Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(497,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.497");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.j (of order \(4\), degree \(2\), 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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.1698758656.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 497.3 | ||
Root | \(-1.69230i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.497 |
Dual form | 930.2.j.c.683.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | −0.292893 | − | 1.70711i | −0.169102 | − | 0.985599i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −0.489528 | + | 2.18183i | −0.218924 | + | 0.975742i | ||||
\(6\) | −1.41421 | − | 1.00000i | −0.577350 | − | 0.408248i | ||||
\(7\) | −0.474719 | − | 0.474719i | −0.179427 | − | 0.179427i | 0.611679 | − | 0.791106i | \(-0.290494\pi\) |
−0.791106 | + | 0.611679i | \(0.790494\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −2.82843 | + | 1.00000i | −0.942809 | + | 0.333333i | ||||
\(10\) | 1.19663 | + | 1.88893i | 0.378409 | + | 0.597333i | ||||
\(11\) | 4.08557i | 1.23184i | 0.787807 | + | 0.615922i | \(0.211217\pi\) | ||||
−0.787807 | + | 0.615922i | \(0.788783\pi\) | |||||||
\(12\) | −1.70711 | + | 0.292893i | −0.492799 | + | 0.0845510i | ||||
\(13\) | −3.10651 | + | 3.10651i | −0.861591 | + | 0.861591i | −0.991523 | − | 0.129932i | \(-0.958524\pi\) |
0.129932 | + | 0.991523i | \(0.458524\pi\) | |||||||
\(14\) | −0.671354 | −0.179427 | ||||||||
\(15\) | 3.86799 | + | 0.196635i | 0.998710 | + | 0.0507709i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −4.06462 | + | 4.06462i | −0.985816 | + | 0.985816i | −0.999901 | − | 0.0140848i | \(-0.995517\pi\) |
0.0140848 | + | 0.999901i | \(0.495517\pi\) | |||||||
\(18\) | −1.29289 | + | 2.70711i | −0.304738 | + | 0.638071i | ||||
\(19\) | − | 1.57129i | − | 0.360478i | −0.983623 | − | 0.180239i | \(-0.942313\pi\) | ||
0.983623 | − | 0.180239i | \(-0.0576871\pi\) | |||||||
\(20\) | 2.18183 | + | 0.489528i | 0.487871 | + | 0.109462i | ||||
\(21\) | −0.671354 | + | 0.949437i | −0.146501 | + | 0.207184i | ||||
\(22\) | 2.88893 | + | 2.88893i | 0.615922 | + | 0.615922i | ||||
\(23\) | −1.06051 | − | 1.06051i | −0.221131 | − | 0.221131i | 0.587844 | − | 0.808974i | \(-0.299977\pi\) |
−0.808974 | + | 0.587844i | \(0.799977\pi\) | |||||||
\(24\) | −1.00000 | + | 1.41421i | −0.204124 | + | 0.288675i | ||||
\(25\) | −4.52072 | − | 2.13613i | −0.904145 | − | 0.427226i | ||||
\(26\) | 4.39327i | 0.861591i | ||||||||
\(27\) | 2.53553 | + | 4.53553i | 0.487964 | + | 0.872864i | ||||
\(28\) | −0.474719 | + | 0.474719i | −0.0897134 | + | 0.0897134i | ||||
\(29\) | −1.87899 | −0.348920 | −0.174460 | − | 0.984664i | \(-0.555818\pi\) | ||||
−0.174460 | + | 0.984664i | \(0.555818\pi\) | |||||||
\(30\) | 2.87412 | − | 2.59604i | 0.524741 | − | 0.473970i | ||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 6.97450 | − | 1.19663i | 1.21410 | − | 0.208307i | ||||
\(34\) | 5.74825i | 0.985816i | ||||||||
\(35\) | 1.26814 | − | 0.803365i | 0.214355 | − | 0.135793i | ||||
\(36\) | 1.00000 | + | 2.82843i | 0.166667 | + | 0.471405i | ||||
\(37\) | −2.00000 | − | 2.00000i | −0.328798 | − | 0.328798i | 0.523331 | − | 0.852129i | \(-0.324689\pi\) |
−0.852129 | + | 0.523331i | \(0.824689\pi\) | |||||||
\(38\) | −1.11107 | − | 1.11107i | −0.180239 | − | 0.180239i | ||||
\(39\) | 6.21302 | + | 4.39327i | 0.994880 | + | 0.703486i | ||||
\(40\) | 1.88893 | − | 1.19663i | 0.298666 | − | 0.189205i | ||||
\(41\) | 7.26358i | 1.13438i | 0.823587 | + | 0.567191i | \(0.191970\pi\) | ||||
−0.823587 | + | 0.567191i | \(0.808030\pi\) | |||||||
\(42\) | 0.196635 | + | 1.14607i | 0.0303414 | + | 0.176843i | ||||
\(43\) | 1.16702 | − | 1.16702i | 0.177968 | − | 0.177968i | −0.612501 | − | 0.790470i | \(-0.709837\pi\) |
0.790470 | + | 0.612501i | \(0.209837\pi\) | |||||||
\(44\) | 4.08557 | 0.615922 | ||||||||
\(45\) | −0.797231 | − | 6.66066i | −0.118844 | − | 0.992913i | ||||
\(46\) | −1.49978 | −0.221131 | ||||||||
\(47\) | −0.520724 | + | 0.520724i | −0.0759555 | + | 0.0759555i | −0.744064 | − | 0.668108i | \(-0.767104\pi\) |
0.668108 | + | 0.744064i | \(0.267104\pi\) | |||||||
\(48\) | 0.292893 | + | 1.70711i | 0.0422755 | + | 0.246400i | ||||
\(49\) | − | 6.54928i | − | 0.935612i | ||||||
\(50\) | −4.70711 | + | 1.68616i | −0.665685 | + | 0.238459i | ||||
\(51\) | 8.12925 | + | 5.74825i | 1.13832 | + | 0.804915i | ||||
\(52\) | 3.10651 | + | 3.10651i | 0.430796 | + | 0.430796i | ||||
\(53\) | −2.48339 | − | 2.48339i | −0.341120 | − | 0.341120i | 0.515668 | − | 0.856788i | \(-0.327544\pi\) |
−0.856788 | + | 0.515668i | \(0.827544\pi\) | |||||||
\(54\) | 5.00000 | + | 1.41421i | 0.680414 | + | 0.192450i | ||||
\(55\) | −8.91399 | − | 2.00000i | −1.20196 | − | 0.269680i | ||||
\(56\) | 0.671354i | 0.0897134i | ||||||||
\(57\) | −2.68235 | + | 0.460219i | −0.355287 | + | 0.0609575i | ||||
\(58\) | −1.32865 | + | 1.32865i | −0.174460 | + | 0.174460i | ||||
\(59\) | 4.40554 | 0.573552 | 0.286776 | − | 0.957998i | \(-0.407416\pi\) | ||||
0.286776 | + | 0.957998i | \(0.407416\pi\) | |||||||
\(60\) | 0.196635 | − | 3.86799i | 0.0253855 | − | 0.499355i | ||||
\(61\) | 11.2340 | 1.43836 | 0.719181 | − | 0.694823i | \(-0.244517\pi\) | ||||
0.719181 | + | 0.694823i | \(0.244517\pi\) | |||||||
\(62\) | 0.707107 | − | 0.707107i | 0.0898027 | − | 0.0898027i | ||||
\(63\) | 1.81743 | + | 0.867988i | 0.228974 | + | 0.109356i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −5.25714 | − | 8.29859i | −0.652068 | − | 1.02931i | ||||
\(66\) | 4.08557 | − | 5.77786i | 0.502899 | − | 0.711206i | ||||
\(67\) | −5.37233 | − | 5.37233i | −0.656334 | − | 0.656334i | 0.298177 | − | 0.954511i | \(-0.403622\pi\) |
−0.954511 | + | 0.298177i | \(0.903622\pi\) | |||||||
\(68\) | 4.06462 | + | 4.06462i | 0.492908 | + | 0.492908i | ||||
\(69\) | −1.49978 | + | 2.12101i | −0.180552 | + | 0.255340i | ||||
\(70\) | 0.328646 | − | 1.46478i | 0.0392808 | − | 0.175074i | ||||
\(71\) | 4.42871i | 0.525592i | 0.964851 | + | 0.262796i | \(0.0846445\pi\) | ||||
−0.964851 | + | 0.262796i | \(0.915355\pi\) | |||||||
\(72\) | 2.70711 | + | 1.29289i | 0.319036 | + | 0.152369i | ||||
\(73\) | −7.86799 | + | 7.86799i | −0.920878 | + | 0.920878i | −0.997092 | − | 0.0762132i | \(-0.975717\pi\) |
0.0762132 | + | 0.997092i | \(0.475717\pi\) | |||||||
\(74\) | −2.82843 | −0.328798 | ||||||||
\(75\) | −2.32251 | + | 8.34302i | −0.268181 | + | 0.963369i | ||||
\(76\) | −1.57129 | −0.180239 | ||||||||
\(77\) | 1.93949 | − | 1.93949i | 0.221026 | − | 0.221026i | ||||
\(78\) | 7.49978 | − | 1.28676i | 0.849183 | − | 0.145697i | ||||
\(79\) | 9.12702i | 1.02687i | 0.858129 | + | 0.513435i | \(0.171627\pi\) | ||||
−0.858129 | + | 0.513435i | \(0.828373\pi\) | |||||||
\(80\) | 0.489528 | − | 2.18183i | 0.0547309 | − | 0.243935i | ||||
\(81\) | 7.00000 | − | 5.65685i | 0.777778 | − | 0.628539i | ||||
\(82\) | 5.13613 | + | 5.13613i | 0.567191 | + | 0.567191i | ||||
\(83\) | −8.35783 | − | 8.35783i | −0.917391 | − | 0.917391i | 0.0794483 | − | 0.996839i | \(-0.474684\pi\) |
−0.996839 | + | 0.0794483i | \(0.974684\pi\) | |||||||
\(84\) | 0.949437 | + | 0.671354i | 0.103592 | + | 0.0732507i | ||||
\(85\) | −6.87855 | − | 10.8580i | −0.746084 | − | 1.17772i | ||||
\(86\) | − | 1.65041i | − | 0.177968i | ||||||
\(87\) | 0.550343 | + | 3.20764i | 0.0590030 | + | 0.343895i | ||||
\(88\) | 2.88893 | − | 2.88893i | 0.307961 | − | 0.307961i | ||||
\(89\) | 5.69230 | 0.603382 | 0.301691 | − | 0.953406i | \(-0.402449\pi\) | ||||
0.301691 | + | 0.953406i | \(0.402449\pi\) | |||||||
\(90\) | −5.27353 | − | 4.14607i | −0.555879 | − | 0.437034i | ||||
\(91\) | 2.94944 | 0.309185 | ||||||||
\(92\) | −1.06051 | + | 1.06051i | −0.110565 | + | 0.110565i | ||||
\(93\) | −0.292893 | − | 1.70711i | −0.0303716 | − | 0.177019i | ||||
\(94\) | 0.736416i | 0.0759555i | ||||||||
\(95\) | 3.42827 | + | 0.769189i | 0.351734 | + | 0.0789172i | ||||
\(96\) | 1.41421 | + | 1.00000i | 0.144338 | + | 0.102062i | ||||
\(97\) | 8.34915 | + | 8.34915i | 0.847728 | + | 0.847728i | 0.989849 | − | 0.142121i | \(-0.0453923\pi\) |
−0.142121 | + | 0.989849i | \(0.545392\pi\) | |||||||
\(98\) | −4.63104 | − | 4.63104i | −0.467806 | − | 0.467806i | ||||
\(99\) | −4.08557 | − | 11.5557i | −0.410615 | − | 1.16139i | ||||
\(100\) | −2.13613 | + | 4.52072i | −0.213613 | + | 0.452072i | ||||
\(101\) | − | 12.5702i | − | 1.25078i | −0.780311 | − | 0.625392i | \(-0.784939\pi\) | ||
0.780311 | − | 0.625392i | \(-0.215061\pi\) | |||||||
\(102\) | 9.81287 | − | 1.68362i | 0.971619 | − | 0.166703i | ||||
\(103\) | −0.449657 | + | 0.449657i | −0.0443060 | + | 0.0443060i | −0.728913 | − | 0.684607i | \(-0.759974\pi\) |
0.684607 | + | 0.728913i | \(0.259974\pi\) | |||||||
\(104\) | 4.39327 | 0.430796 | ||||||||
\(105\) | −1.74286 | − | 1.92955i | −0.170086 | − | 0.188305i | ||||
\(106\) | −3.51205 | −0.341120 | ||||||||
\(107\) | −5.00412 | + | 5.00412i | −0.483766 | + | 0.483766i | −0.906332 | − | 0.422566i | \(-0.861130\pi\) |
0.422566 | + | 0.906332i | \(0.361130\pi\) | |||||||
\(108\) | 4.53553 | − | 2.53553i | 0.436432 | − | 0.243982i | ||||
\(109\) | 7.47661i | 0.716129i | 0.933697 | + | 0.358064i | \(0.116563\pi\) | ||||
−0.933697 | + | 0.358064i | \(0.883437\pi\) | |||||||
\(110\) | −7.71736 | + | 4.88893i | −0.735821 | + | 0.466141i | ||||
\(111\) | −2.82843 | + | 4.00000i | −0.268462 | + | 0.379663i | ||||
\(112\) | 0.474719 | + | 0.474719i | 0.0448567 | + | 0.0448567i | ||||
\(113\) | −6.30315 | − | 6.30315i | −0.592950 | − | 0.592950i | 0.345477 | − | 0.938427i | \(-0.387717\pi\) |
−0.938427 | + | 0.345477i | \(0.887717\pi\) | |||||||
\(114\) | −1.57129 | + | 2.22214i | −0.147165 | + | 0.208122i | ||||
