1.85050 | − | 2.57304i | 0.171079 | − | 0.237878i | ||||
\(118\) | −5.12840 | + | 5.12840i | −0.472108 | + | 0.472108i | ||||
\(119\) | −9.96530 | + | 7.24021i | −0.913517 | + | 0.663709i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.4311 | + | 14.1175i | 1.76646 | + | 1.28341i | ||||
\(122\) | −4.18494 | + | 0.662830i | −0.378887 | + | 0.0600098i | ||||
\(123\) | 2.39852 | + | 1.46186i | 0.216267 | + | 0.131811i | ||||
\(124\) | 10.6608i | 0.957366i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.73738 | − | 2.88852i | −0.511127 | − | 0.257330i | ||||
\(127\) | −9.31862 | + | 4.74807i | −0.826894 | + | 0.421323i | −0.815602 | − | 0.578613i | \(-0.803594\pi\) |
−0.0112913 | + | 0.999936i | \(0.503594\pi\) | |||||||
\(128\) | 0.156434 | + | 0.987688i | 0.0138270 | + | 0.0873001i | ||||
\(129\) | −3.26138 | − | 0.248751i | −0.287148 | − | 0.0219013i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.4805 | + | 15.8015i | 1.00306 | + | 1.38059i | 0.923432 | + | 0.383762i | \(0.125372\pi\) |
0.0796236 | + | 0.996825i | \(0.474628\pi\) | |||||||
\(132\) | 9.97216 | + | 2.36864i | 0.867965 | + | 0.206164i | ||||
\(133\) | −1.80615 | + | 11.4036i | −0.156613 | + | 0.988816i | ||||
\(134\) | 0.400605 | + | 1.23294i | 0.0346070 | + | 0.106510i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.77773 | − | 5.47129i | 0.152439 | − | 0.469159i | ||||
\(137\) | −10.6831 | − | 5.44330i | −0.912717 | − | 0.465053i | −0.0664369 | − | 0.997791i | \(-0.521163\pi\) |
−0.846280 | + | 0.532738i | \(0.821163\pi\) | |||||||
\(138\) | −0.216828 | − | 2.67251i | −0.0184576 | − | 0.227500i | ||||
\(139\) | 22.1318 | + | 7.19107i | 1.87720 | + | 0.609939i | 0.988451 | + | 0.151540i | \(0.0484232\pi\) |
0.888747 | + | 0.458399i | \(0.151577\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.34819 | + | 5.39540i | 0.534614 | + | 0.454375i | ||||
\(142\) | 4.03104 | + | 0.638455i | 0.338278 | + | 0.0535779i | ||||
\(143\) | 4.42062 | + | 4.42062i | 0.369671 | + | 0.369671i | ||||
\(144\) | 2.96076 | − | 0.483612i | 0.246730 | − | 0.0403010i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.183742 | − | 0.252900i | 0.0152066 | − | 0.0209301i | ||||
\(147\) | 3.17470 | − | 2.72474i | 0.261845 | − | 0.224733i | ||||
\(148\) | −0.100380 | − | 0.197006i | −0.00825116 | − | 0.0161938i | ||||
\(149\) | −14.7140 | −1.20542 | −0.602711 | − | 0.797960i | \(-0.705913\pi\) | ||||
−0.602711 | + | 0.797960i | \(0.705913\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.54879 | −0.695691 | −0.347845 | − | 0.937552i | \(-0.613087\pi\) | ||||
−0.347845 | + | 0.937552i | \(0.613087\pi\) | |||||||
\(152\) | −2.44804 | − | 4.80455i | −0.198562 | − | 0.389701i | ||||
\(153\) | −16.4394 | − | 5.25384i | −1.32905 | − | 0.424748i | ||||
\(154\) | 7.44757 | − | 10.2507i | 0.600142 | − | 0.826025i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.69224 | + | 0.696163i | 0.135487 | + | 0.0557377i | ||||
\(157\) | 17.5864 | + | 17.5864i | 1.40355 | + | 1.40355i | 0.788446 | + | 0.615104i | \(0.210886\pi\) |
0.615104 | + | 0.788446i | \(0.289114\pi\) | |||||||
\(158\) | 0.933375 | + | 0.147832i | 0.0742553 | + | 0.0117609i | ||||
\(159\) | 6.81045 | − | 8.01312i | 0.540104 | − | 0.635482i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.15239 | − | 1.02427i | −0.248443 | − | 0.0807240i | ||||
\(162\) | −1.49373 | − | 8.87518i | −0.117358 | − | 0.697300i | ||||
\(163\) | −1.79029 | − | 0.912200i | −0.140227 | − | 0.0714490i | 0.382469 | − | 0.923968i | \(-0.375074\pi\) |
−0.522696 | + | 0.852519i | \(0.675074\pi\) | |||||||
\(164\) | −0.501139 | + | 1.54235i | −0.0391324 | + | 0.120437i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.33760 | + | 7.19438i | 0.181433 | + | 0.558392i | ||||
\(167\) | 2.32146 | − | 14.6571i | 0.179640 | − | 1.13420i | −0.718837 | − | 0.695179i | \(-0.755325\pi\) |
0.898477 | − | 0.439021i | \(-0.144675\pi\) | |||||||
\(168\) | 0.857043 | − | 3.60821i | 0.0661223 | − | 0.278379i | ||||
\(169\) | −6.98518 | − | 9.61428i | −0.537322 | − | 0.739560i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.3780 | + | 7.41367i | −1.09951 | + | 0.566937i | ||||
\(172\) | −0.295415 | − | 1.86518i | −0.0225252 | − | 0.142218i | ||||
\(173\) | 4.46800 | − | 2.27656i | 0.339696 | − | 0.173084i | −0.275818 | − | 0.961210i | \(-0.588949\pi\) |
0.615514 | + | 0.788126i | \(0.288949\pi\) | |||||||
\(174\) | −6.70263 | + | 4.12968i | −0.508125 | + | 0.313070i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.91761i | 0.446057i | ||||||||
\(177\) | −6.53772 | + | 10.7267i | −0.491405 | + | 0.806265i | ||||
\(178\) | 8.54762 | − | 1.35381i | 0.640672 | − | 0.101472i | ||||
\(179\) | −2.56353 | − | 1.86252i | −0.191607 | − | 0.139211i | 0.487846 | − | 0.872930i | \(-0.337783\pi\) |
−0.679453 | + | 0.733719i | \(0.737783\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.04884 | + | 3.66820i | −0.375278 | + | 0.272655i | −0.759396 | − | 0.650629i | \(-0.774505\pi\) |
0.384118 | + | 0.923284i | \(0.374505\pi\) | |||||||
\(182\) | 1.59951 | − | 1.59951i | 0.118563 | − | 0.118563i | ||||
\(183\) | −6.77345 | + | 2.82484i | −0.500707 | + | 0.208818i | ||||
\(184\) | 1.47228 | − | 0.478373i | 0.108538 | − | 0.0352661i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.35392 | + | 17.9443i | 0.319245 | + | 1.31574i | ||||
\(187\) | 15.4553 | − | 30.3327i | 1.13020 | − | 2.21815i | ||||
\(188\) | −2.18372 | + | 4.28579i | −0.159264 | + | 0.312573i | ||||
\(189\) | −10.8369 | − | 2.51881i | −0.788270 | − | 0.183216i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.9806 | − | 6.49209i | 1.44574 | − | 0.469751i | 0.522062 | − | 0.852908i | \(-0.325163\pi\) |
0.923683 | + | 0.383157i | \(0.125163\pi\) | |||||||
\(192\) | 0.666690 | + | 1.59860i | 0.0481142 | + | 0.115369i | ||||
\(193\) | −7.00922 | + | 7.00922i | −0.504535 | + | 0.504535i | −0.912844 | − | 0.408309i | \(-0.866119\pi\) |
0.408309 | + | 0.912844i | \(0.366119\pi\) | |||||||
\(194\) | 9.76009 | − | 7.09112i | 0.700734 | − | 0.509113i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.95413 | + | 1.41976i | 0.139580 | + | 0.101411i | ||||
\(197\) | 10.0821 | − | 1.59685i | 0.718320 | − | 0.113771i | 0.213435 | − | 0.976957i | \(-0.431535\pi\) |
0.504885 | + | 0.863186i | \(0.331535\pi\) | |||||||
\(198\) | 17.7526 | − | 0.0857583i | 1.26162 | − | 0.00609458i | ||||
\(199\) | 15.1147i | 1.07146i | 0.844391 | + | 0.535728i | \(0.179963\pi\) | ||||
−0.844391 | + | 0.535728i | \(0.820037\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.17784 | + | 1.91169i | 0.0830786 | + | 0.134840i | ||||
\(202\) | 0.276463 | − | 0.140865i | 0.0194519 | − | 0.00991123i | ||||
\(203\) | 1.52246 | + | 9.61241i | 0.106856 | + | 0.674659i | ||||
\(204\) | 0.757790 | − | 9.93538i | 0.0530559 | − | 0.695616i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.19267 | + | 7.14709i | 0.361790 | + | 0.497962i | ||||
\(207\) | −1.45644 | − | 4.40986i | −0.101229 | − | 0.306506i | ||||
\(208\) | −0.165266 | + | 1.04345i | −0.0114592 | + | 0.0723503i | ||||
\(209\) | −9.86055 | − | 30.3476i | −0.682068 | − | 2.09919i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.22728 | + | 3.77719i | −0.0844897 | + | 0.260033i | −0.984372 | − | 0.176099i | \(-0.943652\pi\) |
0.899883 | + | 0.436132i | \(0.143652\pi\) | |||||||
\(212\) | 5.40982 | + | 2.75644i | 0.371548 | + | 0.189313i | ||||
\(213\) | 7.04585 | − | 0.571647i | 0.482774 | − | 0.0391686i | ||||
\(214\) | −5.63809 | − | 1.83193i | −0.385412 | − | 0.125228i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.78608 | − | 2.02321i | 0.325652 | − | 0.137662i | ||||
\(217\) | 22.5454 | + | 3.57084i | 1.53048 | + | 0.242404i | ||||
\(218\) | 1.33473 | + | 1.33473i | 0.0903996 | + | 0.0903996i | ||||
\(219\) | 0.205992 | − | 0.500725i | 0.0139196 | − | 0.0338359i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.57235 | − | 4.91692i | 0.240302 | − | 0.330748i | ||||
\(222\) | −0.249419 | − | 0.290608i | −0.0167399 | − | 0.0195043i | ||||
\(223\) | 6.07755 | + | 11.9279i | 0.406983 | + | 0.798748i | 0.999979 | − | 0.00645660i | \(-0.00205521\pi\) |
−0.592996 | + | 0.805205i | \(0.702055\pi\) | |||||||
\(224\) | 2.14116 | 0.143062 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.48225 | 0.564231 | ||||||||
\(227\) | 0.388579 | + | 0.762629i | 0.0257909 | + | 0.0506175i | 0.903542 | − | 0.428499i | \(-0.140957\pi\) |
−0.877752 | + | 0.479116i | \(0.840957\pi\) | |||||||
\(228\) | −6.08278 | − | 7.08729i | −0.402842 | − | 0.469367i | ||||
