Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,2,Mod(107,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([10, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.l (of order \(20\), degree \(8\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.98878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{20})\) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 107.6 | ||
Character | \(\chi\) | \(=\) | 750.107 |
Dual form | 750.2.l.a.743.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{13}{20}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.891007 | + | 0.453990i | 0.630037 | + | 0.321020i | ||||
\(3\) | −1.31434 | − | 1.12805i | −0.758835 | − | 0.651283i | ||||
\(4\) | 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 | \(0.617396\pi\) | |||||||
\(8\) | 0.156434 | + | 0.987688i | 0.0553079 | + | 0.349201i | ||||
\(9\) | 0.454984 | + | 2.96530i | 0.151661 | + | 0.988433i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.62798 | + | 1.82864i | −1.69690 | + | 0.551357i | −0.988068 | − | 0.154020i | \(-0.950778\pi\) |
−0.708833 | + | 0.705376i | \(0.750778\pi\) | |||||||
\(12\) | 0.140065 | − | 1.72638i | 0.0404334 | − | 0.498362i | ||||
\(13\) | 0.479621 | + | 0.941310i | 0.133023 | + | 0.261072i | 0.947904 | − | 0.318556i | \(-0.103198\pi\) |
−0.814881 | + | 0.579628i | \(0.803198\pi\) | |||||||
\(14\) | 0.661655 | + | 2.03636i | 0.176835 | + | 0.544241i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.309017 | + | 0.951057i | −0.0772542 | + | 0.237764i | ||||
\(17\) | 5.68203 | − | 0.899945i | 1.37809 | − | 0.218269i | 0.576969 | − | 0.816766i | \(-0.304235\pi\) |
0.801125 | + | 0.598497i | \(0.204235\pi\) | |||||||
\(18\) | −0.940823 | + | 2.84866i | −0.221754 | + | 0.671435i | ||||
\(19\) | −3.16950 | + | 4.36244i | −0.727133 | + | 1.00081i | 0.272123 | + | 0.962262i | \(0.412274\pi\) |
−0.999257 | + | 0.0385508i | \(0.987726\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.282042 | − | 3.69786i | −0.0615467 | − | 0.806939i | ||||
\(22\) | −5.84476 | − | 0.925718i | −1.24611 | − | 0.197364i | ||||
\(23\) | −0.702799 | + | 1.37932i | −0.146544 | + | 0.287608i | −0.952597 | − | 0.304235i | \(-0.901599\pi\) |
0.806054 | + | 0.591843i | \(0.201599\pi\) | |||||||
\(24\) | 0.908558 | − | 1.47463i | 0.185459 | − | 0.301007i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.05646i | 0.207188i | ||||||||
\(27\) | 2.74701 | − | 4.41066i | 0.528663 | − | 0.848832i | ||||
\(28\) | −0.334951 | + | 2.11480i | −0.0632998 | + | 0.399659i | ||||
\(29\) | −3.67723 | + | 2.67167i | −0.682845 | + | 0.496116i | −0.874300 | − | 0.485386i | \(-0.838679\pi\) |
0.191455 | + | 0.981501i | \(0.438679\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.62475 | + | 6.26624i | 1.54905 | + | 1.12545i | 0.944324 | + | 0.329017i | \(0.106718\pi\) |
0.604726 | + | 0.796433i | \(0.293282\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 9.45990 | + | 3.94521i | 1.64676 | + | 0.686774i | ||||
\(34\) | 5.47129 | + | 1.77773i | 0.938319 | + | 0.304878i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.13154 | + | 2.11105i | −0.355257 | + | 0.351841i | ||||
\(37\) | 0.197006 | − | 0.100380i | 0.0323876 | − | 0.0165023i | −0.437722 | − | 0.899111i | \(-0.644214\pi\) |
0.470109 | + | 0.882608i | \(0.344214\pi\) | |||||||
\(38\) | −4.80455 | + | 2.44804i | −0.779402 | + | 0.397125i | ||||
\(39\) | 0.431463 | − | 1.77824i | 0.0690894 | − | 0.284747i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.54235 | + | 0.501139i | 0.240874 | + | 0.0782648i | 0.426966 | − | 0.904268i | \(-0.359582\pi\) |
−0.186092 | + | 0.982532i | \(0.559582\pi\) | |||||||
\(42\) | 1.42749 | − | 3.42286i | 0.220267 | − | 0.528159i | ||||
\(43\) | −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 | ||||
\(47\) | −0.752458 | + | 4.75083i | −0.109757 | + | 0.692980i | 0.870039 | + | 0.492983i | \(0.164093\pi\) |
−0.979796 | + | 0.199998i | \(0.935907\pi\) | |||||||
\(48\) | 1.47900 | − | 0.901424i | 0.213475 | − | 0.130109i | ||||
\(49\) | − | 2.41543i | − | 0.345062i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.48331 | − | 5.22681i | −1.18790 | − | 0.731899i | ||||
\(52\) | −0.479621 | + | 0.941310i | −0.0665115 | + | 0.130536i | ||||
\(53\) | 5.99683 | + | 0.949805i | 0.823728 | + | 0.130466i | 0.554049 | − | 0.832484i | \(-0.313082\pi\) |
0.269680 | + | 0.962950i | \(0.413082\pi\) | |||||||
\(54\) | 4.45000 | − | 2.68281i | 0.605569 | − | 0.365084i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.25854 | + | 1.73224i | −0.168180 | + | 0.231480i | ||||
\(57\) | 9.08688 | − | 2.15837i | 1.20359 | − | 0.285883i | ||||
\(58\) | −4.48935 | + | 0.711043i | −0.589480 | + | 0.0933645i | ||||
\(59\) | −2.24119 | + | 6.89769i | −0.291779 | + | 0.898002i | 0.692506 | + | 0.721412i | \(0.256507\pi\) |
−0.984285 | + | 0.176590i | \(0.943493\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.30934 | − | 4.02973i | −0.167644 | − | 0.515954i | 0.831578 | − | 0.555408i | \(-0.187438\pi\) |
−0.999221 | + | 0.0394543i | \(0.987438\pi\) | |||||||
\(62\) | 4.83989 | + | 9.49882i | 0.614667 | + | 1.20635i | ||||
\(63\) | −3.80069 | + | 5.17841i | −0.478842 | + | 0.652418i | ||||
\(64\) | −0.951057 | + | 0.309017i | −0.118882 | + | 0.0386271i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.63774 | + | 7.80992i | 0.817050 | + | 0.961334i | ||||
\(67\) | 0.202800 | + | 1.28043i | 0.0247759 | + | 0.156429i | 0.996975 | − | 0.0777287i | \(-0.0247668\pi\) |
−0.972199 | + | 0.234158i | \(0.924767\pi\) | |||||||
\(68\) | 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 | 0.927283 | − | 0.374360i | \(-0.122138\pi\) |
−0.642584 | + | 0.766215i | \(0.722138\pi\) | |||||||
\(72\) | −2.85761 | + | 0.913257i | −0.336773 | + | 0.107628i | ||||
\(73\) | 0.278530 | + | 0.141918i | 0.0325994 | + | 0.0166102i | 0.470214 | − | 0.882552i | \(-0.344177\pi\) |
−0.437615 | + | 0.899163i | \(0.644177\pi\) | |||||||
\(74\) | 0.221105 | 0.0257030 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.39228 | −0.618537 | ||||||||
\(77\) | −11.2895 | − | 5.75231i | −1.28656 | − | 0.655537i | ||||
\(78\) | 1.19174 | − | 1.38854i | 0.134938 | − | 0.157222i | ||||
\(79\) | −0.555462 | − | 0.764528i | −0.0624944 | − | 0.0860162i | 0.776626 | − | 0.629962i | \(-0.216930\pi\) |
−0.839120 | + | 0.543946i | \(0.816930\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.58598 | + | 2.69833i | −0.953998 | + | 0.299814i | ||||
\(82\) | 1.14673 | + | 1.14673i | 0.126635 | + | 0.126635i | ||||
\(83\) | −1.18337 | − | 7.47149i | −0.129891 | − | 0.820102i | −0.963493 | − | 0.267735i | \(-0.913725\pi\) |
0.833601 | − | 0.552367i | \(-0.186275\pi\) | |||||||
\(84\) | 2.82585 | − | 2.40172i | 0.308325 | − | 0.262050i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.79600 | + | 0.583556i | −0.193668 | + | 0.0629264i | ||||
\(87\) | 7.84692 | + | 0.636640i | 0.841278 | + | 0.0682550i | ||||
\(88\) | −2.68654 | − | 5.27263i | −0.286386 | − | 0.562064i | ||||
\(89\) | −2.67429 | − | 8.23061i | −0.283474 | − | 0.872443i | −0.986852 | − | 0.161627i | \(-0.948326\pi\) |
0.703378 | − | 0.710816i | \(-0.251674\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.699010 | + | 2.15133i | −0.0732762 | + | 0.225521i | ||||
\(92\) | −1.52899 | + | 0.242168i | −0.159408 | + | 0.0252477i | ||||
\(93\) | −4.26719 | − | 17.9652i | −0.442487 | − | 1.86290i | ||||
\(94\) | −2.82728 | + | 3.89142i | −0.291612 | + | 0.401369i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.72703 | − | 0.131724i | 0.176265 | − | 0.0134440i | ||||
\(97\) | −11.9156 | − | 1.88725i | −1.20985 | − | 0.191621i | −0.481262 | − | 0.876577i | \(-0.659821\pi\) |
−0.728584 | + | 0.684956i | \(0.759821\pi\) | |||||||
\(98\) | 1.09658 | − | 2.15217i | 0.110772 | − | 0.217402i | ||||
\(99\) | −7.98311 | − | 15.8566i | −0.802333 | − | 1.59365i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.310282i | 0.0308742i | 0.999881 | + | 0.0154371i | \(0.00491398\pi\) | ||||
−0.999881 | + | 0.0154371i | \(0.995086\pi\) | |||||||
\(102\) | −5.18576 | − | 8.50846i | −0.513467 | − | 0.842463i | ||||
\(103\) | 1.38199 | − | 8.72553i | 0.136171 | − | 0.859752i | −0.821147 | − | 0.570717i | \(-0.806665\pi\) |
0.957318 | − | 0.289035i | \(-0.0933345\pi\) | |||||||
\(104\) | −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 | −0.474831 | − | 0.880077i | \(-0.657491\pi\) |
0.880077 | + | 0.474831i | \(0.157491\pi\) | |||||||
\(108\) | 5.18295 | − | 0.370140i | 0.498730 | − | 0.0356167i | ||||
\(109\) | −1.79521 | − | 0.583300i | −0.171950 | − | 0.0558700i | 0.221777 | − | 0.975098i | \(-0.428814\pi\) |
−0.393727 | + | 0.919227i | \(0.628814\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.372167 | − | 0.0903007i | −0.0353245 | − | 0.00857096i | ||||
\(112\) | −1.90779 | + | 0.972066i | −0.180269 | + | 0.0918516i | ||||