\(115\) | 2.83298 | − | 1.79469i | 0.264177 | − | 0.167356i | ||||
\(116\) | 1.87899i | 0.174460i | ||||||||
\(117\) | 5.68003 | − | 11.8931i | 0.525119 | − | 1.09951i | ||||
\(118\) | 3.11519 | − | 3.11519i | 0.286776 | − | 0.286776i | ||||
\(119\) | 3.85911 | 0.353764 | ||||||||
\(120\) | −2.59604 | − | 2.87412i | −0.236985 | − | 0.262370i | ||||
\(121\) | −5.69186 | −0.517442 | ||||||||
\(122\) | 7.94361 | − | 7.94361i | 0.719181 | − | 0.719181i | ||||
\(123\) | 12.3997 | − | 2.12745i | 1.11804 | − | 0.191826i | ||||
\(124\) | − | 1.00000i | − | 0.0898027i | ||||||
\(125\) | 6.87368 | − | 8.81774i | 0.614801 | − | 0.788682i | ||||
\(126\) | 1.89887 | − | 0.671354i | 0.169165 | − | 0.0598089i | ||||
\(127\) | 13.5138 | + | 13.5138i | 1.19916 | + | 1.19916i | 0.974419 | + | 0.224741i | \(0.0721536\pi\) |
0.224741 | + | 0.974419i | \(0.427846\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | −2.33403 | − | 1.65041i | −0.205500 | − | 0.145310i | ||||
\(130\) | −9.58535 | − | 2.15063i | −0.840691 | − | 0.188623i | ||||
\(131\) | 14.5940i | 1.27509i | 0.770415 | + | 0.637543i | \(0.220049\pi\) | ||||
−0.770415 | + | 0.637543i | \(0.779951\pi\) | |||||||
\(132\) | −1.19663 | − | 6.97450i | −0.104154 | − | 0.607052i | ||||
\(133\) | −0.745919 | + | 0.745919i | −0.0646794 | + | 0.0646794i | ||||
\(134\) | −7.59762 | −0.656334 | ||||||||
\(135\) | −11.1370 | + | 3.31182i | −0.958517 | + | 0.285036i | ||||
\(136\) | 5.74825 | 0.492908 | ||||||||
\(137\) | 6.22752 | − | 6.22752i | 0.532053 | − | 0.532053i | −0.389130 | − | 0.921183i | \(-0.627224\pi\) |
0.921183 | + | 0.389130i | \(0.127224\pi\) | |||||||
\(138\) | 0.439276 | + | 2.56029i | 0.0373936 | + | 0.217946i | ||||
\(139\) | − | 1.35498i | − | 0.114928i | −0.998348 | − | 0.0574638i | \(-0.981699\pi\) | ||
0.998348 | − | 0.0574638i | \(-0.0183014\pi\) | |||||||
\(140\) | −0.803365 | − | 1.26814i | −0.0678967 | − | 0.107178i | ||||
\(141\) | 1.04145 | + | 0.736416i | 0.0877058 | + | 0.0620174i | ||||
\(142\) | 3.13157 | + | 3.13157i | 0.262796 | + | 0.262796i | ||||
\(143\) | −12.6919 | − | 12.6919i | −1.06135 | − | 1.06135i | ||||
\(144\) | 2.82843 | − | 1.00000i | 0.235702 | − | 0.0833333i | ||||
\(145\) | 0.919818 | − | 4.09963i | 0.0763868 | − | 0.340456i | ||||
\(146\) | 11.1270i | 0.920878i | ||||||||
\(147\) | −11.1803 | + | 1.91824i | −0.922138 | + | 0.158214i | ||||
\(148\) | −2.00000 | + | 2.00000i | −0.164399 | + | 0.164399i | ||||
\(149\) | −20.3809 | −1.66967 | −0.834833 | − | 0.550504i | \(-0.814436\pi\) | ||||
−0.834833 | + | 0.550504i | \(0.814436\pi\) | |||||||
\(150\) | 4.25714 | + | 7.54167i | 0.347594 | + | 0.615775i | ||||
\(151\) | −19.4720 | −1.58461 | −0.792303 | − | 0.610128i | \(-0.791118\pi\) | ||||
−0.792303 | + | 0.610128i | \(0.791118\pi\) | |||||||
\(152\) | −1.11107 | + | 1.11107i | −0.0901195 | + | 0.0901195i | ||||
\(153\) | 7.43187 | − | 15.5611i | 0.600831 | − | 1.25804i | ||||
\(154\) | − | 2.74286i | − | 0.221026i | ||||||
\(155\) | −0.489528 | + | 2.18183i | −0.0393198 | + | 0.175248i | ||||
\(156\) | 4.39327 | − | 6.21302i | 0.351743 | − | 0.497440i | ||||
\(157\) | −1.46245 | − | 1.46245i | −0.116716 | − | 0.116716i | 0.646336 | − | 0.763053i | \(-0.276300\pi\) |
−0.763053 | + | 0.646336i | \(0.776300\pi\) | |||||||
\(158\) | 6.45377 | + | 6.45377i | 0.513435 | + | 0.513435i | ||||
\(159\) | −3.51205 | + | 4.96679i | −0.278524 | + | 0.393892i | ||||
\(160\) | −1.19663 | − | 1.88893i | −0.0946023 | − | 0.149333i | ||||
\(161\) | 1.00688i | 0.0793535i | ||||||||
\(162\) | 0.949747 | − | 8.94975i | 0.0746192 | − | 0.703159i | ||||
\(163\) | −2.67135 | + | 2.67135i | −0.209237 | + | 0.209237i | −0.803943 | − | 0.594706i | \(-0.797268\pi\) |
0.594706 | + | 0.803943i | \(0.297268\pi\) | |||||||
\(164\) | 7.26358 | 0.567191 | ||||||||
\(165\) | −0.803365 | + | 15.8029i | −0.0625419 | + | 1.23026i | ||||
\(166\) | −11.8198 | −0.917391 | ||||||||
\(167\) | −3.37465 | + | 3.37465i | −0.261138 | + | 0.261138i | −0.825516 | − | 0.564378i | \(-0.809116\pi\) |
0.564378 | + | 0.825516i | \(0.309116\pi\) | |||||||
\(168\) | 1.14607 | − | 0.196635i | 0.0884214 | − | 0.0151707i | ||||
\(169\) | − | 6.30082i | − | 0.484678i | ||||||
\(170\) | −12.5417 | − | 2.81393i | −0.961902 | − | 0.215818i | ||||
\(171\) | 1.57129 | + | 4.44427i | 0.120159 | + | 0.339862i | ||||
\(172\) | −1.16702 | − | 1.16702i | −0.0889841 | − | 0.0889841i | ||||
\(173\) | −12.6186 | − | 12.6186i | −0.959371 | − | 0.959371i | 0.0398349 | − | 0.999206i | \(-0.487317\pi\) |
−0.999206 | + | 0.0398349i | \(0.987317\pi\) | |||||||
\(174\) | 2.65729 | + | 1.87899i | 0.201449 | + | 0.142446i | ||||
\(175\) | 1.13201 | + | 3.16013i | 0.0855720 | + | 0.238884i | ||||
\(176\) | − | 4.08557i | − | 0.307961i | ||||||
\(177\) | −1.29035 | − | 7.52072i | −0.0969888 | − | 0.565292i | ||||
\(178\) | 4.02506 | − | 4.02506i | 0.301691 | − | 0.301691i | ||||
\(179\) | 22.7264 | 1.69865 | 0.849326 | − | 0.527868i | \(-0.177008\pi\) | ||||
0.849326 | + | 0.527868i | \(0.177008\pi\) | |||||||
\(180\) | −6.66066 | + | 0.797231i | −0.496456 | + | 0.0594221i | ||||
\(181\) | −10.6295 | −0.790082 | −0.395041 | − | 0.918663i | \(-0.629270\pi\) | ||||
−0.395041 | + | 0.918663i | \(0.629270\pi\) | |||||||
\(182\) | 2.08557 | − | 2.08557i | 0.154593 | − | 0.154593i | ||||
\(183\) | −3.29035 | − | 19.1776i | −0.243230 | − | 1.41765i | ||||
\(184\) | 1.49978i | 0.110565i | ||||||||
\(185\) | 5.34271 | − | 3.38459i | 0.392804 | − | 0.248840i | ||||
\(186\) | −1.41421 | − | 1.00000i | −0.103695 | − | 0.0733236i | ||||
\(187\) | −16.6063 | − | 16.6063i | −1.21437 | − | 1.21437i | ||||
\(188\) | 0.520724 | + | 0.520724i | 0.0379777 | + | 0.0379777i | ||||
\(189\) | 0.949437 | − | 3.35677i | 0.0690614 | − | 0.244169i | ||||
\(190\) | 2.96805 | − | 1.88026i | 0.215325 | − | 0.136408i | ||||
\(191\) | − | 0.815538i | − | 0.0590103i | −0.999565 | − | 0.0295051i | \(-0.990607\pi\) | ||
0.999565 | − | 0.0295051i | \(-0.00939314\pi\) | |||||||
\(192\) | 1.70711 | − | 0.292893i | 0.123200 | − | 0.0211377i | ||||
\(193\) | −5.68362 | + | 5.68362i | −0.409116 | + | 0.409116i | −0.881430 | − | 0.472314i | \(-0.843419\pi\) |
0.472314 | + | 0.881430i | \(0.343419\pi\) | |||||||
\(194\) | 11.8075 | 0.847728 | ||||||||
\(195\) | −12.6268 | + | 11.4051i | −0.904224 | + | 0.816736i | ||||
\(196\) | −6.54928 | −0.467806 | ||||||||
\(197\) | −18.3545 | + | 18.3545i | −1.30771 | + | 1.30771i | −0.384640 | + | 0.923067i | \(0.625674\pi\) |
−0.923067 | + | 0.384640i | \(0.874326\pi\) | |||||||
\(198\) | −11.0601 | − | 5.28220i | −0.786005 | − | 0.375390i | ||||
\(199\) | 16.1137i | 1.14227i | 0.820856 | + | 0.571135i | \(0.193497\pi\) | ||||
−0.820856 | + | 0.571135i | \(0.806503\pi\) | |||||||
\(200\) | 1.68616 | + | 4.70711i | 0.119230 | + | 0.332843i | ||||
\(201\) | −7.59762 | + | 10.7447i | −0.535895 | + | 0.757869i | ||||
\(202\) | −8.88849 | − | 8.88849i | −0.625392 | − | 0.625392i | ||||
\(203\) | 0.891992 | + | 0.891992i | 0.0626055 | + | 0.0626055i | ||||
\(204\) | 5.74825 | − | 8.12925i | 0.402458 | − | 0.569161i | ||||
\(205\) | −15.8479 | − | 3.55573i | −1.10686 | − | 0.248343i | ||||
\(206\) | 0.635910i | 0.0443060i | ||||||||
\(207\) | 4.06007 | + | 1.93906i | 0.282194 | + | 0.134774i | ||||
\(208\) | 3.10651 | − | 3.10651i | 0.215398 | − | 0.215398i | ||||
\(209\) | 6.41960 | 0.444053 | ||||||||
\(210\) | −2.59679 | − | 0.132012i | −0.179195 | − | 0.00910966i | ||||
\(211\) | −25.1270 | −1.72982 | −0.864908 | − | 0.501931i | \(-0.832623\pi\) | ||||
−0.864908 | + | 0.501931i | \(0.832623\pi\) | |||||||
\(212\) | −2.48339 | + | 2.48339i | −0.170560 | + | 0.170560i | ||||
\(213\) | 7.56029 | − | 1.29714i | 0.518022 | − | 0.0888786i | ||||
\(214\) | 7.07689i | 0.483766i | ||||||||
\(215\) | 1.97494 | + | 3.11751i | 0.134690 | + | 0.212613i | ||||
\(216\) | 1.41421 | − | 5.00000i | 0.0962250 | − | 0.340207i | ||||
\(217\) | −0.474719 | − | 0.474719i | −0.0322260 | − | 0.0322260i | ||||
\(218\) | 5.28676 | + | 5.28676i | 0.358064 | + | 0.358064i | ||||
\(219\) | 15.7360 | + | 11.1270i | 1.06334 | + | 0.751894i | ||||
\(220\) | −2.00000 | + | 8.91399i | −0.134840 | + | 0.600981i | ||||
\(221\) | − | 25.2536i | − | 1.69874i | ||||||
\(222\) | 0.828427 | + | 4.82843i | 0.0556004 | + | 0.324063i | ||||
\(223\) | −3.60852 | + | 3.60852i | −0.241645 | + | 0.241645i | −0.817530 | − | 0.575886i | \(-0.804657\pi\) |
0.575886 | + | 0.817530i | \(0.304657\pi\) | |||||||
\(224\) | 0.671354 | 0.0448567 | ||||||||
\(225\) | 14.9227 | + | 1.52116i | 0.994845 | + | 0.101411i | ||||
\(226\) | −8.91399 | −0.592950 | ||||||||
\(227\) | 16.2085 | − | 16.2085i | 1.07579 | − | 1.07579i | 0.0789120 | − | 0.996882i | \(-0.474855\pi\) |
0.996882 | − | 0.0789120i | \(-0.0251446\pi\) | |||||||
\(228\) | 0.460219 | + | 2.68235i | 0.0304788 | + | 0.177643i | ||||
\(229\) | 6.64235i | 0.438939i | 0.975619 | + | 0.219470i | \(0.0704327\pi\) | ||||
−0.975619 | + | 0.219470i | \(0.929567\pi\) | |||||||
\(230\) | 0.734185 | − | 3.27226i | 0.0484107 | − | 0.215766i | ||||
\(231\) | −3.87899 | − | 2.74286i | −0.255219 | − | 0.180467i | ||||
\(232\) | 1.32865 | + | 1.32865i | 0.0872299 | + | 0.0872299i | ||||
\(233\) | −9.15146 | − | 9.15146i | −0.599532 | − | 0.599532i | 0.340656 | − | 0.940188i | \(-0.389351\pi\) |
−0.940188 | + | 0.340656i | \(0.889351\pi\) | |||||||
\(234\) | −4.39327 | − | 12.4260i | −0.287197 | − | 0.812316i | ||||
\(235\) | −0.881221 | − | 1.39104i | −0.0574845 | − | 0.0907414i | ||||
\(236\) | − | 4.40554i | − | 0.286776i | ||||||
\(237\) | 15.5808 | − | 2.67324i | 1.01208 | − | 0.173646i | ||||
\(238\) | 2.72880 | − | 2.72880i | 0.176882 | − | 0.176882i | ||||
\(239\) | 26.5471 | 1.71719 | 0.858593 | − | 0.512658i | \(-0.171339\pi\) | ||||