\(229\) | −9.72545 | + | 13.3859i | −0.642676 | + | 0.884567i | −0.998755 | − | 0.0498887i | \(-0.984113\pi\) |
0.356079 | + | 0.934456i | \(0.384113\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.34939 | − | 20.2957i | 0.549350 | − | 1.33536i | ||||
\(232\) | −3.21402 | − | 3.21402i | −0.211011 | − | 0.211011i | ||||
\(233\) | −5.38346 | − | 0.852656i | −0.352682 | − | 0.0558593i | −0.0224200 | − | 0.999749i | \(-0.507137\pi\) |
−0.330262 | + | 0.943889i | \(0.607137\pi\) | |||||||
\(234\) | 3.13271 | + | 0.480671i | 0.204792 | + | 0.0314225i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.89769 | − | 2.24119i | −0.449001 | − | 0.145889i | ||||
\(237\) | 1.63144 | − | 0.132363i | 0.105974 | − | 0.00859790i | ||||
\(238\) | −10.9752 | − | 5.59216i | −0.711418 | − | 0.362486i | ||||
\(239\) | 2.69306 | − | 8.28837i | 0.174199 | − | 0.536130i | −0.825397 | − | 0.564553i | \(-0.809049\pi\) |
0.999596 | + | 0.0284230i | \(0.00904853\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.85699 | − | 24.1813i | −0.506113 | − | 1.55766i | −0.798892 | − | 0.601475i | \(-0.794580\pi\) |
0.292779 | − | 0.956180i | \(-0.405420\pi\) | |||||||
\(242\) | −3.75726 | + | 23.7224i | −0.241526 | + | 1.52494i | ||||
\(243\) | −6.13893 | − | 14.3288i | −0.393813 | − | 0.919191i | ||||
\(244\) | −2.49051 | − | 3.42789i | −0.159439 | − | 0.219448i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.213620 | + | 2.80077i | −0.0136199 | + | 0.178570i | ||||
\(247\) | −0.891162 | − | 5.62657i | −0.0567033 | − | 0.358010i | ||||
\(248\) | −9.49882 | + | 4.83989i | −0.603176 | + | 0.307333i | ||||
\(249\) | 6.87290 | + | 11.1550i | 0.435552 | + | 0.706918i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 21.0935i | − | 1.33141i | −0.746215 | − | 0.665706i | \(-0.768131\pi\) | ||
0.746215 | − | 0.665706i | \(-0.231869\pi\) | |||||||
\(252\) | −0.0310298 | − | 6.42341i | −0.00195469 | − | 0.404637i | ||||
\(253\) | 9.04796 | − | 1.43306i | 0.568840 | − | 0.0900954i | ||||
\(254\) | −8.46113 | − | 6.14737i | −0.530898 | − | 0.385720i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | + | 0.587785i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | −11.8588 | + | 11.8588i | −0.739734 | + | 0.739734i | −0.972526 | − | 0.232792i | \(-0.925214\pi\) |
0.232792 | + | 0.972526i | \(0.425214\pi\) | |||||||
\(258\) | −1.25900 | − | 3.01884i | −0.0783816 | − | 0.187945i | ||||
\(259\) | −0.450251 | + | 0.146295i | −0.0279772 | + | 0.00909035i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.59537 | + | 9.68852i | −0.593938 | + | 0.599704i | ||||
\(262\) | −8.86724 | + | 17.4029i | −0.547820 | + | 1.07516i | ||||
\(263\) | 10.3291 | − | 20.2720i | 0.636919 | − | 1.25002i | −0.316562 | − | 0.948572i | \(-0.602529\pi\) |
0.953481 | − | 0.301453i | \(-0.0974715\pi\) | |||||||
\(264\) | 2.41679 | + | 9.96060i | 0.148743 | + | 0.613033i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −10.9806 | + | 3.56783i | −0.673266 | + | 0.218757i | ||||
\(267\) | 13.8346 | − | 5.76965i | 0.846662 | − | 0.353097i | ||||
\(268\) | −0.916684 | + | 0.916684i | −0.0559954 | + | 0.0559954i | ||||
\(269\) | −8.37684 | + | 6.08613i | −0.510745 | + | 0.371078i | −0.813106 | − | 0.582115i | \(-0.802225\pi\) |
0.302361 | + | 0.953193i | \(0.402225\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.517312 | − | 0.375849i | −0.0314245 | − | 0.0228312i | 0.571962 | − | 0.820280i | \(-0.306182\pi\) |
−0.603387 | + | 0.797449i | \(0.706182\pi\) | |||||||
\(272\) | 5.68203 | − | 0.899945i | 0.344524 | − | 0.0545672i | ||||
\(273\) | 2.03906 | − | 3.34556i | 0.123410 | − | 0.202482i | ||||
\(274\) | − | 11.9899i | − | 0.724336i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.28279 | − | 1.40649i | 0.137408 | − | 0.0846608i | ||||
\(277\) | −27.0524 | + | 13.7839i | −1.62542 | + | 0.828193i | −0.626616 | + | 0.779328i | \(0.715560\pi\) |
−0.998805 | + | 0.0488650i | \(0.984440\pi\) | |||||||
\(278\) | 3.64035 | + | 22.9843i | 0.218334 | + | 1.37851i | ||||
\(279\) | 14.6572 | + | 28.4260i | 0.877501 | + | 1.70182i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.7646 | + | 17.5690i | 0.761473 | + | 1.04808i | 0.997090 | + | 0.0762322i | \(0.0242890\pi\) |
−0.235617 | + | 0.971846i | \(0.575711\pi\) | |||||||
\(282\) | −1.92532 | + | 8.10574i | −0.114651 | + | 0.482690i | ||||
\(283\) | −0.541258 | + | 3.41737i | −0.0321745 | + | 0.203142i | −0.998539 | − | 0.0540343i | \(-0.982792\pi\) |
0.966365 | + | 0.257176i | \(0.0827920\pi\) | |||||||
\(284\) | 1.26119 | + | 3.88154i | 0.0748378 | + | 0.230327i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.93188 | + | 5.94572i | −0.114235 | + | 0.351578i | ||||
\(287\) | 3.09390 | + | 1.57642i | 0.182627 | + | 0.0930531i | ||||
\(288\) | 1.77506 | + | 2.41850i | 0.104596 | + | 0.142512i | ||||
\(289\) | −15.3076 | − | 4.97374i | −0.900446 | − | 0.292573i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.5323 | − | 15.9219i | 0.793275 | − | 0.933361i | ||||
\(292\) | 0.308752 | + | 0.0489016i | 0.0180684 | + | 0.00286175i | ||||
\(293\) | −12.2527 | − | 12.2527i | −0.715808 | − | 0.715808i | 0.251936 | − | 0.967744i | \(-0.418933\pi\) |
−0.967744 | + | 0.251936i | \(0.918933\pi\) | |||||||
\(294\) | 3.86905 | + | 1.59167i | 0.225647 | + | 0.0928283i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.129962 | − | 0.178878i | 0.00755391 | − | 0.0103971i | ||||
\(297\) | 29.8464 | − | 7.39463i | 1.73187 | − | 0.429080i | ||||
\(298\) | −6.68004 | − | 13.1103i | −0.386964 | − | 0.759460i | ||||
\(299\) | 1.63544 | 0.0945802 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.04342 | −0.233059 | ||||||||
\(302\) | −3.88107 | − | 7.61703i | −0.223330 | − | 0.438311i | ||||
\(303\) | 0.407816 | − | 0.350015i | 0.0234284 | − | 0.0201078i | ||||
\(304\) | 3.16950 | − | 4.36244i | 0.181783 | − | 0.250203i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.78215 | − | 17.0328i | −0.159045 | − | 0.973703i | ||||
\(307\) | −16.8133 | − | 16.8133i | −0.959588 | − | 0.959588i | 0.0396263 | − | 0.999215i | \(-0.487383\pi\) |
−0.999215 | + | 0.0396263i | \(0.987383\pi\) | |||||||
\(308\) | 12.5146 | + | 1.98211i | 0.713083 | + | 0.112941i | ||||
\(309\) | 11.6593 | + | 9.90936i | 0.663273 | + | 0.563724i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.39905 | + | 2.40410i | 0.419562 | + | 0.136324i | 0.511187 | − | 0.859470i | \(-0.329206\pi\) |
−0.0916250 | + | 0.995794i | \(0.529206\pi\) | |||||||
\(312\) | 0.147973 | + | 1.82384i | 0.00837732 | + | 0.103255i | ||||
\(313\) | −18.5326 | − | 9.44284i | −1.04753 | − | 0.533741i | −0.156492 | − | 0.987679i | \(-0.550019\pi\) |
−0.891033 | + | 0.453939i | \(0.850019\pi\) | |||||||
\(314\) | −7.68555 | + | 23.6537i | −0.433721 | + | 1.33486i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.292024 | + | 0.898757i | 0.0164276 | + | 0.0505590i | ||||
\(317\) | −0.0339077 | + | 0.214085i | −0.00190445 | + | 0.0120242i | −0.988622 | − | 0.150419i | \(-0.951938\pi\) |
0.986718 | + | 0.162444i | \(0.0519376\pi\) | |||||||
\(318\) | 10.2316 | + | 2.43027i | 0.573761 | + | 0.136283i | ||||
\(319\) | −15.8099 | − | 21.7604i | −0.885183 | − | 1.21835i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.2383 | − | 0.780892i | −0.571445 | − | 0.0435852i | ||||
\(322\) | −0.518520 | − | 3.27381i | −0.0288960 | − | 0.182442i | ||||
\(323\) | −27.6399 | + | 14.0832i | −1.53793 | + | 0.783612i | ||||
\(324\) | 7.22970 | − | 5.36017i | 0.401650 | − | 0.297787i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 2.00929i | − | 0.111284i | ||||||
\(327\) | 2.79176 | + | 1.70153i | 0.154384 | + | 0.0940947i | ||||
\(328\) | −1.60175 | + | 0.253693i | −0.0884421 | + | 0.0140078i | ||||
\(329\) | 8.33214 | + | 6.05366i | 0.459366 | + | 0.333749i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.81535 | − | 4.22510i | 0.319640 | − | 0.232232i | −0.416382 | − | 0.909190i | \(-0.636702\pi\) |
0.736022 | + | 0.676958i | \(0.236702\pi\) | |||||||
\(332\) | −5.34899 | + | 5.34899i | −0.293564 | + | 0.293564i | ||||
\(333\) | −0.538511 | − | 0.387290i | −0.0295102 | − | 0.0212234i | ||||
\(334\) | 14.1135 | − | 4.58575i | 0.772255 | − | 0.250921i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.60403 | − | 0.874463i | 0.196616 | − | 0.0477058i | ||||
\(337\) | −3.06621 | + | 6.01777i | −0.167027 | + | 0.327809i | −0.959315 | − | 0.282339i | \(-0.908890\pi\) |
0.792288 | + | 0.610147i | \(0.208890\pi\) | |||||||
\(338\) | 5.39518 | − | 10.5886i | 0.293459 | − | 0.575946i | ||||