\(113\) | 7.55774 | − | 3.85086i | 0.710972 | − | 0.362258i | −0.0608066 | − | 0.998150i | \(-0.519367\pi\) |
0.771779 | + | 0.635891i | \(0.219367\pi\) | |||||||
\(114\) | 9.07635 | + | 2.20224i | 0.850078 | + | 0.206258i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.32285 | − | 1.40458i | −0.401366 | − | 0.130412i | ||||
\(117\) | −2.57304 | + | 1.85050i | −0.237878 | + | 0.171079i | ||||
\(118\) | −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 | ||||
\(122\) | 0.662830 | − | 4.18494i | 0.0600098 | − | 0.378887i | ||||
\(123\) | −1.46186 | − | 2.39852i | −0.131811 | − | 0.216267i | ||||
\(124\) | 10.6608i | 0.957366i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.73738 | + | 2.88852i | −0.511127 | + | 0.257330i | ||||
\(127\) | 4.74807 | − | 9.31862i | 0.421323 | − | 0.826894i | −0.578613 | − | 0.815602i | \(-0.696406\pi\) |
0.999936 | − | 0.0112913i | \(-0.00359421\pi\) | |||||||
\(128\) | −0.987688 | − | 0.156434i | −0.0873001 | − | 0.0138270i | ||||
\(129\) | 3.26138 | − | 0.248751i | 0.287148 | − | 0.0219013i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.4805 | − | 15.8015i | 1.00306 | − | 1.38059i | 0.0796236 | − | 0.996825i | \(-0.474628\pi\) |
0.923432 | − | 0.383762i | \(-0.125372\pi\) | |||||||
\(132\) | 2.36864 | + | 9.97216i | 0.206164 | + | 0.867965i | ||||
\(133\) | −11.4036 | + | 1.80615i | −0.988816 | + | 0.156613i | ||||
\(134\) | −0.400605 | + | 1.23294i | −0.0346070 | + | 0.106510i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.77773 | + | 5.47129i | 0.152439 | + | 0.469159i | ||||
\(137\) | −5.44330 | − | 10.6831i | −0.465053 | − | 0.912717i | −0.997791 | − | 0.0664369i | \(-0.978837\pi\) |
0.532738 | − | 0.846280i | \(-0.321163\pi\) | |||||||
\(138\) | 2.67251 | + | 0.216828i | 0.227500 | + | 0.0184576i | ||||
\(139\) | −22.1318 | + | 7.19107i | −1.87720 | + | 0.609939i | −0.888747 | + | 0.458399i | \(0.848423\pi\) |
−0.988451 | + | 0.151540i | \(0.951577\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.34819 | − | 5.39540i | 0.534614 | − | 0.454375i | ||||
\(142\) | 0.638455 | + | 4.03104i | 0.0535779 | + | 0.338278i | ||||
\(143\) | −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 | ||||
\(147\) | −2.72474 | + | 3.17470i | −0.224733 | + | 0.261845i | ||||
\(148\) | 0.197006 | + | 0.100380i | 0.0161938 | + | 0.00825116i | ||||
\(149\) | 14.7140 | 1.20542 | 0.602711 | − | 0.797960i | \(-0.294087\pi\) | ||||
0.602711 | + | 0.797960i | \(0.294087\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.54879 | −0.695691 | −0.347845 | − | 0.937552i | \(-0.613087\pi\) | ||||
−0.347845 | + | 0.937552i | \(0.613087\pi\) | |||||||
\(152\) | −4.80455 | − | 2.44804i | −0.389701 | − | 0.198562i | ||||
\(153\) | 5.25384 | + | 16.4394i | 0.424748 | + | 1.32905i | ||||
\(154\) | −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 | \(0.289114\pi\) | |||||||
\(158\) | −0.147832 | − | 0.933375i | −0.0117609 | − | 0.0742553i | ||||
\(159\) | −6.81045 | − | 8.01312i | −0.540104 | − | 0.635482i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.15239 | + | 1.02427i | −0.248443 | + | 0.0807240i | ||||
\(162\) | −8.87518 | − | 1.49373i | −0.697300 | − | 0.117358i | ||||
\(163\) | 0.912200 | + | 1.79029i | 0.0714490 | + | 0.140227i | 0.923968 | − | 0.382469i | \(-0.124926\pi\) |
−0.852519 | + | 0.522696i | \(0.824926\pi\) | |||||||
\(164\) | 0.501139 | + | 1.54235i | 0.0391324 | + | 0.120437i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.33760 | − | 7.19438i | 0.181433 | − | 0.558392i | ||||
\(167\) | −14.6571 | + | 2.32146i | −1.13420 | + | 0.179640i | −0.695179 | − | 0.718837i | \(-0.744675\pi\) |
−0.439021 | + | 0.898477i | \(0.644675\pi\) | |||||||
\(168\) | 3.60821 | − | 0.857043i | 0.278379 | − | 0.0661223i | ||||
\(169\) | 6.98518 | − | 9.61428i | 0.537322 | − | 0.739560i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.3780 | − | 7.41367i | −1.09951 | − | 0.566937i | ||||
\(172\) | −1.86518 | − | 0.295415i | −0.142218 | − | 0.0225252i | ||||
\(173\) | 2.27656 | − | 4.46800i | 0.173084 | − | 0.339696i | −0.788126 | − | 0.615514i | \(-0.788949\pi\) |
0.961210 | + | 0.275818i | \(0.0889486\pi\) | |||||||
\(174\) | 6.70263 | + | 4.12968i | 0.508125 | + | 0.313070i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 5.91761i | − | 0.446057i | ||||||
\(177\) | 10.7267 | − | 6.53772i | 0.806265 | − | 0.491405i | ||||
\(178\) | 1.35381 | − | 8.54762i | 0.101472 | − | 0.640672i | ||||
\(179\) | 2.56353 | − | 1.86252i | 0.191607 | − | 0.139211i | −0.487846 | − | 0.872930i | \(-0.662217\pi\) |
0.679453 | + | 0.733719i | \(0.262217\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.04884 | − | 3.66820i | −0.375278 | − | 0.272655i | 0.384118 | − | 0.923284i | \(-0.374505\pi\) |
−0.759396 | + | 0.650629i | \(0.774505\pi\) | |||||||
\(182\) | −1.59951 | + | 1.59951i | −0.118563 | + | 0.118563i | ||||
\(183\) | −2.82484 | + | 6.77345i | −0.208818 | + | 0.500707i | ||||
\(184\) | −1.47228 | − | 0.478373i | −0.108538 | − | 0.0352661i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.35392 | − | 17.9443i | 0.319245 | − | 1.31574i | ||||
\(187\) | −30.3327 | + | 15.4553i | −2.21815 | + | 1.13020i | ||||
\(188\) | −4.28579 | + | 2.18372i | −0.312573 | + | 0.159264i | ||||
\(189\) | 10.8369 | − | 2.51881i | 0.788270 | − | 0.183216i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.9806 | + | 6.49209i | 1.44574 | + | 0.469751i | 0.923683 | − | 0.383157i | \(-0.125163\pi\) |
0.522062 | + | 0.852908i | \(0.325163\pi\) | |||||||
\(192\) | 1.59860 | + | 0.666690i | 0.115369 | + | 0.0481142i | ||||
\(193\) | −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 | ||||
\(197\) | −1.59685 | + | 10.0821i | −0.113771 | + | 0.718320i | 0.863186 | + | 0.504885i | \(0.168465\pi\) |
−0.976957 | + | 0.213435i | \(0.931535\pi\) | |||||||
\(198\) | 0.0857583 | − | 17.7526i | 0.00609458 | − | 1.26162i | ||||
\(199\) | 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 | ||||
\(202\) | −0.140865 | + | 0.276463i | −0.00991123 | + | 0.0194519i | ||||
\(203\) | −9.61241 | − | 1.52246i | −0.674659 | − | 0.106856i | ||||
\(204\) | −0.757790 | − | 9.93538i | −0.0530559 | − | 0.695616i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.19267 | − | 7.14709i | 0.361790 | − | 0.497962i | ||||
\(207\) | −4.40986 | − | 1.45644i | −0.306506 | − | 0.101229i | ||||
\(208\) | −1.04345 | + | 0.165266i | −0.0723503 | + | 0.0114592i | ||||
\(209\) | 9.86055 | − | 30.3476i | 0.682068 | − | 2.09919i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.22728 | − | 3.77719i | −0.0844897 | − | 0.260033i | 0.899883 | − | 0.436132i | \(-0.143652\pi\) |
−0.984372 | + | 0.176099i | \(0.943652\pi\) | |||||||
\(212\) | 2.75644 | + | 5.40982i | 0.189313 | + | 0.371548i | ||||
\(213\) | 0.571647 | − | 7.04585i | 0.0391686 | − | 0.482774i | ||||
\(214\) | 5.63809 | − | 1.83193i | 0.385412 | − | 0.125228i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.78608 | + | 2.02321i | 0.325652 | + | 0.137662i | ||||
\(217\) | 3.57084 | + | 22.5454i | 0.242404 | + | 1.53048i | ||||
\(218\) | −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 | ||||
\(222\) | −0.290608 | − | 0.249419i | −0.0195043 | − | 0.0167399i | ||||
\(223\) | −11.9279 | − | 6.07755i | −0.798748 | − | 0.406983i | 0.00645660 | − | 0.999979i | \(-0.497945\pi\) |
−0.805205 | + | 0.592996i | \(0.797945\pi\) | |||||||
\(224\) | −2.14116 | −0.143062 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.48225 | 0.564231 | ||||||||
\(227\) | 0.762629 | + | 0.388579i | 0.0506175 | + | 0.0257909i | 0.479116 | − | 0.877752i | \(-0.340957\pi\) |
−0.428499 | + | 0.903542i | \(0.640957\pi\) | |||||||
\(228\) | 7.08729 | + | 6.08278i | 0.469367 | + | 0.402842i | ||||
\(229\) | 9.72545 | + | 13.3859i | 0.642676 | + | 0.884567i | 0.998755 | − | 0.0498887i | \(-0.0158867\pi\) |
−0.356079 | + | 0.934456i | \(0.615887\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.34939 | + | 20.2957i | 0.549350 | + | 1.33536i | ||||
\(232\) | −3.21402 | − | 3.21402i | −0.211011 | − | 0.211011i | ||||
\(233\) | 0.852656 | + | 5.38346i | 0.0558593 | + | 0.352682i | 0.999749 | + | 0.0224200i | \(0.00713710\pi\) |
−0.943889 | + | 0.330262i | \(0.892863\pi\) | |||||||
\(234\) | −3.13271 | + | 0.480671i | −0.204792 | + | 0.0314225i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.89769 | + | 2.24119i | −0.449001 | + | 0.145889i | ||||
\(237\) | −0.132363 | + | 1.63144i | −0.00859790 | + | 0.105974i | ||||
\(238\) | 5.59216 | + | 10.9752i | 0.362486 | + | 0.711418i | ||||
\(239\) | −2.69306 | − | 8.28837i | −0.174199 | − | 0.536130i | 0.825397 | − | 0.564553i | \(-0.190951\pi\) |
−0.999596 | + | 0.0284230i | \(0.990951\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.85699 | + | 24.1813i | −0.506113 | + | 1.55766i | 0.292779 | + | 0.956180i | \(0.405420\pi\) |
−0.798892 | + | 0.601475i | \(0.794580\pi\) | |||||||