0.858593 | + | 0.512658i | \(0.171339\pi\) | |||||||
\(240\) | −3.86799 | − | 0.196635i | −0.249678 | − | 0.0126927i | ||||
\(241\) | −3.60673 | −0.232330 | −0.116165 | − | 0.993230i | \(-0.537060\pi\) | ||||
−0.116165 | + | 0.993230i | \(0.537060\pi\) | |||||||
\(242\) | −4.02475 | + | 4.02475i | −0.258721 | + | 0.258721i | ||||
\(243\) | −11.7071 | − | 10.2929i | −0.751011 | − | 0.660289i | ||||
\(244\) | − | 11.2340i | − | 0.719181i | ||||||
\(245\) | 14.2894 | + | 3.20606i | 0.912916 | + | 0.204828i | ||||
\(246\) | 7.26358 | − | 10.2723i | 0.463109 | − | 0.654935i | ||||
\(247\) | 4.88122 | + | 4.88122i | 0.310585 | + | 0.310585i | ||||
\(248\) | −0.707107 | − | 0.707107i | −0.0449013 | − | 0.0449013i | ||||
\(249\) | −11.8198 | + | 16.7157i | −0.749046 | + | 1.05931i | ||||
\(250\) | −1.37465 | − | 11.0955i | −0.0869406 | − | 0.701742i | ||||
\(251\) | 18.2657i | 1.15292i | 0.817126 | + | 0.576460i | \(0.195566\pi\) | ||||
−0.817126 | + | 0.576460i | \(0.804434\pi\) | |||||||
\(252\) | 0.867988 | − | 1.81743i | 0.0546781 | − | 0.114487i | ||||
\(253\) | 4.33276 | − | 4.33276i | 0.272399 | − | 0.272399i | ||||
\(254\) | 19.1115 | 1.19916 | ||||||||
\(255\) | −16.5212 | + | 14.9227i | −1.03460 | + | 0.934494i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.9380 | − | 17.9380i | 1.11894 | − | 1.11894i | 0.127045 | − | 0.991897i | \(-0.459451\pi\) |
0.991897 | − | 0.127045i | \(-0.0405491\pi\) | |||||||
\(258\) | −2.81743 | + | 0.483394i | −0.175405 | + | 0.0300948i | ||||
\(259\) | 1.89887i | 0.117990i | ||||||||
\(260\) | −8.29859 | + | 5.25714i | −0.514657 | + | 0.326034i | ||||
\(261\) | 5.31459 | − | 1.87899i | 0.328965 | − | 0.116307i | ||||
\(262\) | 10.3195 | + | 10.3195i | 0.637543 | + | 0.637543i | ||||
\(263\) | −9.29859 | − | 9.29859i | −0.573376 | − | 0.573376i | 0.359695 | − | 0.933070i | \(-0.382881\pi\) |
−0.933070 | + | 0.359695i | \(0.882881\pi\) | |||||||
\(264\) | −5.77786 | − | 4.08557i | −0.355603 | − | 0.251449i | ||||
\(265\) | 6.63402 | − | 4.20264i | 0.407525 | − | 0.258166i | ||||
\(266\) | 1.05489i | 0.0646794i | ||||||||
\(267\) | −1.66724 | − | 9.71736i | −0.102033 | − | 0.594693i | ||||
\(268\) | −5.37233 | + | 5.37233i | −0.328167 | + | 0.328167i | ||||
\(269\) | 9.25447 | 0.564255 | 0.282128 | − | 0.959377i | \(-0.408960\pi\) | ||||
0.282128 | + | 0.959377i | \(0.408960\pi\) | |||||||
\(270\) | −5.53321 | + | 10.2168i | −0.336740 | + | 0.621776i | ||||
\(271\) | 28.8012 | 1.74955 | 0.874775 | − | 0.484530i | \(-0.161009\pi\) | ||||
0.874775 | + | 0.484530i | \(0.161009\pi\) | |||||||
\(272\) | 4.06462 | − | 4.06462i | 0.246454 | − | 0.246454i | ||||
\(273\) | −0.863870 | − | 5.03500i | −0.0522838 | − | 0.304732i | ||||
\(274\) | − | 8.80704i | − | 0.532053i | ||||||
\(275\) | 8.72730 | − | 18.4697i | 0.526276 | − | 1.11377i | ||||
\(276\) | 2.12101 | + | 1.49978i | 0.127670 | + | 0.0902762i | ||||
\(277\) | 18.8334 | + | 18.8334i | 1.13159 | + | 1.13159i | 0.989913 | + | 0.141674i | \(0.0452486\pi\) |
0.141674 | + | 0.989913i | \(0.454751\pi\) | |||||||
\(278\) | −0.958112 | − | 0.958112i | −0.0574638 | − | 0.0574638i | ||||
\(279\) | −2.82843 | + | 1.00000i | −0.169334 | + | 0.0598684i | ||||
\(280\) | −1.46478 | − | 0.328646i | −0.0875371 | − | 0.0196404i | ||||
\(281\) | − | 12.6435i | − | 0.754250i | −0.926162 | − | 0.377125i | \(-0.876913\pi\) | ||
0.926162 | − | 0.377125i | \(-0.123087\pi\) | |||||||
\(282\) | 1.25714 | − | 0.215691i | 0.0748616 | − | 0.0128442i | ||||
\(283\) | 13.8139 | − | 13.8139i | 0.821153 | − | 0.821153i | −0.165121 | − | 0.986273i | \(-0.552801\pi\) |
0.986273 | + | 0.165121i | \(0.0528013\pi\) | |||||||
\(284\) | 4.42871 | 0.262796 | ||||||||
\(285\) | 0.308970 | − | 6.07772i | 0.0183018 | − | 0.360013i | ||||
\(286\) | −17.9490 | −1.06135 | ||||||||
\(287\) | 3.44816 | − | 3.44816i | 0.203538 | − | 0.203538i | ||||
\(288\) | 1.29289 | − | 2.70711i | 0.0761845 | − | 0.159518i | ||||
\(289\) | − | 16.0423i | − | 0.943666i | ||||||
\(290\) | −2.24846 | − | 3.54928i | −0.132034 | − | 0.208421i | ||||
\(291\) | 11.8075 | − | 16.6983i | 0.692167 | − | 0.978872i | ||||
\(292\) | 7.86799 | + | 7.86799i | 0.460439 | + | 0.460439i | ||||
\(293\) | 20.2335 | + | 20.2335i | 1.18206 | + | 1.18206i | 0.979211 | + | 0.202844i | \(0.0650185\pi\) |
0.202844 | + | 0.979211i | \(0.434981\pi\) | |||||||
\(294\) | −6.54928 | + | 9.26209i | −0.381962 | + | 0.540176i | ||||
\(295\) | −2.15663 | + | 9.61212i | −0.125564 | + | 0.559639i | ||||
\(296\) | 2.82843i | 0.164399i | ||||||||
\(297\) | −18.5302 | + | 10.3591i | −1.07523 | + | 0.601096i | ||||
\(298\) | −14.4114 | + | 14.4114i | −0.834833 | + | 0.834833i | ||||
\(299\) | 6.58894 | 0.381048 | ||||||||
\(300\) | 8.34302 | + | 2.32251i | 0.481684 | + | 0.134090i | ||||
\(301\) | −1.10801 | −0.0638645 | ||||||||
\(302\) | −13.7688 | + | 13.7688i | −0.792303 | + | 0.792303i | ||||
\(303\) | −21.4587 | + | 3.68173i | −1.23277 | + | 0.211510i | ||||
\(304\) | 1.57129i | 0.0901195i | ||||||||
\(305\) | −5.49934 | + | 24.5106i | −0.314891 | + | 1.40347i | ||||
\(306\) | −5.74825 | − | 16.2585i | −0.328605 | − | 0.929436i | ||||
\(307\) | −7.66447 | − | 7.66447i | −0.437434 | − | 0.437434i | 0.453713 | − | 0.891148i | \(-0.350099\pi\) |
−0.891148 | + | 0.453713i | \(0.850099\pi\) | |||||||
\(308\) | −1.93949 | − | 1.93949i | −0.110513 | − | 0.110513i | ||||
\(309\) | 0.899313 | + | 0.635910i | 0.0511601 | + | 0.0361757i | ||||
\(310\) | 1.19663 | + | 1.88893i | 0.0679643 | + | 0.107284i | ||||
\(311\) | 28.5308i | 1.61783i | 0.587925 | + | 0.808915i | \(0.299945\pi\) | ||||
−0.587925 | + | 0.808915i | \(0.700055\pi\) | |||||||
\(312\) | −1.28676 | − | 7.49978i | −0.0728484 | − | 0.424591i | ||||
\(313\) | 23.0992 | − | 23.0992i | 1.30564 | − | 1.30564i | 0.381116 | − | 0.924527i | \(-0.375540\pi\) |
0.924527 | − | 0.381116i | \(-0.124460\pi\) | |||||||
\(314\) | −2.06822 | −0.116716 | ||||||||
\(315\) | −2.78348 | + | 3.54040i | −0.156831 | + | 0.199479i | ||||
\(316\) | 9.12702 | 0.513435 | ||||||||
\(317\) | −11.3278 | + | 11.3278i | −0.636231 | + | 0.636231i | −0.949624 | − | 0.313393i | \(-0.898534\pi\) |
0.313393 | + | 0.949624i | \(0.398534\pi\) | |||||||
\(318\) | 1.02866 | + | 5.99544i | 0.0576841 | + | 0.336208i | ||||
\(319\) | − | 7.67674i | − | 0.429815i | ||||||
\(320\) | −2.18183 | − | 0.489528i | −0.121968 | − | 0.0273655i | ||||
\(321\) | 10.0082 | + | 7.07689i | 0.558605 | + | 0.394994i | ||||
\(322\) | 0.711974 | + | 0.711974i | 0.0396768 | + | 0.0396768i | ||||
\(323\) | 6.38669 | + | 6.38669i | 0.355365 | + | 0.355365i | ||||
\(324\) | −5.65685 | − | 7.00000i | −0.314270 | − | 0.388889i | ||||
\(325\) | 20.6796 | − | 7.40777i | 1.14710 | − | 0.410909i | ||||
\(326\) | 3.77786i | 0.209237i | ||||||||
\(327\) | 12.7634 | − | 2.18985i | 0.705816 | − | 0.121099i | ||||
\(328\) | 5.13613 | − | 5.13613i | 0.283595 | − | 0.283595i | ||||
\(329\) | 0.494395 | 0.0272569 | ||||||||
\(330\) | 10.6063 | + | 11.7424i | 0.583857 | + | 0.646399i | ||||
\(331\) | −19.6774 | −1.08157 | −0.540783 | − | 0.841162i | \(-0.681872\pi\) | ||||
−0.540783 | + | 0.841162i | \(0.681872\pi\) | |||||||
\(332\) | −8.35783 | + | 8.35783i | −0.458695 | + | 0.458695i | ||||
\(333\) | 7.65685 | + | 3.65685i | 0.419593 | + | 0.200394i | ||||
\(334\) | 4.77248i | 0.261138i | ||||||||
\(335\) | 14.3514 | − | 9.09157i | 0.784100 | − | 0.496726i | ||||
\(336\) | 0.671354 | − | 0.949437i | 0.0366253 | − | 0.0517961i | ||||
\(337\) | −3.40510 | − | 3.40510i | −0.185488 | − | 0.185488i | 0.608254 | − | 0.793742i | \(-0.291870\pi\) |
−0.793742 | + | 0.608254i | \(0.791870\pi\) | |||||||
\(338\) | −4.45535 | − | 4.45535i | −0.242339 | − | 0.242339i | ||||
\(339\) | −8.91399 | + | 12.6063i | −0.484142 | + | 0.684680i | ||||
\(340\) | −10.8580 | + | 6.87855i | −0.588860 | + | 0.373042i | ||||
\(341\) | 4.08557i | 0.221246i | ||||||||
\(342\) | 4.25364 | + | 2.03151i | 0.230011 | + | 0.109851i | ||||
\(343\) | −6.43210 | + | 6.43210i | −0.347301 | + | 0.347301i | ||||
\(344\) | −1.65041 | −0.0889841 | ||||||||
\(345\) | −3.89349 | − | 4.31055i | −0.209618 | − | 0.232072i | ||||
\(346\) | −17.8453 | −0.959371 | ||||||||
\(347\) | 8.75110 | − | 8.75110i | 0.469783 | − | 0.469783i | −0.432061 | − | 0.901844i | \(-0.642213\pi\) |
0.901844 | + | 0.432061i | \(0.142213\pi\) | |||||||
\(348\) | 3.20764 | − | 0.550343i | 0.171947 | − | 0.0295015i | ||||
\(349\) | 30.6845i | 1.64251i | 0.570564 | + | 0.821253i | \(0.306724\pi\) | ||||
−0.570564 | + | 0.821253i | \(0.693276\pi\) | |||||||
\(350\) | 3.03500 | + | 1.43410i | 0.162228 | + | 0.0766558i | ||||
\(351\) | −21.9663 | − | 6.21302i | −1.17248 | − | 0.331627i | ||||
\(352\) | −2.88893 | − | 2.88893i | −0.153981 | − | 0.153981i | ||||
\(353\) | 4.19208 | + | 4.19208i | 0.223122 | + | 0.223122i | 0.809812 | − | 0.586690i | \(-0.199569\pi\) |
−0.586690 | + | 0.809812i | \(0.699569\pi\) | |||||||
\(354\) | −6.23037 | − | 4.40554i | −0.331141 | − | 0.234152i | ||||
\(355\) | −9.66268 | − | 2.16798i | −0.512842 | − | 0.115064i | ||||
\(356\) | − | 5.69230i | − | 0.301691i | ||||||
\(357\) | −1.13031 | − | 6.58790i | −0.0598221 | − | 0.348669i | ||||
\(358\) | 16.0700 | − | 16.0700i | 0.849326 | − | 0.849326i | ||||
\(359\) | 6.95588 | 0.367117 | 0.183559 | − | 0.983009i | \(-0.441238\pi\) | ||||
0.183559 | + | 0.983009i | \(0.441238\pi\) | |||||||
\(360\) | −4.14607 | + | 5.27353i | −0.218517 | + | 0.277939i | ||||
\(361\) | 16.5311 | 0.870056 | ||||||||
\(362\) | −7.51617 | + | 7.51617i | −0.395041 | + | 0.395041i | ||||
\(363\) | 1.66711 | + | 9.71661i | 0.0875004 | + | 0.509990i | ||||
\(364\) | − | 2.94944i | − | 0.154593i | ||||||
\(365\) | −13.3150 | − | 21.0182i | −0.696938 | − | 1.10014i | ||||
\(366\) | −15.8872 | − | 11.2340i | −0.830439 | − | 0.587209i | ||||