\(339\) | 14.2774 | − | 3.46420i | 0.775443 | − | 0.188150i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −59.9987 | + | 19.4947i | −3.24911 | + | 1.05570i | ||||
\(342\) | −13.1331 | − | 9.44517i | −0.710157 | − | 0.510736i | ||||
\(343\) | 14.2552 | − | 14.2552i | 0.769710 | − | 0.769710i | ||||
\(344\) | 1.52777 | − | 1.10999i | 0.0823718 | − | 0.0598466i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.05686 | + | 2.94748i | 0.218098 | + | 0.158458i | ||||
\(347\) | −4.52113 | + | 0.716076i | −0.242707 | + | 0.0384410i | −0.276603 | − | 0.960984i | \(-0.589209\pi\) |
0.0338958 | + | 0.999425i | \(0.489209\pi\) | |||||||
\(348\) | −6.72250 | − | 4.09725i | −0.360364 | − | 0.219636i | ||||
\(349\) | 9.78119i | 0.523575i | 0.965126 | + | 0.261787i | \(0.0843120\pi\) | ||||
−0.965126 | + | 0.261787i | \(0.915688\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.46932 | − | 0.470345i | 0.291931 | − | 0.0251052i | ||||
\(352\) | −5.27263 | + | 2.68654i | −0.281032 | + | 0.143193i | ||||
\(353\) | 1.69571 | + | 10.7063i | 0.0902538 | + | 0.569840i | 0.990827 | + | 0.135136i | \(0.0431471\pi\) |
−0.900573 | + | 0.434704i | \(0.856853\pi\) | |||||||
\(354\) | −12.5256 | − | 0.955350i | −0.665727 | − | 0.0507763i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.08679 | + | 7.00137i | 0.269600 | + | 0.371072i | ||||
\(357\) | −20.7575 | − | 4.93044i | −1.09860 | − | 0.260947i | ||||
\(358\) | 0.495694 | − | 3.12969i | 0.0261982 | − | 0.165409i | ||||
\(359\) | 6.51044 | + | 20.0371i | 0.343608 | + | 1.05752i | 0.962325 | + | 0.271902i | \(0.0876527\pi\) |
−0.618717 | + | 0.785614i | \(0.712347\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.11386 | + | 9.58347i | −0.163887 | + | 0.504393i | ||||
\(362\) | −5.56052 | − | 2.83323i | −0.292254 | − | 0.148911i | ||||
\(363\) | 3.36411 | + | 41.4644i | 0.176570 | + | 2.17632i | ||||
\(364\) | 2.15133 | + | 0.699010i | 0.112760 | + | 0.0366381i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.59203 | − | 4.75273i | −0.292300 | − | 0.248429i | ||||
\(367\) | −26.6770 | − | 4.22522i | −1.39253 | − | 0.220555i | −0.585311 | − | 0.810809i | \(-0.699028\pi\) |
−0.807218 | + | 0.590254i | \(0.799028\pi\) | |||||||
\(368\) | 1.09463 | + | 1.09463i | 0.0570618 | + | 0.0570618i | ||||
\(369\) | 0.784283 | + | 4.80153i | 0.0408281 | + | 0.249958i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.64135 | − | 10.5174i | 0.396719 | − | 0.546037i | ||||
\(372\) | −14.0119 | + | 12.0259i | −0.726483 | + | 0.623516i | ||||
\(373\) | −12.1464 | − | 23.8387i | −0.628917 | − | 1.23432i | −0.957114 | − | 0.289711i | \(-0.906441\pi\) |
0.328197 | − | 0.944609i | \(-0.393559\pi\) | |||||||
\(374\) | 34.0432 | 1.76033 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.81005 | −0.248060 | ||||||||
\(377\) | −2.18003 | − | 4.27854i | −0.112277 | − | 0.220356i | ||||
\(378\) | −2.67559 | − | 10.7993i | −0.137617 | − | 0.555455i | ||||
\(379\) | 9.28018 | − | 12.7731i | 0.476691 | − | 0.656109i | −0.501174 | − | 0.865347i | \(-0.667098\pi\) |
0.977865 | + | 0.209238i | \(0.0670983\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.7525 | − | 6.89175i | −0.858257 | − | 0.353075i | ||||
\(382\) | 14.8555 | + | 14.8555i | 0.760073 | + | 0.760073i | ||||
\(383\) | 15.7705 | + | 2.49780i | 0.805836 | + | 0.127632i | 0.545744 | − | 0.837952i | \(-0.316247\pi\) |
0.260092 | + | 0.965584i | \(0.416247\pi\) | |||||||
\(384\) | −1.12169 | + | 1.31977i | −0.0572411 | + | 0.0673495i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.42739 | − | 3.06314i | −0.479841 | − | 0.155910i | ||||
\(387\) | −3.35207 | − | 4.56717i | −0.170395 | − | 0.232162i | ||||
\(388\) | 10.7492 | + | 5.47700i | 0.545709 | + | 0.278053i | ||||
\(389\) | 3.56490 | − | 10.9716i | 0.180748 | − | 0.556284i | −0.819102 | − | 0.573648i | \(-0.805528\pi\) |
0.999849 | + | 0.0173647i | \(0.00552762\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.75201 | − | 8.46982i | −0.139175 | − | 0.428337i | ||||
\(392\) | −0.377857 | + | 2.38569i | −0.0190847 | + | 0.120496i | ||||
\(393\) | −7.81799 | + | 32.9143i | −0.394365 | + | 1.66031i | ||||
\(394\) | 5.99998 | + | 8.25827i | 0.302275 | + | 0.416046i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 8.13594 | + | 15.7788i | 0.408846 | + | 0.792913i | ||||
\(397\) | 3.27643 | + | 20.6866i | 0.164439 | + | 1.03823i | 0.922486 | + | 0.386030i | \(0.126154\pi\) |
−0.758047 | + | 0.652200i | \(0.773846\pi\) | |||||||
\(398\) | −13.4673 | + | 6.86195i | −0.675057 | + | 0.343958i | ||||
\(399\) | −17.0256 | + | 10.4900i | −0.852348 | + | 0.525155i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 24.4394i | − | 1.22045i | −0.792229 | − | 0.610223i | \(-0.791080\pi\) | ||
0.792229 | − | 0.610223i | \(-0.208920\pi\) | |||||||
\(402\) | −1.16859 | + | 1.91735i | −0.0582842 | + | 0.0956289i | ||||
\(403\) | −11.1240 | + | 1.76187i | −0.554125 | + | 0.0877648i | ||||
\(404\) | 0.251023 | + | 0.182379i | 0.0124889 | + | 0.00907370i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.87354 | + | 5.72046i | −0.390757 | + | 0.283902i | ||||
\(407\) | 0.925189 | − | 0.925189i | 0.0458599 | − | 0.0458599i | ||||
\(408\) | 9.19652 | − | 3.83537i | 0.455296 | − | 0.189879i | ||||
\(409\) | −9.31361 | + | 3.02618i | −0.460528 | + | 0.149635i | −0.530087 | − | 0.847943i | \(-0.677841\pi\) |
0.0695588 | + | 0.997578i | \(0.477841\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.89675 | − | 20.1816i | −0.241539 | − | 0.995483i | ||||
\(412\) | −4.01069 | + | 7.87141i | −0.197592 | + | 0.387797i | ||||
\(413\) | −7.05006 | + | 13.8365i | −0.346911 | + | 0.680851i | ||||
\(414\) | 3.26800 | − | 3.29973i | 0.160614 | − | 0.162173i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.00475 | + | 0.326463i | −0.0492619 | + | 0.0160062i | ||||
\(417\) | 15.5144 | + | 37.2007i | 0.759744 | + | 1.82173i | ||||
\(418\) | 22.5634 | − | 22.5634i | 1.10361 | − | 1.10361i | ||||
\(419\) | −20.8723 | + | 15.1646i | −1.01968 | + | 0.740840i | −0.966217 | − | 0.257730i | \(-0.917026\pi\) |
−0.0534618 | + | 0.998570i | \(0.517026\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.8859 | − | 23.1664i | −1.55402 | − | 1.12906i | −0.940705 | − | 0.339225i | \(-0.889835\pi\) |
−0.613316 | − | 0.789837i | \(-0.710165\pi\) | |||||||
\(422\) | −3.92268 | + | 0.621291i | −0.190953 | + | 0.0302440i | ||||
\(423\) | 0.0697075 | + | 14.4300i | 0.00338930 | + | 0.701610i | ||||
\(424\) | 6.07158i | 0.294862i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.70809 | + | 6.01838i | 0.179658 | + | 0.291591i | ||||
\(427\) | −8.08350 | + | 4.11875i | −0.391188 | + | 0.199320i | ||||
\(428\) | −0.927381 | − | 5.85525i | −0.0448267 | − | 0.283024i | ||||
\(429\) | −0.823500 | + | 10.7969i | −0.0397590 | + | 0.521280i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.61295 | − | 4.97279i | −0.174030 | − | 0.239531i | 0.713088 | − | 0.701074i | \(-0.247296\pi\) |
−0.887118 | + | 0.461543i | \(0.847296\pi\) | |||||||
\(432\) | 3.97553 | + | 3.34591i | 0.191273 | + | 0.160980i | ||||
\(433\) | 2.61783 | − | 16.5283i | 0.125805 | − | 0.794299i | −0.841421 | − | 0.540380i | \(-0.818280\pi\) |
0.967225 | − | 0.253919i | \(-0.0817197\pi\) | |||||||
\(434\) | 7.05375 | + | 21.7092i | 0.338591 | + | 1.04208i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.583300 | + | 1.79521i | −0.0279350 | + | 0.0859752i | ||||
\(437\) | −7.43768 | − | 3.78968i | −0.355792 | − | 0.181285i | ||||
\(438\) | 0.539668 | − | 0.0437846i | 0.0257863 | − | 0.00209211i | ||||
\(439\) | −19.1311 | − | 6.21606i | −0.913076 | − | 0.296676i | −0.185453 | − | 0.982653i | \(-0.559375\pi\) |
−0.727623 | + | 0.685977i | \(0.759375\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.16248 | + | 1.09898i | 0.341070 | + | 0.0523326i | ||||
\(442\) | 6.00282 | + | 0.950753i | 0.285525 | + | 0.0452227i | ||||
\(443\) | −17.1571 | − | 17.1571i | −0.815159 | − | 0.815159i | 0.170243 | − | 0.985402i | \(-0.445545\pi\) |
−0.985402 | + | 0.170243i | \(0.945545\pi\) | |||||||
\(444\) | 0.145699 | − | 0.354167i | 0.00691459 | − | 0.0168080i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.86865 | + | 10.8303i | −0.372591 | + | 0.512828i | ||||
\(447\) | −16.5983 | − | 19.3393i | −0.785071 | − | 0.914716i | ||||
\(448\) | 0.972066 | + | 1.90779i | 0.0459258 | + | 0.0901345i | ||||
\(449\) | 15.9242 | 0.751511 | 0.375755 | − | 0.926719i | \(-0.377383\pi\) | ||||