\(242\) | 23.7224 | − | 3.75726i | 1.52494 | − | 0.241526i | ||||
\(243\) | 14.3288 | + | 6.13893i | 0.919191 | + | 0.393813i | ||||
\(244\) | 2.49051 | − | 3.42789i | 0.159439 | − | 0.219448i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.213620 | − | 2.80077i | −0.0136199 | − | 0.178570i | ||||
\(247\) | −5.62657 | − | 0.891162i | −0.358010 | − | 0.0567033i | ||||
\(248\) | −4.83989 | + | 9.49882i | −0.307333 | + | 0.603176i | ||||
\(249\) | −6.87290 | + | 11.1550i | −0.435552 | + | 0.706918i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.0935i | 1.33141i | 0.746215 | + | 0.665706i | \(0.231869\pi\) | ||||
−0.746215 | + | 0.665706i | \(0.768131\pi\) | |||||||
\(252\) | −6.42341 | − | 0.0310298i | −0.404637 | − | 0.00195469i | ||||
\(253\) | 1.43306 | − | 9.04796i | 0.0900954 | − | 0.568840i | ||||
\(254\) | 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 | −0.232792 | − | 0.972526i | \(-0.574786\pi\) |
0.972526 | + | 0.232792i | \(0.0747863\pi\) | |||||||
\(258\) | 3.01884 | + | 1.25900i | 0.187945 | + | 0.0783816i | ||||
\(259\) | 0.450251 | + | 0.146295i | 0.0279772 | + | 0.00909035i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.59537 | − | 9.68852i | −0.593938 | − | 0.599704i | ||||
\(262\) | 17.4029 | − | 8.86724i | 1.07516 | − | 0.547820i | ||||
\(263\) | 20.2720 | − | 10.3291i | 1.25002 | − | 0.636919i | 0.301453 | − | 0.953481i | \(-0.402529\pi\) |
0.948572 | + | 0.316562i | \(0.102529\pi\) | |||||||
\(264\) | −2.41679 | + | 9.96060i | −0.148743 | + | 0.613033i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −10.9806 | − | 3.56783i | −0.673266 | − | 0.218757i | ||||
\(267\) | −5.76965 | + | 13.8346i | −0.353097 | + | 0.846662i | ||||
\(268\) | −0.916684 | + | 0.916684i | −0.0559954 | + | 0.0559954i | ||||
\(269\) | 8.37684 | + | 6.08613i | 0.510745 | + | 0.371078i | 0.813106 | − | 0.582115i | \(-0.197775\pi\) |
−0.302361 | + | 0.953193i | \(0.597775\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.517312 | + | 0.375849i | −0.0314245 | + | 0.0228312i | −0.603387 | − | 0.797449i | \(-0.706182\pi\) |
0.571962 | + | 0.820280i | \(0.306182\pi\) | |||||||
\(272\) | −0.899945 | + | 5.68203i | −0.0545672 | + | 0.344524i | ||||
\(273\) | 3.34556 | − | 2.03906i | 0.202482 | − | 0.123410i | ||||
\(274\) | − | 11.9899i | − | 0.724336i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.28279 | + | 1.40649i | 0.137408 | + | 0.0846608i | ||||
\(277\) | 13.7839 | − | 27.0524i | 0.828193 | − | 1.62542i | 0.0488650 | − | 0.998805i | \(-0.484440\pi\) |
0.779328 | − | 0.626616i | \(-0.215560\pi\) | |||||||
\(278\) | −22.9843 | − | 3.64035i | −1.37851 | − | 0.218334i | ||||
\(279\) | −14.6572 | + | 28.4260i | −0.877501 | + | 1.70182i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.7646 | − | 17.5690i | 0.761473 | − | 1.04808i | −0.235617 | − | 0.971846i | \(-0.575711\pi\) |
0.997090 | − | 0.0762322i | \(-0.0242890\pi\) | |||||||
\(282\) | 8.10574 | − | 1.92532i | 0.482690 | − | 0.114651i | ||||
\(283\) | −3.41737 | + | 0.541258i | −0.203142 | + | 0.0321745i | −0.257176 | − | 0.966365i | \(-0.582792\pi\) |
0.0540343 | + | 0.998539i | \(0.482792\pi\) | |||||||
\(284\) | −1.26119 | + | 3.88154i | −0.0748378 | + | 0.230327i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.93188 | − | 5.94572i | −0.114235 | − | 0.351578i | ||||
\(287\) | 1.57642 | + | 3.09390i | 0.0930531 | + | 0.182627i | ||||
\(288\) | −2.41850 | − | 1.77506i | −0.142512 | − | 0.104596i | ||||
\(289\) | 15.3076 | − | 4.97374i | 0.900446 | − | 0.292573i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.5323 | + | 15.9219i | 0.793275 | + | 0.933361i | ||||
\(292\) | 0.0489016 | + | 0.308752i | 0.00286175 | + | 0.0180684i | ||||
\(293\) | 12.2527 | + | 12.2527i | 0.715808 | + | 0.715808i | 0.967744 | − | 0.251936i | \(-0.0810673\pi\) |
−0.251936 | + | 0.967744i | \(0.581067\pi\) | |||||||
\(294\) | −3.86905 | + | 1.59167i | −0.225647 | + | 0.0928283i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.129962 | + | 0.178878i | 0.00755391 | + | 0.0103971i | ||||
\(297\) | −7.39463 | + | 29.8464i | −0.429080 | + | 1.73187i | ||||
\(298\) | 13.1103 | + | 6.68004i | 0.759460 | + | 0.386964i | ||||
\(299\) | −1.63544 | −0.0945802 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.04342 | −0.233059 | ||||||||
\(302\) | −7.61703 | − | 3.88107i | −0.438311 | − | 0.223330i | ||||
\(303\) | 0.350015 | − | 0.407816i | 0.0201078 | − | 0.0234284i | ||||
\(304\) | −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 | \(0.987383\pi\) | |||||||
\(308\) | −1.98211 | − | 12.5146i | −0.112941 | − | 0.713083i | ||||
\(309\) | −11.6593 | + | 9.90936i | −0.663273 | + | 0.563724i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.39905 | − | 2.40410i | 0.419562 | − | 0.136324i | −0.0916250 | − | 0.995794i | \(-0.529206\pi\) |
0.511187 | + | 0.859470i | \(0.329206\pi\) | |||||||
\(312\) | 1.82384 | + | 0.147973i | 0.103255 | + | 0.00837732i | ||||
\(313\) | 9.44284 | + | 18.5326i | 0.533741 | + | 1.04753i | 0.987679 | + | 0.156492i | \(0.0500186\pi\) |
−0.453939 | + | 0.891033i | \(0.649981\pi\) | |||||||
\(314\) | 7.68555 | + | 23.6537i | 0.433721 | + | 1.33486i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.292024 | − | 0.898757i | 0.0164276 | − | 0.0505590i | ||||
\(317\) | 0.214085 | − | 0.0339077i | 0.0120242 | − | 0.00190445i | −0.150419 | − | 0.988622i | \(-0.548062\pi\) |
0.162444 | + | 0.986718i | \(0.448062\pi\) | |||||||
\(318\) | −2.43027 | − | 10.2316i | −0.136283 | − | 0.573761i | ||||
\(319\) | 15.8099 | − | 21.7604i | 0.885183 | − | 1.21835i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.2383 | + | 0.780892i | −0.571445 | + | 0.0435852i | ||||
\(322\) | −3.27381 | − | 0.518520i | −0.182442 | − | 0.0288960i | ||||
\(323\) | −14.0832 | + | 27.6399i | −0.783612 | + | 1.53793i | ||||
\(324\) | −7.22970 | − | 5.36017i | −0.401650 | − | 0.297787i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.00929i | 0.111284i | ||||||||
\(327\) | 1.70153 | + | 2.79176i | 0.0940947 | + | 0.154384i | ||||
\(328\) | −0.253693 | + | 1.60175i | −0.0140078 | + | 0.0884421i | ||||
\(329\) | −8.33214 | + | 6.05366i | −0.459366 | + | 0.333749i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.81535 | + | 4.22510i | 0.319640 | + | 0.232232i | 0.736022 | − | 0.676958i | \(-0.236702\pi\) |
−0.416382 | + | 0.909190i | \(0.636702\pi\) | |||||||
\(332\) | 5.34899 | − | 5.34899i | 0.293564 | − | 0.293564i | ||||
\(333\) | 0.387290 | + | 0.538511i | 0.0212234 | + | 0.0295102i | ||||
\(334\) | −14.1135 | − | 4.58575i | −0.772255 | − | 0.250921i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.60403 | + | 0.874463i | 0.196616 | + | 0.0477058i | ||||
\(337\) | 6.01777 | − | 3.06621i | 0.327809 | − | 0.167027i | −0.282339 | − | 0.959315i | \(-0.591110\pi\) |
0.610147 | + | 0.792288i | \(0.291110\pi\) | |||||||
\(338\) | 10.5886 | − | 5.39518i | 0.575946 | − | 0.293459i | ||||
\(339\) | −14.2774 | − | 3.46420i | −0.775443 | − | 0.188150i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −59.9987 | − | 19.4947i | −3.24911 | − | 1.05570i | ||||
\(342\) | −9.44517 | − | 13.1331i | −0.510736 | − | 0.710157i | ||||
\(343\) | 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 | ||||
\(347\) | 0.716076 | − | 4.52113i | 0.0384410 | − | 0.242707i | −0.960984 | − | 0.276603i | \(-0.910791\pi\) |
0.999425 | + | 0.0338958i | \(0.0107914\pi\) | |||||||
\(348\) | 4.09725 | + | 6.72250i | 0.219636 | + | 0.360364i | ||||
\(349\) | 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 | ||||
\(352\) | 2.68654 | − | 5.27263i | 0.143193 | − | 0.281032i | ||||
\(353\) | −10.7063 | − | 1.69571i | −0.569840 | − | 0.0902538i | −0.135136 | − | 0.990827i | \(-0.543147\pi\) |
−0.434704 | + | 0.900573i | \(0.643147\pi\) | |||||||
\(354\) | 12.5256 | − | 0.955350i | 0.665727 | − | 0.0507763i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.08679 | − | 7.00137i | 0.269600 | − | 0.371072i | ||||
\(357\) | −4.93044 | − | 20.7575i | −0.260947 | − | 1.09860i | ||||
\(358\) | 3.12969 | − | 0.495694i | 0.165409 | − | 0.0261982i | ||||
\(359\) | −6.51044 | + | 20.0371i | −0.343608 | + | 1.05752i | 0.618717 | + | 0.785614i | \(0.287653\pi\) |
−0.962325 | + | 0.271902i | \(0.912347\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.11386 | − | 9.58347i | −0.163887 | − | 0.504393i | ||||
\(362\) | −2.83323 | − | 5.56052i | −0.148911 | − | 0.292254i | ||||
\(363\) | −41.4644 | − | 3.36411i | −2.17632 | − | 0.176570i | ||||
\(364\) | −2.15133 | + | 0.699010i | −0.112760 | + | 0.0366381i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.59203 | + | 4.75273i | −0.292300 | + | 0.248429i | ||||
\(367\) | −4.22522 | − | 26.6770i | −0.220555 | − | 1.39253i | −0.810809 | − | 0.585311i | \(-0.800972\pi\) |
0.590254 | − | 0.807218i | \(-0.299028\pi\) | |||||||
\(368\) | −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 | ||||