\(367\) | 3.72774 | + | 3.72774i | 0.194586 | + | 0.194586i | 0.797675 | − | 0.603088i | \(-0.206063\pi\) |
−0.603088 | + | 0.797675i | \(0.706063\pi\) | |||||||
\(368\) | 1.06051 | + | 1.06051i | 0.0552826 | + | 0.0552826i | ||||
\(369\) | −7.26358 | − | 20.5445i | −0.378127 | − | 1.06950i | ||||
\(370\) | 1.38459 | − | 6.17113i | 0.0719816 | − | 0.320822i | ||||
\(371\) | 2.35783i | 0.122412i | ||||||||
\(372\) | −1.70711 | + | 0.292893i | −0.0885094 | + | 0.0151858i | ||||
\(373\) | 2.93906 | − | 2.93906i | 0.152179 | − | 0.152179i | −0.626912 | − | 0.779090i | \(-0.715681\pi\) |
0.779090 | + | 0.626912i | \(0.215681\pi\) | |||||||
\(374\) | −23.4848 | −1.21437 | ||||||||
\(375\) | −17.0661 | − | 9.15146i | −0.881288 | − | 0.472579i | ||||
\(376\) | 0.736416 | 0.0379777 | ||||||||
\(377\) | 5.83710 | − | 5.83710i | 0.300626 | − | 0.300626i | ||||
\(378\) | −1.70224 | − | 3.04495i | −0.0875538 | − | 0.156615i | ||||
\(379\) | 19.7134i | 1.01261i | 0.862354 | + | 0.506305i | \(0.168989\pi\) | ||||
−0.862354 | + | 0.506305i | \(0.831011\pi\) | |||||||
\(380\) | 0.769189 | − | 3.42827i | 0.0394586 | − | 0.175867i | ||||
\(381\) | 19.1115 | − | 27.0277i | 0.979110 | − | 1.38467i | ||||
\(382\) | −0.576673 | − | 0.576673i | −0.0295051 | − | 0.0295051i | ||||
\(383\) | 1.75110 | + | 1.75110i | 0.0894769 | + | 0.0894769i | 0.750428 | − | 0.660952i | \(-0.229847\pi\) |
−0.660952 | + | 0.750428i | \(0.729847\pi\) | |||||||
\(384\) | 1.00000 | − | 1.41421i | 0.0510310 | − | 0.0721688i | ||||
\(385\) | 3.28220 | + | 5.18108i | 0.167277 | + | 0.264052i | ||||
\(386\) | 8.03786i | 0.409116i | ||||||||
\(387\) | −2.13380 | + | 4.46784i | −0.108467 | + | 0.227113i | ||||
\(388\) | 8.34915 | − | 8.34915i | 0.423864 | − | 0.423864i | ||||
\(389\) | 13.1089 | 0.664649 | 0.332324 | − | 0.943165i | \(-0.392167\pi\) | ||||
0.332324 | + | 0.943165i | \(0.392167\pi\) | |||||||
\(390\) | −0.863870 | + | 16.9931i | −0.0437438 | + | 0.860480i | ||||
\(391\) | 8.62111 | 0.435988 | ||||||||
\(392\) | −4.63104 | + | 4.63104i | −0.233903 | + | 0.233903i | ||||
\(393\) | 24.9136 | − | 4.27449i | 1.25672 | − | 0.215620i | ||||
\(394\) | 25.9572i | 1.30771i | ||||||||
\(395\) | −19.9136 | − | 4.46793i | −1.00196 | − | 0.224806i | ||||
\(396\) | −11.5557 | + | 4.08557i | −0.580697 | + | 0.205307i | ||||
\(397\) | −5.49522 | − | 5.49522i | −0.275797 | − | 0.275797i | 0.555631 | − | 0.831429i | \(-0.312477\pi\) |
−0.831429 | + | 0.555631i | \(0.812477\pi\) | |||||||
\(398\) | 11.3941 | + | 11.3941i | 0.571135 | + | 0.571135i | ||||
\(399\) | 1.49184 | + | 1.05489i | 0.0746853 | + | 0.0528105i | ||||
\(400\) | 4.52072 | + | 2.13613i | 0.226036 | + | 0.106806i | ||||
\(401\) | 2.83575i | 0.141611i | 0.997490 | + | 0.0708053i | \(0.0225569\pi\) | ||||
−0.997490 | + | 0.0708053i | \(0.977443\pi\) | |||||||
\(402\) | 2.22529 | + | 12.9699i | 0.110987 | + | 0.646882i | ||||
\(403\) | −3.10651 | + | 3.10651i | −0.154746 | + | 0.154746i | ||||
\(404\) | −12.5702 | −0.625392 | ||||||||
\(405\) | 8.91557 | + | 18.0420i | 0.443018 | + | 0.896513i | ||||
\(406\) | 1.26147 | 0.0626055 | ||||||||
\(407\) | 8.17113 | − | 8.17113i | 0.405028 | − | 0.405028i | ||||
\(408\) | −1.68362 | − | 9.81287i | −0.0833517 | − | 0.485809i | ||||
\(409\) | 3.01333i | 0.148999i | 0.997221 | + | 0.0744997i | \(0.0237360\pi\) | ||||
−0.997221 | + | 0.0744997i | \(0.976264\pi\) | |||||||
\(410\) | −13.7204 | + | 8.69186i | −0.677603 | + | 0.429260i | ||||
\(411\) | −12.4550 | − | 8.80704i | −0.614362 | − | 0.434419i | ||||
\(412\) | 0.449657 | + | 0.449657i | 0.0221530 | + | 0.0221530i | ||||
\(413\) | −2.09139 | − | 2.09139i | −0.102911 | − | 0.102911i | ||||
\(414\) | 4.24202 | − | 1.49978i | 0.208484 | − | 0.0737102i | ||||
\(415\) | 22.3267 | − | 14.1439i | 1.09598 | − | 0.694298i | ||||
\(416\) | − | 4.39327i | − | 0.215398i | ||||||
\(417\) | −2.31309 | + | 0.396863i | −0.113272 | + | 0.0194345i | ||||
\(418\) | 4.53934 | − | 4.53934i | 0.222026 | − | 0.222026i | ||||
\(419\) | −39.6972 | −1.93934 | −0.969669 | − | 0.244423i | \(-0.921401\pi\) | ||||
−0.969669 | + | 0.244423i | \(0.921401\pi\) | |||||||
\(420\) | −1.92955 | + | 1.74286i | −0.0941525 | + | 0.0850429i | ||||
\(421\) | 6.85743 | 0.334210 | 0.167105 | − | 0.985939i | \(-0.446558\pi\) | ||||
0.167105 | + | 0.985939i | \(0.446558\pi\) | |||||||
\(422\) | −17.7675 | + | 17.7675i | −0.864908 | + | 0.864908i | ||||
\(423\) | 0.952107 | − | 1.99356i | 0.0462930 | − | 0.0969300i | ||||
\(424\) | 3.51205i | 0.170560i | ||||||||
\(425\) | 27.0576 | − | 9.69248i | 1.31249 | − | 0.470154i | ||||
\(426\) | 4.42871 | − | 6.26315i | 0.214572 | − | 0.303450i | ||||
\(427\) | −5.33297 | − | 5.33297i | −0.258081 | − | 0.258081i | ||||
\(428\) | 5.00412 | + | 5.00412i | 0.241883 | + | 0.241883i | ||||
\(429\) | −17.9490 | + | 25.3837i | −0.866586 | + | 1.22554i | ||||
\(430\) | 3.60091 | + | 0.807922i | 0.173651 | + | 0.0389615i | ||||
\(431\) | 7.58473i | 0.365343i | 0.983174 | + | 0.182672i | \(0.0584746\pi\) | ||||
−0.983174 | + | 0.182672i | \(0.941525\pi\) | |||||||
\(432\) | −2.53553 | − | 4.53553i | −0.121991 | − | 0.218216i | ||||
\(433\) | 6.55340 | − | 6.55340i | 0.314936 | − | 0.314936i | −0.531882 | − | 0.846818i | \(-0.678515\pi\) |
0.846818 | + | 0.531882i | \(0.178515\pi\) | |||||||
\(434\) | −0.671354 | −0.0322260 | ||||||||
\(435\) | −7.26791 | − | 0.369475i | −0.348470 | − | 0.0177150i | ||||
\(436\) | 7.47661 | 0.358064 | ||||||||
\(437\) | −1.66636 | + | 1.66636i | −0.0797127 | + | 0.0797127i | ||||
\(438\) | 18.9950 | − | 3.25903i | 0.907616 | − | 0.155722i | ||||
\(439\) | − | 11.1508i | − | 0.532199i | −0.963946 | − | 0.266100i | \(-0.914265\pi\) | ||
0.963946 | − | 0.266100i | \(-0.0857350\pi\) | |||||||
\(440\) | 4.88893 | + | 7.71736i | 0.233071 | + | 0.367911i | ||||
\(441\) | 6.54928 | + | 18.5242i | 0.311871 | + | 0.882104i | ||||
\(442\) | −17.8570 | − | 17.8570i | −0.849370 | − | 0.849370i | ||||
\(443\) | 3.68595 | + | 3.68595i | 0.175125 | + | 0.175125i | 0.789227 | − | 0.614102i | \(-0.210482\pi\) |
−0.614102 | + | 0.789227i | \(0.710482\pi\) | |||||||
\(444\) | 4.00000 | + | 2.82843i | 0.189832 | + | 0.134231i | ||||
\(445\) | −2.78654 | + | 12.4196i | −0.132095 | + | 0.588745i | ||||
\(446\) | 5.10322i | 0.241645i | ||||||||
\(447\) | 5.96942 | + | 34.7923i | 0.282344 | + | 1.64562i | ||||
\(448\) | 0.474719 | − | 0.474719i | 0.0224283 | − | 0.0224283i | ||||
\(449\) | −12.8111 | −0.604592 | −0.302296 | − | 0.953214i | \(-0.597753\pi\) | ||||
−0.302296 | + | 0.953214i | \(0.597753\pi\) | |||||||
\(450\) | 11.6275 | − | 9.47630i | 0.548128 | − | 0.446717i | ||||
\(451\) | −29.6759 | −1.39738 | ||||||||
\(452\) | −6.30315 | + | 6.30315i | −0.296475 | + | 0.296475i | ||||
\(453\) | 5.70320 | + | 33.2407i | 0.267960 | + | 1.56178i | ||||
\(454\) | − | 22.9222i | − | 1.07579i | ||||||
\(455\) | −1.44383 | + | 6.43516i | −0.0676879 | + | 0.301685i | ||||
\(456\) | 2.22214 | + | 1.57129i | 0.104061 | + | 0.0735823i | ||||
\(457\) | 20.8096 | + | 20.8096i | 0.973431 | + | 0.973431i | 0.999656 | − | 0.0262250i | \(-0.00834864\pi\) |
−0.0262250 | + | 0.999656i | \(0.508349\pi\) | |||||||
\(458\) | 4.69685 | + | 4.69685i | 0.219470 | + | 0.219470i | ||||
\(459\) | −28.7412 | − | 8.12925i | −1.34153 | − | 0.379441i | ||||
\(460\) | −1.79469 | − | 2.83298i | −0.0836778 | − | 0.132089i | ||||
\(461\) | 10.0281i | 0.467056i | 0.972350 | + | 0.233528i | \(0.0750271\pi\) | ||||
−0.972350 | + | 0.233528i | \(0.924973\pi\) | |||||||
\(462\) | −4.68235 | + | 0.803365i | −0.217843 | + | 0.0373759i | ||||
\(463\) | −3.28991 | + | 3.28991i | −0.152895 | + | 0.152895i | −0.779410 | − | 0.626515i | \(-0.784481\pi\) |
0.626515 | + | 0.779410i | \(0.284481\pi\) | |||||||
\(464\) | 1.87899 | 0.0872299 | ||||||||
\(465\) | 3.86799 | + | 0.196635i | 0.179374 | + | 0.00911873i | ||||
\(466\) | −12.9421 | −0.599532 | ||||||||
\(467\) | 11.2120 | − | 11.2120i | 0.518828 | − | 0.518828i | −0.398389 | − | 0.917217i | \(-0.630431\pi\) |
0.917217 | + | 0.398389i | \(0.130431\pi\) | |||||||
\(468\) | −11.8931 | − | 5.68003i | −0.549756 | − | 0.262559i | ||||
\(469\) | 5.10069i | 0.235528i | ||||||||
\(470\) | −1.60673 | − | 0.360496i | −0.0741129 | − | 0.0166284i | ||||
\(471\) | −2.06822 | + | 2.92490i | −0.0952984 | + | 0.134772i | ||||
\(472\) | −3.11519 | − | 3.11519i | −0.143388 | − | 0.143388i | ||||
\(473\) | 4.76792 | + | 4.76792i | 0.219229 | + | 0.219229i | ||||
\(474\) | 9.12702 | − | 12.9075i | 0.419218 | − | 0.592863i | ||||
\(475\) | −3.35647 | + | 7.10336i | −0.154006 | + | 0.325924i | ||||
\(476\) | − | 3.85911i | − | 0.176882i | ||||||
\(477\) | 9.50749 | + | 4.54070i | 0.435318 | + | 0.207905i | ||||
\(478\) | 18.7716 | − | 18.7716i | 0.858593 | − | 0.858593i | ||||
\(479\) | −5.88990 | −0.269116 | −0.134558 | − | 0.990906i | \(-0.542961\pi\) | ||||
−0.134558 | + | 0.990906i | \(0.542961\pi\) | |||||||
\(480\) | −2.87412 | + | 2.59604i | −0.131185 | + | 0.118492i | ||||
\(481\) | 12.4260 | 0.566579 | ||||||||
\(482\) | −2.55034 | + | 2.55034i | −0.116165 | + | 0.116165i | ||||
\(483\) | 1.71886 | − | 0.294909i | 0.0782107 | − | 0.0134188i | ||||
\(484\) | 5.69186i | 0.258721i | ||||||||
\(485\) | −22.3035 | + | 14.1292i | −1.01275 | + | 0.641576i | ||||
\(486\) | −15.5563 | + | 1.00000i | −0.705650 | + | 0.0453609i | ||||
\(487\) | 24.5134 | + | 24.5134i | 1.11081 | + | 1.11081i | 0.993041 | + | 0.117767i | \(0.0375736\pi\) |
0.117767 | + | 0.993041i | \(0.462426\pi\) | |||||||
\(488\) | −7.94361 | − | 7.94361i | −0.359590 | − | 0.359590i | ||||
\(489\) | 5.34271 | + | 3.77786i | 0.241606 | + | 0.170841i | ||||
\(490\) | 12.3712 | − | 7.83710i | 0.558872 | − | 0.354044i | ||||
\(491\) | 24.6711i | 1.11339i | 0.830717 | + | 0.556696i | \(0.187931\pi\) | ||||