0.375755 | + | 0.926719i | \(0.377383\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.59671 | −0.451891 | ||||||||
\(452\) | 3.85086 | + | 7.55774i | 0.181129 | + | 0.355486i | ||||
\(453\) | −9.64350 | − | 11.2360i | −0.453091 | − | 0.527914i | ||||
\(454\) | −0.503096 | + | 0.692453i | −0.0236115 | + | 0.0324984i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.55330 | − | 8.63736i | 0.166398 | − | 0.404482i | ||||
\(457\) | −2.30257 | − | 2.30257i | −0.107710 | − | 0.107710i | 0.651198 | − | 0.758908i | \(-0.274267\pi\) |
−0.758908 | + | 0.651198i | \(0.774267\pi\) | |||||||
\(458\) | −16.3422 | − | 2.58835i | −0.763621 | − | 0.120946i | ||||
\(459\) | −11.6393 | − | 27.5337i | −0.543274 | − | 1.28516i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.43135 | + | 3.06443i | 0.439262 | + | 0.142725i | 0.520295 | − | 0.853987i | \(-0.325822\pi\) |
−0.0810333 | + | 0.996711i | \(0.525822\pi\) | |||||||
\(462\) | 21.8742 | − | 1.77471i | 1.01768 | − | 0.0825668i | ||||
\(463\) | 20.5992 | + | 10.4958i | 0.957328 | + | 0.487783i | 0.861580 | − | 0.507623i | \(-0.169476\pi\) |
0.0957485 | + | 0.995406i | \(0.469476\pi\) | |||||||
\(464\) | 1.40458 | − | 4.32285i | 0.0652059 | − | 0.200683i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.68432 | − | 5.18379i | −0.0780245 | − | 0.240135i | ||||
\(467\) | 0.726976 | − | 4.58995i | 0.0336405 | − | 0.212397i | −0.965142 | − | 0.261726i | \(-0.915708\pi\) |
0.998783 | + | 0.0493288i | \(0.0157082\pi\) | |||||||
\(468\) | 0.993939 | + | 3.00948i | 0.0459448 | + | 0.139113i | ||||
\(469\) | 1.63156 | + | 2.24565i | 0.0753383 | + | 0.103694i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.27611 | + | 42.9530i | −0.150955 | + | 1.97917i | ||||
\(472\) | −1.13457 | − | 7.16336i | −0.0522226 | − | 0.329721i | ||||
\(473\) | 9.95697 | − | 5.07333i | 0.457822 | − | 0.233272i | ||||
\(474\) | 0.858596 | + | 1.39353i | 0.0394366 | + | 0.0640072i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 12.3178i | − | 0.564585i | ||||||
\(477\) | 18.2145 | − | 0.0879897i | 0.833986 | − | 0.00402877i | ||||
\(478\) | 8.60761 | − | 1.36331i | 0.393703 | − | 0.0623564i | ||||
\(479\) | 12.7801 | + | 9.28530i | 0.583939 | + | 0.424256i | 0.840142 | − | 0.542367i | \(-0.182472\pi\) |
−0.256203 | + | 0.966623i | \(0.582472\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.188977 | − | 0.137300i | 0.00861660 | − | 0.00626032i | ||||
\(482\) | 17.9787 | − | 17.9787i | 0.818908 | − | 0.818908i | ||||
\(483\) | −2.20982 | − | 5.29875i | −0.100550 | − | 0.241101i | ||||
\(484\) | −22.8426 | + | 7.42201i | −1.03830 | + | 0.337364i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 9.98001 | − | 11.9750i | 0.452702 | − | 0.543195i | ||||
\(487\) | −0.0615473 | + | 0.120793i | −0.00278898 | + | 0.00547367i | −0.892397 | − | 0.451252i | \(-0.850978\pi\) |
0.889608 | + | 0.456725i | \(0.150978\pi\) | |||||||
\(488\) | 1.92361 | − | 3.77529i | 0.0870776 | − | 0.170899i | ||||
\(489\) | −0.820608 | − | 3.38207i | −0.0371092 | − | 0.152942i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.65368 | − | 2.81175i | 0.390535 | − | 0.126893i | −0.107166 | − | 0.994241i | \(-0.534178\pi\) |
0.497701 | + | 0.867349i | \(0.334178\pi\) | |||||||
\(492\) | −2.59248 | + | 1.08119i | −0.116878 | + | 0.0487436i | ||||
\(493\) | −18.4898 | + | 18.4898i | −0.832738 | + | 0.832738i | ||||
\(494\) | 4.60873 | − | 3.34844i | 0.207357 | − | 0.150654i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.62475 | − | 6.26624i | −0.387263 | − | 0.281363i | ||||
\(497\) | 8.63111 | − | 1.36703i | 0.387158 | − | 0.0613198i | ||||
\(498\) | −6.81893 | + | 11.1881i | −0.305564 | + | 0.501349i | ||||
\(499\) | − | 27.5900i | − | 1.23510i | −0.786532 | − | 0.617549i | \(-0.788126\pi\) | ||
0.786532 | − | 0.617549i | \(-0.211874\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.8831 | − | 13.4828i | 0.977667 | − | 0.602368i | ||||
\(502\) | 18.7945 | − | 9.57626i | 0.838838 | − | 0.427409i | ||||
\(503\) | 1.71307 | + | 10.8159i | 0.0763820 | + | 0.482257i | 0.995993 | + | 0.0894274i | \(0.0285037\pi\) |
−0.919611 | + | 0.392829i | \(0.871496\pi\) | |||||||
\(504\) | 5.70921 | − | 2.94381i | 0.254308 | − | 0.131128i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.38455 | + | 7.41120i | 0.239372 | + | 0.329468i | ||||
\(507\) | 4.75677 | − | 20.0263i | 0.211256 | − | 0.889401i | ||||
\(508\) | 1.63607 | − | 10.3298i | 0.0725891 | − | 0.458309i | ||||
\(509\) | −2.83257 | − | 8.71775i | −0.125551 | − | 0.386407i | 0.868450 | − | 0.495777i | \(-0.165117\pi\) |
−0.994001 | + | 0.109370i | \(0.965117\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.206834 | − | 0.636570i | 0.00914980 | − | 0.0281602i | ||||
\(512\) | −0.891007 | − | 0.453990i | −0.0393773 | − | 0.0200637i | ||||
\(513\) | −25.9633 | − | 10.5346i | −1.14631 | − | 0.465114i | ||||
\(514\) | −15.9501 | − | 5.18250i | −0.703529 | − | 0.228590i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.11823 | − | 2.49230i | 0.0932500 | − | 0.109717i | ||||
\(517\) | −28.1136 | − | 4.45276i | −1.23643 | − | 0.195832i | ||||
\(518\) | −0.334760 | − | 0.334760i | −0.0147085 | − | 0.0147085i | ||||
\(519\) | 8.03233 | + | 3.30439i | 0.352580 | + | 0.145047i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.3932 | − | 18.4342i | 0.586767 | − | 0.807615i | −0.407650 | − | 0.913138i | \(-0.633652\pi\) |
0.994417 | + | 0.105523i | \(0.0336517\pi\) | |||||||
\(522\) | −12.9887 | − | 4.15104i | −0.568502 | − | 0.181686i | ||||
\(523\) | −16.3751 | − | 32.1380i | −0.716035 | − | 1.40530i | −0.905902 | − | 0.423488i | \(-0.860806\pi\) |
0.189867 | − | 0.981810i | \(-0.439194\pi\) | |||||||
\(524\) | −19.5318 | −0.853250 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.7518 | 0.992025 | ||||||||
\(527\) | 27.8432 | + | 54.6453i | 1.21287 | + | 2.38039i | ||||
\(528\) | −7.77776 | + | 6.67539i | −0.338484 | + | 0.290509i | ||||
\(529\) | −12.1105 | + | 16.6686i | −0.526542 | + | 0.724723i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −21.4734 | + | 3.50747i | −0.931866 | + | 0.152211i | ||||
\(532\) | −8.16406 | − | 8.16406i | −0.353957 | − | 0.353957i | ||||
\(533\) | −1.69218 | − | 0.268016i | −0.0732966 | − | 0.0116090i | ||||
\(534\) | 11.4216 | + | 9.70732i | 0.494259 | + | 0.420077i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.23294 | − | 0.400605i | −0.0532548 | − | 0.0173035i | ||||
\(537\) | −0.443825 | − | 5.47038i | −0.0191525 | − | 0.236064i | ||||
\(538\) | −9.22579 | − | 4.70077i | −0.397752 | − | 0.202665i | ||||
\(539\) | −4.41696 | + | 13.5940i | −0.190252 | + | 0.585536i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.6711 | + | 32.8422i | 0.458786 | + | 1.41200i | 0.866633 | + | 0.498947i | \(0.166280\pi\) |
−0.407847 | + | 0.913050i | \(0.633720\pi\) | |||||||
\(542\) | 0.100029 | − | 0.631560i | 0.00429663 | − | 0.0271278i | ||||
\(543\) | −10.5166 | − | 2.49797i | −0.451312 | − | 0.107198i | ||||
\(544\) | 3.38144 | + | 4.65416i | 0.144978 | + | 0.199545i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.90663 | + | 0.297966i | 0.167188 | + | 0.0127518i | ||||
\(547\) | 3.53445 | + | 22.3156i | 0.151122 | + | 0.954148i | 0.940390 | + | 0.340098i | \(0.110460\pi\) |
−0.789268 | + | 0.614049i | \(0.789540\pi\) | |||||||
\(548\) | 10.6831 | − | 5.44330i | 0.456359 | − | 0.232526i | ||||
\(549\) | −11.3536 | − | 5.71604i | −0.484561 | − | 0.243955i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.5096i | 1.04414i | ||||||||
\(552\) | 2.28956 | + | 1.39545i | 0.0974500 | + | 0.0593942i | ||||
\(553\) | 1.99850 | − | 0.316532i | 0.0849851 | − | 0.0134603i | ||||
\(554\) | −24.5631 | − | 17.8461i | −1.04358 | − | 0.758209i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.8265 | + | 13.6782i | −0.798420 | + | 0.580086i | ||||
\(557\) | 3.76017 | − | 3.76017i | 0.159323 | − | 0.159323i | −0.622943 | − | 0.782267i | \(-0.714063\pi\) |
0.782267 | + | 0.622943i | \(0.214063\pi\) | |||||||
\(558\) | −18.6735 | + | 25.9647i | −0.790513 | + | 1.09918i | ||||
\(559\) | 1.89740 | − | 0.616502i | 0.0802513 | − | 0.0260752i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 57.3019 | − | 13.9034i | 2.41929 | − | 0.587003i | ||||
\(562\) | −9.85907 | + | 19.3495i | −0.415880 | + | 0.816210i | ||||
\(563\) | 11.0089 | − | 21.6061i | 0.463969 | − | 0.910590i | −0.533913 | − | 0.845539i | \(-0.679279\pi\) |
0.997882 | − | 0.0650508i | \(-0.0207209\pi\) | |||||||
\(564\) | −8.09634 | + | 1.96445i | −0.340918 | + | 0.0827185i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.29063 | + | 1.06919i | −0.138315 | + | 0.0449414i | ||||