\(372\) | 12.0259 | − | 14.0119i | 0.623516 | − | 0.726483i | ||||
\(373\) | 23.8387 | + | 12.1464i | 1.23432 | + | 0.628917i | 0.944609 | − | 0.328197i | \(-0.106441\pi\) |
0.289711 | + | 0.957114i | \(0.406441\pi\) | |||||||
\(374\) | −34.0432 | −1.76033 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.81005 | −0.248060 | ||||||||
\(377\) | −4.27854 | − | 2.18003i | −0.220356 | − | 0.112277i | ||||
\(378\) | 10.7993 | + | 2.67559i | 0.555455 | + | 0.137617i | ||||
\(379\) | −9.28018 | − | 12.7731i | −0.476691 | − | 0.656109i | 0.501174 | − | 0.865347i | \(-0.332902\pi\) |
−0.977865 | + | 0.209238i | \(0.932902\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.7525 | + | 6.89175i | −0.858257 | + | 0.353075i | ||||
\(382\) | 14.8555 | + | 14.8555i | 0.760073 | + | 0.760073i | ||||
\(383\) | −2.49780 | − | 15.7705i | −0.127632 | − | 0.805836i | −0.965584 | − | 0.260092i | \(-0.916247\pi\) |
0.837952 | − | 0.545744i | \(-0.183753\pi\) | |||||||
\(384\) | 1.12169 | + | 1.31977i | 0.0572411 | + | 0.0673495i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.42739 | + | 3.06314i | −0.479841 | + | 0.155910i | ||||
\(387\) | −4.56717 | − | 3.35207i | −0.232162 | − | 0.170395i | ||||
\(388\) | −5.47700 | − | 10.7492i | −0.278053 | − | 0.545709i | ||||
\(389\) | −3.56490 | − | 10.9716i | −0.180748 | − | 0.556284i | 0.819102 | − | 0.573648i | \(-0.194472\pi\) |
−0.999849 | + | 0.0173647i | \(0.994472\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.75201 | + | 8.46982i | −0.139175 | + | 0.428337i | ||||
\(392\) | 2.38569 | − | 0.377857i | 0.120496 | − | 0.0190847i | ||||
\(393\) | −32.9143 | + | 7.81799i | −1.66031 | + | 0.394365i | ||||
\(394\) | −5.99998 | + | 8.25827i | −0.302275 | + | 0.416046i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 8.13594 | − | 15.7788i | 0.408846 | − | 0.792913i | ||||
\(397\) | 20.6866 | + | 3.27643i | 1.03823 | + | 0.164439i | 0.652200 | − | 0.758047i | \(-0.273846\pi\) |
0.386030 | + | 0.922486i | \(0.373846\pi\) | |||||||
\(398\) | −6.86195 | + | 13.4673i | −0.343958 | + | 0.675057i | ||||
\(399\) | 17.0256 | + | 10.4900i | 0.852348 | + | 0.525155i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.4394i | 1.22045i | 0.792229 | + | 0.610223i | \(0.208920\pi\) | ||||
−0.792229 | + | 0.610223i | \(0.791080\pi\) | |||||||
\(402\) | 1.91735 | − | 1.16859i | 0.0956289 | − | 0.0582842i | ||||
\(403\) | −1.76187 | + | 11.1240i | −0.0877648 | + | 0.554125i | ||||
\(404\) | −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 | ||||
\(408\) | 3.83537 | − | 9.19652i | 0.189879 | − | 0.455296i | ||||
\(409\) | 9.31361 | + | 3.02618i | 0.460528 | + | 0.149635i | 0.530087 | − | 0.847943i | \(-0.322159\pi\) |
−0.0695588 | + | 0.997578i | \(0.522159\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.89675 | + | 20.1816i | −0.241539 | + | 0.995483i | ||||
\(412\) | 7.87141 | − | 4.01069i | 0.387797 | − | 0.197592i | ||||
\(413\) | −13.8365 | + | 7.05006i | −0.680851 | + | 0.346911i | ||||
\(414\) | −3.26800 | − | 3.29973i | −0.160614 | − | 0.162173i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.00475 | − | 0.326463i | −0.0492619 | − | 0.0160062i | ||||
\(417\) | 37.2007 | + | 15.5144i | 1.82173 | + | 0.759744i | ||||
\(418\) | 22.5634 | − | 22.5634i | 1.10361 | − | 1.10361i | ||||
\(419\) | 20.8723 | + | 15.1646i | 1.01968 | + | 0.740840i | 0.966217 | − | 0.257730i | \(-0.0829745\pi\) |
0.0534618 | + | 0.998570i | \(0.482974\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.8859 | + | 23.1664i | −1.55402 | + | 1.12906i | −0.613316 | + | 0.789837i | \(0.710165\pi\) |
−0.940705 | + | 0.339225i | \(0.889835\pi\) | |||||||
\(422\) | 0.621291 | − | 3.92268i | 0.0302440 | − | 0.190953i | ||||
\(423\) | −14.4300 | − | 0.0697075i | −0.701610 | − | 0.00338930i | ||||
\(424\) | 6.07158i | 0.294862i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.70809 | − | 6.01838i | 0.179658 | − | 0.291591i | ||||
\(427\) | 4.11875 | − | 8.08350i | 0.199320 | − | 0.391188i | ||||
\(428\) | 5.85525 | + | 0.927381i | 0.283024 | + | 0.0448267i | ||||
\(429\) | 0.823500 | + | 10.7969i | 0.0397590 | + | 0.521280i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.61295 | + | 4.97279i | −0.174030 | + | 0.239531i | −0.887118 | − | 0.461543i | \(-0.847296\pi\) |
0.713088 | + | 0.701074i | \(0.247296\pi\) | |||||||
\(432\) | 3.34591 | + | 3.97553i | 0.160980 | + | 0.191273i | ||||
\(433\) | 16.5283 | − | 2.61783i | 0.794299 | − | 0.125805i | 0.253919 | − | 0.967225i | \(-0.418280\pi\) |
0.540380 | + | 0.841421i | \(0.318280\pi\) | |||||||
\(434\) | −7.05375 | + | 21.7092i | −0.338591 | + | 1.04208i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.583300 | − | 1.79521i | −0.0279350 | − | 0.0859752i | ||||
\(437\) | −3.78968 | − | 7.43768i | −0.181285 | − | 0.355792i | ||||
\(438\) | 0.0437846 | − | 0.539668i | 0.00209211 | − | 0.0257863i | ||||
\(439\) | 19.1311 | − | 6.21606i | 0.913076 | − | 0.296676i | 0.185453 | − | 0.982653i | \(-0.440625\pi\) |
0.727623 | + | 0.685977i | \(0.240625\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.16248 | − | 1.09898i | 0.341070 | − | 0.0523326i | ||||
\(442\) | 0.950753 | + | 6.00282i | 0.0452227 | + | 0.285525i | ||||
\(443\) | 17.1571 | + | 17.1571i | 0.815159 | + | 0.815159i | 0.985402 | − | 0.170243i | \(-0.0544552\pi\) |
−0.170243 | + | 0.985402i | \(0.554455\pi\) | |||||||
\(444\) | −0.145699 | − | 0.354167i | −0.00691459 | − | 0.0168080i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.86865 | − | 10.8303i | −0.372591 | − | 0.512828i | ||||
\(447\) | −19.3393 | − | 16.5983i | −0.914716 | − | 0.785071i | ||||
\(448\) | −1.90779 | − | 0.972066i | −0.0901345 | − | 0.0459258i | ||||
\(449\) | −15.9242 | −0.751511 | −0.375755 | − | 0.926719i | \(-0.622617\pi\) | ||||
−0.375755 | + | 0.926719i | \(0.622617\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.59671 | −0.451891 | ||||||||
\(452\) | 7.55774 | + | 3.85086i | 0.355486 | + | 0.181129i | ||||
\(453\) | 11.2360 | + | 9.64350i | 0.527914 | + | 0.453091i | ||||
\(454\) | 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 | \(0.774267\pi\) | |||||||
\(458\) | 2.58835 | + | 16.3422i | 0.120946 | + | 0.763621i | ||||
\(459\) | 11.6393 | − | 27.5337i | 0.543274 | − | 1.28516i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.43135 | − | 3.06443i | 0.439262 | − | 0.142725i | −0.0810333 | − | 0.996711i | \(-0.525822\pi\) |
0.520295 | + | 0.853987i | \(0.325822\pi\) | |||||||
\(462\) | −1.77471 | + | 21.8742i | −0.0825668 | + | 1.01768i | ||||
\(463\) | −10.4958 | − | 20.5992i | −0.487783 | − | 0.957328i | −0.995406 | − | 0.0957485i | \(-0.969476\pi\) |
0.507623 | − | 0.861580i | \(-0.330524\pi\) | |||||||
\(464\) | −1.40458 | − | 4.32285i | −0.0652059 | − | 0.200683i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.68432 | + | 5.18379i | −0.0780245 | + | 0.240135i | ||||
\(467\) | −4.58995 | + | 0.726976i | −0.212397 | + | 0.0336405i | −0.261726 | − | 0.965142i | \(-0.584292\pi\) |
0.0493288 | + | 0.998783i | \(0.484292\pi\) | |||||||
\(468\) | −3.00948 | − | 0.993939i | −0.139113 | − | 0.0459448i | ||||
\(469\) | −1.63156 | + | 2.24565i | −0.0753383 | + | 0.103694i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.27611 | − | 42.9530i | −0.150955 | − | 1.97917i | ||||
\(472\) | −7.16336 | − | 1.13457i | −0.329721 | − | 0.0522226i | ||||
\(473\) | 5.07333 | − | 9.95697i | 0.233272 | − | 0.457822i | ||||
\(474\) | −0.858596 | + | 1.39353i | −0.0394366 | + | 0.0640072i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.3178i | 0.564585i | ||||||||
\(477\) | −0.0879897 | + | 18.2145i | −0.00402877 | + | 0.833986i | ||||
\(478\) | 1.36331 | − | 8.60761i | 0.0623564 | − | 0.393703i | ||||
\(479\) | −12.7801 | + | 9.28530i | −0.583939 | + | 0.424256i | −0.840142 | − | 0.542367i | \(-0.817528\pi\) |
0.256203 | + | 0.966623i | \(0.417528\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.188977 | + | 0.137300i | 0.00861660 | + | 0.00626032i | ||||
\(482\) | −17.9787 | + | 17.9787i | −0.818908 | + | 0.818908i | ||||
\(483\) | 5.29875 | + | 2.20982i | 0.241101 | + | 0.100550i | ||||
\(484\) | 22.8426 | + | 7.42201i | 1.03830 | + | 0.337364i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 9.98001 | + | 11.9750i | 0.452702 | + | 0.543195i | ||||
\(487\) | 0.120793 | − | 0.0615473i | 0.00547367 | − | 0.00278898i | −0.451252 | − | 0.892397i | \(-0.649022\pi\) |
0.456725 | + | 0.889608i | \(0.349022\pi\) | |||||||
\(488\) | 3.77529 | − | 1.92361i | 0.170899 | − | 0.0870776i | ||||
\(489\) | 0.820608 | − | 3.38207i | 0.0371092 | − | 0.152942i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.65368 | + | 2.81175i | 0.390535 | + | 0.126893i | 0.497701 | − | 0.867349i | \(-0.334178\pi\) |
−0.107166 | + | 0.994241i | \(0.534178\pi\) | |||||||
\(492\) | 1.08119 | − | 2.59248i | 0.0487436 | − | 0.116878i | ||||