−0.830717 | + | 0.556696i | \(0.812069\pi\) | |||||||
\(492\) | −2.12745 | − | 12.3997i | −0.0959131 | − | 0.559022i | ||||
\(493\) | 7.63739 | − | 7.63739i | 0.343971 | − | 0.343971i | ||||
\(494\) | 6.90309 | 0.310585 | ||||||||
\(495\) | 27.2126 | − | 3.25714i | 1.22311 | − | 0.146398i | ||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | 2.10239 | − | 2.10239i | 0.0943052 | − | 0.0943052i | ||||
\(498\) | 3.46193 | + | 20.1776i | 0.155133 | + | 0.904179i | ||||
\(499\) | − | 38.4311i | − | 1.72041i | −0.509945 | − | 0.860207i | \(-0.670334\pi\) | ||
0.509945 | − | 0.860207i | \(-0.329666\pi\) | |||||||
\(500\) | −8.81774 | − | 6.87368i | −0.394341 | − | 0.307400i | ||||
\(501\) | 6.74930 | + | 4.77248i | 0.301537 | + | 0.213219i | ||||
\(502\) | 12.9158 | + | 12.9158i | 0.576460 | + | 0.576460i | ||||
\(503\) | 17.8215 | + | 17.8215i | 0.794623 | + | 0.794623i | 0.982242 | − | 0.187619i | \(-0.0600769\pi\) |
−0.187619 | + | 0.982242i | \(0.560077\pi\) | |||||||
\(504\) | −0.671354 | − | 1.89887i | −0.0299045 | − | 0.0845826i | ||||
\(505\) | 27.4260 | + | 6.15348i | 1.22044 | + | 0.273826i | ||||
\(506\) | − | 6.12745i | − | 0.272399i | ||||||
\(507\) | −10.7562 | + | 1.84547i | −0.477698 | + | 0.0819601i | ||||
\(508\) | 13.5138 | − | 13.5138i | 0.599580 | − | 0.599580i | ||||
\(509\) | −26.2585 | −1.16389 | −0.581944 | − | 0.813229i | \(-0.697708\pi\) | ||||
−0.581944 | + | 0.813229i | \(0.697708\pi\) | |||||||
\(510\) | −1.13031 | + | 22.2341i | −0.0500508 | + | 0.984545i | ||||
\(511\) | 7.47016 | 0.330460 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 7.12663 | − | 3.98405i | 0.314648 | − | 0.175900i | ||||
\(514\) | − | 25.3682i | − | 1.11894i | ||||||
\(515\) | −0.760953 | − | 1.20119i | −0.0335316 | − | 0.0529308i | ||||
\(516\) | −1.65041 | + | 2.33403i | −0.0726552 | + | 0.102750i | ||||
\(517\) | −2.12745 | − | 2.12745i | −0.0935653 | − | 0.0935653i | ||||
\(518\) | 1.34271 | + | 1.34271i | 0.0589952 | + | 0.0589952i | ||||
\(519\) | −17.8453 | + | 25.2371i | −0.783323 | + | 1.10779i | ||||
\(520\) | −2.15063 | + | 9.58535i | −0.0943113 | + | 0.420345i | ||||
\(521\) | − | 27.7886i | − | 1.21744i | −0.793384 | − | 0.608721i | \(-0.791683\pi\) | ||
0.793384 | − | 0.608721i | \(-0.208317\pi\) | |||||||
\(522\) | 2.42933 | − | 5.08663i | 0.106329 | − | 0.222636i | ||||
\(523\) | −18.1124 | + | 18.1124i | −0.792001 | + | 0.792001i | −0.981819 | − | 0.189818i | \(-0.939210\pi\) |
0.189818 | + | 0.981819i | \(0.439210\pi\) | |||||||
\(524\) | 14.5940 | 0.637543 | ||||||||
\(525\) | 5.06313 | − | 2.85805i | 0.220973 | − | 0.124735i | ||||
\(526\) | −13.1502 | −0.573376 | ||||||||
\(527\) | −4.06462 | + | 4.06462i | −0.177058 | + | 0.177058i | ||||
\(528\) | −6.97450 | + | 1.19663i | −0.303526 | + | 0.0520768i | ||||
\(529\) | − | 20.7507i | − | 0.902203i | ||||||
\(530\) | 1.71925 | − | 7.66268i | 0.0746793 | − | 0.332845i | ||||
\(531\) | −12.4607 | + | 4.40554i | −0.540750 | + | 0.191184i | ||||
\(532\) | 0.745919 | + | 0.745919i | 0.0323397 | + | 0.0323397i | ||||
\(533\) | −22.5644 | − | 22.5644i | −0.977373 | − | 0.977373i | ||||
\(534\) | −8.05012 | − | 5.69230i | −0.348363 | − | 0.246330i | ||||
\(535\) | −8.46846 | − | 13.3678i | −0.366123 | − | 0.577939i | ||||
\(536\) | 7.59762i | 0.328167i | ||||||||
\(537\) | −6.65642 | − | 38.7964i | −0.287246 | − | 1.67419i | ||||
\(538\) | 6.54390 | − | 6.54390i | 0.282128 | − | 0.282128i | ||||
\(539\) | 26.7575 | 1.15253 | ||||||||
\(540\) | 3.31182 | + | 11.1370i | 0.142518 | + | 0.479258i | ||||
\(541\) | 28.7637 | 1.23665 | 0.618323 | − | 0.785924i | \(-0.287812\pi\) | ||||
0.618323 | + | 0.785924i | \(0.287812\pi\) | |||||||
\(542\) | 20.3655 | − | 20.3655i | 0.874775 | − | 0.874775i | ||||
\(543\) | 3.11330 | + | 18.1456i | 0.133604 | + | 0.778704i | ||||
\(544\) | − | 5.74825i | − | 0.246454i | ||||||
\(545\) | −16.3126 | − | 3.66001i | −0.698757 | − | 0.156778i | ||||
\(546\) | −4.17113 | − | 2.94944i | −0.178508 | − | 0.126224i | ||||
\(547\) | −10.2072 | − | 10.2072i | −0.436428 | − | 0.436428i | 0.454380 | − | 0.890808i | \(-0.349861\pi\) |
−0.890808 | + | 0.454380i | \(0.849861\pi\) | |||||||
\(548\) | −6.22752 | − | 6.22752i | −0.266027 | − | 0.266027i | ||||
\(549\) | −31.7745 | + | 11.2340i | −1.35610 | + | 0.479454i | ||||
\(550\) | −6.88893 | − | 19.2312i | −0.293745 | − | 0.820021i | ||||
\(551\) | 2.95243i | 0.125778i | ||||||||
\(552\) | 2.56029 | − | 0.439276i | 0.108973 | − | 0.0186968i | ||||
\(553\) | 4.33276 | − | 4.33276i | 0.184248 | − | 0.184248i | ||||
\(554\) | 26.6344 | 1.13159 | ||||||||
\(555\) | −7.34271 | − | 8.12925i | −0.311681 | − | 0.345067i | ||||
\(556\) | −1.35498 | −0.0574638 | ||||||||
\(557\) | −12.7383 | + | 12.7383i | −0.539739 | + | 0.539739i | −0.923452 | − | 0.383713i | \(-0.874645\pi\) |
0.383713 | + | 0.923452i | \(0.374645\pi\) | |||||||
\(558\) | −1.29289 | + | 2.70711i | −0.0547325 | + | 0.114601i | ||||
\(559\) | 7.25070i | 0.306672i | ||||||||
\(560\) | −1.26814 | + | 0.803365i | −0.0535888 | + | 0.0339484i | ||||
\(561\) | −23.4848 | + | 33.2126i | −0.991531 | + | 1.40224i | ||||
\(562\) | −8.94032 | − | 8.94032i | −0.377125 | − | 0.377125i | ||||
\(563\) | −1.84999 | − | 1.84999i | −0.0779678 | − | 0.0779678i | 0.667047 | − | 0.745015i | \(-0.267558\pi\) |
−0.745015 | + | 0.667047i | \(0.767558\pi\) | |||||||
\(564\) | 0.736416 | − | 1.04145i | 0.0310087 | − | 0.0438529i | ||||
\(565\) | 16.8379 | − | 10.6668i | 0.708377 | − | 0.448756i | ||||
\(566\) | − | 19.5358i | − | 0.821153i | ||||||
\(567\) | −6.00844 | − | 0.637616i | −0.252331 | − | 0.0267774i | ||||
\(568\) | 3.13157 | − | 3.13157i | 0.131398 | − | 0.131398i | ||||
\(569\) | −28.0100 | −1.17424 | −0.587121 | − | 0.809499i | \(-0.699739\pi\) | ||||
−0.587121 | + | 0.809499i | \(0.699739\pi\) | |||||||
\(570\) | −4.07912 | − | 4.51607i | −0.170856 | − | 0.189157i | ||||
\(571\) | 41.3740 | 1.73145 | 0.865724 | − | 0.500522i | \(-0.166859\pi\) | ||||
0.865724 | + | 0.500522i | \(0.166859\pi\) | |||||||
\(572\) | −12.6919 | + | 12.6919i | −0.530673 | + | 0.530673i | ||||
\(573\) | −1.39221 | + | 0.238866i | −0.0581604 | + | 0.00997875i | ||||
\(574\) | − | 4.87643i | − | 0.203538i | ||||||
\(575\) | 2.52887 | + | 7.05963i | 0.105461 | + | 0.294407i | ||||
\(576\) | −1.00000 | − | 2.82843i | −0.0416667 | − | 0.117851i | ||||
\(577\) | −3.56082 | − | 3.56082i | −0.148239 | − | 0.148239i | 0.629092 | − | 0.777331i | \(-0.283427\pi\) |
−0.777331 | + | 0.629092i | \(0.783427\pi\) | |||||||
\(578\) | −11.3436 | − | 11.3436i | −0.471833 | − | 0.471833i | ||||
\(579\) | 11.3672 | + | 8.03786i | 0.472407 | + | 0.334042i | ||||
\(580\) | −4.09963 | − | 0.919818i | −0.170228 | − | 0.0381934i | ||||
\(581\) | 7.93523i | 0.329209i | ||||||||
\(582\) | −3.45833 | − | 20.1566i | −0.143352 | − | 0.835519i | ||||
\(583\) | 10.1461 | − | 10.1461i | 0.420207 | − | 0.420207i | ||||
\(584\) | 11.1270 | 0.460439 | ||||||||
\(585\) | 23.1680 | + | 18.2148i | 0.957880 | + | 0.753090i | ||||
\(586\) | 28.6145 | 1.18206 | ||||||||
\(587\) | 17.7934 | − | 17.7934i | 0.734413 | − | 0.734413i | −0.237078 | − | 0.971491i | \(-0.576190\pi\) |
0.971491 | + | 0.237078i | \(0.0761896\pi\) | |||||||
\(588\) | 1.91824 | + | 11.1803i | 0.0791069 | + | 0.461069i | ||||
\(589\) | − | 1.57129i | − | 0.0647438i | ||||||
\(590\) | 5.27182 | + | 8.32176i | 0.217037 | + | 0.342602i | ||||
\(591\) | 36.7091 | + | 25.9572i | 1.51001 | + | 1.06774i | ||||
\(592\) | 2.00000 | + | 2.00000i | 0.0821995 | + | 0.0821995i | ||||
\(593\) | −33.6090 | − | 33.6090i | −1.38016 | − | 1.38016i | −0.844325 | − | 0.535832i | \(-0.819998\pi\) |
−0.535832 | − | 0.844325i | \(-0.680002\pi\) | |||||||
\(594\) | −5.77786 | + | 20.4278i | −0.237069 | + | 0.838164i | ||||
\(595\) | −1.88914 | + | 8.41989i | −0.0774472 | + | 0.345182i | ||||
\(596\) | 20.3809i | 0.834833i | ||||||||
\(597\) | 27.5078 | − | 4.71959i | 1.12582 | − | 0.193160i | ||||
\(598\) | 4.65908 | − | 4.65908i | 0.190524 | − | 0.190524i | ||||
\(599\) | 6.77010 | 0.276619 | 0.138309 | − | 0.990389i | \(-0.455833\pi\) | ||||
0.138309 | + | 0.990389i | \(0.455833\pi\) | |||||||
\(600\) | 7.54167 | − | 4.25714i | 0.307887 | − | 0.173797i | ||||
\(601\) | 45.8051 | 1.86843 | 0.934215 | − | 0.356711i | \(-0.116102\pi\) | ||||
0.934215 | + | 0.356711i | \(0.116102\pi\) | |||||||
\(602\) | −0.783480 | + | 0.783480i | −0.0319323 | + | 0.0319323i | ||||
\(603\) | 20.5676 | + | 9.82291i | 0.837576 | + | 0.400020i | ||||
\(604\) | 19.4720i | 0.792303i | ||||||||
\(605\) | 2.78632 | − | 12.4186i | 0.113280 | − | 0.504890i | ||||
\(606\) | −12.5702 | + | 17.7770i | −0.510631 | + | 0.722141i | ||||
\(607\) | 20.7241 | + | 20.7241i | 0.841165 | + | 0.841165i | 0.989010 | − | 0.147845i | \(-0.0472338\pi\) |
−0.147845 | + | 0.989010i | \(0.547234\pi\) | |||||||
\(608\) | 1.11107 | + | 1.11107i | 0.0450597 | + | 0.0450597i | ||||
\(609\) | 1.26147 | − | 1.78398i | 0.0511172 | − | 0.0722906i | ||||
\(610\) | 13.4430 | + | 21.2202i | 0.544289 | + | 0.859181i | ||||
\(611\) | − | 3.23527i | − | 0.130885i | ||||||
\(612\) | −15.5611 | − | 7.43187i | −0.629021 | − | 0.300415i | ||||
\(613\) | −25.8175 | + | 25.8175i | −1.04276 | + | 1.04276i | −0.0437155 | + | 0.999044i | \(0.513920\pi\) |
−0.999044 | + | 0.0437155i | \(0.986080\pi\) | |||||||
\(614\) | −10.8392 | −0.437434 | ||||||||
\(615\) | −1.42827 | + | 28.0955i | −0.0575936 | + | 1.13292i | ||||
\(616\) | −2.74286 | −0.110513 | ||||||||
\(617\) | −13.0922 | + | 13.0922i | −0.527073 | + | 0.527073i | −0.919698 | − | 0.392626i | \(-0.871567\pi\) |
0.392626 | + | 0.919698i | \(0.371567\pi\) | |||||||
\(618\) | 1.08557 | − | 0.186254i | 0.0436679 | − | 0.00749223i | ||||
\(619\) | 6.70426i | 0.269467i | 0.990882 | + | 0.134734i | \(0.0430178\pi\) | ||||