\(567\) | −8.91407 | − | 17.0848i | −0.374356 | − | 0.717493i | ||||
\(568\) | −2.88591 | + | 2.88591i | −0.121090 | + | 0.121090i | ||||
\(569\) | 24.5934 | − | 17.8681i | 1.03101 | − | 0.749071i | 0.0624977 | − | 0.998045i | \(-0.480093\pi\) |
0.968510 | + | 0.248974i | \(0.0800934\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.57335 | + | 3.32274i | 0.191389 | + | 0.139052i | 0.679353 | − | 0.733811i | \(-0.262260\pi\) |
−0.487964 | + | 0.872864i | \(0.662260\pi\) | |||||||
\(572\) | −6.17473 | + | 0.977982i | −0.258179 | + | 0.0408915i | ||||
\(573\) | 31.0720 | + | 18.9379i | 1.29805 | + | 0.791141i | ||||
\(574\) | 3.47236i | 0.144934i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.34904 | + | 2.67957i | −0.0562101 | + | 0.111649i | ||||
\(577\) | 22.8994 | − | 11.6678i | 0.953316 | − | 0.485739i | 0.0930933 | − | 0.995657i | \(-0.470324\pi\) |
0.860223 | + | 0.509919i | \(0.170324\pi\) | |||||||
\(578\) | −2.51787 | − | 15.8972i | −0.104729 | − | 0.661236i | ||||
\(579\) | −17.1193 | − | 1.30572i | −0.711454 | − | 0.0542639i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.52039 | + | 13.1037i | 0.394972 | + | 0.543633i | ||||
\(582\) | 20.3301 | + | 4.82891i | 0.842708 | + | 0.200165i | ||||
\(583\) | −5.62058 | + | 35.4869i | −0.232781 | + | 1.46972i | ||||
\(584\) | 0.0965991 | + | 0.297301i | 0.00399730 | + | 0.0123024i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.35461 | − | 16.4798i | 0.221197 | − | 0.680773i | ||||
\(587\) | 12.8802 | + | 6.56280i | 0.531623 | + | 0.270876i | 0.699129 | − | 0.714995i | \(-0.253571\pi\) |
−0.167506 | + | 0.985871i | \(0.553571\pi\) | |||||||
\(588\) | 0.338318 | + | 4.16995i | 0.0139520 | + | 0.171966i | ||||
\(589\) | 54.6723 | + | 17.7641i | 2.25273 | + | 0.731957i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.4720 | + | 11.4500i | 0.554163 | + | 0.470990i | ||||
\(592\) | 0.218383 | + | 0.0345885i | 0.00897549 | + | 0.00142158i | ||||
\(593\) | −27.1124 | − | 27.1124i | −1.11337 | − | 1.11337i | −0.992691 | − | 0.120680i | \(-0.961492\pi\) |
−0.120680 | − | 0.992691i | \(-0.538508\pi\) | |||||||
\(594\) | 20.1387 | + | 23.2363i | 0.826299 | + | 0.953396i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.64870 | − | 11.9039i | 0.354265 | − | 0.487603i | ||||
\(597\) | −19.8659 | + | 17.0503i | −0.813058 | + | 0.697821i | ||||
\(598\) | 0.742476 | + | 1.45719i | 0.0303621 | + | 0.0595890i | ||||
\(599\) | −22.2597 | −0.909506 | −0.454753 | − | 0.890618i | \(-0.650272\pi\) | ||||
−0.454753 | + | 0.890618i | \(0.650272\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.661317 | −0.0269757 | −0.0134878 | − | 0.999909i | \(-0.504293\pi\) | ||||
−0.0134878 | + | 0.999909i | \(0.504293\pi\) | |||||||
\(602\) | −1.83568 | − | 3.60272i | −0.0748165 | − | 0.146836i | ||||
\(603\) | −1.18393 | + | 3.70457i | −0.0482135 | + | 0.150862i | ||||
\(604\) | 5.02485 | − | 6.91612i | 0.204458 | − | 0.281413i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.497011 | + | 0.204463i | 0.0201897 | + | 0.00830576i | ||||
\(607\) | 25.2285 | + | 25.2285i | 1.02399 | + | 1.02399i | 0.999705 | + | 0.0242876i | \(0.00773174\pi\) |
0.0242876 | + | 0.999705i | \(0.492268\pi\) | |||||||
\(608\) | 5.32589 | + | 0.843538i | 0.215993 | + | 0.0342100i | ||||
\(609\) | −10.9166 | + | 12.8444i | −0.442362 | + | 0.520480i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.83290 | − | 1.57031i | −0.195518 | − | 0.0635278i | ||||
\(612\) | 13.9133 | − | 10.2117i | 0.562412 | − | 0.412782i | ||||
\(613\) | 22.2583 | + | 11.3412i | 0.899003 | + | 0.458065i | 0.841485 | − | 0.540280i | \(-0.181682\pi\) |
0.0575173 | + | 0.998345i | \(0.481682\pi\) | |||||||
\(614\) | 7.34770 | − | 22.6139i | 0.296529 | − | 0.912623i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.91542 | + | 12.0504i | 0.157757 | + | 0.485525i | ||||
\(617\) | 4.87738 | − | 30.7946i | 0.196356 | − | 1.23974i | −0.670775 | − | 0.741661i | \(-0.734038\pi\) |
0.867131 | − | 0.498081i | \(-0.165962\pi\) | |||||||
\(618\) | −3.53610 | + | 14.8873i | −0.142243 | + | 0.598853i | ||||
\(619\) | 2.12975 | + | 2.93135i | 0.0856019 | + | 0.117821i | 0.849670 | − | 0.527314i | \(-0.176801\pi\) |
−0.764068 | + | 0.645135i | \(0.776801\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.15311 | − | 6.88882i | 0.166659 | − | 0.276439i | ||||
\(622\) | 1.21703 | + | 7.68404i | 0.0487985 | + | 0.308102i | ||||
\(623\) | 16.5103 | − | 8.41243i | 0.661472 | − | 0.337037i | ||||
\(624\) | −1.55788 | + | 0.959853i | −0.0623651 | + | 0.0384249i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 20.7996i | − | 0.831321i | ||||||
\(627\) | 28.7639 | − | 47.1939i | 1.14872 | − | 1.88474i | ||||
\(628\) | −24.5648 | + | 3.89068i | −0.980241 | + | 0.155255i | ||||
\(629\) | −1.02906 | − | 0.747655i | −0.0410312 | − | 0.0298109i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.12680 | − | 2.99829i | 0.164285 | − | 0.119360i | −0.502605 | − | 0.864516i | \(-0.667625\pi\) |
0.666890 | + | 0.745156i | \(0.267625\pi\) | |||||||
\(632\) | −0.668222 | + | 0.668222i | −0.0265805 | + | 0.0265805i | ||||
\(633\) | −6.34896 | + | 2.64781i | −0.252349 | + | 0.105241i | ||||
\(634\) | −0.206145 | + | 0.0669805i | −0.00818706 | + | 0.00266014i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.47967 | + | 10.2198i | 0.0983253 | + | 0.405240i | ||||
\(637\) | −1.15849 | + | 2.27367i | −0.0459012 | + | 0.0900861i | ||||
\(638\) | 12.2112 | − | 23.9657i | 0.483444 | − | 0.948813i | ||||
\(639\) | 8.69945 | + | 8.61580i | 0.344145 | + | 0.340836i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −45.1681 | + | 14.6760i | −1.78403 | + | 0.579668i | −0.999198 | − | 0.0400355i | \(-0.987253\pi\) |
−0.784836 | + | 0.619703i | \(0.787253\pi\) | |||||||
\(642\) | −3.95230 | − | 9.47689i | −0.155985 | − | 0.374023i | ||||
\(643\) | 17.9186 | − | 17.9186i | 0.706639 | − | 0.706639i | −0.259188 | − | 0.965827i | \(-0.583455\pi\) |
0.965827 | + | 0.259188i | \(0.0834550\pi\) | |||||||
\(644\) | 2.68158 | − | 1.94828i | 0.105669 | − | 0.0767731i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −25.0965 | − | 18.2337i | −0.987409 | − | 0.717395i | ||||
\(647\) | −7.06356 | + | 1.11876i | −0.277697 | + | 0.0439829i | −0.293730 | − | 0.955889i | \(-0.594897\pi\) |
0.0160323 | + | 0.999871i | \(0.494897\pi\) | |||||||
\(648\) | 8.05816 | + | 4.00825i | 0.316554 | + | 0.157459i | ||||
\(649\) | − | 42.9184i | − | 1.68469i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.7391 | + | 33.6604i | 0.812831 | + | 1.31926i | ||||
\(652\) | 1.79029 | − | 0.912200i | 0.0701133 | − | 0.0357245i | ||||
\(653\) | 3.64054 | + | 22.9855i | 0.142465 | + | 0.899490i | 0.950583 | + | 0.310470i | \(0.100486\pi\) |
−0.808118 | + | 0.589021i | \(0.799514\pi\) | |||||||
\(654\) | −0.248642 | + | 3.25995i | −0.00972269 | + | 0.127474i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.953223 | − | 1.31200i | −0.0372171 | − | 0.0512250i | ||||
\(657\) | 0.890494 | − | 0.294102i | 0.0347415 | − | 0.0114740i | ||||
\(658\) | −1.61113 | + | 10.1723i | −0.0628085 | + | 0.396557i | ||||
\(659\) | −1.14382 | − | 3.52031i | −0.0445568 | − | 0.137132i | 0.926303 | − | 0.376779i | \(-0.122968\pi\) |
−0.970860 | + | 0.239647i | \(0.922968\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.4157 | + | 35.1339i | −0.444019 | + | 1.36655i | 0.439537 | + | 0.898224i | \(0.355143\pi\) |
−0.883556 | + | 0.468326i | \(0.844857\pi\) | |||||||
\(662\) | 6.40470 | + | 3.26336i | 0.248926 | + | 0.126834i | ||||
\(663\) | 10.4923 | − | 0.851267i | 0.407488 | − | 0.0330605i | ||||
\(664\) | −7.19438 | − | 2.33760i | −0.279196 | − | 0.0907163i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.100599 | − | 0.655643i | 0.00389815 | − | 0.0254056i | ||||
\(667\) | −6.94972 | − | 1.10073i | −0.269094 | − | 0.0426203i | ||||
\(668\) | 10.4933 | + | 10.4933i | 0.405999 | + | 0.405999i | ||||
\(669\) | −8.82147 | + | 21.4432i | −0.341058 | + | 0.829044i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.7379 | − | 20.2849i | 0.568949 | − | 0.783092i | ||||
\(672\) | 2.41535 | + | 2.81421i | 0.0931740 | + | 0.108561i | ||||
\(673\) | 0.542210 | + | 1.06415i | 0.0209006 | + | 0.0410198i | 0.901221 | − | 0.433360i | \(-0.142672\pi\) |
−0.880320 | + | 0.474380i | \(0.842672\pi\) | |||||||
\(674\) | −6.75390 | −0.260151 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.8839 | 0.457073 | ||||||||