\(493\) | −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 | ||||
\(497\) | −1.36703 | + | 8.63111i | −0.0613198 | + | 0.387158i | ||||
\(498\) | −11.1881 | + | 6.81893i | −0.501349 | + | 0.305564i | ||||
\(499\) | − | 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 | ||||
\(502\) | −9.57626 | + | 18.7945i | −0.427409 | + | 0.838838i | ||||
\(503\) | −10.8159 | − | 1.71307i | −0.482257 | − | 0.0763820i | −0.0894274 | − | 0.995993i | \(-0.528504\pi\) |
−0.392829 | + | 0.919611i | \(0.628504\pi\) | |||||||
\(504\) | −5.70921 | − | 2.94381i | −0.254308 | − | 0.131128i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.38455 | − | 7.41120i | 0.239372 | − | 0.329468i | ||||
\(507\) | −20.0263 | + | 4.75677i | −0.889401 | + | 0.211256i | ||||
\(508\) | 10.3298 | − | 1.63607i | 0.458309 | − | 0.0725891i | ||||
\(509\) | 2.83257 | − | 8.71775i | 0.125551 | − | 0.386407i | −0.868450 | − | 0.495777i | \(-0.834883\pi\) |
0.994001 | + | 0.109370i | \(0.0348833\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.206834 | + | 0.636570i | 0.00914980 | + | 0.0281602i | ||||
\(512\) | −0.453990 | − | 0.891007i | −0.0200637 | − | 0.0393773i | ||||
\(513\) | 10.5346 | + | 25.9633i | 0.465114 | + | 1.14631i | ||||
\(514\) | 15.9501 | − | 5.18250i | 0.703529 | − | 0.228590i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.11823 | + | 2.49230i | 0.0932500 | + | 0.109717i | ||||
\(517\) | −4.45276 | − | 28.1136i | −0.195832 | − | 1.23643i | ||||
\(518\) | 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 | 0.994417 | − | 0.105523i | \(-0.0336517\pi\) |
−0.407650 | + | 0.913138i | \(0.633652\pi\) | |||||||
\(522\) | −4.15104 | − | 12.9887i | −0.181686 | − | 0.568502i | ||||
\(523\) | 32.1380 | + | 16.3751i | 1.40530 | + | 0.716035i | 0.981810 | − | 0.189867i | \(-0.0608055\pi\) |
0.423488 | + | 0.905902i | \(0.360806\pi\) | |||||||
\(524\) | 19.5318 | 0.853250 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.7518 | 0.992025 | ||||||||
\(527\) | 54.6453 | + | 27.8432i | 2.38039 | + | 1.21287i | ||||
\(528\) | −6.67539 | + | 7.77776i | −0.290509 | + | 0.338484i | ||||
\(529\) | 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 | ||||
\(533\) | 0.268016 | + | 1.69218i | 0.0116090 | + | 0.0732966i | ||||
\(534\) | −11.4216 | + | 9.70732i | −0.494259 | + | 0.420077i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.23294 | + | 0.400605i | −0.0532548 | + | 0.0173035i | ||||
\(537\) | −5.47038 | − | 0.443825i | −0.236064 | − | 0.0191525i | ||||
\(538\) | 4.70077 | + | 9.22579i | 0.202665 | + | 0.397752i | ||||
\(539\) | 4.41696 | + | 13.5940i | 0.190252 | + | 0.585536i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.6711 | − | 32.8422i | 0.458786 | − | 1.41200i | −0.407847 | − | 0.913050i | \(-0.633720\pi\) |
0.866633 | − | 0.498947i | \(-0.166280\pi\) | |||||||
\(542\) | −0.631560 | + | 0.100029i | −0.0271278 | + | 0.00429663i | ||||
\(543\) | 2.49797 | + | 10.5166i | 0.107198 | + | 0.451312i | ||||
\(544\) | −3.38144 | + | 4.65416i | −0.144978 | + | 0.199545i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.90663 | − | 0.297966i | 0.167188 | − | 0.0127518i | ||||
\(547\) | 22.3156 | + | 3.53445i | 0.954148 | + | 0.151122i | 0.614049 | − | 0.789268i | \(-0.289540\pi\) |
0.340098 | + | 0.940390i | \(0.389540\pi\) | |||||||
\(548\) | 5.44330 | − | 10.6831i | 0.232526 | − | 0.456359i | ||||
\(549\) | 11.3536 | − | 5.71604i | 0.484561 | − | 0.243955i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 24.5096i | − | 1.04414i | ||||||
\(552\) | 1.39545 | + | 2.28956i | 0.0593942 | + | 0.0974500i | ||||
\(553\) | 0.316532 | − | 1.99850i | 0.0134603 | − | 0.0849851i | ||||
\(554\) | 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 | −0.782267 | − | 0.622943i | \(-0.785937\pi\) |
0.622943 | + | 0.782267i | \(0.285937\pi\) | |||||||
\(558\) | −25.9647 | + | 18.6735i | −1.09918 | + | 0.790513i | ||||
\(559\) | −1.89740 | − | 0.616502i | −0.0802513 | − | 0.0260752i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 57.3019 | + | 13.9034i | 2.41929 | + | 0.587003i | ||||
\(562\) | 19.3495 | − | 9.85907i | 0.816210 | − | 0.415880i | ||||
\(563\) | 21.6061 | − | 11.0089i | 0.910590 | − | 0.463969i | 0.0650508 | − | 0.997882i | \(-0.479279\pi\) |
0.845539 | + | 0.533913i | \(0.179279\pi\) | |||||||
\(564\) | 8.09634 | + | 1.96445i | 0.340918 | + | 0.0827185i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.29063 | − | 1.06919i | −0.138315 | − | 0.0449414i | ||||
\(567\) | −17.0848 | − | 8.91407i | −0.717493 | − | 0.374356i | ||||
\(568\) | −2.88591 | + | 2.88591i | −0.121090 | + | 0.121090i | ||||
\(569\) | −24.5934 | − | 17.8681i | −1.03101 | − | 0.749071i | −0.0624977 | − | 0.998045i | \(-0.519907\pi\) |
−0.968510 | + | 0.248974i | \(0.919907\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.57335 | − | 3.32274i | 0.191389 | − | 0.139052i | −0.487964 | − | 0.872864i | \(-0.662260\pi\) |
0.679353 | + | 0.733811i | \(0.262260\pi\) | |||||||
\(572\) | 0.977982 | − | 6.17473i | 0.0408915 | − | 0.258179i | ||||
\(573\) | −18.9379 | − | 31.0720i | −0.791141 | − | 1.29805i | ||||
\(574\) | 3.47236i | 0.144934i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.34904 | − | 2.67957i | −0.0562101 | − | 0.111649i | ||||
\(577\) | −11.6678 | + | 22.8994i | −0.485739 | + | 0.953316i | 0.509919 | + | 0.860223i | \(0.329676\pi\) |
−0.995657 | + | 0.0930933i | \(0.970324\pi\) | |||||||
\(578\) | 15.8972 | + | 2.51787i | 0.661236 | + | 0.104729i | ||||
\(579\) | 17.1193 | − | 1.30572i | 0.711454 | − | 0.0542639i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.52039 | − | 13.1037i | 0.394972 | − | 0.543633i | ||||
\(582\) | 4.82891 | + | 20.3301i | 0.200165 | + | 0.842708i | ||||
\(583\) | −35.4869 | + | 5.62058i | −1.46972 | + | 0.232781i | ||||
\(584\) | −0.0965991 | + | 0.297301i | −0.00399730 | + | 0.0123024i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.35461 | + | 16.4798i | 0.221197 | + | 0.680773i | ||||
\(587\) | 6.56280 | + | 12.8802i | 0.270876 | + | 0.531623i | 0.985871 | − | 0.167506i | \(-0.0535713\pi\) |
−0.714995 | + | 0.699129i | \(0.753571\pi\) | |||||||
\(588\) | −4.16995 | − | 0.338318i | −0.171966 | − | 0.0139520i | ||||
\(589\) | −54.6723 | + | 17.7641i | −2.25273 | + | 0.731957i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.4720 | − | 11.4500i | 0.554163 | − | 0.470990i | ||||
\(592\) | 0.0345885 | + | 0.218383i | 0.00142158 | + | 0.00897549i | ||||
\(593\) | 27.1124 | + | 27.1124i | 1.11337 | + | 1.11337i | 0.992691 | + | 0.120680i | \(0.0385075\pi\) |
0.120680 | + | 0.992691i | \(0.461492\pi\) | |||||||
\(594\) | −20.1387 | + | 23.2363i | −0.826299 | + | 0.953396i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.64870 | + | 11.9039i | 0.354265 | + | 0.487603i | ||||
\(597\) | 17.0503 | − | 19.8659i | 0.697821 | − | 0.813058i | ||||
\(598\) | −1.45719 | − | 0.742476i | −0.0595890 | − | 0.0303621i | ||||
\(599\) | 22.2597 | 0.909506 | 0.454753 | − | 0.890618i | \(-0.349728\pi\) | ||||
0.454753 | + | 0.890618i | \(0.349728\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.661317 | −0.0269757 | −0.0134878 | − | 0.999909i | \(-0.504293\pi\) | ||||
−0.0134878 | + | 0.999909i | \(0.504293\pi\) | |||||||
\(602\) | −3.60272 | − | 1.83568i | −0.146836 | − | 0.0748165i | ||||
\(603\) | −3.70457 | + | 1.18393i | −0.150862 | + | 0.0482135i | ||||
\(604\) | −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 | \(0.492268\pi\) | |||||||
\(608\) | −0.843538 | − | 5.32589i | −0.0342100 | − | 0.215993i | ||||
\(609\) | 10.9166 | + | 12.8444i | 0.442362 | + | 0.520480i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.83290 | + | 1.57031i | −0.195518 | + | 0.0635278i | ||||
\(612\) | −10.2117 | + | 13.9133i | −0.412782 | + | 0.562412i | ||||
\(613\) | −11.3412 | − | 22.2583i | −0.458065 | − | 0.899003i | −0.998345 | − | 0.0575173i | \(-0.981682\pi\) |
0.540280 | − | 0.841485i | \(-0.318318\pi\) | |||||||
\(614\) | −7.34770 | − | 22.6139i | −0.296529 | − | 0.912623i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.91542 | − | 12.0504i | 0.157757 | − | 0.485525i | ||||
\(617\) | −30.7946 | + | 4.87738i | −1.23974 | + | 0.196356i | −0.741661 | − | 0.670775i | \(-0.765962\pi\) |
−0.498081 | + | 0.867131i | \(0.665962\pi\) | |||||||
\(618\) | −14.8873 | + | 3.53610i | −0.598853 | + | 0.142243i | ||||
\(619\) | −2.12975 | + | 2.93135i | −0.0856019 | + | 0.117821i | −0.849670 | − | 0.527314i | \(-0.823199\pi\) |
0.764068 | + | 0.645135i | \(0.223199\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.15311 | + | 6.88882i | 0.166659 | + | 0.276439i | ||||
\(622\) | 7.68404 | + | 1.21703i | 0.308102 | + | 0.0487985i | ||||
\(623\) | 8.41243 | − | 16.5103i | 0.337037 | − | 0.661472i | ||||
\(624\) | 1.55788 | + | 0.959853i | 0.0623651 | + | 0.0384249i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 20.7996i | 0.831321i | ||||||||