−0.990882 | + | 0.134734i | \(0.956982\pi\) | |||||||
\(620\) | 2.18183 | + | 0.489528i | 0.0876242 | + | 0.0196599i | ||||
\(621\) | 2.12101 | − | 7.49890i | 0.0851132 | − | 0.300921i | ||||
\(622\) | 20.1743 | + | 20.1743i | 0.808915 | + | 0.808915i | ||||
\(623\) | −2.70224 | − | 2.70224i | −0.108263 | − | 0.108263i | ||||
\(624\) | −6.21302 | − | 4.39327i | −0.248720 | − | 0.175872i | ||||
\(625\) | 15.8739 | + | 19.3137i | 0.634956 | + | 0.772548i | ||||
\(626\) | − | 32.6672i | − | 1.30564i | ||||||
\(627\) | −1.88026 | − | 10.9589i | −0.0750902 | − | 0.437658i | ||||
\(628\) | −1.46245 | + | 1.46245i | −0.0583581 | + | 0.0583581i | ||||
\(629\) | 16.2585 | 0.648269 | ||||||||
\(630\) | 0.535224 | + | 4.47166i | 0.0213238 | + | 0.178155i | ||||
\(631\) | −20.5580 | −0.818399 | −0.409200 | − | 0.912445i | \(-0.634192\pi\) | ||||
−0.409200 | + | 0.912445i | \(0.634192\pi\) | |||||||
\(632\) | 6.45377 | − | 6.45377i | 0.256717 | − | 0.256717i | ||||
\(633\) | 7.35953 | + | 42.8945i | 0.292515 | + | 1.70490i | ||||
\(634\) | 16.0199i | 0.636231i | ||||||||
\(635\) | −36.1002 | + | 22.8694i | −1.43259 | + | 0.907546i | ||||
\(636\) | 4.96679 | + | 3.51205i | 0.196946 | + | 0.139262i | ||||
\(637\) | 20.3454 | + | 20.3454i | 0.806115 | + | 0.806115i | ||||
\(638\) | −5.42827 | − | 5.42827i | −0.214907 | − | 0.214907i | ||||
\(639\) | −4.42871 | − | 12.5263i | −0.175197 | − | 0.495532i | ||||
\(640\) | −1.88893 | + | 1.19663i | −0.0746666 | + | 0.0473011i | ||||
\(641\) | − | 21.5740i | − | 0.852120i | −0.904695 | − | 0.426060i | \(-0.859901\pi\) | ||
0.904695 | − | 0.426060i | \(-0.140099\pi\) | |||||||
\(642\) | 12.0810 | − | 2.07277i | 0.476799 | − | 0.0818059i | ||||
\(643\) | −21.5307 | + | 21.5307i | −0.849087 | + | 0.849087i | −0.990019 | − | 0.140933i | \(-0.954990\pi\) |
0.140933 | + | 0.990019i | \(0.454990\pi\) | |||||||
\(644\) | 1.00688 | 0.0396768 | ||||||||
\(645\) | 4.74348 | − | 4.28453i | 0.186774 | − | 0.168703i | ||||
\(646\) | 9.03214 | 0.355365 | ||||||||
\(647\) | 10.5743 | − | 10.5743i | 0.415720 | − | 0.415720i | −0.468005 | − | 0.883726i | \(-0.655027\pi\) |
0.883726 | + | 0.468005i | \(0.155027\pi\) | |||||||
\(648\) | −8.94975 | − | 0.949747i | −0.351579 | − | 0.0373096i | ||||
\(649\) | 17.9991i | 0.706527i | ||||||||
\(650\) | 9.38459 | − | 19.8608i | 0.368094 | − | 0.779003i | ||||
\(651\) | −0.671354 | + | 0.949437i | −0.0263124 | + | 0.0372114i | ||||
\(652\) | 2.67135 | + | 2.67135i | 0.104618 | + | 0.104618i | ||||
\(653\) | −21.0078 | − | 21.0078i | −0.822099 | − | 0.822099i | 0.164310 | − | 0.986409i | \(-0.447460\pi\) |
−0.986409 | + | 0.164310i | \(0.947460\pi\) | |||||||
\(654\) | 7.47661 | − | 10.5735i | 0.292358 | − | 0.413457i | ||||
\(655\) | −31.8416 | − | 7.14418i | −1.24415 | − | 0.279146i | ||||
\(656\) | − | 7.26358i | − | 0.283595i | ||||||
\(657\) | 14.3860 | − | 30.1220i | 0.561253 | − | 1.17517i | ||||
\(658\) | 0.349590 | − | 0.349590i | 0.0136284 | − | 0.0136284i | ||||
\(659\) | 26.4009 | 1.02843 | 0.514216 | − | 0.857661i | \(-0.328083\pi\) | ||||
0.514216 | + | 0.857661i | \(0.328083\pi\) | |||||||
\(660\) | 15.8029 | + | 0.803365i | 0.615128 | + | 0.0312709i | ||||
\(661\) | −29.3162 | −1.14027 | −0.570135 | − | 0.821551i | \(-0.693109\pi\) | ||||
−0.570135 | + | 0.821551i | \(0.693109\pi\) | |||||||
\(662\) | −13.9140 | + | 13.9140i | −0.540783 | + | 0.540783i | ||||
\(663\) | −43.1106 | + | 7.39661i | −1.67428 | + | 0.287260i | ||||
\(664\) | 11.8198i | 0.458695i | ||||||||
\(665\) | −1.26232 | − | 1.99261i | −0.0489506 | − | 0.0772703i | ||||
\(666\) | 8.00000 | − | 2.82843i | 0.309994 | − | 0.109599i | ||||
\(667\) | 1.99268 | + | 1.99268i | 0.0771568 | + | 0.0771568i | ||||
\(668\) | 3.37465 | + | 3.37465i | 0.130569 | + | 0.130569i | ||||
\(669\) | 7.21704 | + | 5.10322i | 0.279027 | + | 0.197302i | ||||
\(670\) | 3.71925 | − | 16.5767i | 0.143687 | − | 0.640413i | ||||
\(671\) | 45.8971i | 1.77184i | ||||||||
\(672\) | −0.196635 | − | 1.14607i | −0.00758536 | − | 0.0442107i | ||||
\(673\) | −21.6844 | + | 21.6844i | −0.835870 | + | 0.835870i | −0.988312 | − | 0.152442i | \(-0.951286\pi\) |
0.152442 | + | 0.988312i | \(0.451286\pi\) | |||||||
\(674\) | −4.81554 | −0.185488 | ||||||||
\(675\) | −1.77396 | − | 25.9201i | −0.0682798 | − | 0.997666i | ||||
\(676\) | −6.30082 | −0.242339 | ||||||||
\(677\) | −31.1572 | + | 31.1572i | −1.19747 | + | 1.19747i | −0.222544 | + | 0.974923i | \(0.571436\pi\) |
−0.974923 | + | 0.222544i | \(0.928564\pi\) | |||||||
\(678\) | 2.61085 | + | 15.2171i | 0.100269 | + | 0.584411i | ||||
\(679\) | − | 7.92700i | − | 0.304210i | ||||||
\(680\) | −2.81393 | + | 12.5417i | −0.107909 | + | 0.480951i | ||||
\(681\) | −32.4169 | − | 22.9222i | −1.24222 | − | 0.878382i | ||||
\(682\) | 2.88893 | + | 2.88893i | 0.110623 | + | 0.110623i | ||||
\(683\) | 27.6523 | + | 27.6523i | 1.05809 | + | 1.05809i | 0.998206 | + | 0.0598802i | \(0.0190719\pi\) |
0.0598802 | + | 0.998206i | \(0.480928\pi\) | |||||||
\(684\) | 4.44427 | − | 1.57129i | 0.169931 | − | 0.0600797i | ||||
\(685\) | 10.5388 | + | 16.6359i | 0.402668 | + | 0.635625i | ||||
\(686\) | 9.09636i | 0.347301i | ||||||||
\(687\) | 11.3392 | − | 1.94550i | 0.432618 | − | 0.0742255i | ||||
\(688\) | −1.16702 | + | 1.16702i | −0.0444921 | + | 0.0444921i | ||||
\(689\) | 15.4294 | 0.587813 | ||||||||
\(690\) | −5.80113 | − | 0.294909i | −0.220845 | − | 0.0112270i | ||||
\(691\) | −13.4710 | −0.512462 | −0.256231 | − | 0.966616i | \(-0.582481\pi\) | ||||
−0.256231 | + | 0.966616i | \(0.582481\pi\) | |||||||
\(692\) | −12.6186 | + | 12.6186i | −0.479686 | + | 0.479686i | ||||
\(693\) | −3.54623 | + | 7.42521i | −0.134710 | + | 0.282061i | ||||
\(694\) | − | 12.3759i | − | 0.469783i | ||||||
\(695\) | 2.95632 | + | 0.663299i | 0.112140 | + | 0.0251604i | ||||
\(696\) | 1.87899 | − | 2.65729i | 0.0712229 | − | 0.100724i | ||||
\(697\) | −29.5237 | − | 29.5237i | −1.11829 | − | 1.11829i | ||||
\(698\) | 21.6972 | + | 21.6972i | 0.821253 | + | 0.821253i | ||||
\(699\) | −12.9421 | + | 18.3029i | −0.489516 | + | 0.692280i | ||||
\(700\) | 3.16013 | − | 1.13201i | 0.119442 | − | 0.0427860i | ||||
\(701\) | 6.91995i | 0.261363i | 0.991424 | + | 0.130682i | \(0.0417165\pi\) | ||||
−0.991424 | + | 0.130682i | \(0.958283\pi\) | |||||||
\(702\) | −19.9258 | + | 11.1393i | −0.752052 | + | 0.420425i | ||||
\(703\) | −3.14257 | + | 3.14257i | −0.118524 | + | 0.118524i | ||||
\(704\) | −4.08557 | −0.153981 | ||||||||
\(705\) | −2.11655 | + | 1.91176i | −0.0797138 | + | 0.0720012i | ||||
\(706\) | 5.92849 | 0.223122 | ||||||||
\(707\) | −5.96732 | + | 5.96732i | −0.224424 | + | 0.224424i | ||||
\(708\) | −7.52072 | + | 1.29035i | −0.282646 | + | 0.0484944i | ||||
\(709\) | − | 19.1112i | − | 0.717735i | −0.933389 | − | 0.358867i | \(-0.883163\pi\) | ||
0.933389 | − | 0.358867i | \(-0.116837\pi\) | |||||||
\(710\) | −8.36554 | + | 5.29955i | −0.313953 | + | 0.198889i | ||||
\(711\) | −9.12702 | − | 25.8151i | −0.342290 | − | 0.968142i | ||||
\(712\) | −4.02506 | − | 4.02506i | −0.150846 | − | 0.150846i | ||||
\(713\) | −1.06051 | − | 1.06051i | −0.0397162 | − | 0.0397162i | ||||
\(714\) | −5.45760 | − | 3.85911i | −0.204245 | − | 0.144423i | ||||
\(715\) | 33.9044 | − | 21.4784i | 1.26795 | − | 0.803247i | ||||
\(716\) | − | 22.7264i | − | 0.849326i | ||||||
\(717\) | −7.77545 | − | 45.3187i | −0.290380 | − | 1.69246i | ||||
\(718\) | 4.91855 | − | 4.91855i | 0.183559 | − | 0.183559i | ||||
\(719\) | 40.0027 | 1.49185 | 0.745925 | − | 0.666030i | \(-0.232008\pi\) | ||||
0.745925 | + | 0.666030i | \(0.232008\pi\) | |||||||
\(720\) | 0.797231 | + | 6.66066i | 0.0297110 | + | 0.248228i | ||||
\(721\) | 0.426921 | 0.0158994 | ||||||||
\(722\) | 11.6892 | − | 11.6892i | 0.435028 | − | 0.435028i | ||||
\(723\) | 1.05639 | + | 6.15707i | 0.0392874 | + | 0.228984i | ||||
\(724\) | 10.6295i | 0.395041i | ||||||||
\(725\) | 8.49440 | + | 4.01377i | 0.315474 | + | 0.149068i | ||||
\(726\) | 8.04950 | + | 5.69186i | 0.298745 | + | 0.211245i | ||||
\(727\) | −13.2741 | − | 13.2741i | −0.492311 | − | 0.492311i | 0.416723 | − | 0.909034i | \(-0.363179\pi\) |
−0.909034 | + | 0.416723i | \(0.863179\pi\) | |||||||
\(728\) | −2.08557 | − | 2.08557i | −0.0772963 | − | 0.0772963i | ||||
\(729\) | −14.1421 | + | 23.0000i | −0.523783 | + | 0.851852i | ||||
\(730\) | −24.2772 | − | 5.44699i | −0.898540 | − | 0.201602i | ||||
\(731\) | 9.48696i | 0.350888i | ||||||||
\(732\) | −19.1776 | + | 3.29035i | −0.708824 | + | 0.121615i | ||||
\(733\) | −8.25491 | + | 8.25491i | −0.304902 | + | 0.304902i | −0.842928 | − | 0.538026i | \(-0.819170\pi\) |
0.538026 | + | 0.842928i | \(0.319170\pi\) | |||||||
\(734\) | 5.27182 | 0.194586 | ||||||||
\(735\) | 1.28782 | − | 25.3326i | 0.0475019 | − | 0.934405i | ||||
\(736\) | 1.49978 | 0.0552826 | ||||||||
\(737\) | 21.9490 | − | 21.9490i | 0.808502 | − | 0.808502i | ||||
\(738\) | −19.6633 | − | 9.39104i | −0.723816 | − | 0.345689i | ||||
\(739\) | − | 27.7673i | − | 1.02143i | −0.859749 | − | 0.510717i | \(-0.829380\pi\) | ||
0.859749 | − | 0.510717i | \(-0.170620\pi\) | |||||||
\(740\) | −3.38459 | − | 5.34271i | −0.124420 | − | 0.196402i | ||||
\(741\) | 6.90309 | − | 9.76244i | 0.253591 | − | 0.358632i | ||||
\(742\) | 1.66724 | + | 1.66724i | 0.0612061 | + | 0.0612061i | ||||
\(743\) | −22.1612 | − | 22.1612i | −0.813015 | − | 0.813015i | 0.172070 | − | 0.985085i | \(-0.444955\pi\) |
−0.985085 | + | 0.172070i | \(0.944955\pi\) | |||||||
\(744\) | −1.00000 | + | 1.41421i | −0.0366618 | + | 0.0518476i | ||||
\(745\) | 9.97701 | − | 44.4675i | 0.365529 | − | 1.62916i | ||||
\(746\) | − | 4.15645i | − | 0.152179i | ||||||
\(747\) | 31.9973 | + | 15.2817i | 1.17072 | + | 0.559127i | ||||