\(677\) | −15.6087 | − | 30.6338i | −0.599892 | − | 1.17735i | −0.968790 | − | 0.247884i | \(-0.920265\pi\) |
0.368898 | − | 0.929470i | \(-0.379735\pi\) | |||||||
\(678\) | 9.56844 | + | 11.1486i | 0.367474 | + | 0.428158i | ||||
\(679\) | 15.1832 | − | 20.8979i | 0.582679 | − | 0.801988i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.564016 | + | 1.37101i | −0.0216132 | + | 0.0525373i | ||||
\(682\) | −44.6088 | − | 44.6088i | −1.70816 | − | 1.70816i | ||||
\(683\) | 44.5125 | + | 7.05008i | 1.70322 | + | 0.269764i | 0.930849 | − | 0.365405i | \(-0.119070\pi\) |
0.772373 | + | 0.635169i | \(0.219070\pi\) | |||||||
\(684\) | 2.45340 | − | 15.9897i | 0.0938081 | − | 0.611382i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 19.1733 | + | 6.22977i | 0.732038 | + | 0.237854i | ||||
\(687\) | −28.5645 | + | 2.31751i | −1.08980 | + | 0.0884185i | ||||
\(688\) | 1.68260 | + | 0.857327i | 0.0641485 | + | 0.0326853i | ||||
\(689\) | −1.98215 | + | 6.10043i | −0.0755138 | + | 0.232408i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.10289 | + | 3.39434i | 0.0419558 | + | 0.129127i | 0.969840 | − | 0.243741i | \(-0.0783746\pi\) |
−0.927885 | + | 0.372867i | \(0.878375\pi\) | |||||||
\(692\) | −0.784450 | + | 4.95282i | −0.0298203 | + | 0.188278i | ||||
\(693\) | 36.0941 | − | 11.9207i | 1.37110 | − | 0.452832i | ||||
\(694\) | −2.69058 | − | 3.70326i | −0.102133 | − | 0.140574i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.598727 | − | 7.84991i | 0.0226947 | − | 0.297550i | ||||
\(697\) | 1.45946 | + | 9.21466i | 0.0552809 | + | 0.349030i | ||||
\(698\) | −8.71510 | + | 4.44057i | −0.329871 | + | 0.168078i | ||||
\(699\) | −4.95215 | − | 8.03754i | −0.187308 | − | 0.304008i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.6139i | 0.740807i | 0.928871 | + | 0.370403i | \(0.120781\pi\) | ||||
−0.928871 | + | 0.370403i | \(0.879219\pi\) | |||||||
\(702\) | 2.90210 | + | 4.65967i | 0.109533 | + | 0.175868i | ||||
\(703\) | −1.17758 | + | 0.186511i | −0.0444133 | + | 0.00703438i | ||||
\(704\) | −4.78745 | − | 3.47829i | −0.180434 | − | 0.131093i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.76956 | + | 6.37146i | −0.330047 | + | 0.239793i | ||||
\(707\) | 0.469776 | − | 0.469776i | 0.0176677 | − | 0.0176677i | ||||
\(708\) | −4.83527 | − | 11.5941i | −0.181721 | − | 0.435733i | ||||
\(709\) | −22.4237 | + | 7.28590i | −0.842140 | + | 0.273628i | −0.698150 | − | 0.715951i | \(-0.745993\pi\) |
−0.143990 | + | 0.989579i | \(0.545993\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.01433 | + | 1.99496i | 0.0755432 | + | 0.0748168i | ||||
\(712\) | −3.92891 | + | 7.71092i | −0.147242 | + | 0.288979i | ||||
\(713\) | −7.49238 | + | 14.7046i | −0.280592 | + | 0.550692i | ||||
\(714\) | −5.03066 | − | 20.7335i | −0.188268 | − | 0.775930i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.01361 | − | 0.979183i | 0.112624 | − | 0.0365938i | ||||
\(717\) | 13.9317 | − | 5.81015i | 0.520287 | − | 0.216984i | ||||
\(718\) | −14.8975 | + | 14.8975i | −0.555969 | + | 0.555969i | ||||
\(719\) | 30.2210 | − | 21.9569i | 1.12705 | − | 0.818853i | 0.141791 | − | 0.989897i | \(-0.454714\pi\) |
0.985263 | + | 0.171044i | \(0.0547140\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.3031 | + | 11.1183i | 0.569916 | + | 0.414068i | ||||
\(722\) | −9.95259 | + | 1.57634i | −0.370397 | + | 0.0586651i | ||||
\(723\) | 22.9194 | − | 37.6046i | 0.852381 | − | 1.39853i | ||||
\(724\) | − | 6.24071i | − | 0.231934i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −35.4178 | + | 21.8219i | −1.31448 | + | 0.809886i | ||||
\(727\) | 37.8579 | − | 19.2896i | 1.40407 | − | 0.715411i | 0.422476 | − | 0.906374i | \(-0.361161\pi\) |
0.981597 | + | 0.190964i | \(0.0611612\pi\) | |||||||
\(728\) | 0.353862 | + | 2.23419i | 0.0131150 | + | 0.0828047i | ||||
\(729\) | 11.9078 | − | 24.2323i | 0.441031 | − | 0.897492i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.38561 | − | 8.78903i | −0.236180 | − | 0.325074i | ||||
\(732\) | 1.69599 | − | 7.14023i | 0.0626855 | − | 0.263911i | ||||
\(733\) | 6.98056 | − | 44.0735i | 0.257833 | − | 1.62789i | −0.430565 | − | 0.902559i | \(-0.641686\pi\) |
0.688398 | − | 0.725333i | \(-0.258314\pi\) | |||||||
\(734\) | −8.34641 | − | 25.6876i | −0.308072 | − | 0.948147i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.478373 | + | 1.47228i | −0.0176331 | + | 0.0542690i | ||||
\(737\) | −6.83537 | − | 3.48279i | −0.251784 | − | 0.128290i | ||||
\(738\) | −3.92214 | + | 2.87865i | −0.144376 | + | 0.105965i | ||||
\(739\) | −8.01855 | − | 2.60538i | −0.294967 | − | 0.0958406i | 0.157795 | − | 0.987472i | \(-0.449561\pi\) |
−0.452762 | + | 0.891631i | \(0.649561\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.38996 | − | 7.51837i | 0.234741 | − | 0.276194i | ||||
\(742\) | 12.8402 | + | 2.03368i | 0.471378 | + | 0.0746589i | ||||
\(743\) | 24.9192 | + | 24.9192i | 0.914196 | + | 0.914196i | 0.996599 | − | 0.0824029i | \(-0.0262594\pi\) |
−0.0824029 | + | 0.996599i | \(0.526259\pi\) | |||||||
\(744\) | −17.0765 | − | 7.02502i | −0.626053 | − | 0.257550i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 15.7261 | − | 21.6451i | 0.575772 | − | 0.792482i | ||||
\(747\) | −6.90844 | + | 21.6168i | −0.252767 | + | 0.790916i | ||||
\(748\) | 15.4553 | + | 30.3327i | 0.565101 | + | 1.10907i | ||||
\(749\) | −12.6933 | −0.463804 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.40064 | −0.306544 | −0.153272 | − | 0.988184i | \(-0.548981\pi\) | ||||
−0.153272 | + | 0.988184i | \(0.548981\pi\) | |||||||
\(752\) | −2.18372 | − | 4.28579i | −0.0796320 | − | 0.156287i | ||||
\(753\) | 27.7241 | − | 23.7946i | 1.01032 | − | 0.867125i | ||||
\(754\) | 2.82250 | − | 3.88484i | 0.102789 | − | 0.141477i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 8.40754 | − | 7.28674i | 0.305779 | − | 0.265016i | ||||
\(757\) | −5.57829 | − | 5.57829i | −0.202746 | − | 0.202746i | 0.598429 | − | 0.801176i | \(-0.295792\pi\) |
−0.801176 | + | 0.598429i | \(0.795792\pi\) | |||||||
\(758\) | 15.5940 | + | 2.46985i | 0.566400 | + | 0.0897089i | ||||
\(759\) | 12.0901 | + | 10.2755i | 0.438843 | + | 0.372978i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.92036 | − | 1.92364i | −0.214613 | − | 0.0697320i | 0.199737 | − | 0.979849i | \(-0.435991\pi\) |
−0.414350 | + | 0.910118i | \(0.635991\pi\) | |||||||
\(762\) | −1.46488 | − | 18.0554i | −0.0530669 | − | 0.654077i | ||||
\(763\) | 3.60114 | + | 1.83487i | 0.130370 | + | 0.0664268i | ||||
\(764\) | −6.49209 | + | 19.9806i | −0.234875 | + | 0.722872i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.93411 | + | 15.1856i | 0.178276 | + | 0.548679i | ||||
\(767\) | 1.19862 | − | 7.56779i | 0.0432796 | − | 0.273257i | ||||
\(768\) | −1.68517 | − | 0.400270i | −0.0608082 | − | 0.0144435i | ||||
\(769\) | −2.22958 | − | 3.06876i | −0.0804008 | − | 0.110662i | 0.766922 | − | 0.641740i | \(-0.221787\pi\) |
−0.847323 | + | 0.531078i | \(0.821787\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.9640 | − | 2.20914i | −1.04311 | − | 0.0795601i | ||||
\(772\) | −1.55066 | − | 9.79050i | −0.0558096 | − | 0.352368i | ||||
\(773\) | −30.3587 | + | 15.4685i | −1.09193 | + | 0.556364i | −0.904742 | − | 0.425960i | \(-0.859936\pi\) |
−0.187185 | + | 0.982325i | \(0.559936\pi\) | |||||||
\(774\) | 2.54757 | − | 5.06017i | 0.0915704 | − | 0.181884i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 12.0641i | 0.433077i | ||||||||
\(777\) | −0.700189 | − | 0.426754i | −0.0251192 | − | 0.0153097i | ||||
\(778\) | 11.3942 | − | 1.80467i | 0.408503 | − | 0.0647005i | ||||
\(779\) | 7.07466 | + | 5.14004i | 0.253476 | + | 0.184161i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.5390 | + | 14.1959i | −0.699159 | + | 0.507969i | ||||
\(782\) | 6.29727 | − | 6.29727i | 0.225190 | − | 0.225190i | ||||
\(783\) | −23.5581 | − | 1.68240i | −0.841898 | − | 0.0601240i | ||||
\(784\) | −2.29721 | + | 0.746410i | −0.0820433 | + | 0.0266575i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −32.8761 | + | 7.97690i | −1.17265 | + | 0.284527i | ||||
\(787\) | −14.2544 | + | 27.9758i | −0.508114 | + | 0.997230i | 0.484371 | + | 0.874863i | \(0.339049\pi\) |
−0.992485 | + | 0.122367i | \(0.960951\pi\) | |||||||
\(788\) | −4.63424 | + | 9.09520i | −0.165088 | + | 0.324003i | ||||
\(789\) | 38.2961 | − | 9.29197i | 1.36338 | − | 0.330803i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.2729 | − | 5.61232i | 0.614155 | − | 0.199551i | ||||