\(627\) | −47.1939 | + | 28.7639i | −1.88474 | + | 1.14872i | ||||
\(628\) | −3.89068 | + | 24.5648i | −0.155255 | + | 0.980241i | ||||
\(629\) | 1.02906 | − | 0.747655i | 0.0410312 | − | 0.0298109i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.12680 | + | 2.99829i | 0.164285 | + | 0.119360i | 0.666890 | − | 0.745156i | \(-0.267625\pi\) |
−0.502605 | + | 0.864516i | \(0.667625\pi\) | |||||||
\(632\) | 0.668222 | − | 0.668222i | 0.0265805 | − | 0.0265805i | ||||
\(633\) | −2.64781 | + | 6.34896i | −0.105241 | + | 0.252349i | ||||
\(634\) | 0.206145 | + | 0.0669805i | 0.00818706 | + | 0.00266014i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.47967 | − | 10.2198i | 0.0983253 | − | 0.405240i | ||||
\(637\) | 2.27367 | − | 1.15849i | 0.0900861 | − | 0.0459012i | ||||
\(638\) | 23.9657 | − | 12.2112i | 0.948813 | − | 0.483444i | ||||
\(639\) | −8.69945 | + | 8.61580i | −0.344145 | + | 0.340836i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −45.1681 | − | 14.6760i | −1.78403 | − | 0.579668i | −0.784836 | − | 0.619703i | \(-0.787253\pi\) |
−0.999198 | + | 0.0400355i | \(0.987253\pi\) | |||||||
\(642\) | −9.47689 | − | 3.95230i | −0.374023 | − | 0.155985i | ||||
\(643\) | 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 | ||||
\(647\) | 1.11876 | − | 7.06356i | 0.0439829 | − | 0.277697i | −0.955889 | − | 0.293730i | \(-0.905103\pi\) |
0.999871 | + | 0.0160323i | \(0.00510347\pi\) | |||||||
\(648\) | −4.00825 | − | 8.05816i | −0.157459 | − | 0.316554i | ||||
\(649\) | − | 42.9184i | − | 1.68469i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.7391 | − | 33.6604i | 0.812831 | − | 1.31926i | ||||
\(652\) | −0.912200 | + | 1.79029i | −0.0357245 | + | 0.0701133i | ||||
\(653\) | −22.9855 | − | 3.64054i | −0.899490 | − | 0.142465i | −0.310470 | − | 0.950583i | \(-0.600486\pi\) |
−0.589021 | + | 0.808118i | \(0.700486\pi\) | |||||||
\(654\) | 0.248642 | + | 3.25995i | 0.00972269 | + | 0.127474i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.953223 | + | 1.31200i | −0.0372171 | + | 0.0512250i | ||||
\(657\) | −0.294102 | + | 0.890494i | −0.0114740 | + | 0.0347415i | ||||
\(658\) | −10.1723 | + | 1.61113i | −0.396557 | + | 0.0628085i | ||||
\(659\) | 1.14382 | − | 3.52031i | 0.0445568 | − | 0.137132i | −0.926303 | − | 0.376779i | \(-0.877032\pi\) |
0.970860 | + | 0.239647i | \(0.0770317\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.4157 | − | 35.1339i | −0.444019 | − | 1.36655i | −0.883556 | − | 0.468326i | \(-0.844857\pi\) |
0.439537 | − | 0.898224i | \(-0.355143\pi\) | |||||||
\(662\) | 3.26336 | + | 6.40470i | 0.126834 | + | 0.248926i | ||||
\(663\) | 0.851267 | − | 10.4923i | 0.0330605 | − | 0.407488i | ||||
\(664\) | 7.19438 | − | 2.33760i | 0.279196 | − | 0.0907163i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.100599 | + | 0.655643i | 0.00389815 | + | 0.0254056i | ||||
\(667\) | −1.10073 | − | 6.94972i | −0.0426203 | − | 0.269094i | ||||
\(668\) | −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 | ||||
\(672\) | 2.81421 | + | 2.41535i | 0.108561 | + | 0.0931740i | ||||
\(673\) | −1.06415 | − | 0.542210i | −0.0410198 | − | 0.0209006i | 0.433360 | − | 0.901221i | \(-0.357328\pi\) |
−0.474380 | + | 0.880320i | \(0.657328\pi\) | |||||||
\(674\) | 6.75390 | 0.260151 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.8839 | 0.457073 | ||||||||
\(677\) | −30.6338 | − | 15.6087i | −1.17735 | − | 0.599892i | −0.247884 | − | 0.968790i | \(-0.579735\pi\) |
−0.929470 | + | 0.368898i | \(0.879735\pi\) | |||||||
\(678\) | −11.1486 | − | 9.56844i | −0.428158 | − | 0.367474i | ||||
\(679\) | −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 | ||||
\(683\) | −7.05008 | − | 44.5125i | −0.269764 | − | 1.70322i | −0.635169 | − | 0.772373i | \(-0.719070\pi\) |
0.365405 | − | 0.930849i | \(-0.380930\pi\) | |||||||
\(684\) | −2.45340 | − | 15.9897i | −0.0938081 | − | 0.611382i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 19.1733 | − | 6.22977i | 0.732038 | − | 0.237854i | ||||
\(687\) | 2.31751 | − | 28.5645i | 0.0884185 | − | 1.08980i | ||||
\(688\) | −0.857327 | − | 1.68260i | −0.0326853 | − | 0.0641485i | ||||
\(689\) | 1.98215 | + | 6.10043i | 0.0755138 | + | 0.232408i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.10289 | − | 3.39434i | 0.0419558 | − | 0.129127i | −0.927885 | − | 0.372867i | \(-0.878375\pi\) |
0.969840 | + | 0.243741i | \(0.0783746\pi\) | |||||||
\(692\) | 4.95282 | − | 0.784450i | 0.188278 | − | 0.0298203i | ||||
\(693\) | 11.9207 | − | 36.0941i | 0.452832 | − | 1.37110i | ||||
\(694\) | 2.69058 | − | 3.70326i | 0.102133 | − | 0.140574i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.598727 | + | 7.84991i | 0.0226947 | + | 0.297550i | ||||
\(697\) | 9.21466 | + | 1.45946i | 0.349030 | + | 0.0552809i | ||||
\(698\) | −4.44057 | + | 8.71510i | −0.168078 | + | 0.329871i | ||||
\(699\) | 4.95215 | − | 8.03754i | 0.187308 | − | 0.304008i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 19.6139i | − | 0.740807i | −0.928871 | − | 0.370403i | \(-0.879219\pi\) | ||
0.928871 | − | 0.370403i | \(-0.120781\pi\) | |||||||
\(702\) | 4.65967 | + | 2.90210i | 0.175868 | + | 0.109533i | ||||
\(703\) | −0.186511 | + | 1.17758i | −0.00703438 | + | 0.0444133i | ||||
\(704\) | 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 | ||||
\(708\) | 11.5941 | + | 4.83527i | 0.435733 | + | 0.181721i | ||||
\(709\) | 22.4237 | + | 7.28590i | 0.842140 | + | 0.273628i | 0.698150 | − | 0.715951i | \(-0.254007\pi\) |
0.143990 | + | 0.989579i | \(0.454007\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.01433 | − | 1.99496i | 0.0755432 | − | 0.0748168i | ||||
\(712\) | 7.71092 | − | 3.92891i | 0.288979 | − | 0.147242i | ||||
\(713\) | −14.7046 | + | 7.49238i | −0.550692 | + | 0.280592i | ||||
\(714\) | 5.03066 | − | 20.7335i | 0.188268 | − | 0.775930i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.01361 | + | 0.979183i | 0.112624 | + | 0.0365938i | ||||
\(717\) | −5.81015 | + | 13.9317i | −0.216984 | + | 0.520287i | ||||
\(718\) | −14.8975 | + | 14.8975i | −0.555969 | + | 0.555969i | ||||
\(719\) | −30.2210 | − | 21.9569i | −1.12705 | − | 0.818853i | −0.141791 | − | 0.989897i | \(-0.545286\pi\) |
−0.985263 | + | 0.171044i | \(0.945286\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.3031 | − | 11.1183i | 0.569916 | − | 0.414068i | ||||
\(722\) | 1.57634 | − | 9.95259i | 0.0586651 | − | 0.370397i | ||||
\(723\) | 37.6046 | − | 22.9194i | 1.39853 | − | 0.852381i | ||||
\(724\) | − | 6.24071i | − | 0.231934i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −35.4178 | − | 21.8219i | −1.31448 | − | 0.809886i | ||||
\(727\) | −19.2896 | + | 37.8579i | −0.715411 | + | 1.40407i | 0.190964 | + | 0.981597i | \(0.438839\pi\) |
−0.906374 | + | 0.422476i | \(0.861161\pi\) | |||||||
\(728\) | −2.23419 | − | 0.353862i | −0.0828047 | − | 0.0131150i | ||||
\(729\) | −11.9078 | − | 24.2323i | −0.441031 | − | 0.897492i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.38561 | + | 8.78903i | −0.236180 | + | 0.325074i | ||||
\(732\) | −7.14023 | + | 1.69599i | −0.263911 | + | 0.0626855i | ||||
\(733\) | 44.0735 | − | 6.98056i | 1.62789 | − | 0.257833i | 0.725333 | − | 0.688398i | \(-0.241686\pi\) |
0.902559 | + | 0.430565i | \(0.141686\pi\) | |||||||
\(734\) | 8.34641 | − | 25.6876i | 0.308072 | − | 0.948147i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.478373 | − | 1.47228i | −0.0176331 | − | 0.0542690i | ||||
\(737\) | −3.48279 | − | 6.83537i | −0.128290 | − | 0.251784i | ||||
\(738\) | −2.87865 | + | 3.92214i | −0.105965 | + | 0.144376i | ||||
\(739\) | 8.01855 | − | 2.60538i | 0.294967 | − | 0.0958406i | −0.157795 | − | 0.987472i | \(-0.550439\pi\) |
0.452762 | + | 0.891631i | \(0.350439\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.38996 | + | 7.51837i | 0.234741 | + | 0.276194i | ||||
\(742\) | 2.03368 | + | 12.8402i | 0.0746589 | + | 0.471378i | ||||
\(743\) | −24.9192 | − | 24.9192i | −0.914196 | − | 0.914196i | 0.0824029 | − | 0.996599i | \(-0.473741\pi\) |
−0.996599 | + | 0.0824029i | \(0.973741\pi\) | |||||||
\(744\) | 17.0765 | − | 7.02502i | 0.626053 | − | 0.257550i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 15.7261 | + | 21.6451i | 0.575772 | + | 0.792482i | ||||
\(747\) | 21.6168 | − | 6.90844i | 0.790916 | − | 0.252767i | ||||
\(748\) | −30.3327 | − | 15.4553i | −1.10907 | − | 0.565101i | ||||
\(749\) | 12.6933 | 0.463804 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.40064 | −0.306544 | −0.153272 | − | 0.988184i | \(-0.548981\pi\) | ||||
−0.153272 | + | 0.988184i | \(0.548981\pi\) | |||||||
\(752\) | −4.28579 | − | 2.18372i | −0.156287 | − | 0.0796320i | ||||
\(753\) | 23.7946 | − | 27.7241i | 0.867125 | − | 1.01032i | ||||
\(754\) | −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 | \(0.795792\pi\) | |||||||