\(748\) | −16.6063 | + | 16.6063i | −0.607186 | + | 0.607186i | ||||
\(749\) | 4.75110 | 0.173601 | ||||||||
\(750\) | −18.5386 | + | 5.59648i | −0.676934 | + | 0.204354i | ||||
\(751\) | −14.3357 | −0.523117 | −0.261558 | − | 0.965188i | \(-0.584236\pi\) | ||||
−0.261558 | + | 0.965188i | \(0.584236\pi\) | |||||||
\(752\) | 0.520724 | − | 0.520724i | 0.0189889 | − | 0.0189889i | ||||
\(753\) | 31.1815 | − | 5.34989i | 1.13632 | − | 0.194961i | ||||
\(754\) | − | 8.25491i | − | 0.300626i | ||||||
\(755\) | 9.53207 | − | 42.4844i | 0.346908 | − | 1.54617i | ||||
\(756\) | −3.35677 | − | 0.949437i | −0.122084 | − | 0.0345307i | ||||
\(757\) | −32.6821 | − | 32.6821i | −1.18785 | − | 1.18785i | −0.977660 | − | 0.210192i | \(-0.932591\pi\) |
−0.210192 | − | 0.977660i | \(-0.567409\pi\) | |||||||
\(758\) | 13.9395 | + | 13.9395i | 0.506305 | + | 0.506305i | ||||
\(759\) | −8.66553 | − | 6.12745i | −0.314539 | − | 0.222413i | ||||
\(760\) | −1.88026 | − | 2.96805i | −0.0682041 | − | 0.107663i | ||||
\(761\) | 15.8679i | 0.575211i | 0.957749 | + | 0.287605i | \(0.0928591\pi\) | ||||
−0.957749 | + | 0.287605i | \(0.907141\pi\) | |||||||
\(762\) | −5.59762 | − | 32.6253i | −0.202780 | − | 1.18189i | ||||
\(763\) | 3.54928 | − | 3.54928i | 0.128493 | − | 0.128493i | ||||
\(764\) | −0.815538 | −0.0295051 | ||||||||
\(765\) | 30.3135 | + | 23.8326i | 1.09599 | + | 0.861671i | ||||
\(766\) | 2.47642 | 0.0894769 | ||||||||
\(767\) | −13.6859 | + | 13.6859i | −0.494168 | + | 0.494168i | ||||
\(768\) | −0.292893 | − | 1.70711i | −0.0105689 | − | 0.0615999i | ||||
\(769\) | − | 25.7022i | − | 0.926845i | −0.886138 | − | 0.463422i | \(-0.846621\pi\) | ||
0.886138 | − | 0.463422i | \(-0.153379\pi\) | |||||||
\(770\) | 5.98444 | + | 1.34271i | 0.215664 | + | 0.0483878i | ||||
\(771\) | −35.8760 | − | 25.3682i | −1.29204 | − | 0.913612i | ||||
\(772\) | 5.68362 | + | 5.68362i | 0.204558 | + | 0.204558i | ||||
\(773\) | 29.4146 | + | 29.4146i | 1.05797 | + | 1.05797i | 0.998213 | + | 0.0597568i | \(0.0190325\pi\) |
0.0597568 | + | 0.998213i | \(0.480967\pi\) | |||||||
\(774\) | 1.65041 | + | 4.66806i | 0.0593228 | + | 0.167790i | ||||
\(775\) | −4.52072 | − | 2.13613i | −0.162389 | − | 0.0767320i | ||||
\(776\) | − | 11.8075i | − | 0.423864i | ||||||
\(777\) | 3.24158 | − | 0.556167i | 0.116291 | − | 0.0199524i | ||||
\(778\) | 9.26941 | − | 9.26941i | 0.332324 | − | 0.332324i | ||||
\(779\) | 11.4132 | 0.408919 | ||||||||
\(780\) | 11.4051 | + | 12.6268i | 0.408368 | + | 0.452112i | ||||
\(781\) | −18.0938 | −0.647447 | ||||||||
\(782\) | 6.09604 | − | 6.09604i | 0.217994 | − | 0.217994i | ||||
\(783\) | −4.76424 | − | 8.52222i | −0.170260 | − | 0.304559i | ||||
\(784\) | 6.54928i | 0.233903i | ||||||||
\(785\) | 3.90672 | − | 2.47490i | 0.139437 | − | 0.0883330i | ||||
\(786\) | 14.5940 | − | 20.6391i | 0.520552 | − | 0.736171i | ||||
\(787\) | 5.55205 | + | 5.55205i | 0.197909 | + | 0.197909i | 0.799103 | − | 0.601194i | \(-0.205308\pi\) |
−0.601194 | + | 0.799103i | \(0.705308\pi\) | |||||||
\(788\) | 18.3545 | + | 18.3545i | 0.653853 | + | 0.653853i | ||||
\(789\) | −13.1502 | + | 18.5972i | −0.468159 | + | 0.662077i | ||||
\(790\) | −17.2403 | + | 10.9217i | −0.613383 | + | 0.388577i | ||||
\(791\) | 5.98444i | 0.212782i | ||||||||
\(792\) | −5.28220 | + | 11.0601i | −0.187695 | + | 0.393002i | ||||
\(793\) | −34.8984 | + | 34.8984i | −1.23928 | + | 1.23928i | ||||
\(794\) | −7.77142 | −0.275797 | ||||||||
\(795\) | −9.11742 | − | 10.0941i | −0.323361 | − | 0.357999i | ||||
\(796\) | 16.1137 | 0.571135 | ||||||||
\(797\) | −1.64459 | + | 1.64459i | −0.0582542 | + | 0.0582542i | −0.735634 | − | 0.677380i | \(-0.763116\pi\) |
0.677380 | + | 0.735634i | \(0.263116\pi\) | |||||||
\(798\) | 1.80081 | − | 0.308970i | 0.0637479 | − | 0.0109374i | ||||
\(799\) | − | 4.23310i | − | 0.149756i | ||||||
\(800\) | 4.70711 | − | 1.68616i | 0.166421 | − | 0.0596149i | ||||
\(801\) | −16.1002 | + | 5.69230i | −0.568874 | + | 0.201127i | ||||
\(802\) | 2.00518 | + | 2.00518i | 0.0708053 | + | 0.0708053i | ||||
\(803\) | −32.1452 | − | 32.1452i | −1.13438 | − | 1.13438i | ||||
\(804\) | 10.7447 | + | 7.59762i | 0.378935 | + | 0.267947i | ||||
\(805\) | −2.19684 | − | 0.492898i | −0.0774285 | − | 0.0173724i | ||||
\(806\) | 4.39327i | 0.154746i | ||||||||
\(807\) | −2.71057 | − | 15.7984i | −0.0954166 | − | 0.556129i | ||||
\(808\) | −8.88849 | + | 8.88849i | −0.312696 | + | 0.312696i | ||||
\(809\) | −36.8202 | −1.29453 | −0.647265 | − | 0.762265i | \(-0.724087\pi\) | ||||
−0.647265 | + | 0.762265i | \(0.724087\pi\) | |||||||
\(810\) | 19.0619 | + | 6.45334i | 0.669765 | + | 0.226747i | ||||
\(811\) | 51.4403 | 1.80631 | 0.903156 | − | 0.429312i | \(-0.141244\pi\) | ||||
0.903156 | + | 0.429312i | \(0.141244\pi\) | |||||||
\(812\) | 0.891992 | − | 0.891992i | 0.0313028 | − | 0.0313028i | ||||
\(813\) | −8.43568 | − | 49.1668i | −0.295852 | − | 1.72435i | ||||
\(814\) | − | 11.5557i | − | 0.405028i | ||||||
\(815\) | −4.52072 | − | 7.13613i | −0.158354 | − | 0.249968i | ||||
\(816\) | −8.12925 | − | 5.74825i | −0.284581 | − | 0.201229i | ||||
\(817\) | −1.83372 | − | 1.83372i | −0.0641536 | − | 0.0641536i | ||||
\(818\) | 2.13074 | + | 2.13074i | 0.0744997 | + | 0.0744997i | ||||
\(819\) | −8.34227 | + | 2.94944i | −0.291502 | + | 0.103062i | ||||
\(820\) | −3.55573 | + | 15.8479i | −0.124171 | + | 0.553432i | ||||
\(821\) | − | 26.0911i | − | 0.910587i | −0.890341 | − | 0.455293i | \(-0.849534\pi\) | ||
0.890341 | − | 0.455293i | \(-0.150466\pi\) | |||||||
\(822\) | −15.0346 | + | 2.57952i | −0.524391 | + | 0.0899712i | ||||
\(823\) | 1.58219 | − | 1.58219i | 0.0551518 | − | 0.0551518i | −0.678993 | − | 0.734145i | \(-0.737583\pi\) |
0.734145 | + | 0.678993i | \(0.237583\pi\) | |||||||
\(824\) | 0.635910 | 0.0221530 | ||||||||
\(825\) | −34.0860 | − | 9.48878i | −1.18672 | − | 0.330357i | ||||
\(826\) | −2.95767 | −0.102911 | ||||||||
\(827\) | −32.0545 | + | 32.0545i | −1.11464 | + | 1.11464i | −0.122128 | + | 0.992514i | \(0.538972\pi\) |
−0.992514 | + | 0.122128i | \(0.961028\pi\) | |||||||
\(828\) | 1.93906 | − | 4.06007i | 0.0673869 | − | 0.141097i | ||||
\(829\) | 19.2021i | 0.666917i | 0.942765 | + | 0.333458i | \(0.108216\pi\) | ||||
−0.942765 | + | 0.333458i | \(0.891784\pi\) | |||||||
\(830\) | 5.78610 | − | 25.7886i | 0.200838 | − | 0.895137i | ||||
\(831\) | 26.6344 | − | 37.6667i | 0.923938 | − | 1.30665i | ||||
\(832\) | −3.10651 | − | 3.10651i | −0.107699 | − | 0.107699i | ||||
\(833\) | 26.6204 | + | 26.6204i | 0.922341 | + | 0.922341i | ||||
\(834\) | −1.35498 | + | 1.91622i | −0.0469190 | + | 0.0663534i | ||||
\(835\) | −5.71091 | − | 9.01489i | −0.197634 | − | 0.311973i | ||||
\(836\) | − | 6.41960i | − | 0.222026i | ||||||
\(837\) | 2.53553 | + | 4.53553i | 0.0876409 | + | 0.156771i | ||||
\(838\) | −28.0702 | + | 28.0702i | −0.969669 | + | 0.969669i | ||||
\(839\) | −4.58696 | −0.158359 | −0.0791797 | − | 0.996860i | \(-0.525230\pi\) | ||||
−0.0791797 | + | 0.996860i | \(0.525230\pi\) | |||||||
\(840\) | −0.132012 | + | 2.59679i | −0.00455483 | + | 0.0895977i | ||||
\(841\) | −25.4694 | −0.878255 | ||||||||
\(842\) | 4.84893 | − | 4.84893i | 0.167105 | − | 0.167105i | ||||
\(843\) | −21.5839 | + | 3.70320i | −0.743387 | + | 0.127545i | ||||
\(844\) | 25.1270i | 0.864908i | ||||||||
\(845\) | 13.7473 | + | 3.08443i | 0.472921 | + | 0.106108i | ||||
\(846\) | −0.736416 | − | 2.08290i | −0.0253185 | − | 0.0716115i | ||||
\(847\) | 2.70203 | + | 2.70203i | 0.0928429 | + | 0.0928429i | ||||
\(848\) | 2.48339 | + | 2.48339i | 0.0852801 | + | 0.0852801i | ||||
\(849\) | −27.6279 | − | 19.5358i | −0.948186 | − | 0.670468i | ||||
\(850\) | 12.2790 | − | 25.9862i | 0.421166 | − | 0.891320i | ||||
\(851\) | 4.24202i | 0.145415i | ||||||||
\(852\) | −1.29714 | − | 7.56029i | −0.0444393 | − | 0.259011i | ||||
\(853\) | −28.9519 | + | 28.9519i | −0.991296 | + | 0.991296i | −0.999962 | − | 0.00866672i | \(-0.997241\pi\) |
0.00866672 | + | 0.999962i | \(0.497241\pi\) | |||||||
\(854\) | −7.54196 | −0.258081 | ||||||||
\(855\) | −10.4658 | + | 1.25268i | −0.357923 | + | 0.0428407i | ||||
\(856\) | 7.07689 | 0.241883 | ||||||||
\(857\) | 20.9236 | − | 20.9236i | 0.714736 | − | 0.714736i | −0.252786 | − | 0.967522i | \(-0.581347\pi\) |
0.967522 | + | 0.252786i | \(0.0813468\pi\) | |||||||
\(858\) | 5.25714 | + | 30.6409i | 0.179476 | + | 1.04606i | ||||
\(859\) | − | 41.8628i | − | 1.42834i | −0.699971 | − | 0.714171i | \(-0.746804\pi\) | ||
0.699971 | − | 0.714171i | \(-0.253196\pi\) | |||||||
\(860\) | 3.11751 | − | 1.97494i | 0.106306 | − | 0.0673448i | ||||
\(861\) | −6.89632 | − | 4.87643i | −0.235026 | − | 0.166188i | ||||
\(862\) | 5.36321 | + | 5.36321i | 0.182672 | + | 0.182672i | ||||
\(863\) | −14.0730 | − | 14.0730i | −0.479049 | − | 0.479049i | 0.425778 | − | 0.904827i | \(-0.360000\pi\) |
−0.904827 | + | 0.425778i | \(0.860000\pi\) | |||||||
\(864\) | −5.00000 | − | 1.41421i | −0.170103 | − | 0.0481125i | ||||
\(865\) | 33.7086 | − | 21.3544i | 1.14613 | − | 0.726070i | ||||
\(866\) | − | 9.26791i | − | 0.314936i | ||||||
\(867\) | −27.3860 | + | 4.69869i | −0.930076 | + | 0.159576i | ||||
\(868\) | −0.474719 | + | 0.474719i | −0.0161130 | + | 0.0161130i | ||||
\(869\) | −37.2890 | −1.26494 | ||||||||
\(870\) | −5.40045 | + | 4.87793i | −0.183092 | + | 0.165377i | ||||
\(871\) | 33.3784 | 1.13098 | ||||||||
\(872\) | 5.28676 | − | 5.28676i | 0.179032 | − | 0.179032i | ||||
\(873\) | −31.9641 | − | 15.2658i | −1.08182 | − | 0.516670i | ||||
\(874\) | 2.35659i | 0.0797127i | ||||||||
\(875\) | −7.44901 | + | 0.922878i | −0.251822 | + | 0.0311990i | ||||
\(876\) | 11.1270 | − | 15.7360i | 0.375947 | − | 0.531669i | ||||
\(877\) | −25.1682 | − | 25.1682i | −0.849868 | − | 0.849868i | 0.140248 | − | 0.990116i | \(-0.455210\pi\) |