\(792\) | −10.3654 | + | 14.4126i | −0.368317 | + | 0.512129i | ||||
\(793\) | 3.16524 | − | 3.16524i | 0.112401 | − | 0.112401i | ||||
\(794\) | −16.9444 | + | 12.3108i | −0.601334 | + | 0.436895i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.2281 | − | 8.88422i | −0.433413 | − | 0.314893i | ||||
\(797\) | −10.4366 | + | 1.65300i | −0.369685 | + | 0.0585523i | −0.338513 | − | 0.940962i | \(-0.609924\pi\) |
−0.0311718 | + | 0.999514i | \(0.509924\pi\) | |||||||
\(798\) | −17.0761 | − | 10.4076i | −0.604488 | − | 0.368425i | ||||
\(799\) | 27.6716i | 0.978949i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 23.1894 | + | 11.6749i | 0.819358 | + | 0.412511i | ||||
\(802\) | 21.7757 | − | 11.0953i | 0.768926 | − | 0.391787i | ||||
\(803\) | 0.289381 | + | 1.82708i | 0.0102120 | + | 0.0644762i | ||||
\(804\) | −2.23890 | − | 0.170765i | −0.0789601 | − | 0.00602243i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.62002 | − | 9.11167i | −0.233180 | − | 0.320945i | ||||
\(807\) | −17.4488 | − | 4.14454i | −0.614227 | − | 0.145895i | ||||
\(808\) | −0.0485388 | + | 0.306462i | −0.00170759 | + | 0.0107813i | ||||
\(809\) | 4.15772 | + | 12.7961i | 0.146178 | + | 0.449889i | 0.997161 | − | 0.0753048i | \(-0.0239930\pi\) |
−0.850983 | + | 0.525193i | \(0.823993\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.32531 | − | 19.4673i | 0.222112 | − | 0.683590i | −0.776460 | − | 0.630166i | \(-0.782987\pi\) |
0.998572 | − | 0.0534235i | \(-0.0170133\pi\) | |||||||
\(812\) | −8.67148 | − | 4.41834i | −0.304309 | − | 0.155053i | ||||
\(813\) | −0.0895624 | − | 1.10390i | −0.00314109 | − | 0.0387156i | ||||
\(814\) | 1.24438 | + | 0.404322i | 0.0436154 | + | 0.0141715i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7.59247 | + | 6.45294i | 0.265790 | + | 0.225898i | ||||
\(817\) | −10.0575 | − | 1.59296i | −0.351869 | − | 0.0557306i | ||||
\(818\) | −6.92463 | − | 6.92463i | −0.242114 | − | 0.242114i | ||||
\(819\) | 6.69738 | − | 1.09395i | 0.234025 | − | 0.0382257i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.1279 | − | 15.3163i | 0.388368 | − | 0.534543i | −0.569409 | − | 0.822054i | \(-0.692828\pi\) |
0.957777 | + | 0.287512i | \(0.0928280\pi\) | |||||||
\(822\) | 15.7588 | − | 13.5253i | 0.549652 | − | 0.471748i | ||||
\(823\) | 7.17013 | + | 14.0722i | 0.249935 | + | 0.490525i | 0.981553 | − | 0.191190i | \(-0.0612345\pi\) |
−0.731618 | + | 0.681715i | \(0.761235\pi\) | |||||||
\(824\) | −8.83429 | −0.307757 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.5291 | −0.540326 | ||||||||
\(827\) | 3.08387 | + | 6.05244i | 0.107237 | + | 0.210464i | 0.938389 | − | 0.345581i | \(-0.112318\pi\) |
−0.831152 | + | 0.556045i | \(0.812318\pi\) | |||||||
\(828\) | 4.42372 | + | 1.41377i | 0.153735 | + | 0.0491317i | ||||
\(829\) | 11.0240 | − | 15.1733i | 0.382880 | − | 0.526989i | −0.573465 | − | 0.819230i | \(-0.694401\pi\) |
0.956345 | + | 0.292241i | \(0.0944010\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −48.6333 | − | 20.0071i | −1.68707 | − | 0.694038i | ||||
\(832\) | −0.747028 | − | 0.747028i | −0.0258985 | − | 0.0258985i | ||||
\(833\) | 13.7246 | + | 2.17376i | 0.475528 | + | 0.0753162i | ||||
\(834\) | −26.1027 | + | 30.7122i | −0.903862 | + | 1.06348i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 30.3476 | + | 9.86055i | 1.04960 | + | 0.341034i | ||||
\(837\) | −20.8274 | + | 51.3306i | −0.719899 | + | 1.77424i | ||||
\(838\) | −22.9876 | − | 11.7128i | −0.794093 | − | 0.404611i | ||||
\(839\) | −5.00273 | + | 15.3968i | −0.172713 | + | 0.531557i | −0.999522 | − | 0.0309268i | \(-0.990154\pi\) |
0.826808 | + | 0.562484i | \(0.190154\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.57725 | − | 7.93197i | −0.0888709 | − | 0.273516i | ||||
\(842\) | 6.16556 | − | 38.9278i | 0.212479 | − | 1.34154i | ||||
\(843\) | −8.69245 | + | 36.5959i | −0.299384 | + | 1.26043i | ||||
\(844\) | −2.33443 | − | 3.21307i | −0.0803545 | − | 0.110598i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12.8256 | + | 6.61319i | −0.440952 | + | 0.227366i | ||||
\(847\) | 8.04490 | + | 50.7935i | 0.276426 | + | 1.74529i | ||||
\(848\) | −5.40982 | + | 2.75644i | −0.185774 | + | 0.0946566i | ||||
\(849\) | −5.10216 | + | 3.14358i | −0.175106 | + | 0.107887i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 0.342281i | − | 0.0117332i | ||||||
\(852\) | −3.67898 | + | 6.03622i | −0.126040 | + | 0.206797i | ||||
\(853\) | 32.4823 | − | 5.14470i | 1.11217 | − | 0.176151i | 0.426803 | − | 0.904345i | \(-0.359640\pi\) |
0.685371 | + | 0.728194i | \(0.259640\pi\) | |||||||
\(854\) | −7.33967 | − | 5.33258i | −0.251158 | − | 0.182477i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.79605 | − | 3.48453i | 0.163926 | − | 0.119099i | ||||
\(857\) | 14.2417 | − | 14.2417i | 0.486489 | − | 0.486489i | −0.420708 | − | 0.907196i | \(-0.638218\pi\) |
0.907196 | + | 0.420708i | \(0.138218\pi\) | |||||||
\(858\) | −9.99398 | + | 4.16795i | −0.341189 | + | 0.142291i | ||||
\(859\) | 29.9968 | − | 9.74655i | 1.02348 | − | 0.332548i | 0.251269 | − | 0.967917i | \(-0.419152\pi\) |
0.772208 | + | 0.635369i | \(0.219152\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.41813 | + | 5.84472i | 0.0483299 | + | 0.199188i | ||||
\(862\) | 2.79055 | − | 5.47676i | 0.0950465 | − | 0.186539i | ||||
\(863\) | 9.85205 | − | 19.3357i | 0.335368 | − | 0.658196i | −0.660318 | − | 0.750986i | \(-0.729579\pi\) |
0.995686 | + | 0.0927901i | \(0.0295785\pi\) | |||||||
\(864\) | −1.17637 | + | 5.06124i | −0.0400211 | + | 0.172187i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 15.9153 | − | 5.17119i | 0.540824 | − | 0.175724i | ||||
\(867\) | −10.7306 | − | 25.7300i | −0.364431 | − | 0.873838i | ||||
\(868\) | −16.1407 | + | 16.1407i | −0.547852 | + | 0.547852i | ||||
\(869\) | −4.52418 | + | 3.28701i | −0.153472 | + | 0.111504i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.10801 | − | 0.805017i | −0.0375435 | − | 0.0272770i | ||||
\(872\) | −1.86436 | + | 0.295286i | −0.0631352 | + | 0.00999963i | ||||
\(873\) | 36.1920 | − | 0.174834i | 1.22491 | − | 0.00591723i | ||||
\(874\) | − | 8.34750i | − | 0.282358i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.284016 | + | 0.460970i | 0.00959602 | + | 0.0155747i | ||||
\(877\) | 6.74142 | − | 3.43493i | 0.227642 | − | 0.115989i | −0.336450 | − | 0.941701i | \(-0.609226\pi\) |
0.564092 | + | 0.825712i | \(0.309226\pi\) | |||||||
\(878\) | −3.14677 | − | 19.8679i | −0.106198 | − | 0.670510i | ||||
\(879\) | 2.28250 | − | 29.9258i | 0.0769868 | − | 1.00937i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.8656 | + | 25.9662i | 0.635597 | + | 0.874825i | 0.998371 | − | 0.0570525i | \(-0.0181702\pi\) |
−0.362774 | + | 0.931877i | \(0.618170\pi\) | |||||||
\(882\) | 2.27249 | + | 6.88074i | 0.0765189 | + | 0.231687i | ||||
\(883\) | 4.49099 | − | 28.3550i | 0.151134 | − | 0.954222i | −0.789241 | − | 0.614083i | \(-0.789526\pi\) |
0.940375 | − | 0.340139i | \(-0.110474\pi\) | |||||||
\(884\) | 1.87810 | + | 5.78018i | 0.0631672 | + | 0.194409i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.49794 | − | 23.0763i | 0.251898 | − | 0.775263i | ||||
\(887\) | −10.8136 | − | 5.50981i | −0.363086 | − | 0.185001i | 0.262924 | − | 0.964816i | \(-0.415313\pi\) |
−0.626010 | + | 0.779815i | \(0.715313\pi\) | |||||||
\(888\) | 0.381711 | − | 0.0309692i | 0.0128094 | − | 0.00103926i | ||||
\(889\) | −21.2974 | − | 6.91994i | −0.714291 | − | 0.232087i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 43.3875 | + | 30.8868i | 1.45353 | + | 1.03475i | ||||
\(892\) | −13.2221 | − | 2.09418i | −0.442710 | − | 0.0701183i | ||||
\(893\) | 18.3403 | + | 18.3403i | 0.613736 | + | 0.613736i | ||||
\(894\) | 9.69597 | − | 23.5690i | 0.324282 | − | 0.788265i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.25854 | + | 1.73224i | −0.0420450 | + | 0.0578699i | ||||
\(897\) | 1.84487 | + | 2.14953i | 0.0615985 | + | 0.0717708i | ||||
\(898\) | 7.22945 | + | 14.1886i | 0.241250 | + | 0.473479i | ||||
\(899\) | 48.4565 | 1.61611 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.9289 | 1.16365 | ||||||||
\(902\) | −4.35682 | − | 8.55073i | −0.145066 | − | 0.284708i | ||||
\(903\) | −4.56120 | − | 5.31444i | −0.151787 | − | 0.176853i | ||||
\(904\) | −4.98574 | + | 6.86228i | −0.165823 | + | 0.228236i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.63331 | − | 13.6935i | 0.187154 | − | 0.454935i | ||||
\(907\) | −18.7112 | − | 18.7112i | −0.621295 | − | 0.621295i | 0.324567 | − | 0.945863i | \(-0.394781\pi\) |