\(758\) | −2.46985 | − | 15.5940i | −0.0897089 | − | 0.566400i | ||||
\(759\) | −12.0901 | + | 10.2755i | −0.438843 | + | 0.372978i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.92036 | + | 1.92364i | −0.214613 | + | 0.0697320i | −0.414350 | − | 0.910118i | \(-0.635991\pi\) |
0.199737 | + | 0.979849i | \(0.435991\pi\) | |||||||
\(762\) | −18.0554 | − | 1.46488i | −0.654077 | − | 0.0530669i | ||||
\(763\) | −1.83487 | − | 3.60114i | −0.0664268 | − | 0.130370i | ||||
\(764\) | 6.49209 | + | 19.9806i | 0.234875 | + | 0.722872i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.93411 | − | 15.1856i | 0.178276 | − | 0.548679i | ||||
\(767\) | −7.56779 | + | 1.19862i | −0.273257 | + | 0.0432796i | ||||
\(768\) | 0.400270 | + | 1.68517i | 0.0144435 | + | 0.0608082i | ||||
\(769\) | 2.22958 | − | 3.06876i | 0.0804008 | − | 0.110662i | −0.766922 | − | 0.641740i | \(-0.778213\pi\) |
0.847323 | + | 0.531078i | \(0.178213\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.9640 | + | 2.20914i | −1.04311 | + | 0.0795601i | ||||
\(772\) | −9.79050 | − | 1.55066i | −0.352368 | − | 0.0558096i | ||||
\(773\) | −15.4685 | + | 30.3587i | −0.556364 | + | 1.09193i | 0.425960 | + | 0.904742i | \(0.359936\pi\) |
−0.982325 | + | 0.187185i | \(0.940064\pi\) | |||||||
\(774\) | −2.54757 | − | 5.06017i | −0.0915704 | − | 0.181884i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 12.0641i | − | 0.433077i | ||||||
\(777\) | −0.426754 | − | 0.700189i | −0.0153097 | − | 0.0251192i | ||||
\(778\) | 1.80467 | − | 11.3942i | 0.0647005 | − | 0.408503i | ||||
\(779\) | −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 | ||||
\(783\) | 1.68240 | + | 23.5581i | 0.0601240 | + | 0.841898i | ||||
\(784\) | 2.29721 | + | 0.746410i | 0.0820433 | + | 0.0266575i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −32.8761 | − | 7.97690i | −1.17265 | − | 0.284527i | ||||
\(787\) | 27.9758 | − | 14.2544i | 0.997230 | − | 0.508114i | 0.122367 | − | 0.992485i | \(-0.460951\pi\) |
0.874863 | + | 0.484371i | \(0.160951\pi\) | |||||||
\(788\) | −9.09520 | + | 4.63424i | −0.324003 | + | 0.165088i | ||||
\(789\) | −38.2961 | − | 9.29197i | −1.36338 | − | 0.330803i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.2729 | + | 5.61232i | 0.614155 | + | 0.199551i | ||||
\(792\) | 14.4126 | − | 10.3654i | 0.512129 | − | 0.368317i | ||||
\(793\) | 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 | ||||
\(797\) | 1.65300 | − | 10.4366i | 0.0585523 | − | 0.369685i | −0.940962 | − | 0.338513i | \(-0.890076\pi\) |
0.999514 | − | 0.0311718i | \(-0.00992392\pi\) | |||||||
\(798\) | 10.4076 | + | 17.0761i | 0.368425 | + | 0.604488i | ||||
\(799\) | 27.6716i | 0.978949i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 23.1894 | − | 11.6749i | 0.819358 | − | 0.412511i | ||||
\(802\) | −11.0953 | + | 21.7757i | −0.391787 | + | 0.768926i | ||||
\(803\) | −1.82708 | − | 0.289381i | −0.0644762 | − | 0.0102120i | ||||
\(804\) | 2.23890 | − | 0.170765i | 0.0789601 | − | 0.00602243i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.62002 | + | 9.11167i | −0.233180 | + | 0.320945i | ||||
\(807\) | −4.14454 | − | 17.4488i | −0.145895 | − | 0.614227i | ||||
\(808\) | −0.306462 | + | 0.0485388i | −0.0107813 | + | 0.00170759i | ||||
\(809\) | −4.15772 | + | 12.7961i | −0.146178 | + | 0.449889i | −0.997161 | − | 0.0753048i | \(-0.976007\pi\) |
0.850983 | + | 0.525193i | \(0.176007\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.32531 | + | 19.4673i | 0.222112 | + | 0.683590i | 0.998572 | + | 0.0534235i | \(0.0170133\pi\) |
−0.776460 | + | 0.630166i | \(0.782987\pi\) | |||||||
\(812\) | −4.41834 | − | 8.67148i | −0.155053 | − | 0.304309i | ||||
\(813\) | 1.10390 | + | 0.0895624i | 0.0387156 | + | 0.00314109i | ||||
\(814\) | −1.24438 | + | 0.404322i | −0.0436154 | + | 0.0141715i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7.59247 | − | 6.45294i | 0.265790 | − | 0.225898i | ||||
\(817\) | −1.59296 | − | 10.0575i | −0.0557306 | − | 0.351869i | ||||
\(818\) | 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 | 0.957777 | − | 0.287512i | \(-0.0928280\pi\) |
−0.569409 | + | 0.822054i | \(0.692828\pi\) | |||||||
\(822\) | −13.5253 | + | 15.7588i | −0.471748 | + | 0.549652i | ||||
\(823\) | −14.0722 | − | 7.17013i | −0.490525 | − | 0.249935i | 0.191190 | − | 0.981553i | \(-0.438765\pi\) |
−0.681715 | + | 0.731618i | \(0.738765\pi\) | |||||||
\(824\) | 8.83429 | 0.307757 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.5291 | −0.540326 | ||||||||
\(827\) | 6.05244 | + | 3.08387i | 0.210464 | + | 0.107237i | 0.556045 | − | 0.831152i | \(-0.312318\pi\) |
−0.345581 | + | 0.938389i | \(0.612318\pi\) | |||||||
\(828\) | −1.41377 | − | 4.42372i | −0.0491317 | − | 0.153735i | ||||
\(829\) | −11.0240 | − | 15.1733i | −0.382880 | − | 0.526989i | 0.573465 | − | 0.819230i | \(-0.305599\pi\) |
−0.956345 | + | 0.292241i | \(0.905599\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −48.6333 | + | 20.0071i | −1.68707 | + | 0.694038i | ||||
\(832\) | −0.747028 | − | 0.747028i | −0.0258985 | − | 0.0258985i | ||||
\(833\) | −2.17376 | − | 13.7246i | −0.0753162 | − | 0.475528i | ||||
\(834\) | 26.1027 | + | 30.7122i | 0.903862 | + | 1.06348i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 30.3476 | − | 9.86055i | 1.04960 | − | 0.341034i | ||||
\(837\) | 51.3306 | − | 20.8274i | 1.77424 | − | 0.719899i | ||||
\(838\) | 11.7128 | + | 22.9876i | 0.404611 | + | 0.794093i | ||||
\(839\) | 5.00273 | + | 15.3968i | 0.172713 | + | 0.531557i | 0.999522 | − | 0.0309268i | \(-0.00984587\pi\) |
−0.826808 | + | 0.562484i | \(0.809846\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.57725 | + | 7.93197i | −0.0888709 | + | 0.273516i | ||||
\(842\) | −38.9278 | + | 6.16556i | −1.34154 | + | 0.212479i | ||||
\(843\) | −36.5959 | + | 8.69245i | −1.26043 | + | 0.299384i | ||||
\(844\) | 2.33443 | − | 3.21307i | 0.0803545 | − | 0.110598i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12.8256 | − | 6.61319i | −0.440952 | − | 0.227366i | ||||
\(847\) | 50.7935 | + | 8.04490i | 1.74529 | + | 0.276426i | ||||
\(848\) | −2.75644 | + | 5.40982i | −0.0946566 | + | 0.185774i | ||||
\(849\) | 5.10216 | + | 3.14358i | 0.175106 | + | 0.107887i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.342281i | 0.0117332i | ||||||||
\(852\) | 6.03622 | − | 3.67898i | 0.206797 | − | 0.126040i | ||||
\(853\) | 5.14470 | − | 32.4823i | 0.176151 | − | 1.11217i | −0.728194 | − | 0.685371i | \(-0.759640\pi\) |
0.904345 | − | 0.426803i | \(-0.140360\pi\) | |||||||
\(854\) | 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 | −0.907196 | − | 0.420708i | \(-0.861782\pi\) |
0.420708 | + | 0.907196i | \(0.361782\pi\) | |||||||
\(858\) | −4.16795 | + | 9.99398i | −0.142291 | + | 0.341189i | ||||
\(859\) | −29.9968 | − | 9.74655i | −1.02348 | − | 0.332548i | −0.251269 | − | 0.967917i | \(-0.580848\pi\) |
−0.772208 | + | 0.635369i | \(0.780848\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.41813 | − | 5.84472i | 0.0483299 | − | 0.199188i | ||||
\(862\) | −5.47676 | + | 2.79055i | −0.186539 | + | 0.0950465i | ||||
\(863\) | 19.3357 | − | 9.85205i | 0.658196 | − | 0.335368i | −0.0927901 | − | 0.995686i | \(-0.529579\pi\) |
0.750986 | + | 0.660318i | \(0.229579\pi\) | |||||||
\(864\) | 1.17637 | + | 5.06124i | 0.0400211 | + | 0.172187i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 15.9153 | + | 5.17119i | 0.540824 | + | 0.175724i | ||||
\(867\) | −25.7300 | − | 10.7306i | −0.873838 | − | 0.364431i | ||||
\(868\) | −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 | ||||
\(872\) | 0.295286 | − | 1.86436i | 0.00999963 | − | 0.0631352i | ||||
\(873\) | 0.174834 | − | 36.1920i | 0.00591723 | − | 1.22491i | ||||
\(874\) | − | 8.34750i | − | 0.282358i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.284016 | − | 0.460970i | 0.00959602 | − | 0.0155747i | ||||
\(877\) | −3.43493 | + | 6.74142i | −0.115989 | + | 0.227642i | −0.941701 | − | 0.336450i | \(-0.890774\pi\) |
0.825712 | + | 0.564092i | \(0.190774\pi\) | |||||||
\(878\) | 19.8679 | + | 3.14677i | 0.670510 | + | 0.106198i | ||||
\(879\) | −2.28250 | − | 29.9258i | −0.0769868 | − | 1.00937i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.8656 | − | 25.9662i | 0.635597 | − | 0.874825i | −0.362774 | − | 0.931877i | \(-0.618170\pi\) |
0.998371 | + | 0.0570525i | \(0.0181702\pi\) | |||||||
\(882\) | 6.88074 | + | 2.27249i | 0.231687 | + | 0.0765189i | ||||
\(883\) | 28.3550 | − | 4.49099i | 0.954222 | − | 0.151134i | 0.340139 | − | 0.940375i | \(-0.389526\pi\) |
0.614083 | + | 0.789241i | \(0.289526\pi\) | |||||||
\(884\) | −1.87810 | + | 5.78018i | −0.0631672 | + | 0.194409i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.49794 | + | 23.0763i | 0.251898 | + | 0.775263i | ||||