−0.990116 | + | 0.140248i | \(0.955210\pi\) | |||||||
\(878\) | −7.88481 | − | 7.88481i | −0.266100 | − | 0.266100i | ||||
\(879\) | 28.6145 | − | 40.4671i | 0.965144 | − | 1.36492i | ||||
\(880\) | 8.91399 | + | 2.00000i | 0.300491 | + | 0.0674200i | ||||
\(881\) | 55.8080i | 1.88022i | 0.340872 | + | 0.940110i | \(0.389278\pi\) | ||||
−0.340872 | + | 0.940110i | \(0.610722\pi\) | |||||||
\(882\) | 17.7296 | + | 8.46753i | 0.596987 | + | 0.285116i | ||||
\(883\) | 11.1283 | − | 11.1283i | 0.374497 | − | 0.374497i | −0.494615 | − | 0.869112i | \(-0.664691\pi\) |
0.869112 | + | 0.494615i | \(0.164691\pi\) | |||||||
\(884\) | −25.2536 | −0.849370 | ||||||||
\(885\) | 17.0406 | + | 0.866283i | 0.572813 | + | 0.0291198i | ||||
\(886\) | 5.21272 | 0.175125 | ||||||||
\(887\) | 27.8846 | − | 27.8846i | 0.936272 | − | 0.936272i | −0.0618158 | − | 0.998088i | \(-0.519689\pi\) |
0.998088 | + | 0.0618158i | \(0.0196891\pi\) | |||||||
\(888\) | 4.82843 | − | 0.828427i | 0.162031 | − | 0.0278002i | ||||
\(889\) | − | 12.8305i | − | 0.430323i | ||||||
\(890\) | 6.81160 | + | 10.7524i | 0.228325 | + | 0.360420i | ||||
\(891\) | 23.1115 | + | 28.5990i | 0.774263 | + | 0.958102i | ||||
\(892\) | 3.60852 | + | 3.60852i | 0.120822 | + | 0.120822i | ||||
\(893\) | 0.818208 | + | 0.818208i | 0.0273803 | + | 0.0273803i | ||||
\(894\) | 28.8229 | + | 20.3809i | 0.963982 | + | 0.681638i | ||||
\(895\) | −11.1252 | + | 49.5851i | −0.371875 | + | 1.65745i | ||||
\(896\) | − | 0.671354i | − | 0.0224283i | ||||||
\(897\) | −1.92986 | − | 11.2480i | −0.0644360 | − | 0.375561i | ||||
\(898\) | −9.05880 | + | 9.05880i | −0.302296 | + | 0.302296i | ||||
\(899\) | −1.87899 | −0.0626678 | ||||||||
\(900\) | 1.52116 | − | 14.9227i | 0.0507054 | − | 0.497422i | ||||
\(901\) | 20.1881 | 0.672564 | ||||||||
\(902\) | −20.9840 | + | 20.9840i | −0.698691 | + | 0.698691i | ||||
\(903\) | 0.324528 | + | 1.89149i | 0.0107996 | + | 0.0629448i | ||||
\(904\) | 8.91399i | 0.296475i | ||||||||
\(905\) | 5.20342 | − | 23.1916i | 0.172968 | − | 0.770916i | ||||
\(906\) | 27.5375 | + | 19.4720i | 0.914872 | + | 0.646912i | ||||
\(907\) | −23.9940 | − | 23.9940i | −0.796709 | − | 0.796709i | 0.185866 | − | 0.982575i | \(-0.440491\pi\) |
−0.982575 | + | 0.185866i | \(0.940491\pi\) | |||||||
\(908\) | −16.2085 | − | 16.2085i | −0.537897 | − | 0.537897i | ||||
\(909\) | 12.5702 | + | 35.5540i | 0.416928 | + | 1.17925i | ||||
\(910\) | 3.52940 | + | 5.57129i | 0.116998 | + | 0.184686i | ||||
\(911\) | 5.18069i | 0.171644i | 0.996310 | + | 0.0858219i | \(0.0273516\pi\) | ||||
−0.996310 | + | 0.0858219i | \(0.972648\pi\) | |||||||
\(912\) | 2.68235 | − | 0.460219i | 0.0888216 | − | 0.0152394i | ||||
\(913\) | 34.1465 | − | 34.1465i | 1.13008 | − | 1.13008i | ||||
\(914\) | 29.4292 | 0.973431 | ||||||||
\(915\) | 43.4528 | + | 2.20899i | 1.43651 | + | 0.0730269i | ||||
\(916\) | 6.64235 | 0.219470 | ||||||||
\(917\) | 6.92805 | − | 6.92805i | 0.228785 | − | 0.228785i | ||||
\(918\) | −26.0714 | + | 14.5749i | −0.860483 | + | 0.481042i | ||||
\(919\) | 37.4389i | 1.23500i | 0.786573 | + | 0.617498i | \(0.211854\pi\) | ||||
−0.786573 | + | 0.617498i | \(0.788146\pi\) | |||||||
\(920\) | −3.27226 | − | 0.734185i | −0.107883 | − | 0.0242054i | ||||
\(921\) | −10.8392 | + | 15.3289i | −0.357164 | + | 0.505106i | ||||
\(922\) | 7.09095 | + | 7.09095i | 0.233528 | + | 0.233528i | ||||
\(923\) | −13.7578 | − | 13.7578i | −0.452845 | − | 0.452845i | ||||
\(924\) | −2.74286 | + | 3.87899i | −0.0902335 | + | 0.127609i | ||||
\(925\) | 4.76919 | + | 13.3137i | 0.156810 | + | 0.437752i | ||||
\(926\) | 4.65264i | 0.152895i | ||||||||
\(927\) | 0.822164 | − | 1.72148i | 0.0270034 | − | 0.0565407i | ||||
\(928\) | 1.32865 | − | 1.32865i | 0.0436150 | − | 0.0436150i | ||||
\(929\) | 10.3349 | 0.339079 | 0.169539 | − | 0.985523i | \(-0.445772\pi\) | ||||
0.169539 | + | 0.985523i | \(0.445772\pi\) | |||||||
\(930\) | 2.87412 | − | 2.59604i | 0.0942462 | − | 0.0851275i | ||||
\(931\) | −10.2908 | −0.337268 | ||||||||
\(932\) | −9.15146 | + | 9.15146i | −0.299766 | + | 0.299766i | ||||
\(933\) | 48.7050 | − | 8.35646i | 1.59453 | − | 0.273578i | ||||
\(934\) | − | 15.8561i | − | 0.518828i | ||||||
\(935\) | 44.3613 | − | 28.1028i | 1.45077 | − | 0.919059i | ||||
\(936\) | −12.4260 | + | 4.39327i | −0.406158 | + | 0.143599i | ||||
\(937\) | 15.8855 | + | 15.8855i | 0.518958 | + | 0.518958i | 0.917256 | − | 0.398298i | \(-0.130399\pi\) |
−0.398298 | + | 0.917256i | \(0.630399\pi\) | |||||||
\(938\) | 3.60673 | + | 3.60673i | 0.117764 | + | 0.117764i | ||||
\(939\) | −46.1984 | − | 32.6672i | −1.50763 | − | 1.06605i | ||||
\(940\) | −1.39104 | + | 0.881221i | −0.0453707 | + | 0.0287422i | ||||
\(941\) | − | 28.9714i | − | 0.944442i | −0.881480 | − | 0.472221i | \(-0.843452\pi\) | ||
0.881480 | − | 0.472221i | \(-0.156548\pi\) | |||||||
\(942\) | 0.605767 | + | 3.53067i | 0.0197369 | + | 0.115035i | ||||
\(943\) | 7.70307 | − | 7.70307i | 0.250846 | − | 0.250846i | ||||
\(944\) | −4.40554 | −0.143388 | ||||||||
\(945\) | 6.85911 | + | 3.71474i | 0.223127 | + | 0.120840i | ||||
\(946\) | 6.74286 | 0.219229 | ||||||||
\(947\) | −34.7182 | + | 34.7182i | −1.12819 | + | 1.12819i | −0.137718 | + | 0.990471i | \(0.543977\pi\) |
−0.990471 | + | 0.137718i | \(0.956023\pi\) | |||||||
\(948\) | −2.67324 | − | 15.5808i | −0.0868228 | − | 0.506041i | ||||
\(949\) | − | 48.8840i | − | 1.58684i | ||||||
\(950\) | 2.64945 | + | 7.39622i | 0.0859594 | + | 0.239965i | ||||
\(951\) | 22.6555 | + | 16.0199i | 0.734656 | + | 0.519480i | ||||
\(952\) | −2.72880 | − | 2.72880i | −0.0884409 | − | 0.0884409i | ||||
\(953\) | 3.05595 | + | 3.05595i | 0.0989919 | + | 0.0989919i | 0.754868 | − | 0.655876i | \(-0.227701\pi\) |
−0.655876 | + | 0.754868i | \(0.727701\pi\) | |||||||
\(954\) | 9.93358 | − | 3.51205i | 0.321611 | − | 0.113707i | ||||
\(955\) | 1.77936 | + | 0.399229i | 0.0575788 | + | 0.0129187i | ||||
\(956\) | − | 26.5471i | − | 0.858593i | ||||||
\(957\) | −13.1050 | + | 2.24846i | −0.423625 | + | 0.0726825i | ||||
\(958\) | −4.16479 | + | 4.16479i | −0.134558 | + | 0.134558i | ||||
\(959\) | −5.91264 | −0.190929 | ||||||||
\(960\) | −0.196635 | + | 3.86799i | −0.00634636 | + | 0.124839i | ||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 8.78654 | − | 8.78654i | 0.283289 | − | 0.283289i | ||||
\(963\) | 9.14967 | − | 19.1579i | 0.294844 | − | 0.617355i | ||||
\(964\) | 3.60673i | 0.116165i | ||||||||
\(965\) | −9.61838 | − | 15.1830i | −0.309627 | − | 0.488757i | ||||
\(966\) | 1.00688 | − | 1.42395i | 0.0323959 | − | 0.0458148i | ||||
\(967\) | −33.8479 | − | 33.8479i | −1.08847 | − | 1.08847i | −0.995686 | − | 0.0927884i | \(-0.970422\pi\) |
−0.0927884 | − | 0.995686i | \(-0.529578\pi\) | |||||||
\(968\) | 4.02475 | + | 4.02475i | 0.129360 | + | 0.129360i | ||||
\(969\) | 9.03214 | − | 12.7734i | 0.290154 | − | 0.410340i | ||||
\(970\) | −5.78010 | + | 25.7619i | −0.185588 | + | 0.827164i | ||||
\(971\) | − | 58.2910i | − | 1.87065i | −0.353793 | − | 0.935324i | \(-0.615108\pi\) | ||
0.353793 | − | 0.935324i | \(-0.384892\pi\) | |||||||
\(972\) | −10.2929 | + | 11.7071i | −0.330145 | + | 0.375506i | ||||
\(973\) | −0.643232 | + | 0.643232i | −0.0206211 | + | 0.0206211i | ||||
\(974\) | 34.6672 | 1.11081 | ||||||||
\(975\) | −18.7028 | − | 33.1326i | −0.598968 | − | 1.06109i | ||||
\(976\) | −11.2340 | −0.359590 | ||||||||
\(977\) | 1.11995 | − | 1.11995i | 0.0358304 | − | 0.0358304i | −0.688965 | − | 0.724795i | \(-0.741934\pi\) |
0.724795 | + | 0.688965i | \(0.241934\pi\) | |||||||
\(978\) | 6.44922 | − | 1.10651i | 0.206223 | − | 0.0353823i | ||||
\(979\) | 23.2563i | 0.743273i | ||||||||
\(980\) | 3.20606 | − | 14.2894i | 0.102414 | − | 0.456458i | ||||
\(981\) | −7.47661 | − | 21.1470i | −0.238710 | − | 0.675173i | ||||
\(982\) | 17.4451 | + | 17.4451i | 0.556696 | + | 0.556696i | ||||
\(983\) | 36.6650 | + | 36.6650i | 1.16943 | + | 1.16943i | 0.982343 | + | 0.187087i | \(0.0599047\pi\) |
0.187087 | + | 0.982343i | \(0.440095\pi\) | |||||||
\(984\) | −10.2723 | − | 7.26358i | −0.327468 | − | 0.231555i | ||||
\(985\) | −31.0613 | − | 49.0315i | −0.989696 | − | 1.56227i | ||||
\(986\) | − | 10.8009i | − | 0.343971i | ||||||
\(987\) | −0.144805 | − | 0.843985i | −0.00460919 | − | 0.0268644i | ||||
\(988\) | 4.88122 | − | 4.88122i | 0.155292 | − | 0.155292i | ||||
\(989\) | −2.47525 | −0.0787085 | ||||||||
\(990\) | 16.9391 | − | 21.5453i | 0.538359 | − | 0.684756i | ||||
\(991\) | 60.1248 | 1.90993 | 0.954964 | − | 0.296722i | \(-0.0958934\pi\) | ||||
0.954964 | + | 0.296722i | \(0.0958934\pi\) | |||||||
\(992\) | −0.707107 | + | 0.707107i | −0.0224507 | + | 0.0224507i | ||||
\(993\) | 5.76337 | + | 33.5914i | 0.182895 | + | 1.06599i | ||||
\(994\) | − | 2.97323i | − | 0.0943052i | ||||||
\(995\) | −35.1573 | − | 7.88810i | −1.11456 | − | 0.250070i | ||||
\(996\) | 16.7157 | + | 11.8198i | 0.529656 | + | 0.374523i | ||||
\(997\) | −15.0323 | − | 15.0323i | −0.476079 | − | 0.476079i | 0.427796 | − | 0.903875i | \(-0.359290\pi\) |
−0.903875 | + | 0.427796i | \(0.859290\pi\) | |||||||
\(998\) | −27.1749 | − | 27.1749i | −0.860207 | − | 0.860207i | ||||
\(999\) | 4.00000 | − | 14.1421i | 0.126554 | − | 0.447437i |
(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 | 930.2.j.c.497.3 | ✓ | 8 | |
3.2 | odd | 2 | 930.2.j.f.497.2 | yes | 8 | ||
5.3 | odd | 4 | 930.2.j.f.683.2 | yes | 8 | ||
15.8 | even | 4 | inner | 930.2.j.c.683.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.j.c.497.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
930.2.j.c.683.3 | yes | 8 | 15.8 | even | 4 | inner | |
930.2.j.f.497.2 | yes | 8 | 3.2 | odd | 2 | ||
930.2.j.f.683.2 | yes | 8 | 5.3 | odd | 4 |