−0.945863 | + | 0.324567i | \(0.894781\pi\) | |||||||
\(908\) | −0.845381 | − | 0.133895i | −0.0280549 | − | 0.00444347i | ||||
\(909\) | 0.920078 | + | 0.141173i | 0.0305171 | + | 0.00468243i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.0222 | − | 12.0293i | −1.22660 | − | 0.398547i | −0.377119 | − | 0.926165i | \(-0.623085\pi\) |
−0.849482 | + | 0.527618i | \(0.823085\pi\) | |||||||
\(912\) | 9.30911 | − | 0.755271i | 0.308255 | − | 0.0250095i | ||||
\(913\) | −39.8854 | − | 20.3226i | −1.32002 | − | 0.672581i | ||||
\(914\) | 1.00626 | − | 3.09695i | 0.0332842 | − | 0.102438i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.11297 | − | 15.7361i | −0.168937 | − | 0.519935i | ||||
\(917\) | −6.54220 | + | 41.3058i | −0.216042 | + | 1.36404i | ||||
\(918\) | 19.2486 | − | 22.8707i | 0.635297 | − | 0.754845i | ||||
\(919\) | 13.4831 | + | 18.5579i | 0.444766 | + | 0.612168i | 0.971263 | − | 0.238009i | \(-0.0764948\pi\) |
−0.526497 | + | 0.850177i | \(0.676495\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.13209 | − | 41.0648i | 0.103206 | − | 1.35313i | ||||
\(922\) | 1.55131 | + | 9.79461i | 0.0510898 | + | 0.322568i | ||||
\(923\) | −3.84176 | + | 1.95747i | −0.126453 | + | 0.0644311i | ||||
\(924\) | 11.5119 | + | 18.6843i | 0.378715 | + | 0.614669i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 23.1191i | 0.759740i | ||||||||
\(927\) | 0.128027 | + | 26.5026i | 0.00420496 | + | 0.870459i | ||||
\(928\) | 4.48935 | − | 0.711043i | 0.147370 | − | 0.0233411i | ||||
\(929\) | 0.473139 | + | 0.343755i | 0.0155232 | + | 0.0112782i | 0.595520 | − | 0.803341i | \(-0.296946\pi\) |
−0.579997 | + | 0.814619i | \(0.696946\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.5372 | − | 7.65572i | 0.345342 | − | 0.250906i | ||||
\(932\) | 3.85413 | − | 3.85413i | 0.126246 | − | 0.126246i | ||||
\(933\) | 5.18673 | + | 12.4368i | 0.169806 | + | 0.407163i | ||||
\(934\) | 4.41971 | − | 1.43605i | 0.144617 | − | 0.0469891i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.23023 | + | 2.25188i | −0.0728974 | + | 0.0736051i | ||||
\(937\) | 25.3343 | − | 49.7213i | 0.827634 | − | 1.62432i | 0.0473659 | − | 0.998878i | \(-0.484917\pi\) |
0.780268 | − | 0.625445i | \(-0.215083\pi\) | |||||||
\(938\) | −1.26017 | + | 2.47323i | −0.0411461 | + | 0.0807538i | ||||
\(939\) | −8.49469 | − | 35.0102i | −0.277214 | − | 1.14251i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.5712 | + | 4.08462i | −0.409808 | + | 0.133155i | −0.506664 | − | 0.862144i | \(-0.669121\pi\) |
0.0968556 | + | 0.995298i | \(0.469121\pi\) | |||||||
\(942\) | −39.7588 | + | 16.5812i | −1.29541 | + | 0.540246i | ||||
\(943\) | −1.77519 | + | 1.77519i | −0.0578082 | + | 0.0578082i | ||||
\(944\) | 5.86752 | − | 4.26300i | 0.190972 | − | 0.138749i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.04074 | + | 6.56848i | 0.293940 | + | 0.213560i | ||||
\(947\) | −17.8550 | + | 2.82795i | −0.580210 | + | 0.0918962i | −0.439639 | − | 0.898174i | \(-0.644894\pi\) |
−0.140571 | + | 0.990071i | \(0.544894\pi\) | |||||||
\(948\) | −0.851854 | + | 1.39767i | −0.0276669 | + | 0.0453941i | ||||
\(949\) | 0.330250i | 0.0107204i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.319630 | + | 0.196933i | −0.0103647 | + | 0.00638600i | ||||
\(952\) | 10.9752 | − | 5.59216i | 0.355709 | − | 0.181243i | ||||
\(953\) | −8.17990 | − | 51.6458i | −0.264973 | − | 1.67297i | −0.657671 | − | 0.753305i | \(-0.728458\pi\) |
0.392698 | − | 0.919667i | \(-0.371542\pi\) | |||||||
\(954\) | 8.34763 | + | 16.1893i | 0.270264 | + | 0.524149i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.12250 | + | 7.05051i | 0.165673 | + | 0.228030i | ||||
\(957\) | 10.7662 | − | 45.3265i | 0.348022 | − | 1.46520i | ||||
\(958\) | −2.47121 | + | 15.6026i | −0.0798412 | + | 0.504097i | ||||
\(959\) | −7.93318 | − | 24.4158i | −0.256176 | − | 0.788428i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.5409 | − | 78.6068i | 0.823900 | − | 2.53570i | ||||
\(962\) | 0.208129 | + | 0.106047i | 0.00671033 | + | 0.00341909i | ||||
\(963\) | −10.5230 | − | 14.3375i | −0.339098 | − | 0.462019i | ||||
\(964\) | 24.1813 | + | 7.85699i | 0.778828 | + | 0.253056i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.71798 | − | 4.37455i | 0.119624 | − | 0.140749i | ||||
\(967\) | 30.7047 | + | 4.86314i | 0.987395 | + | 0.156388i | 0.629187 | − | 0.777254i | \(-0.283388\pi\) |
0.358208 | + | 0.933642i | \(0.383388\pi\) | |||||||
\(968\) | −16.9834 | − | 16.9834i | −0.545867 | − | 0.545867i | ||||
\(969\) | −49.6895 | − | 20.4416i | −1.59626 | − | 0.656679i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.2468 | + | 34.7493i | −0.810210 | + | 1.11516i | 0.181081 | + | 0.983468i | \(0.442040\pi\) |
−0.991291 | + | 0.131690i | \(0.957960\pi\) | |||||||
\(972\) | 15.2006 | + | 3.45574i | 0.487559 | + | 0.110843i | ||||
\(973\) | 22.6208 | + | 44.3957i | 0.725188 | + | 1.42326i | ||||
\(974\) | −0.135570 | −0.00434393 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.23711 | 0.135627 | ||||||||
\(977\) | 26.9394 | + | 52.8715i | 0.861867 | + | 1.69151i | 0.711276 | + | 0.702912i | \(0.248117\pi\) |
0.150590 | + | 0.988596i | \(0.451883\pi\) | |||||||
\(978\) | 2.64090 | − | 2.26659i | 0.0844466 | − | 0.0724777i | ||||
\(979\) | −30.1017 | + | 41.4314i | −0.962054 | + | 1.32415i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.912865 | + | 5.58874i | 0.0291455 | + | 0.178435i | ||||
\(982\) | 6.43398 | + | 6.43398i | 0.205317 | + | 0.205317i | ||||
\(983\) | −37.5537 | − | 5.94792i | −1.19778 | − | 0.189709i | −0.474492 | − | 0.880260i | \(-0.657368\pi\) |
−0.723284 | + | 0.690550i | \(0.757368\pi\) | |||||||
\(984\) | −2.14031 | − | 1.81907i | −0.0682305 | − | 0.0579899i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −24.8687 | − | 8.08033i | −0.791981 | − | 0.257330i | ||||
\(987\) | 1.44255 | + | 17.7801i | 0.0459168 | + | 0.565948i | ||||
\(988\) | 5.07580 | + | 2.58625i | 0.161483 | + | 0.0822796i | ||||
\(989\) | 0.903372 | − | 2.78029i | 0.0287255 | − | 0.0884081i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.31171 | + | 28.6585i | 0.295796 | + | 0.910367i | 0.982953 | + | 0.183858i | \(0.0588585\pi\) |
−0.687157 | + | 0.726509i | \(0.741141\pi\) | |||||||
\(992\) | 1.66771 | − | 10.5295i | 0.0529499 | − | 0.334313i | ||||
\(993\) | 12.1132 | + | 2.87721i | 0.384402 | + | 0.0913054i | ||||
\(994\) | 5.13648 | + | 7.06976i | 0.162919 | + | 0.224239i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −13.0644 | − | 0.996443i | −0.413960 | − | 0.0315735i | ||||
\(997\) | −5.29952 | − | 33.4599i | −0.167838 | − | 1.05968i | −0.917463 | − | 0.397822i | \(-0.869766\pi\) |
0.749625 | − | 0.661863i | \(-0.230234\pi\) | |||||||
\(998\) | 24.5829 | − | 12.5256i | 0.778157 | − | 0.396491i | ||||
\(999\) | −0.0984382 | − | 1.14467i | −0.00311445 | − | 0.0362158i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 750.2.l.b.257.10 | 80 | ||
3.2 | odd | 2 | inner | 750.2.l.b.257.4 | 80 | ||
5.2 | odd | 4 | 750.2.l.c.743.5 | 80 | |||
5.3 | odd | 4 | 750.2.l.a.743.6 | 80 | |||
5.4 | even | 2 | 150.2.l.a.47.1 | ✓ | 80 | ||
15.2 | even | 4 | 750.2.l.c.743.6 | 80 | |||
15.8 | even | 4 | 750.2.l.a.743.5 | 80 | |||
15.14 | odd | 2 | 150.2.l.a.47.7 | yes | 80 | ||
25.6 | even | 5 | 750.2.l.a.107.5 | 80 | |||
25.8 | odd | 20 | inner | 750.2.l.b.143.4 | 80 | ||
25.17 | odd | 20 | 150.2.l.a.83.7 | yes | 80 | ||
25.19 | even | 10 | 750.2.l.c.107.6 | 80 | |||
75.8 | even | 20 | inner | 750.2.l.b.143.10 | 80 | ||
75.17 | even | 20 | 150.2.l.a.83.1 | yes | 80 | ||
75.44 | odd | 10 | 750.2.l.c.107.5 | 80 | |||
75.56 | odd | 10 | 750.2.l.a.107.6 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.l.a.47.1 | ✓ | 80 | 5.4 | even | 2 | ||
150.2.l.a.47.7 | yes | 80 | 15.14 | odd | 2 | ||
150.2.l.a.83.1 | yes | 80 | 75.17 | even | 20 | ||
150.2.l.a.83.7 | yes | 80 | 25.17 | odd | 20 | ||
750.2.l.a.107.5 | 80 | 25.6 | even | 5 | |||
750.2.l.a.107.6 | 80 | 75.56 | odd | 10 | |||
750.2.l.a.743.5 | 80 | 15.8 | even | 4 | |||
750.2.l.a.743.6 | 80 | 5.3 | odd | 4 | |||
750.2.l.b.143.4 | 80 | 25.8 | odd | 20 | inner | ||
750.2.l.b.143.10 | 80 | 75.8 | even | 20 | inner | ||
750.2.l.b.257.4 | 80 | 3.2 | odd | 2 | inner | ||
750.2.l.b.257.10 | 80 | 1.1 | even | 1 | trivial | ||
750.2.l.c.107.5 | 80 | 75.44 | odd | 10 | |||
750.2.l.c.107.6 | 80 | 25.19 | even | 10 | |||
750.2.l.c.743.5 | 80 | 5.2 | odd | 4 | |||
750.2.l.c.743.6 | 80 | 15.2 | even | 4 |