\(887\) | −5.50981 | − | 10.8136i | −0.185001 | − | 0.363086i | 0.779815 | − | 0.626010i | \(-0.215313\pi\) |
−0.964816 | + | 0.262924i | \(0.915313\pi\) | |||||||
\(888\) | 0.0309692 | − | 0.381711i | 0.00103926 | − | 0.0128094i | ||||
\(889\) | 21.2974 | − | 6.91994i | 0.714291 | − | 0.232087i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 43.3875 | − | 30.8868i | 1.45353 | − | 1.03475i | ||||
\(892\) | −2.09418 | − | 13.2221i | −0.0701183 | − | 0.442710i | ||||
\(893\) | −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 | ||||
\(897\) | 2.14953 | + | 1.84487i | 0.0717708 | + | 0.0615985i | ||||
\(898\) | −14.1886 | − | 7.22945i | −0.473479 | − | 0.241250i | ||||
\(899\) | −48.4565 | −1.61611 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.9289 | 1.16365 | ||||||||
\(902\) | −8.55073 | − | 4.35682i | −0.284708 | − | 0.145066i | ||||
\(903\) | 5.31444 | + | 4.56120i | 0.176853 | + | 0.151787i | ||||
\(904\) | 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 | \(0.894781\pi\) | |||||||
\(908\) | 0.133895 | + | 0.845381i | 0.00444347 | + | 0.0280549i | ||||
\(909\) | −0.920078 | + | 0.141173i | −0.0305171 | + | 0.00468243i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.0222 | + | 12.0293i | −1.22660 | + | 0.398547i | −0.849482 | − | 0.527618i | \(-0.823085\pi\) |
−0.377119 | + | 0.926165i | \(0.623085\pi\) | |||||||
\(912\) | −0.755271 | + | 9.30911i | −0.0250095 | + | 0.308255i | ||||
\(913\) | 20.3226 | + | 39.8854i | 0.672581 | + | 1.32002i | ||||
\(914\) | −1.00626 | − | 3.09695i | −0.0332842 | − | 0.102438i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.11297 | + | 15.7361i | −0.168937 | + | 0.519935i | ||||
\(917\) | 41.3058 | − | 6.54220i | 1.36404 | − | 0.216042i | ||||
\(918\) | 22.8707 | − | 19.2486i | 0.754845 | − | 0.635297i | ||||
\(919\) | −13.4831 | + | 18.5579i | −0.444766 | + | 0.612168i | −0.971263 | − | 0.238009i | \(-0.923505\pi\) |
0.526497 | + | 0.850177i | \(0.323505\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.13209 | + | 41.0648i | 0.103206 | + | 1.35313i | ||||
\(922\) | 9.79461 | + | 1.55131i | 0.322568 | + | 0.0510898i | ||||
\(923\) | −1.95747 | + | 3.84176i | −0.0644311 | + | 0.126453i | ||||
\(924\) | −11.5119 | + | 18.6843i | −0.378715 | + | 0.614669i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 23.1191i | − | 0.759740i | ||||||
\(927\) | 26.5026 | + | 0.128027i | 0.870459 | + | 0.00420496i | ||||
\(928\) | 0.711043 | − | 4.48935i | 0.0233411 | − | 0.147370i | ||||
\(929\) | −0.473139 | + | 0.343755i | −0.0155232 | + | 0.0112782i | −0.595520 | − | 0.803341i | \(-0.703054\pi\) |
0.579997 | + | 0.814619i | \(0.303054\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.5372 | + | 7.65572i | 0.345342 | + | 0.250906i | ||||
\(932\) | −3.85413 | + | 3.85413i | −0.126246 | + | 0.126246i | ||||
\(933\) | −12.4368 | − | 5.18673i | −0.407163 | − | 0.169806i | ||||
\(934\) | −4.41971 | − | 1.43605i | −0.144617 | − | 0.0469891i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.23023 | − | 2.25188i | −0.0728974 | − | 0.0736051i | ||||
\(937\) | −49.7213 | + | 25.3343i | −1.62432 | + | 0.827634i | −0.625445 | + | 0.780268i | \(0.715083\pi\) |
−0.998878 | + | 0.0473659i | \(0.984917\pi\) | |||||||
\(938\) | −2.47323 | + | 1.26017i | −0.0807538 | + | 0.0411461i | ||||
\(939\) | 8.49469 | − | 35.0102i | 0.277214 | − | 1.14251i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.5712 | − | 4.08462i | −0.409808 | − | 0.133155i | 0.0968556 | − | 0.995298i | \(-0.469121\pi\) |
−0.506664 | + | 0.862144i | \(0.669121\pi\) | |||||||
\(942\) | 16.5812 | − | 39.7588i | 0.540246 | − | 1.29541i | ||||
\(943\) | −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 | ||||
\(947\) | 2.82795 | − | 17.8550i | 0.0918962 | − | 0.580210i | −0.898174 | − | 0.439639i | \(-0.855106\pi\) |
0.990071 | − | 0.140571i | \(-0.0448937\pi\) | |||||||
\(948\) | −1.39767 | + | 0.851854i | −0.0453941 | + | 0.0276669i | ||||
\(949\) | 0.330250i | 0.0107204i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.319630 | − | 0.196933i | −0.0103647 | − | 0.00638600i | ||||
\(952\) | −5.59216 | + | 10.9752i | −0.181243 | + | 0.355709i | ||||
\(953\) | 51.6458 | + | 8.17990i | 1.67297 | + | 0.264973i | 0.919667 | − | 0.392698i | \(-0.128458\pi\) |
0.753305 | + | 0.657671i | \(0.228458\pi\) | |||||||
\(954\) | −8.34763 | + | 16.1893i | −0.270264 | + | 0.524149i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.12250 | − | 7.05051i | 0.165673 | − | 0.228030i | ||||
\(957\) | −45.3265 | + | 10.7662i | −1.46520 | + | 0.348022i | ||||
\(958\) | −15.6026 | + | 2.47121i | −0.504097 | + | 0.0798412i | ||||
\(959\) | 7.93318 | − | 24.4158i | 0.256176 | − | 0.788428i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.5409 | + | 78.6068i | 0.823900 | + | 2.53570i | ||||
\(962\) | 0.106047 | + | 0.208129i | 0.00341909 | + | 0.00671033i | ||||
\(963\) | 14.3375 | + | 10.5230i | 0.462019 | + | 0.339098i | ||||
\(964\) | −24.1813 | + | 7.85699i | −0.778828 | + | 0.253056i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.71798 | + | 4.37455i | 0.119624 | + | 0.140749i | ||||
\(967\) | 4.86314 | + | 30.7047i | 0.156388 | + | 0.987395i | 0.933642 | + | 0.358208i | \(0.116612\pi\) |
−0.777254 | + | 0.629187i | \(0.783388\pi\) | |||||||
\(968\) | 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 | −0.991291 | − | 0.131690i | \(-0.957960\pi\) |
0.181081 | − | 0.983468i | \(-0.442040\pi\) | |||||||
\(972\) | 3.45574 | + | 15.2006i | 0.110843 | + | 0.487559i | ||||
\(973\) | −44.3957 | − | 22.6208i | −1.42326 | − | 0.725188i | ||||
\(974\) | 0.135570 | 0.00434393 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.23711 | 0.135627 | ||||||||
\(977\) | 52.8715 | + | 26.9394i | 1.69151 | + | 0.861867i | 0.988596 | + | 0.150590i | \(0.0481174\pi\) |
0.702912 | + | 0.711276i | \(0.251883\pi\) | |||||||
\(978\) | 2.26659 | − | 2.64090i | 0.0724777 | − | 0.0844466i | ||||
\(979\) | 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 | ||||
\(983\) | 5.94792 | + | 37.5537i | 0.189709 | + | 1.19778i | 0.880260 | + | 0.474492i | \(0.157368\pi\) |
−0.690550 | + | 0.723284i | \(0.742632\pi\) | |||||||
\(984\) | 2.14031 | − | 1.81907i | 0.0682305 | − | 0.0579899i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −24.8687 | + | 8.08033i | −0.791981 | + | 0.257330i | ||||
\(987\) | 17.7801 | + | 1.44255i | 0.565948 | + | 0.0459168i | ||||
\(988\) | −2.58625 | − | 5.07580i | −0.0822796 | − | 0.161483i | ||||
\(989\) | −0.903372 | − | 2.78029i | −0.0287255 | − | 0.0884081i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.31171 | − | 28.6585i | 0.295796 | − | 0.910367i | −0.687157 | − | 0.726509i | \(-0.741141\pi\) |
0.982953 | − | 0.183858i | \(-0.0588585\pi\) | |||||||
\(992\) | −10.5295 | + | 1.66771i | −0.334313 | + | 0.0529499i | ||||
\(993\) | −2.87721 | − | 12.1132i | −0.0913054 | − | 0.384402i | ||||
\(994\) | −5.13648 | + | 7.06976i | −0.162919 | + | 0.224239i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −13.0644 | + | 0.996443i | −0.413960 | + | 0.0315735i | ||||
\(997\) | −33.4599 | − | 5.29952i | −1.05968 | − | 0.167838i | −0.397822 | − | 0.917463i | \(-0.630234\pi\) |
−0.661863 | + | 0.749625i | \(0.730234\pi\) | |||||||
\(998\) | 12.5256 | − | 24.5829i | 0.396491 | − | 0.778157i | ||||
\(999\) | 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.a.107.6 | 80 | ||
3.2 | odd | 2 | inner | 750.2.l.a.107.5 | 80 | ||
5.2 | odd | 4 | 150.2.l.a.83.1 | yes | 80 | ||
5.3 | odd | 4 | 750.2.l.b.143.10 | 80 | |||
5.4 | even | 2 | 750.2.l.c.107.5 | 80 | |||
15.2 | even | 4 | 150.2.l.a.83.7 | yes | 80 | ||
15.8 | even | 4 | 750.2.l.b.143.4 | 80 | |||
15.14 | odd | 2 | 750.2.l.c.107.6 | 80 | |||
25.3 | odd | 20 | inner | 750.2.l.a.743.5 | 80 | ||
25.4 | even | 10 | 150.2.l.a.47.7 | yes | 80 | ||
25.21 | even | 5 | 750.2.l.b.257.4 | 80 | |||
25.22 | odd | 20 | 750.2.l.c.743.6 | 80 | |||
75.29 | odd | 10 | 150.2.l.a.47.1 | ✓ | 80 | ||
75.47 | even | 20 | 750.2.l.c.743.5 | 80 | |||
75.53 | even | 20 | inner | 750.2.l.a.743.6 | 80 | ||
75.71 | odd | 10 | 750.2.l.b.257.10 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.l.a.47.1 | ✓ | 80 | 75.29 | odd | 10 | ||
150.2.l.a.47.7 | yes | 80 | 25.4 | even | 10 | ||
150.2.l.a.83.1 | yes | 80 | 5.2 | odd | 4 | ||
150.2.l.a.83.7 | yes | 80 | 15.2 | even | 4 | ||
750.2.l.a.107.5 | 80 | 3.2 | odd | 2 | inner | ||
750.2.l.a.107.6 | 80 | 1.1 | even | 1 | trivial | ||
750.2.l.a.743.5 | 80 | 25.3 | odd | 20 | inner | ||
750.2.l.a.743.6 | 80 | 75.53 | even | 20 | inner | ||
750.2.l.b.143.4 | 80 | 15.8 | even | 4 | |||
750.2.l.b.143.10 | 80 | 5.3 | odd | 4 | |||
750.2.l.b.257.4 | 80 | 25.21 | even | 5 | |||
750.2.l.b.257.10 | 80 | 75.71 | odd | 10 | |||
750.2.l.c.107.5 | 80 | 5.4 | even | 2 | |||
750.2.l.c.107.6 | 80 | 15.14 | odd | 2 | |||
750.2.l.c.743.5 | 80 | 75.47 | even | 20 | |||
750.2.l.c.743.6 | 80 | 25.22 | odd | 20 |